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中級arXiv

LIBERO-Pro2.0:条件が変わるとロボット基盤モデルの成功率は平均26.5ポイント低下(華中科技大、清華大)

Xueyang Zhou, Yangming Xu, Qianjiang Li, Guiyao Tie, Junhao Wu, Ziheng Huang, Guowen Zhang, Zhijie Yuan, Di Wu, Duanfeng Chu, Pan Zhou, Lichao Sun, Yongchao ChenHuazhong University of Science and Technology; Tsinghua University; Wuhan University of Technology; Lehigh University; University of Toronto
30秒で読む

華中科技大学と清華大学などはプレプリントで、LIBEROベンチマークで63.8から98.5%を出すロボット制御モデル17種が、作業途中に物体、目標、カメラ、ロボット状態を変えると成功率が平均26.5ポイント下がったと報告した。Physical Intelligenceのpi0.5を頑健性の教示80件で微調整すると、未知の摂動課題での成功率は70.1%となり、既存方策の28.0から47.9%を上回った。

研究課題

ロボット基盤モデルがLIBEROで出す満点に近い成績は汎化能力の表れか、それとも学習データに近い条件でだけ通用する成績か。

問題

LIBEROは卓上マニピュレーションの事実上の標準となり、多くのモデルが飽和に近い。著者らは、上位モデルが物体を取り除いても手を伸ばし、指示を無意味なトークンに替えても同じ軌道を出し、物体を動かしても学習時の位置へ向かう例を確認した。

従来の手法

従来のベンチマークは学習に近い条件で成功を再現できるかを測る。LIBERO-Plusなどの拡張版も摂動を加えたが、多くはエピソード開始前に固定する静的な摂動だった。

新しい手法

LIBERO-Pro2.0は課題条件、環境、観測、実行、ロボット状態、言語の6次元に、静的摂動22種と実行中の介入20種を加え、摂動課題1,648件を作った。各課題は6回の人手確認で物理的な妥当性を検証した。モデル生成と人の教示による学習軌跡3万9,390本も公開し、VLAモデル、ワールドアクションモデル、頑健性特化手法など17方策を評価した。

結果

静的摂動で平均成功率は33.9から71.2%(25.1から41.8ポイント低下)、実行中の摂動で35.3から81.8%(16.7から32.5ポイント低下)となり、平均26.5ポイント下がった。OpenVLA-OFTは静的摂動で97.1%から58.9%、pi0.5は93.3%から66.7%に落ちた。順位も逆転し、FastWAMは通常条件でpi0.5を上回る(97.8%対93.3%)が、実行中の摂動では70.1%と73.8%のpi0.5に及ばなかった。pi0.5を8課題、各10本の軌跡で学習させると未知課題の平均頑健性は70.1%と元のpi0.5より22.2ポイント高まり、経路障害物の課題では96.3%と、全比較モデル(20%未満)を大きく上回った。

限界

プレプリントであり、実験はすべてLIBEROの単腕卓上シミュレーションで行われ、実環境での頑健性は測っていない。複数のモデルが実行次元でほぼ0%となったのは、摂動の定義方法の影響もありうる。微調整の効果は、試験と同じ種類の摂動の教示から得られたものだ。

産業への影響

Physical Intelligence、エヌビディア、オープンソース勢のロボット基盤モデルを比較する導入企業やSIerにとって、ベンチマーク対策と実際の頑健性を見分ける試験が生まれた。順位の逆転は、LIBEROの通常スコアだけでモデルを選ぶべきでないことを示す。独自VLAを開発する国内メーカーも数カ月以内にこの指標の開示を求められる可能性が高く、実環境版の試験はなお空白だ。

論文全文

LIBERO-Pro2.0: A Benchmark for Evaluating the Robustness of Embodied Foundation Models

Xueyang Zhou, Yangming Xu, Qianjiang Li, Guiyao Tie, Junhao Wu, Ziheng Huang, Guowen Zhang, Zhijie Yuan, Di Wu, Duanfeng Chu, Pan Zhou, Lichao Sun, Yongchao Chen

CC BY 4.0 のもとで公開された論文です。出典を明記して転載しています。原文は arXiv:2610.24587(PDF)。

Abstract

LIBERO has emerged as a widely adopted benchmark for evaluating robotic manipulation policies. However, strong performance on LIBERO does not necessarily indicate robust embodied capabilities, as models may exploit benchmark-specific regularities rather than generalize to diverse operating conditions. In this work, we introduce LIBERO-Pro2.0, a comprehensive benchmark for systematically evaluating the robustness of embodied foundation models under distribution shifts. LIBERO-Pro2.0 encompasses 22 static perturbations and 20 runtime interventions across six dimensions: Condition, Environment, Observation, Execution, Robot State Configuration, and Language, yielding 1,648 validated shifted task instances. To support robustness-oriented learning, we further collect 39,390 training trajectories through model-generated and human demonstrations. All shifted task instances undergo six rounds of iterative human review and correction to ensure physical plausibility and task validity. We evaluate 17 representative robot policies spanning vision-language-action models, world-action models, and robustness-oriented policies. Our results reveal substantial robustness gaps across all evaluated paradigms: under runtime distribution shifts, the evaluated models exhibit an average performance drop of 26.5 percentage points, with individual drops reaching 32.5 points. These findings highlight the gap between nominal benchmark performance and robustness under distribution shifts, underscoring the need for systematic robustness evaluation of embodied foundation models.

Webpage | GitHub | Hugging Face | Leaderboard | Community

Figure 1: Overview of LIBERO-Pro2.0. Built upon LIBERO, our benchmark introduces 22 static distribution shifts and 20 runtime interventions across six dimensions: condition, environment, observation, robot, execution, and language. The left and right panels illustrate representative static and runtime perturbations, respectively.

1 Introduction

Reliable evaluation is essential for measuring progress in embodied intelligence (Yu et al., 2020; James et al., 2020; Mees et al., 2022; Gu et al., 2023; Mu et al., 2025; Zhang et al., 2025). LIBERO has emerged as a de facto standard for tabletop manipulation (Liu et al., 2023), with increasingly many systems approaching saturated performance under its standard protocol (Kim et al., 2025b; Black et al., 2025; Kim et al., 2025a; Qu et al., 2025; Lee et al., 2025; Fang et al., 2026). Yet a fundamental question remains: do these high success rates reflect generalizable embodied capabilities, or merely strong performance within a familiar training–evaluation distribution?

To examine this question, we revisit high-performing systems on LIBERO and observe three striking failure patterns under simple task variations: (1) when the target object is replaced or even removed, models still execute the original grasping behavior; (2) when the task instruction is replaced with meaningless tokens, models continue to produce nearly identical action trajectories; and (3) when the target object is moved away from its familiar position, models still move toward the location commonly seen during training. These qualitative observations motivate a systematic evaluation of sensitivity to task-relevant visual, linguistic, and spatial changes, but do not by themselves establish memorization as the underlying failure mechanism.

These failures expose a broader limitation of current evaluation protocols. Standard benchmarks largely test whether a policy can reproduce successful behavior under conditions close to those seen during training (Yu et al., 2020; James et al., 2020; Mees et al., 2022; Gu et al., 2023; Liu et al., 2023), while deployment requires the same system to remain effective when the scene changes before execution, when unexpected events occur during interaction (Li et al., 2024; Fei et al., 2026; Zhang et al., 2026), and when an initial action fails. Consequently, nominal task success alone does not characterize robustness when operating conditions change. A meaningful evaluation protocol should therefore separate training from evaluation distributions and explicitly test both generalization to static shifts and adaptation to runtime interventions.

To this end, we introduce LIBERO-Pro2.0, a large-scale robustness benchmark for embodied foundation models under static distribution shifts and runtime interventions. LIBERO-Pro2.0 defines 42 perturbation types (22 static and 20 runtime), yielding 1,648 perturbed task variants. These perturbations span scene and object configurations, visual observations, camera settings, robot states, among others. We reserve 8 comprehensively perturbed tasks for evaluation and release the remaining perturbations for training, collecting 39,390 training trajectories. Each perturbed task undergoes six rounds of human verification to ensure validity and reproducibility. We evaluate 17 representative policies spanning vision-language-action models, world-action models, and robustness-oriented policies. Results reveal substantial robustness degradation under both static and runtime distribution shifts, with runtime shifts causing an average performance drop of 26.5 percentage points. Moreover, robustness varies substantially across perturbation types. High nominal success does not guarantee small robustness losses or preservation of policy rankings under distribution shifts. Our main contributions are threefold:

  • We introduce LIBERO-Pro2.0, a large-scale robustness benchmark for embodied foundation models, extending LIBERO beyond nominal task success to systematically evaluate robustness under both static distribution shifts and runtime interventions.
  • We develop a comprehensive perturbation suite with 42 perturbation types, yielding 1,648 perturbed task variants and 39,390 training trajectories across diverse environments, observations, instructions, robot states, and execution conditions, with rigorous human verification.
  • We conduct a large-scale evaluation of 17 representative policies across different model paradigms, revealing substantial robustness degradation under both static and runtime shifts and showing that nominal LIBERO performance does not consistently reflect robustness.
Figure 2: Failure patterns under task variations. Examples for the task “Pick up the alphabet soup and put it in the basket.” The policy behaves similarly despite changes to the target object, instruction, or object position.

2 Preliminaries

2.1 Embodied Manipulation Tasks

We consider a language-conditioned manipulation task \mathcal{T}=(\ell,e,\mathcal{G}), where \ell is the task instruction, e specifies the environment configuration, and \mathcal{G} is the task-success predicate. Starting from an initial state s_{0}, a policy \pi interacts with the environment for a finite episode horizon T_{\mathrm{ep}}, receiving an observation o_{t} and producing an action a_{t}\sim\pi(\cdot\mid o_{t},\ell_{t}) at each step. The instruction input satisfies \ell_{t}=\ell by default; D20 permits semantics-preserving restatements during execution without changing the task objective or success predicate. The resulting trajectory is \tau=(s_{0},a_{0},\ldots,s_{T_{\mathrm{ep}}}), and an episode is successful if \mathcal{G}(\tau)=1.

2.2 Evaluation under Distribution Shifts

The original LIBERO evaluation distribution closely resembles its training distribution. In real-world deployment, however, operating conditions can deviate substantially from those encountered during training, making the original evaluation insufficient for assessing policy generalization. We therefore introduce controlled distribution shifts into the LIBERO evaluation setting. Given the original evaluation distribution \mathcal{D}_{\mathrm{eval}}, an evaluation transformation \phi parameterized by \eta induces a shifted distribution \mathcal{D}_{\mathrm{eval}}^{\phi}=\phi(\mathcal{D}_{\mathrm{eval}};\eta), while preserving the task objective and success criterion. Performance under \mathcal{D}_{\mathrm{eval}}^{\phi} measures policy generalization when evaluation conditions deviate from those represented during training.

2.3 Static Shifts and Runtime Interventions

We distinguish two types of evaluation transformations according to their temporal behavior during an episode. A static shift \phi_{S} is configured before policy execution, yielding \mathcal{T}^{S}=\phi_{S}(\mathcal{T};\eta). Its intervention parameters or fault rules remain fixed throughout the episod. In contrast, a runtime intervention \phi^{D} is applied during policy execution, with its occurrence and configuration determined by the interaction history \tau_{0:t}, i.e., \phi^{D}(\mathcal{T};t,\tau_{0:t},\eta). Static shifts evaluate generalization under shifted but stationary conditions, whereas runtime interventions evaluate policy robustness to changes that arise during interaction.

3 LIBERO-Pro2.0

LIBERO-Pro2.0 extends LIBERO with robustness evaluation under relevant variations in environments, observations, robot states, execution processes, and task instructions, while preserving task validity and feasibility. An overview of LIBERO-Pro2.0 and its evaluation dimensions is shown in Fig. 3.

Figure 3: Cases of LIBERO-Pro2.0.

3.1 Systematic Distribution Shift Design

We consider two forms of distribution shift according to when the operating condition changes: Static Distribution Shifts and Runtime Distribution Shifts.Static shifts are configured before execution, with intervention parameters or fault rules held fixed throughout an episode, while runtime shifts occur during task execution and alter the environment, observation, robot state, or execution process. The former evaluates out-of-distribution generalization, while the latter evaluates online adaptation and recovery.

Static distribution shifts.

Static distribution shifts characterize changes that are established before execution and remain stationary throughout an episode. Let \phi^{S}\in\Phi^{S} denote a static shift operator and \eta its configuration. Applying \phi^{S} to a nominal task \mathcal{T} induces a shifted task \mathcal{T}^{S}=\phi^{S}(\mathcal{T};\eta), where \eta is specified before the rollout and held fixed throughout execution. LIBERO-Pro2.0 instantiates 22 static distribution shifts over the task environment, observation process, robot configuration, and language condition, covering object configuration and appearance, scene composition, camera and observation conditions, robot initialization and calibration, temporal configuration, and instruction expression. These shifts reflect deployment-relevant variations that arise in real-world robotic manipulation, making robustness to such out-of-distribution conditions essential for deployment.

Figure 4: Perturbation distribution in LIBERO-Pro2.0.
Runtime distribution shifts.

Runtime distribution shifts characterize changes that emerge after task execution has begun. Let \phi^{D}\in\Phi^{D} denote a runtime shift operator and \eta its configuration. Each shift is associated with a trigger function g_{\phi}(\tau_{0:t}) defined over the interaction trajectory \tau_{0:t}; the trigger determines when the shift is introduced, while \eta specifies its realization and temporal extent. LIBERO-Pro2.0 instantiates 20 runtime distribution shifts over the task environment, observation process, robot and action execution, and language condition, covering object or receiver relocation, dynamic occlusion and obstacles, camera and observation failures, frame-stream and synchronization anomalies, transient latency, action-execution disruptions, robot-state changes, semantics-preserving instruction restatements, and recoverable execution failures. These shifts capture execution-time changes that can occur during real-world deployment, where a robust policy must continuously adapt its behavior and recover from unexpected deviations to maintain stable task execution.

3.2 Data Collection

LIBERO-Pro2.0 is built from the 40 tasks in LIBERO-Goal, LIBERO-Spatial, LIBERO-Object, and LIBERO-10. Using random seed 142, we sample two tasks from each suite for held-out evaluation, yielding 8 evaluation tasks and 32 training tasks. After applying all applicable distribution shifts and filtering invalid task–shift combinations, the training and evaluation sets contain 1,313 and 335 valid instances, respectively, for a total of 1,648 validated shifted task instances. For robustness-oriented learning, we collect 30 trajectories for each training instance, yielding 39,390 trajectories from \pi_{0.5}, GPT-5.6 Sol with Codex, and human demonstrations. All authors conduct six rounds of iterative human review and correction over all 1,648 distribution-shift instances. In each round, every instance is executed twice using \pi_{0.5}, producing approximately 3,296 rollout videos per round and 19,776 reviewed rollouts across six rounds, totaling more than 82 hours of footage. Reviewers verify that each shift is correctly realized and that tasks remain semantically valid and physically executable, including spatial consistency after relocation, valid occlusions or obstacles, feasible execution paths, and correct runtime triggering. Temporal and action-stream shifts are additionally checked against execution logs when necessary. Invalid or ambiguous instances are corrected and re-evaluated, while task–shift combinations that fail validation are removed.

4 Experiments

Table 1: Leaderboard of robot-policy robustness under static distribution shifts. Category scores and Avg. report mean success rates (%) over valid suite–perturbation entries across four LIBERO suites. Base denotes nominal success, and \Delta=\mathrm{Avg.}-\mathrm{Base} is measured in percentage points. All calculations precede rounding. OpenVLA-OFT variants follow LIBERO-Plus (Fei et al., 2026): w excludes wrist-camera input, m uses joint fine-tuning across the four original suites, and + uses mixed fine-tuning on LIBERO-Plus data.
  • Vision-Language-Action Policies
    Cond. S01–S05, S07–S09
    データなし
    Env. S06, S10–S14, S22
    データなし
    Obs. S15–S16, S19
    データなし
    Exec. S20
    データなし
    Robot S17–S18
    データなし
    Lang. S21
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • OpenVLA (Kim et al., 2025b)
    Cond. S01–S05, S07–S09
    25.2
    Env. S06, S10–S14, S22
    37.6
    Obs. S15–S16, S19
    34.4
    Exec. S20
    0.0
    Robot S17–S18
    54.0
    Lang. S21
    67.5
    Avg.
    33.9
    Base
    64.6
    \Delta
    -30.7
  • OpenVLA-OFT (Kim et al., 2025a)
    Cond. S01–S05, S07–S09
    44.1
    Env. S06, S10–S14, S22
    82.0
    Obs. S15–S16, S19
    46.3
    Exec. S20
    0.0
    Robot S17–S18
    66.5
    Lang. S21
    94.6
    Avg.
    58.9
    Base
    97.1
    \Delta
    -38.2
  • OpenVLA-OFTw (Kim et al., 2025a)
    Cond. S01–S05, S07–S09
    40.1
    Env. S06, S10–S14, S22
    64.9
    Obs. S15–S16, S19
    67.6
    Exec. S20
    0.4
    Robot S17–S18
    55.4
    Lang. S21
    90.0
    Avg.
    53.8
    Base
    89.2
    \Delta
    -35.4
  • OpenVLA-OFTm (Kim et al., 2025a)
    Cond. S01–S05, S07–S09
    45.9
    Env. S06, S10–S14, S22
    78.3
    Obs. S15–S16, S19
    49.7
    Exec. S20
    0.0
    Robot S17–S18
    72.1
    Lang. S21
    92.1
    Avg.
    59.3
    Base
    92.5
    \Delta
    -33.2
  • OpenVLA-OFT+ (Fei et al., 2026)
    Cond. S01–S05, S07–S09
    47.2
    Env. S06, S10–S14, S22
    78.5
    Obs. S15–S16, S19
    45.0
    Exec. S20
    0.0
    Robot S17–S18
    73.8
    Lang. S21
    90.0
    Avg.
    59.2
    Base
    92.1
    \Delta
    -32.9
  • UniVLA (Bu et al., 2025)
    Cond. S01–S05, S07–S09
    39.8
    Env. S06, S10–S14, S22
    59.5
    Obs. S15–S16, S19
    58.1
    Exec. S20
    0.0
    Robot S17–S18
    79.6
    Lang. S21
    91.7
    Avg.
    52.9
    Base
    92.1
    \Delta
    -39.2
  • \pi_{0} (Black et al., 2025)
    Cond. S01–S05, S07–S09
    25.0
    Env. S06, S10–S14, S22
    53.8
    Obs. S15–S16, S19
    60.0
    Exec. S20
    5.0
    Robot S17–S18
    19.2
    Lang. S21
    46.3
    Avg.
    38.6
    Base
    63.8
    \Delta
    -25.1
  • \pi_{0}-FAST (Pertsch et al., 2025)
    Cond. S01–S05, S07–S09
    43.8
    Env. S06, S10–S14, S22
    71.5
    Obs. S15–S16, S19
    39.9
    Exec. S20
    0.0
    Robot S17–S18
    57.7
    Lang. S21
    81.2
    Avg.
    53.2
    Base
    80.4
    \Delta
    -27.3
  • \pi_{0.5} (Physical Intelligence et al., 2025)
    Cond. S01–S05, S07–S09
    60.7
    Env. S06, S10–S14, S22
    83.9
    Obs. S15–S16, S19
    43.3
    Exec. S20
    0.8
    Robot S17–S18
    85.0
    Lang. S21
    93.3
    Avg.
    66.7
    Base
    93.3
    \Delta
    -26.6
  • X-VLA (Zheng et al., 2025)
    Cond. S01–S05, S07–S09
    42.1
    Env. S06, S10–S14, S22
    81.7
    Obs. S15–S16, S19
    49.3
    Exec. S20
    71.7
    Robot S17–S18
    61.7
    Lang. S21
    90.8
    Avg.
    61.2
    Base
    95.0
    \Delta
    -33.8
  • GR00T N1.7 (Bjorck et al., 2025)
    Cond. S01–S05, S07–S09
    46.6
    Env. S06, S10–S14, S22
    79.2
    Obs. S15–S16, S19
    48.5
    Exec. S20
    0.0
    Robot S17–S18
    77.9
    Lang. S21
    88.8
    Avg.
    60.0
    Base
    90.4
    \Delta
    -30.4
  • MolmoAct2 (Fang et al., 2026)
    Cond. S01–S05, S07–S09
    63.8
    Env. S06, S10–S14, S22
    85.0
    Obs. S15–S16, S19
    65.1
    Exec. S20
    0.0
    Robot S17–S18
    85.0
    Lang. S21
    94.6
    Avg.
    71.2
    Base
    97.2
    \Delta
    -26.0
  • World-Action Models
    Cond. S01–S05, S07–S09
    データなし
    Env. S06, S10–S14, S22
    データなし
    Obs. S15–S16, S19
    データなし
    Exec. S20
    データなし
    Robot S17–S18
    データなし
    Lang. S21
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • Cosmos Policy (Kim et al., 2026)
    Cond. S01–S05, S07–S09
    56.9
    Env. S06, S10–S14, S22
    89.3
    Obs. S15–S16, S19
    70.8
    Exec. S20
    4.2
    Robot S17–S18
    82.5
    Lang. S21
    93.3
    Avg.
    70.8
    Base
    97.5
    \Delta
    -26.7
  • FastWAM (Yuan et al., 2026)
    Cond. S01–S05, S07–S09
    43.8
    Env. S06, S10–S14, S22
    84.7
    Obs. S15–S16, S19
    5.2
    Exec. S20
    2.8
    Robot S17–S18
    87.5
    Lang. S21
    90.3
    Avg.
    55.9
    Base
    97.8
    \Delta
    -41.8
  • LingBot-VA (Li et al., 2026)
    Cond. S01–S05, S07–S09
    52.2
    Env. S06, S10–S14, S22
    86.1
    Obs. S15–S16, S19
    35.7
    Exec. S20
    86.7
    Robot S17–S18
    98.3
    Lang. S21
    97.1
    Avg.
    68.7
    Base
    98.5
    \Delta
    -29.7
  • Robustness-Oriented Policies
    Cond. S01–S05, S07–S09
    データなし
    Env. S06, S10–S14, S22
    データなし
    Obs. S15–S16, S19
    データなし
    Exec. S20
    データなし
    Robot S17–S18
    データなし
    Lang. S21
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • Anchor-Align (Dalal et al., 2026)
    Cond. S01–S05, S07–S09
    43.2
    Env. S06, S10–S14, S22
    74.3
    Obs. S15–S16, S19
    38.6
    Exec. S20
    0.8
    Robot S17–S18
    76.5
    Lang. S21
    90.8
    Avg.
    55.9
    Base
    91.3
    \Delta
    -35.4
  • RIPT-VLA (Tan et al., 2025)
    Cond. S01–S05, S07–S09
    40.6
    Env. S06, S10–S14, S22
    76.0
    Obs. S15–S16, S19
    42.8
    Exec. S20
    0.0
    Robot S17–S18
    65.0
    Lang. S21
    86.7
    Avg.
    54.8
    Base
    87.9
    \Delta
    -33.1
Table 2: Leaderboard of robot-policy robustness under runtime distribution shifts.
  • Vision-Language-Action Policies
    Cond. D01–D06
    データなし
    Env. D07–D09
    データなし
    Obs. D10–D13
    データなし
    Exec. D14–D16
    データなし
    Robot D17–D19
    データなし
    Lang. D20
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • OpenVLA (Kim et al., 2025b)
    Cond. D01–D06
    20.6
    Env. D07–D09
    41.9
    Obs. D10–D13
    41.3
    Exec. D14–D16
    53.6
    Robot D17–D19
    29.9
    Lang. D20
    63.8
    Avg.
    36.4
    Base
    64.6
    \Delta
    -28.2
  • OpenVLA-OFT (Kim et al., 2025a)
    Cond. D01–D06
    42.8
    Env. D07–D09
    63.1
    Obs. D10–D13
    80.4
    Exec. D14–D16
    85.3
    Robot D17–D19
    57.6
    Lang. D20
    95.4
    Avg.
    64.6
    Base
    97.1
    \Delta
    -32.5
  • OpenVLA-OFTw (Kim et al., 2025a)
    Cond. D01–D06
    34.9
    Env. D07–D09
    77.8
    Obs. D10–D13
    74.6
    Exec. D14–D16
    81.0
    Robot D17–D19
    54.0
    Lang. D20
    91.7
    Avg.
    61.9
    Base
    89.2
    \Delta
    -27.3
  • OpenVLA-OFTm (Kim et al., 2025a)
    Cond. D01–D06
    39.6
    Env. D07–D09
    61.4
    Obs. D10–D13
    80.4
    Exec. D14–D16
    85.7
    Robot D17–D19
    63.6
    Lang. D20
    93.8
    Avg.
    64.3
    Base
    92.5
    \Delta
    -28.2
  • OpenVLA-OFT+ (Fei et al., 2026)
    Cond. D01–D06
    41.3
    Env. D07–D09
    56.9
    Obs. D10–D13
    79.8
    Exec. D14–D16
    84.2
    Robot D17–D19
    64.0
    Lang. D20
    93.8
    Avg.
    63.8
    Base
    92.1
    \Delta
    -28.3
  • UniVLA (Bu et al., 2025)
    Cond. D01–D06
    30.9
    Env. D07–D09
    71.7
    Obs. D10–D13
    78.9
    Exec. D14–D16
    81.5
    Robot D17–D19
    56.2
    Lang. D20
    90.8
    Avg.
    61.0
    Base
    92.1
    \Delta
    -31.1
  • \pi_{0} (Black et al., 2025)
    Cond. D01–D06
    24.9
    Env. D07–D09
    56.9
    Obs. D10–D13
    52.7
    Exec. D14–D16
    30.8
    Robot D17–D19
    7.2
    Lang. D20
    61.3
    Avg.
    35.3
    Base
    63.8
    \Delta
    -28.4
  • \pi_{0}-FAST (Pertsch et al., 2025)
    Cond. D01–D06
    45.6
    Env. D07–D09
    45.4
    Obs. D10–D13
    60.9
    Exec. D14–D16
    70.0
    Robot D17–D19
    58.3
    Lang. D20
    79.2
    Avg.
    55.9
    Base
    80.4
    \Delta
    -24.5
  • \pi_{0.5} (Physical Intelligence et al., 2025)
    Cond. D01–D06
    60.5
    Env. D07–D09
    58.1
    Obs. D10–D13
    86.6
    Exec. D14–D16
    88.9
    Robot D17–D19
    77.5
    Lang. D20
    94.2
    Avg.
    73.8
    Base
    93.3
    \Delta
    -19.5
  • X-VLA (Zheng et al., 2025)
    Cond. D01–D06
    41.7
    Env. D07–D09
    59.7
    Obs. D10–D13
    93.6
    Exec. D14–D16
    70.1
    Robot D17–D19
    70.1
    Lang. D20
    95.0
    Avg.
    66.0
    Base
    95.0
    \Delta
    -29.0
  • GR00T N1.7 (Bjorck et al., 2025)
    Cond. D01–D06
    41.7
    Env. D07–D09
    66.0
    Obs. D10–D13
    77.9
    Exec. D14–D16
    82.4
    Robot D17–D19
    60.3
    Lang. D20
    89.6
    Avg.
    63.9
    Base
    90.4
    \Delta
    -26.6
  • MolmoAct2 (Fang et al., 2026)
    Cond. D01–D06
    58.6
    Env. D07–D09
    74.2
    Obs. D10–D13
    90.3
    Exec. D14–D16
    90.4
    Robot D17–D19
    79.0
    Lang. D20
    94.2
    Avg.
    76.9
    Base
    97.2
    \Delta
    -20.3
  • World-Action Models
    Cond. D01–D06
    データなし
    Env. D07–D09
    データなし
    Obs. D10–D13
    データなし
    Exec. D14–D16
    データなし
    Robot D17–D19
    データなし
    Lang. D20
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • Cosmos Policy (Kim et al., 2026)
    Cond. D01–D06
    45.6
    Env. D07–D09
    84.7
    Obs. D10–D13
    87.9
    Exec. D14–D16
    85.6
    Robot D17–D19
    70.6
    Lang. D20
    95.8
    Avg.
    72.2
    Base
    97.5
    \Delta
    -25.3
  • FastWAM (Yuan et al., 2026)
    Cond. D01–D06
    43.6
    Env. D07–D09
    67.1
    Obs. D10–D13
    90.7
    Exec. D14–D16
    89.9
    Robot D17–D19
    71.4
    Lang. D20
    93.2
    Avg.
    70.1
    Base
    97.8
    \Delta
    -27.6
  • LingBot-VA (Li et al., 2026)
    Cond. D01–D06
    77.3
    Env. D07–D09
    81.5
    Obs. D10–D13
    90.5
    Exec. D14–D16
    96.8
    Robot D17–D19
    59.3
    Lang. D20
    96.7
    Avg.
    81.8
    Base
    98.5
    \Delta
    -16.7
  • Robustness-Oriented Policies
    Cond. D01–D06
    データなし
    Env. D07–D09
    データなし
    Obs. D10–D13
    データなし
    Exec. D14–D16
    データなし
    Robot D17–D19
    データなし
    Lang. D20
    データなし
    Avg.
    データなし
    Base
    データなし
    \Delta
    データなし
  • Anchor-Align (Dalal et al., 2026)
    Cond. D01–D06
    42.4
    Env. D07–D09
    47.4
    Obs. D10–D13
    77.4
    Exec. D14–D16
    87.5
    Robot D17–D19
    58.8
    Lang. D20
    88.3
    Avg.
    61.6
    Base
    91.3
    \Delta
    -29.7
  • RIPT-VLA (Tan et al., 2025)
    Cond. D01–D06
    39.4
    Env. D07–D09
    58.6
    Obs. D10–D13
    74.5
    Exec. D14–D16
    79.6
    Robot D17–D19
    54.3
    Lang. D20
    89.6
    Avg.
    60.1
    Base
    87.9
    \Delta
    -27.8

4.1 Experimental Setup

We evaluate 17 representative robot manipulation policies spanning different policy paradigms, using their official checkpoints and inference settings. Experiments are conducted on the 8 held-out tasks of LIBERO-Pro2.0 under nominal execution, 22 static shifts, and 20 runtime shifts. Additional experimental details are provided in Appendix C. Our evaluation is organized around the following research questions:

  • Overall Performance Landscape: How robust are current robot policies under diverse static and runtime distribution shifts?
  • RQ1: What limits robustness under runtime distribution shifts?
  • RQ2: Does robustness compose under compound distribution shifts?
  • RQ3: Can robustness be learned from limited demonstrations and transferred to held-out tasks?

4.2 Overall Performance Landscape

Finding 1: High nominal performance does not imply strong robustness.

Table 1 and Table 2 show that, despite nominal success rates ranging from 63.8% to 98.5%, all policies degrade substantially under distribution shifts. Static shifts reduce average success rates to 33.9%–71.2% (25.1–41.8 points drop), while runtime shifts reduce them to 35.3%–81.8% (16.7–32.5 points drop). Moreover, robustness rankings do not consistently follow nominal performance. For example, FastWAM achieves higher nominal performance (97.8%) than \pi_{0.5} (93.3%), but its runtime robustness decreases to 70.1%, lower than \pi_{0.5} (73.8%). This ranking reversal indicates that nominal task success does not necessarily predict robustness under runtime distribution shifts. Therefore, robustness evaluation reveals additional capabilities beyond standard task solving metrics.

Finding 2: Static evaluation does not fully characterize runtime robustness. Figure 5 compares semantically matched static–runtime perturbation pairs, including object relocation, goal relocation, path obstruction, occlusion, camera changes, and language variation. Despite similar perturbation mechanisms, their effects differ across static and runtime settings. For example, averaged across the four suites, LingBot-VA achieves 56.7% success under static receiver-pose changes (S02), compared with 29.2% under runtime receiver-pose updates (D02). Camera changes exhibit the opposite pattern: 6.3% under S15 versus 60.8% under D07. These contrasting patterns show that static evaluation alone does not fully characterize runtime robustness.

Finding 3: Different perturbation categories expose heterogeneous robustness bottlenecks.

Robustness varies substantially across perturbation dimensions. Language variations remain relatively easy, with all models achieving over 46% success under S21, whereas execution-related shifts are considerably more challenging, reducing OpenVLA-OFT and \pi_{0} to 0.0% and 5.0% under S20. Runtime shifts further expose distinct weaknesses in observation, execution, and physical-state adaptation, showing that robustness is inherently multidimensional.

Figure 5: Comparison between matched static and runtime perturbations. Each pair contains a static shift occurring before execution and its runtime counterpart triggered during execution, including object pose changes (S01/D01, S02/D02), path constraints (S05/D05), occlusion (S12/D04), camera changes (S15/D07), robot-state variations (S17/D19), and language variations (S21/D20).

4.3 RQ1: What Limits Robustness under Runtime Distribution Shifts?

Table 3: Feedback utilization gain G_{\mathrm{feedback}} (pp) across dynamic perturbation categories.
  • OpenVLA-OFT
    Cond. D01–D06
    -26.6
    Env. D07–D09
    -22.8
    Obs. D10–D13
    -15.0
    Exec. D14–D16
    -8.7
    Robot D17–D19
    -27.3
    Lang. D20
    -1.1
    Avg.
    -19.8
  • \pi_{0.5}
    Cond. D01–D06
    -3.5
    Env. D07–D09
    -19.2
    Obs. D10–D13
    -3.2
    Exec. D14–D16
    -5.3
    Robot D17–D19
    +7.5
    Lang. D20
    +2.1
    Avg.
    -4.1
  • Anchor-Align
    Cond. D01–D06
    -15.1
    Env. D07–D09
    -19.5
    Obs. D10–D13
    -12.9
    Exec. D14–D16
    -10.8
    Robot D17–D19
    -8.9
    Lang. D20
    -7.9
    Avg.
    -13.4
  • FastWAM
    Cond. D01–D06
    -15.6
    Env. D07–D09
    -9.2
    Obs. D10–D13
    -1.4
    Exec. D14–D16
    -7.5
    Robot D17–D19
    -6.8
    Lang. D20
    -3.3
    Avg.
    -8.7
  • Cosmos Policy
    Cond. D01–D06
    -11.8
    Env. D07–D09
    -10.3
    Obs. D10–D13
    -6.4
    Exec. D14–D16
    -13.2
    Robot D17–D19
    +1.1
    Lang. D20
    -5.4
    Avg.
    -8.4

We investigate why policies fail under runtime distribution shifts through three controlled interventions targeting feedback utilization, closed-loop update frequency, and post-perturbation recovery.

RQ1-A: Can Policies Use Updated Observations?

We examine whether policies can exploit observations updated after runtime perturbations. Under live feedback, the policy continuously receives post-perturbation visual observations, whereas under freeze feedback, it repeatedly receives the last observation before the perturbation and therefore does not receive updated visual observations. Here, S_{1} denotes the success rate under a dynamic perturbation, while S_{0} denotes the success rate under the corresponding no-perturbation condition. Therefore, S_{1,\mathrm{live}} and S_{1,\mathrm{freeze}} measure performance with and without access to updated observations after a perturbation, whereas S_{0,\mathrm{live}} and S_{0,\mathrm{freeze}} capture the normal feedback effect in the absence of perturbations. We define

G_{\mathrm{feedback}}=(S_{1,\mathrm{live}}-S_{1,\mathrm{freeze}})-(S_{0,\mathrm{live}}-S_{0,\mathrm{freeze}}),

where positive values indicate a larger live-versus-freeze benefit under perturbation than in the corresponding no-perturbation condition. Table 3 summarizes the results, with complete results in Appendix A.2. (1) Reduced feedback benefit under perturbations. Negative values indicate that the benefit of updated visual observations is smaller than under nominal execution, not that updated observations provide no benefit. For example, under D01, OpenVLA-OFT achieves 5.4% success with live observations and 0.0% with frozen observations, despite G_{\mathrm{feedback}}=-46.1 percentage points. (2) Feedback benefit depends on perturbation type. Although most category-level contrasts are negative, \pi_{0.5} and Cosmos Policy obtain positive average contrasts of 7.5 and 1.1 percentage points, respectively, on robot-state changes (D17–D19).

Figure 6: Effect of policy execution horizon on robustness to dynamic perturbations. Panels (a)–(e) report task success rates under five representative perturbation types; panel (f) shows the average across these perturbations.
RQ1-B: Does Closed-Loop Update Frequency Limit Robustness?

We study whether action chunking delays the use of updated observations by fixing the prediction horizon H and varying the number of executed actions K before re-observation. Detailed horizon settings are shown in Appendix C.5. We evaluate target replanning (D01), goal replanning (D02), feasibility replanning (D03), path replanning (D05), and recovery replanning (D18) under execution ratios K/H. Figure 6 presents the results. (1) Replanning frequency exhibits a non-monotonic effect. Average success increases from 21.6\% at K/H=1 to 24.1\% at 1/2, but drops to 19.2\% at 1/8, showing that more frequent re-observation does not uniformly improve robustness. (2) Frequency sensitivity is policy-dependent. FastWAM and Cosmos Policy benefit more from shorter execution intervals, whereas Anchor-Align performs better with longer horizons. OpenVLA-OFT remains weak across settings, indicating that update frequency alone cannot compensate for limited perturbation handling.

Table 4: Average performance and intervention gains in RQ1-C. \Delta denotes the change in success rate relative to normal continuation.
  • OpenVLA-OFT
    Continue
    64.6
    \bm{\Delta_{\mathrm{Hold}}}
    -15.7
    \bm{\Delta_{\mathrm{Retry}}}
    -40.8
    \bm{\Delta_{\mathrm{Reset}}}
    -31.6
  • \pi_{0.5}
    Continue
    73.8
    \bm{\Delta_{\mathrm{Hold}}}
    +18.9
    \bm{\Delta_{\mathrm{Retry}}}
    -24.1
    \bm{\Delta_{\mathrm{Reset}}}
    +0.7
  • Anchor-Align
    Continue
    61.6
    \bm{\Delta_{\mathrm{Hold}}}
    +28.1
    \bm{\Delta_{\mathrm{Retry}}}
    -16.8
    \bm{\Delta_{\mathrm{Reset}}}
    +0.9
  • FastWAM
    Continue
    70.1
    \bm{\Delta_{\mathrm{Hold}}}
    +24.3
    \bm{\Delta_{\mathrm{Retry}}}
    -20.9
    \bm{\Delta_{\mathrm{Reset}}}
    -0.4
  • Cosmos Policy
    Continue
    72.2
    \bm{\Delta_{\mathrm{Hold}}}
    +26.0
    \bm{\Delta_{\mathrm{Retry}}}
    -23.0
    \bm{\Delta_{\mathrm{Reset}}}
    +2.5
RQ1-C: How Do Interventions Affect Recovery after a Runtime Shift?

We compare three recovery interventions following runtime shifts: Hold pauses execution, Retry replays actions from an unperturbed reference trajectory, and Reset restores the robot to its pre-perturbation pose. The baseline, Continue, proceeds under the perturbed condition without an additional recovery intervention. For each intervention I, we report the success-rate change \Delta_{I}=S_{I}-S_{\mathrm{continue}} in percentage points. Table 4 summarizes the average effects, with per-perturbation results in Appendix A.3. (1) Hold has policy-dependent effects. Hold increases average success by 18.9–28.1 percentage points for four of the five policies, but decreases it by 15.7 points for OpenVLA-OFT. (2) Retry reduces success on average. Retry lowers average success by 16.8–40.8 percentage points across all five policies, although it improves performance under some individual perturbations. (3) Reset has small average effects for most policies. The average change ranges from -0.4 to +2.5 percentage points for \pi_{0.5}, Anchor-Align, FastWAM, and Cosmos Policy, whereas OpenVLA-OFT declines by 31.6 points.

4.4 RQ2: Does Robustness Compose?

Real-world perturbations often occur jointly, raising the question of whether robustness to individual shifts transfers to compound settings. For a model m and perturbation composition \mathcal{C}=\{c_{1},\dots,c_{k}\}, we define the weakest-single gap as \Delta_{m}(\mathcal{C})=p_{m}(\mathcal{C})-\min_{c_{i}\in\mathcal{C}}p_{m}(c_{i}). A negative value indicates lower success than the weakest constituent perturbation; it does not by itself establish an interaction effect beyond independent failure accumulation. Figure 7 summarizes these gaps, while Appendix A.4 reports detailed success rates.

Figure 7: Weakest-single gap \Delta_{m}(\mathcal{C}) under composed perturbations. The heatmap compares static–static, static–dynamic, dynamic–dynamic, and three-way compositions across policies.
Robustness to individual perturbations does not reliably compose.

Table 5 shows that P02 (S09+S13), P06 (S09+D13), and T03 (S09+S22+D13) reduce success to only 9.2\%–12.9\%, although their constituent perturbations remain individually manageable (69.6\%–99.2\%). Thus, robustness to isolated shifts can collapse when multiple assumptions are violated jointly.

Recovery capability is also non-compositional.

As shown in Appendix A.4, \pi_{0.5} performs well on D02, D18, and D20 individually, yet drops to 22.9\% on P08 (D02+D18) and 17.5\% on P10 (D18+D20). This indicates that recovery from one runtime disturbance does not guarantee recovery under concurrent shifts.

Table 5: Key evidence for non-compositional robustness. Although all models perform reasonably well on the constituent perturbations S09, S13, D13, and S22, they all collapse on the composed settings P02, P06, and T03.
  • OpenVLA-OFT
    S09
    69.6
    S13
    94.2
    D13
    69.6
    S22
    93.3
    P02: S09+S13
    12.5
    P06: S09+D13
    12.5
    T03: S09+S22+D13
    12.5
  • \pi_{0.5}
    S09
    70.0
    S13
    92.5
    D13
    83.8
    S22
    94.2
    P02: S09+S13
    12.5
    P06: S09+D13
    12.1
    T03: S09+S22+D13
    12.9
  • Anchor-Align
    S09
    72.5
    S13
    86.7
    D13
    79.6
    S22
    87.9
    P02: S09+S13
    10.0
    P06: S09+D13
    11.3
    T03: S09+S22+D13
    11.7
  • FastWAM
    S09
    80.3
    S13
    91.2
    D13
    83.7
    S22
    88.3
    P02: S09+S13
    9.2
    P06: S09+D13
    11.7
    T03: S09+S22+D13
    10.0
  • Cosmos Policy
    S09
    87.5
    S13
    99.2
    D13
    81.7
    S22
    96.7
    P02: S09+S13
    12.9
    P06: S09+D13
    11.7
    T03: S09+S22+D13
    12.1

4.5 RQ3: Can Robustness Be Learned and Generalized?

Table 6: Transfer of robustness from training set to tasks held out from additional fine-tuning. Each column reports the average success rate over a static–dynamic perturbation pair. Gain denotes the improvement of Ours over \pi_{0.5}.
  • OpenVLA-OFT
    Object Pose
    20.8
    Receiver Pose
    24.4
    Path Obstacle
    14.8
    Camera Calibration
    26.9
    Robot State
    52.9
    Total
    28.0
  • \pi_{0.5}
    Object Pose
    61.9
    Receiver Pose
    71.0
    Path Obstacle
    19.8
    Camera Calibration
    8.1
    Robot State
    78.7
    Total
    47.9
  • Anchor-Align
    Object Pose
    27.9
    Receiver Pose
    39.4
    Path Obstacle
    12.1
    Camera Calibration
    6.0
    Robot State
    65.4
    Total
    30.2
  • FastWAM
    Object Pose
    28.8
    Receiver Pose
    16.0
    Path Obstacle
    19.3
    Camera Calibration
    8.3
    Robot State
    83.1
    Total
    31.1
  • Cosmos Policy
    Object Pose
    42.9
    Receiver Pose
    39.2
    Path Obstacle
    11.7
    Camera Calibration
    57.1
    Robot State
    82.9
    Total
    46.7
  • Ours
    Object Pose
    68.8
    Receiver Pose
    73.2
    Path Obstacle
    96.3
    Camera Calibration
    20.8
    Robot State
    91.7
    Total
    70.1
  • Gain
    Object Pose
    +6.9
    Receiver Pose
    +2.1
    Path Obstacle
    +76.5
    Camera Calibration
    +12.7
    Robot State
    +12.9
    Total
    +22.2

We ask whether robustness can be learned from limited demonstrations and transferred to tasks held out from additional fine-tuning. We train \pi_{0.5} on eight training tasks with ten trajectories per task, while keeping all evaluation tasks disjoint. We consider five semantically matched static–dynamic perturbation families: S01/D01 (object pose), S02/D02 (receiver pose), S05/D05 (path obstacle), S15/D07 (camera calibration), and S17/D19 (robot state). Training details are provided in Appendix C.6.

Robustness can be learned from limited demonstrations.

After robustness-oriented fine-tuning, our model achieves 70.1\% average robustness on unseen tasks, outperforming existing policies (28.0\%–47.9\%) in Table 6. The largest gain appears on path changes (S05/D05), where our model reaches 96.3\%, compared with below 20\% for all baselines.

Generalization depends on perturbation semantics.

Learned robustness transfers well in receiver pose (73.2\%) and robot-state shifts (91.7\%), but remains limited under camera calibration shifts (20.8\%). This suggests robustness generalizes better when perturbation semantics preserve stable task constraints than when they require broader perception–action recalibration.

5 Related Work

Embodied Foundation Models. Recent advances in large-scale robot datasets and foundation models have significantly improved the generalization capabilities of robotic manipulation policies. Datasets such as Open X-Embodiment and DROID provide diverse demonstrations across tasks, environments, and robotic platforms (Open X-Embodiment Collaboration et al., 2023; Khazatsky et al., 2024). Building on these resources, vision-language-action (VLA) models, including OpenVLA, \pi_{0}, and OpenVLA-OFT, learn generalizable visuomotor policies from large-scale multimodal data (Kim et al., 2025b; Black et al., 2025; Kim et al., 2025a). More recently, world-action models such as Cosmos Policy, LingBot-VA, and FastWAM have explored predictive world representations to support action generation and visuomotor control (Kim et al., 2026; Li et al., 2026; Yuan et al., 2026).

Robot Manipulation Benchmarks and Robustness Evaluation. Existing benchmarks, including Meta-World, RLBench, CALVIN, ManiSkill2, and LIBERO, provide standardized protocols for evaluating multi-task and language-conditioned robotic manipulation (Yu et al., 2020; James et al., 2020; Mees et al., 2022; Gu et al., 2023; Liu et al., 2023). Recent benchmarks such as RoboCasa, RoboTwin, and VLABench further expand task complexity and scene diversity (Nasiriany et al., 2024; Mu et al., 2025; Zhang et al., 2025), while RoboDojo introduces a unified simulation-and-real-world evaluation framework covering diverse manipulation capabilities (Chen et al., 2026). Beyond nominal task success, recent studies investigate policy robustness through environmental variations, domain randomization, and controlled perturbations (Li et al., 2024; Chen et al., 2025; Zhang et al., 2026). In particular, LIBERO-PRO exposes the reliance of VLA models on memorized behaviors under changes in objects, initial states, instructions, and environments (Zhou et al., 2025), while LIBERO-Plus evaluates robustness under progressively challenging static distribution shifts (Fei et al., 2026). Despite these advances, existing benchmarks primarily emphasize task diversity or robustness to pre-execution variations, leaving adaptation to disturbances arising during execution insufficiently evaluated. LIBERO-Pro2.0 addresses this critical gap by systematically assessing both static generalization and runtime robustness within a unified benchmark.

6 Conclusion

We present LIBERO-Pro2.0, a systematic benchmark for evaluating the robustness of embodied foundation models under static distribution shifts and runtime interventions. Our evaluation reveals substantial robustness gaps that remain hidden by strong nominal performance, while further analyses highlight challenges in online adaptation, recovery, compound robustness, and robustness transfer. We hope LIBERO-Pro2.0 provides a practical foundation for developing embodied policies that remain reliable under diverse and evolving deployment conditions.

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Appendix A Additional Experimental Results

This appendix provides the complete LIBERO-Pro2.0 results supplementing the feedback-utilization, recovery-intervention, and robustness-composition analyses in the main paper.

A.1 Main Results

Table 7: Static and runtime perturbation results on LIBERO-Goal. All values are reported in percentages (%).
  • OpenVLA
    S1
    1.7
    S2
    8.3
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    48.3
    S7
    35.0
    S8
    33.3
    S9
    43.3
    S10
    46.7
    S11
    41.7
    S12
    0.0
    S13
    31.7
    S14
    16.7
    S15
    1.7
    S16
    0.0
    S17
    15.0
    S18
    51.7
    S19
    46.7
    S20
    0.0
    S21
    63.3
    S22
    43.3
  • OpenVLA-OFT
    S1
    33.3
    S2
    0.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    86.7
    S7
    58.3
    S8
    83.3
    S9
    81.7
    S10
    91.7
    S11
    85.0
    S12
    55.0
    S13
    90.0
    S14
    93.3
    S15
    0.0
    S16
    8.3
    S17
    0.0
    S18
    81.7
    S19
    90.0
    S20
    0.0
    S21
    88.3
    S22
    88.3
  • OpenVLA-OFTw
    S1
    20.0
    S2
    1.7
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    76.7
    S7
    55.0
    S8
    86.7
    S9
    81.7
    S10
    86.7
    S11
    90.0
    S12
    0.0
    S13
    78.3
    S14
    75.0
    S15
    43.3
    S16
    0.0
    S17
    40.0
    S18
    76.7
    S19
    86.7
    S20
    0.0
    S21
    85.0
    S22
    83.3
  • OpenVLA-OFTm
    S1
    40.0
    S2
    1.7
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    76.7
    S7
    55.0
    S8
    73.3
    S9
    71.7
    S10
    80.0
    S11
    56.7
    S12
    53.3
    S13
    85.0
    S14
    86.7
    S15
    0.0
    S16
    1.7
    S17
    0.0
    S18
    75.0
    S19
    86.7
    S20
    0.0
    S21
    80.0
    S22
    85.0
  • OpenVLA-OFT+
    S1
    28.3
    S2
    1.7
    S3
    0.0
    S4
    5.0
    S5
    0.0
    S6
    60.0
    S7
    45.0
    S8
    60.0
    S9
    56.7
    S10
    55.0
    S11
    63.3
    S12
    65.0
    S13
    76.7
    S14
    88.3
    S15
    0.0
    S16
    0.0
    S17
    0.0
    S18
    83.3
    S19
    78.3
    S20
    0.0
    S21
    80.0
    S22
    81.7
  • UniVLA
    S1
    3.3
    S2
    5.0
    S3
    5.0
    S4
    8.3
    S5
    0.0
    S6
    61.7
    S7
    81.7
    S8
    76.7
    S9
    85.0
    S10
    76.7
    S11
    76.7
    S12
    0.0
    S13
    73.3
    S14
    78.3
    S15
    26.7
    S16
    0.0
    S17
    40.0
    S18
    85.0
    S19
    83.3
    S20
    0.0
    S21
    83.3
    S22
    83.3
  • \pi_{0}
    S1
    3.3
    S2
    0.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    48.3
    S7
    51.7
    S8
    58.3
    S9
    56.7
    S10
    55.0
    S11
    45.0
    S12
    63.3
    S13
    65.0
    S14
    43.3
    S15
    50.0
    S16
    51.7
    S17
    30.0
    S18
    1.7
    S19
    51.7
    S20
    13.3
    S21
    40.0
    S22
    51.7
  • \pi_{0}-FAST
    S1
    55.0
    S2
    36.7
    S3
    8.3
    S4
    8.3
    S5
    0.0
    S6
    71.7
    S7
    88.3
    S8
    71.7
    S9
    76.7
    S10
    86.7
    S11
    63.3
    S12
    78.3
    S13
    93.3
    S14
    88.3
    S15
    0.0
    S16
    25.0
    S17
    43.3
    S18
    50.0
    S19
    90.0
    S20
    0.0
    S21
    93.3
    S22
    91.7
  • \pi_{0.5}
    S1
    73.3
    S2
    51.7
    S3
    15.0
    S4
    61.7
    S5
    6.7
    S6
    95.0
    S7
    75.0
    S8
    93.3
    S9
    96.7
    S10
    93.3
    S11
    95.0
    S12
    66.7
    S13
    96.7
    S14
    95.0
    S15
    0.0
    S16
    0.0
    S17
    50.0
    S18
    93.3
    S19
    95.0
    S20
    0.0
    S21
    96.7
    S22
    98.3
  • X-VLA
    S1
    23.3
    S2
    0.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    93.3
    S7
    93.3
    S8
    96.7
    S9
    100.0
    S10
    95.0
    S11
    85.0
    S12
    46.7
    S13
    93.3
    S14
    96.7
    S15
    0.0
    S16
    0.0
    S17
    65.0
    S18
    28.3
    S19
    98.3
    S20
    48.3
    S21
    95.0
    S22
    95.0
  • GR00T N1.7
    S1
    21.7
    S2
    1.7
    S3
    30.0
    S4
    0.0
    S5
    0.0
    S6
    73.3
    S7
    75.0
    S8
    85.0
    S9
    81.7
    S10
    86.7
    S11
    73.3
    S12
    71.7
    S13
    83.3
    S14
    80.0
    S15
    0.0
    S16
    0.0
    S17
    30.0
    S18
    85.0
    S19
    90.0
    S20
    0.0
    S21
    81.7
    S22
    83.3
  • MolmoAct2
    S1
    73.3
    S2
    46.7
    S3
    6.7
    S4
    28.3
    S5
    3.3
    S6
    86.7
    S7
    66.7
    S8
    100.0
    S9
    96.7
    S10
    98.3
    S11
    61.7
    S12
    86.7
    S13
    96.7
    S14
    96.7
    S15
    1.7
    S16
    55.0
    S17
    58.3
    S18
    96.7
    S19
    98.3
    S20
    0.0
    S21
    93.3
    S22
    95.0
  • Anchor-Align
    S1
    35.0
    S2
    5.0
    S3
    0.0
    S4
    5.0
    S5
    0.0
    S6
    61.7
    S7
    50.0
    S8
    90.0
    S9
    91.7
    S10
    80.0
    S11
    56.7
    S12
    85.0
    S13
    83.3
    S14
    83.3
    S15
    0.0
    S16
    0.0
    S17
    21.7
    S18
    91.7
    S19
    91.7
    S20
    0.0
    S21
    91.7
    S22
    90.0
  • RIPT-VLA
    S1
    20.0
    S2
    0.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    73.3
    S7
    48.3
    S8
    55.0
    S9
    58.3
    S10
    65.0
    S11
    66.7
    S12
    55.0
    S13
    60.0
    S14
    66.7
    S15
    0.0
    S16
    0.0
    S17
    1.7
    S18
    56.7
    S19
    71.7
    S20
    0.0
    S21
    63.3
    S22
    61.7
  • Cosmos Policy
    S1
    56.7
    S2
    43.3
    S3
    23.3
    S4
    13.3
    S5
    23.3
    S6
    73.3
    S7
    90.0
    S8
    80.0
    S9
    90.0
    S10
    96.7
    S11
    83.3
    S12
    96.7
    S13
    100.0
    S14
    96.7
    S15
    23.3
    S16
    53.3
    S17
    56.7
    S18
    96.7
    S19
    100.0
    S20
    16.7
    S21
    86.7
    S22
    96.7
  • FastWAM
    S1
    43.3
    S2
    0.0
    S3
    0.0
    S4
    1.7
    S5
    0.0
    S6
    85.0
    S7
    55.0
    S8
    81.7
    S9
    91.7
    S10
    90.0
    S11
    86.7
    S12
    76.7
    S13
    76.7
    S14
    76.7
    S15
    0.0
    S16
    0.0
    S17
    63.3
    S18
    90.0
    S19
    0.0
    S20
    0.0
    S21
    76.7
    S22
    83.3
  • LingBot-VA
    S1
    38.3
    S2
    5.0
    S3
    45.0
    S4
    3.3
    S5
    78.3
    S6
    58.3
    S7
    46.7
    S8
    88.3
    S9
    48.3
    S10
    86.7
    S11
    90.0
    S12
    90.0
    S13
    88.3
    S14
    93.3
    S15
    0.0
    S16
    0.0
    S17
    96.7
    S18
    95.0
    S19
    66.7
    S20
    73.3
    S21
    90.0
    S22
    91.7
Table 8: Static and runtime perturbation results on LIBERO-Object. All values are reported in percentages (%).
  • OpenVLA
    S1
    0.0
    S2
    3.3
    S3
    6.7
    S4
    3.3
    S5
    0.0
    S6
    0.0
    S7
    45.0
    S8
    80.0
    S9
    81.7
    S10
    78.3
    S11
    11.7
    S12
    0.0
    S13
    76.7
    S14
    5.0
    S15
    10.0
    S16
    0.0
    S17
    36.7
    S18
    88.3
    S19
    88.3
    S20
    0.0
    S21
    81.7
    S22
    75.0
  • OpenVLA-OFT
    S1
    8.3
    S2
    1.7
    S3
    0.0
    S4
    16.7
    S5
    1.7
    S6
    0.0
    S7
    95.0
    S8
    91.7
    S9
    60.0
    S10
    98.3
    S11
    80.0
    S12
    70.0
    S13
    98.3
    S14
    100.0
    S15
    10.0
    S16
    20.0
    S17
    51.7
    S18
    100.0
    S19
    96.7
    S20
    0.0
    S21
    96.7
    S22
    100.0
  • OpenVLA-OFTw
    S1
    0.0
    S2
    0.0
    S3
    1.7
    S4
    0.0
    S5
    0.0
    S6
    0.0
    S7
    95.0
    S8
    98.3
    S9
    100.0
    S10
    100.0
    S11
    61.7
    S12
    0.0
    S13
    98.3
    S14
    86.7
    S15
    50.0
    S16
    45.0
    S17
    96.7
    S18
    15.0
    S19
    100.0
    S20
    0.0
    S21
    100.0
    S22
    98.3
  • OpenVLA-OFTm
    S1
    43.3
    S2
    6.7
    S3
    1.7
    S4
    3.3
    S5
    0.0
    S6
    0.0
    S7
    76.7
    S8
    93.3
    S9
    40.0
    S10
    98.3
    S11
    66.7
    S12
    98.3
    S13
    86.7
    S14
    93.3
    S15
    3.3
    S16
    5.0
    S17
    86.7
    S18
    100.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • OpenVLA-OFT+
    S1
    48.3
    S2
    63.3
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    0.0
    S7
    81.7
    S8
    93.3
    S9
    83.3
    S10
    100.0
    S11
    68.3
    S12
    100.0
    S13
    95.0
    S14
    100.0
    S15
    0.0
    S16
    3.3
    S17
    91.7
    S18
    100.0
    S19
    100.0
    S20
    0.0
    S21
    100.0
    S22
    98.3
  • UniVLA
    S1
    5.0
    S2
    3.3
    S3
    3.3
    S4
    35.0
    S5
    0.0
    S6
    0.0
    S7
    78.3
    S8
    91.7
    S9
    100.0
    S10
    86.7
    S11
    26.7
    S12
    0.0
    S13
    100.0
    S14
    51.7
    S15
    0.0
    S16
    0.0
    S17
    66.7
    S18
    98.3
    S19
    100.0
    S20
    0.0
    S21
    96.7
    S22
    93.3
  • \pi_{0}
    S1
    1.7
    S2
    0.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    0.0
    S7
    61.7
    S8
    78.3
    S9
    81.7
    S10
    81.7
    S11
    41.7
    S12
    71.7
    S13
    88.3
    S14
    80.0
    S15
    85.0
    S16
    76.7
    S17
    20.0
    S18
    0.0
    S19
    73.3
    S20
    1.7
    S21
    41.7
    S22
    85.0
  • \pi_{0}-FAST
    S1
    56.7
    S2
    65.0
    S3
    0.0
    S4
    1.7
    S5
    5.0
    S6
    0.0
    S7
    83.3
    S8
    96.7
    S9
    100.0
    S10
    95.0
    S11
    83.3
    S12
    100.0
    S13
    100.0
    S14
    95.0
    S15
    0.0
    S16
    20.0
    S17
    93.3
    S18
    95.0
    S19
    91.7
    S20
    0.0
    S21
    98.3
    S22
    93.3
  • \pi_{0.5}
    S1
    88.3
    S2
    85.0
    S3
    21.7
    S4
    56.7
    S5
    3.3
    S6
    0.0
    S7
    71.7
    S8
    61.7
    S9
    51.7
    S10
    96.7
    S11
    75.0
    S12
    95.0
    S13
    98.3
    S14
    98.3
    S15
    0.0
    S16
    3.3
    S17
    98.3
    S18
    100.0
    S19
    100.0
    S20
    0.0
    S21
    100.0
    S22
    100.0
  • X-VLA
    S1
    10.0
    S2
    0.0
    S3
    0.0
    S4
    5.0
    S5
    18.3
    S6
    0.0
    S7
    78.3
    S8
    88.3
    S9
    100.0
    S10
    98.3
    S11
    65.0
    S12
    80.0
    S13
    100.0
    S14
    98.3
    S15
    0.0
    S16
    18.3
    S17
    96.7
    S18
    25.0
    S19
    98.3
    S20
    91.7
    S21
    100.0
    S22
    100.0
  • GR00T N1.7
    S1
    30.0
    S2
    45.0
    S3
    5.0
    S4
    0.0
    S5
    3.3
    S6
    0.0
    S7
    66.7
    S8
    93.3
    S9
    95.0
    S10
    96.7
    S11
    68.3
    S12
    98.3
    S13
    100.0
    S14
    95.0
    S15
    0.0
    S16
    0.0
    S17
    86.7
    S18
    100.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    96.7
  • MolmoAct2
    S1
    100.0
    S2
    80.0
    S3
    5.0
    S4
    96.7
    S5
    5.0
    S6
    0.0
    S7
    76.7
    S8
    100.0
    S9
    100.0
    S10
    100.0
    S11
    85.0
    S12
    100.0
    S13
    100.0
    S14
    100.0
    S15
    0.0
    S16
    100.0
    S17
    98.3
    S18
    96.7
    S19
    98.3
    S20
    0.0
    S21
    100.0
    S22
    100.0
  • Anchor-Align
    S1
    1.7
    S2
    50.0
    S3
    0.0
    S4
    0.0
    S5
    0.0
    S6
    0.0
    S7
    58.3
    S8
    100.0
    S9
    96.7
    S10
    33.3
    S11
    68.3
    S12
    96.7
    S13
    91.7
    S14
    100.0
    S15
    0.0
    S16
    0.0
    S17
    95.0
    S18
    100.0
    S19
    96.7
    S20
    0.0
    S21
    96.7
    S22
    100.0
  • RIPT-VLA
    S1
    5.0
    S2
    0.0
    S3
    0.0
    S4
    16.7
    S5
    0.0
    S6
    0.0
    S7
    95.0
    S8
    90.0
    S9
    68.3
    S10
    96.7
    S11
    76.7
    S12
    88.3
    S13
    96.7
    S14
    96.7
    S15
    1.7
    S16
    1.7
    S17
    60.0
    S18
    96.7
    S19
    98.3
    S20
    0.0
    S21
    95.0
    S22
    96.7
  • Cosmos Policy
    S1
    50.0
    S2
    36.7
    S3
    20.0
    S4
    3.3
    S5
    0.0
    S6
    20.0
    S7
    100.0
    S8
    100.0
    S9
    96.7
    S10
    100.0
    S11
    86.7
    S12
    100.0
    S13
    100.0
    S14
    100.0
    S15
    20.0
    S16
    66.7
    S17
    66.7
    S18
    86.7
    S19
    96.7
    S20
    0.0
    S21
    100.0
    S22
    100.0
  • FastWAM
    S1
    39.7
    S2
    7.7
    S3
    0.0
    S4
    1.7
    S5
    0.0
    S6
    0.0
    S7
    81.7
    S8
    99.0
    S9
    100.0
    S10
    100.0
    S11
    81.7
    S12
    100.0
    S13
    100.0
    S14
    100.0
    S15
    0.0
    S16
    0.0
    S17
    98.3
    S18
    100.0
    S19
    38.0
    S20
    0.0
    S21
    100.0
    S22
    100.0
  • LingBot-VA
    S1
    73.3
    S2
    95.0
    S3
    100.0
    S4
    15.0
    S5
    100.0
    S6
    75.0
    S7
    40.0
    S8
    100.0
    S9
    0.0
    S10
    100.0
    S11
    98.3
    S12
    100.0
    S13
    96.7
    S14
    100.0
    S15
    5.0
    S16
    31.7
    S17
    100.0
    S18
    100.0
    S19
    100.0
    S20
    88.3
    S21
    100.0
    S22
    98.3
Table 9: Static and runtime perturbation results on LIBERO-Spatial. All values are reported in percentages (%).
  • OpenVLA
    S1
    15.0
    S2
    5.0
    S3
    3.3
    S4
    N/A
    S5
    0.0
    S6
    70.0
    S7
    88.3
    S8
    70.0
    S9
    68.3
    S10
    36.7
    S11
    71.7
    S12
    0.0
    S13
    73.3
    S14
    38.3
    S15
    40.0
    S16
    28.3
    S17
    83.3
    S18
    83.3
    S19
    88.3
    S20
    0.0
    S21
    75.0
    S22
    80.0
  • OpenVLA-OFT
    S1
    73.3
    S2
    76.7
    S3
    30.0
    S4
    N/A
    S5
    0.0
    S6
    80.0
    S7
    100.0
    S8
    93.3
    S9
    98.3
    S10
    88.3
    S11
    100.0
    S12
    98.3
    S13
    93.3
    S14
    98.3
    S15
    51.7
    S16
    81.7
    S17
    96.7
    S18
    86.7
    S19
    100.0
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • OpenVLA-OFTw
    S1
    40.0
    S2
    15.0
    S3
    5.0
    S4
    N/A
    S5
    1.7
    S6
    75.0
    S7
    98.3
    S8
    91.7
    S9
    98.3
    S10
    48.3
    S11
    96.7
    S12
    6.7
    S13
    98.3
    S14
    98.3
    S15
    93.3
    S16
    90.0
    S17
    100.0
    S18
    10.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • OpenVLA-OFTm
    S1
    73.3
    S2
    96.7
    S3
    28.3
    S4
    N/A
    S5
    0.0
    S6
    75.0
    S7
    100.0
    S8
    95.0
    S9
    95.0
    S10
    70.0
    S11
    95.0
    S12
    53.3
    S13
    90.0
    S14
    98.3
    S15
    41.7
    S16
    65.0
    S17
    100.0
    S18
    93.3
    S19
    100.0
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • OpenVLA-OFT+
    S1
    66.7
    S2
    98.3
    S3
    35.0
    S4
    N/A
    S5
    0.0
    S6
    81.7
    S7
    96.7
    S8
    95.0
    S9
    95.0
    S10
    86.7
    S11
    88.3
    S12
    66.7
    S13
    98.3
    S14
    98.3
    S15
    38.3
    S16
    56.7
    S17
    98.3
    S18
    100.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    98.3
  • UniVLA
    S1
    18.3
    S2
    55.0
    S3
    10.0
    S4
    N/A
    S5
    0.0
    S6
    75.0
    S7
    98.3
    S8
    98.3
    S9
    98.3
    S10
    68.3
    S11
    98.3
    S12
    1.7
    S13
    51.7
    S14
    95.0
    S15
    73.3
    S16
    80.0
    S17
    98.3
    S18
    98.3
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    95.0
  • \pi_{0}
    S1
    6.7
    S2
    0.0
    S3
    8.3
    S4
    N/A
    S5
    0.0
    S6
    40.0
    S7
    61.7
    S8
    71.7
    S9
    65.0
    S10
    55.0
    S11
    66.7
    S12
    61.7
    S13
    56.7
    S14
    60.0
    S15
    58.3
    S16
    71.7
    S17
    55.0
    S18
    10.0
    S19
    68.3
    S20
    3.3
    S21
    60.0
    S22
    60.0
  • \pi_{0}-FAST
    S1
    83.3
    S2
    90.0
    S3
    25.0
    S4
    N/A
    S5
    0.0
    S6
    83.3
    S7
    98.3
    S8
    93.3
    S9
    100.0
    S10
    95.0
    S11
    98.3
    S12
    96.7
    S13
    91.7
    S14
    100.0
    S15
    15.0
    S16
    96.7
    S17
    93.3
    S18
    78.3
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • \pi_{0.5}
    S1
    95.0
    S2
    100.0
    S3
    40.0
    S4
    N/A
    S5
    6.7
    S6
    85.0
    S7
    100.0
    S8
    98.3
    S9
    93.3
    S10
    96.7
    S11
    100.0
    S12
    81.7
    S13
    100.0
    S14
    100.0
    S15
    0.0
    S16
    100.0
    S17
    98.3
    S18
    100.0
    S19
    100.0
    S20
    0.0
    S21
    98.3
    S22
    98.3
  • X-VLA
    S1
    40.0
    S2
    1.7
    S3
    3.3
    S4
    N/A
    S5
    0.0
    S6
    63.3
    S7
    98.3
    S8
    95.0
    S9
    93.3
    S10
    81.7
    S11
    90.0
    S12
    31.7
    S13
    88.3
    S14
    98.3
    S15
    31.7
    S16
    48.3
    S17
    93.3
    S18
    65.0
    S19
    95.0
    S20
    98.3
    S21
    93.3
    S22
    91.7
  • GR00T N1.7
    S1
    85.0
    S2
    76.7
    S3
    23.3
    S4
    N/A
    S5
    0.0
    S6
    81.7
    S7
    100.0
    S8
    95.0
    S9
    95.0
    S10
    95.0
    S11
    93.3
    S12
    98.3
    S13
    100.0
    S14
    100.0
    S15
    23.3
    S16
    98.3
    S17
    96.7
    S18
    100.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • MolmoAct2
    S1
    75.0
    S2
    95.0
    S3
    31.7
    S4
    N/A
    S5
    0.0
    S6
    85.0
    S7
    100.0
    S8
    88.3
    S9
    100.0
    S10
    95.0
    S11
    100.0
    S12
    98.3
    S13
    98.3
    S14
    100.0
    S15
    40.0
    S16
    98.3
    S17
    96.7
    S18
    100.0
    S19
    100.0
    S20
    0.0
    S21
    96.7
    S22
    98.3
  • Anchor-Align
    S1
    95.0
    S2
    95.0
    S3
    36.7
    S4
    N/A
    S5
    0.0
    S6
    21.7
    S7
    100.0
    S8
    68.3
    S9
    81.7
    S10
    91.7
    S11
    98.3
    S12
    98.3
    S13
    93.3
    S14
    96.7
    S15
    0.0
    S16
    95.0
    S17
    100.0
    S18
    100.0
    S19
    98.3
    S20
    0.0
    S21
    98.3
    S22
    100.0
  • RIPT-VLA
    S1
    78.3
    S2
    76.7
    S3
    26.7
    S4
    N/A
    S5
    0.0
    S6
    75.0
    S7
    98.3
    S8
    93.3
    S9
    95.0
    S10
    88.3
    S11
    100.0
    S12
    98.3
    S13
    91.7
    S14
    96.7
    S15
    48.3
    S16
    81.7
    S17
    100.0
    S18
    93.3
    S19
    100.0
    S20
    0.0
    S21
    100.0
    S22
    100.0
  • Cosmos Policy
    S1
    73.3
    S2
    56.7
    S3
    53.3
    S4
    N/A
    S5
    13.3
    S6
    90.0
    S7
    100.0
    S8
    93.3
    S9
    96.7
    S10
    90.0
    S11
    90.0
    S12
    93.3
    S13
    96.7
    S14
    96.7
    S15
    63.3
    S16
    93.3
    S17
    83.3
    S18
    93.3
    S19
    90.0
    S20
    0.0
    S21
    90.0
    S22
    100.0
  • FastWAM
    S1
    40.0
    S2
    49.0
    S3
    27.0
    S4
    N/A
    S5
    1.0
    S6
    81.0
    S7
    98.0
    S8
    95.0
    S9
    91.0
    S10
    88.0
    S11
    91.0
    S12
    77.0
    S13
    88.0
    S14
    94.0
    S15
    0.0
    S16
    23.0
    S17
    92.0
    S18
    98.0
    S19
    1.0
    S20
    11.0
    S21
    88.0
    S22
    85.0
  • LingBot-VA
    S1
    83.3
    S2
    75.0
    S3
    30.0
    S4
    N/A
    S5
    93.3
    S6
    0.0
    S7
    0.0
    S8
    91.7
    S9
    0.0
    S10
    98.3
    S11
    100.0
    S12
    93.3
    S13
    100.0
    S14
    98.3
    S15
    13.3
    S16
    21.7
    S17
    100.0
    S18
    100.0
    S19
    96.7
    S20
    93.3
    S21
    100.0
    S22
    100.0
Table 10: Static and runtime perturbation results on LIBERO-10. All values are reported in percentages (%).
  • OpenVLA
    S1
    18.3
    S2
    5.0
    S3
    26.7
    S4
    0.0
    S5
    13.3
    S6
    1.7
    S7
    55.0
    S8
    53.3
    S9
    18.3
    S10
    36.7
    S11
    43.3
    S12
    0.0
    S13
    46.7
    S14
    38.3
    S15
    28.3
    S16
    31.7
    S17
    23.3
    S18
    50.0
    S19
    50.0
    S20
    0.0
    S21
    50.0
    S22
    41.7
  • OpenVLA-OFT
    S1
    30.0
    S2
    26.7
    S3
    36.7
    S4
    0.0
    S5
    46.7
    S6
    33.3
    S7
    91.7
    S8
    95.0
    S9
    38.3
    S10
    80.0
    S11
    96.7
    S12
    41.7
    S13
    95.0
    S14
    68.3
    S15
    0.0
    S16
    6.7
    S17
    23.3
    S18
    91.7
    S19
    90.0
    S20
    0.0
    S21
    95.0
    S22
    85.0
  • OpenVLA-OFTw
    S1
    35.0
    S2
    8.3
    S3
    33.3
    S4
    3.3
    S5
    61.7
    S6
    11.7
    S7
    78.3
    S8
    85.0
    S9
    46.7
    S10
    70.0
    S11
    66.7
    S12
    0.0
    S13
    75.0
    S14
    70.0
    S15
    73.3
    S16
    60.0
    S17
    41.7
    S18
    63.3
    S19
    71.7
    S20
    1.7
    S21
    76.7
    S22
    66.7
  • OpenVLA-OFTm
    S1
    31.7
    S2
    30.0
    S3
    56.7
    S4
    0.0
    S5
    66.7
    S6
    15.0
    S7
    95.0
    S8
    100.0
    S9
    46.7
    S10
    90.0
    S11
    95.0
    S12
    90.0
    S13
    91.7
    S14
    73.3
    S15
    10.0
    S16
    88.3
    S17
    43.3
    S18
    78.3
    S19
    96.7
    S20
    0.0
    S21
    91.7
    S22
    88.3
  • OpenVLA-OFT+
    S1
    36.7
    S2
    35.0
    S3
    48.3
    S4
    0.0
    S5
    68.3
    S6
    10.0
    S7
    90.0
    S8
    86.7
    S9
    43.3
    S10
    83.3
    S11
    85.0
    S12
    91.7
    S13
    85.0
    S14
    88.3
    S15
    0.0
    S16
    75.0
    S17
    41.7
    S18
    75.0
    S19
    90.0
    S20
    0.0
    S21
    81.7
    S22
    85.0
  • UniVLA
    S1
    36.7
    S2
    28.3
    S3
    36.7
    S4
    6.7
    S5
    30.0
    S6
    35.0
    S7
    63.3
    S8
    68.3
    S9
    5.0
    S10
    66.7
    S11
    75.0
    S12
    0.0
    S13
    86.7
    S14
    26.7
    S15
    73.3
    S16
    78.3
    S17
    61.7
    S18
    88.3
    S19
    83.3
    S20
    0.0
    S21
    88.3
    S22
    81.7
  • \pi_{0}
    S1
    0.0
    S2
    1.7
    S3
    18.3
    S4
    0.0
    S5
    31.7
    S6
    10.0
    S7
    55.0
    S8
    43.3
    S9
    18.3
    S10
    51.7
    S11
    50.0
    S12
    45.0
    S13
    40.0
    S14
    41.7
    S15
    41.7
    S16
    41.7
    S17
    31.7
    S18
    5.0
    S19
    50.0
    S20
    1.7
    S21
    43.3
    S22
    48.3
  • \pi_{0}-FAST
    S1
    3.3
    S2
    0.0
    S3
    21.7
    S4
    0.0
    S5
    31.7
    S6
    3.3
    S7
    23.3
    S8
    16.7
    S9
    18.3
    S10
    36.7
    S11
    31.7
    S12
    31.7
    S13
    33.3
    S14
    33.3
    S15
    0.0
    S16
    20.0
    S17
    6.7
    S18
    1.7
    S19
    21.7
    S20
    0.0
    S21
    35.0
    S22
    26.7
  • \pi_{0.5}
    S1
    36.7
    S2
    20.0
    S3
    68.3
    S4
    76.7
    S5
    53.3
    S6
    25.0
    S7
    71.7
    S8
    70.0
    S9
    38.3
    S10
    83.3
    S11
    81.7
    S12
    63.3
    S13
    75.0
    S14
    75.0
    S15
    0.0
    S16
    50.0
    S17
    70.0
    S18
    70.0
    S19
    71.7
    S20
    3.3
    S21
    78.3
    S22
    80.0
  • X-VLA
    S1
    16.7
    S2
    16.7
    S3
    13.3
    S4
    3.3
    S5
    86.7
    S6
    50.0
    S7
    100.0
    S8
    95.0
    S9
    28.3
    S10
    100.0
    S11
    91.7
    S12
    55.0
    S13
    100.0
    S14
    100.0
    S15
    48.3
    S16
    53.3
    S17
    95.0
    S18
    25.0
    S19
    100.0
    S20
    48.3
    S21
    75.0
    S22
    98.3
  • GR00T N1.7
    S1
    15.0
    S2
    23.3
    S3
    33.3
    S4
    0.0
    S5
    61.7
    S6
    5.0
    S7
    80.0
    S8
    80.0
    S9
    41.7
    S10
    65.0
    S11
    71.7
    S12
    51.7
    S13
    86.7
    S14
    80.0
    S15
    3.3
    S16
    86.7
    S17
    50.0
    S18
    75.0
    S19
    83.3
    S20
    0.0
    S21
    76.7
    S22
    81.7
  • MolmoAct2
    S1
    41.7
    S2
    28.3
    S3
    83.3
    S4
    86.7
    S5
    60.0
    S6
    18.3
    S7
    81.7
    S8
    78.3
    S9
    41.7
    S10
    91.7
    S11
    95.0
    S12
    56.7
    S13
    76.7
    S14
    76.7
    S15
    23.3
    S16
    80.0
    S17
    60.0
    S18
    73.3
    S19
    86.7
    S20
    0.0
    S21
    88.3
    S22
    83.3
  • Anchor-Align
    S1
    26.7
    S2
    20.0
    S3
    38.3
    S4
    0.0
    S5
    36.7
    S6
    16.7
    S7
    70.0
    S8
    68.3
    S9
    20.0
    S10
    73.3
    S11
    63.3
    S12
    83.3
    S13
    78.3
    S14
    73.3
    S15
    0.0
    S16
    21.7
    S17
    31.7
    S18
    71.7
    S19
    60.0
    S20
    3.3
    S21
    76.7
    S22
    61.7
  • RIPT-VLA
    S1
    23.3
    S2
    16.7
    S3
    23.3
    S4
    0.0
    S5
    45.0
    S6
    16.7
    S7
    90.0
    S8
    96.7
    S9
    38.3
    S10
    78.3
    S11
    93.3
    S12
    45.0
    S13
    85.0
    S14
    75.0
    S15
    0.0
    S16
    21.7
    S17
    26.7
    S18
    85.0
    S19
    88.3
    S20
    0.0
    S21
    88.3
    S22
    83.3
  • Cosmos Policy
    S1
    76.7
    S2
    70.0
    S3
    33.3
    S4
    3.3
    S5
    20.0
    S6
    33.3
    S7
    90.0
    S8
    90.0
    S9
    66.7
    S10
    90.0
    S11
    90.0
    S12
    100.0
    S13
    100.0
    S14
    90.0
    S15
    46.7
    S16
    100.0
    S17
    83.3
    S18
    93.3
    S19
    96.7
    S20
    0.0
    S21
    96.7
    S22
    90.0
  • FastWAM
    S1
    25.0
    S2
    6.7
    S3
    15.0
    S4
    0.0
    S5
    78.3
    S6
    31.7
    S7
    96.7
    S8
    95.0
    S9
    38.3
    S10
    100.0
    S11
    100.0
    S12
    93.3
    S13
    100.0
    S14
    100.0
    S15
    0.0
    S16
    0.0
    S17
    86.7
    S18
    71.7
    S19
    0.0
    S20
    0.0
    S21
    96.7
    S22
    85.0
  • LingBot-VA
    S1
    46.7
    S2
    51.7
    S3
    88.3
    S4
    0.0
    S5
    83.3
    S6
    38.3
    S7
    0.0
    S8
    98.3
    S9
    0.0
    S10
    76.7
    S11
    80.0
    S12
    90.0
    S13
    91.7
    S14
    85.0
    S15
    6.7
    S16
    26.7
    S17
    98.3
    S18
    96.7
    S19
    60.0
    S20
    91.7
    S21
    98.3
    S22
    93.3

A.2 Complete Feedback Utilization Results

Table 11 reports all five policies under live and frozen observations, with and without each dynamic perturbation.

Table 11: Complete feedback-utilization results. Success rates are percentages; 0/1 denotes absence/presence of a perturbation, and live/freeze denotes the visual-observation condition. Live allows the policy to receive updated observations and infer actions normally, whereas Freeze holds the visual observation fixed at its pre-event value for a specified interval. For each model, the freeze duration is set to one-eighth of the number of inference steps required to complete unperturbed tasks, with freezing initiated immediately before the perturbation event. The feedback gain G_{\mathrm{feedback}}=(S_{1,\mathrm{live}}-S_{1,\mathrm{freeze}})-(S_{0,\mathrm{live}}-S_{0,\mathrm{freeze}}) is measured in percentage points. The two panels cover D01–D10 and D11–D20, respectively.
  • OpenVLA-OFT
    (a): D01–D10 D01
    データなし
    (a): D01–D10 D02
    データなし
    (a): D01–D10 D03
    データなし
    (a): D01–D10 D04
    データなし
    (a): D01–D10 D05
    データなし
    (a): D01–D10 D06
    データなし
    (a): D01–D10 D07
    データなし
    (a): D01–D10 D08
    データなし
    (a): D01–D10 D09
    データなし
    (a): D01–D10 D10
    データなし
  • S_{0,\mathrm{live}}
    (a): D01–D10 D01
    97.1
    (a): D01–D10 D02
    97.1
    (a): D01–D10 D03
    97.1
    (a): D01–D10 D04
    97.1
    (a): D01–D10 D05
    97.1
    (a): D01–D10 D06
    97.1
    (a): D01–D10 D07
    97.1
    (a): D01–D10 D08
    97.1
    (a): D01–D10 D09
    97.1
    (a): D01–D10 D10
    97.1
  • S_{0,\mathrm{freeze}}
    (a): D01–D10 D01
    45.6
    (a): D01–D10 D02
    43.8
    (a): D01–D10 D03
    33.8
    (a): D01–D10 D04
    50.0
    (a): D01–D10 D05
    42.5
    (a): D01–D10 D06
    55.0
    (a): D01–D10 D07
    48.1
    (a): D01–D10 D08
    48.1
    (a): D01–D10 D09
    48.1
    (a): D01–D10 D10
    48.1
  • S_{1,\mathrm{live}}
    (a): D01–D10 D01
    5.4
    (a): D01–D10 D02
    24.3
    (a): D01–D10 D03
    17.6
    (a): D01–D10 D04
    95.8
    (a): D01–D10 D05
    16.8
    (a): D01–D10 D06
    95.3
    (a): D01–D10 D07
    38.3
    (a): D01–D10 D08
    56.7
    (a): D01–D10 D09
    94.2
    (a): D01–D10 D10
    87.9
  • S_{1,\mathrm{freeze}}
    (a): D01–D10 D01
    0.0
    (a): D01–D10 D02
    3.8
    (a): D01–D10 D03
    0.0
    (a): D01–D10 D04
    41.9
    (a): D01–D10 D05
    13.8
    (a): D01–D10 D06
    43.6
    (a): D01–D10 D07
    21.3
    (a): D01–D10 D08
    41.3
    (a): D01–D10 D09
    48.1
    (a): D01–D10 D10
    47.5
  • \mathbf{G_{\mathrm{feedback}}}
    (a): D01–D10 D01
    -46.1
    (a): D01–D10 D02
    -32.8
    (a): D01–D10 D03
    -45.8
    (a): D01–D10 D04
    6.9
    (a): D01–D10 D05
    -51.5
    (a): D01–D10 D06
    9.6
    (a): D01–D10 D07
    -31.9
    (a): D01–D10 D08
    -33.6
    (a): D01–D10 D09
    -2.9
    (a): D01–D10 D10
    -8.6
  • \pi_{0.5}
    (a): D01–D10 D01
    データなし
    (a): D01–D10 D02
    データなし
    (a): D01–D10 D03
    データなし
    (a): D01–D10 D04
    データなし
    (a): D01–D10 D05
    データなし
    (a): D01–D10 D06
    データなし
    (a): D01–D10 D07
    データなし
    (a): D01–D10 D08
    データなし
    (a): D01–D10 D09
    データなし
    (a): D01–D10 D10
    データなし
  • S_{0,\mathrm{live}}
    (a): D01–D10 D01
    93.3
    (a): D01–D10 D02
    93.3
    (a): D01–D10 D03
    93.3
    (a): D01–D10 D04
    93.3
    (a): D01–D10 D05
    93.3
    (a): D01–D10 D06
    93.3
    (a): D01–D10 D07
    93.3
    (a): D01–D10 D08
    93.3
    (a): D01–D10 D09
    93.3
    (a): D01–D10 D10
    93.3
  • S_{0,\mathrm{freeze}}
    (a): D01–D10 D01
    86.9
    (a): D01–D10 D02
    91.3
    (a): D01–D10 D03
    80.0
    (a): D01–D10 D04
    83.8
    (a): D01–D10 D05
    85.6
    (a): D01–D10 D06
    92.9
    (a): D01–D10 D07
    85.6
    (a): D01–D10 D08
    85.6
    (a): D01–D10 D09
    85.6
    (a): D01–D10 D10
    85.6
  • S_{1,\mathrm{live}}
    (a): D01–D10 D01
    50.4
    (a): D01–D10 D02
    76.9
    (a): D01–D10 D03
    19.8
    (a): D01–D10 D04
    92.9
    (a): D01–D10 D05
    21.1
    (a): D01–D10 D06
    97.4
    (a): D01–D10 D07
    16.3
    (a): D01–D10 D08
    65.8
    (a): D01–D10 D09
    92.1
    (a): D01–D10 D10
    88.8
  • S_{1,\mathrm{freeze}}
    (a): D01–D10 D01
    41.3
    (a): D01–D10 D02
    64.4
    (a): D01–D10 D03
    15.6
    (a): D01–D10 D04
    85.6
    (a): D01–D10 D05
    41.3
    (a): D01–D10 D06
    92.1
    (a): D01–D10 D07
    38.8
    (a): D01–D10 D08
    83.8
    (a): D01–D10 D09
    86.3
    (a): D01–D10 D10
    86.3
  • \mathbf{G_{\mathrm{feedback}}}
    (a): D01–D10 D01
    2.7
    (a): D01–D10 D02
    10.5
    (a): D01–D10 D03
    -9.1
    (a): D01–D10 D04
    -2.3
    (a): D01–D10 D05
    -27.8
    (a): D01–D10 D06
    4.8
    (a): D01–D10 D07
    -30.2
    (a): D01–D10 D08
    -25.6
    (a): D01–D10 D09
    -1.9
    (a): D01–D10 D10
    -5.2
  • Anchor-Align
    (a): D01–D10 D01
    データなし
    (a): D01–D10 D02
    データなし
    (a): D01–D10 D03
    データなし
    (a): D01–D10 D04
    データなし
    (a): D01–D10 D05
    データなし
    (a): D01–D10 D06
    データなし
    (a): D01–D10 D07
    データなし
    (a): D01–D10 D08
    データなし
    (a): D01–D10 D09
    データなし
    (a): D01–D10 D10
    データなし
  • S_{0,\mathrm{live}}
    (a): D01–D10 D01
    91.3
    (a): D01–D10 D02
    91.3
    (a): D01–D10 D03
    91.3
    (a): D01–D10 D04
    91.3
    (a): D01–D10 D05
    91.3
    (a): D01–D10 D06
    91.3
    (a): D01–D10 D07
    91.3
    (a): D01–D10 D08
    91.3
    (a): D01–D10 D09
    91.3
    (a): D01–D10 D10
    91.3
  • S_{0,\mathrm{freeze}}
    (a): D01–D10 D01
    78.1
    (a): D01–D10 D02
    83.8
    (a): D01–D10 D03
    56.9
    (a): D01–D10 D04
    72.5
    (a): D01–D10 D05
    72.5
    (a): D01–D10 D06
    78.6
    (a): D01–D10 D07
    74.4
    (a): D01–D10 D08
    74.4
    (a): D01–D10 D09
    74.4
    (a): D01–D10 D10
    74.4
  • S_{1,\mathrm{live}}
    (a): D01–D10 D01
    16.3
    (a): D01–D10 D02
    38.2
    (a): D01–D10 D03
    15.3
    (a): D01–D10 D04
    88.8
    (a): D01–D10 D05
    13.9
    (a): D01–D10 D06
    79.8
    (a): D01–D10 D07
    12.1
    (a): D01–D10 D08
    39.2
    (a): D01–D10 D09
    90.8
    (a): D01–D10 D10
    75.4
  • S_{1,\mathrm{freeze}}
    (a): D01–D10 D01
    16.3
    (a): D01–D10 D02
    30.0
    (a): D01–D10 D03
    11.3
    (a): D01–D10 D04
    74.4
    (a): D01–D10 D05
    25.6
    (a): D01–D10 D06
    80.0
    (a): D01–D10 D07
    19.4
    (a): D01–D10 D08
    57.5
    (a): D01–D10 D09
    73.1
    (a): D01–D10 D10
    75.6
  • \mathbf{G_{\mathrm{feedback}}}
    (a): D01–D10 D01
    -13.1
    (a): D01–D10 D02
    0.7
    (a): D01–D10 D03
    -30.3
    (a): D01–D10 D04
    -4.4
    (a): D01–D10 D05
    -30.5
    (a): D01–D10 D06
    -12.9
    (a): D01–D10 D07
    -24.2
    (a): D01–D10 D08
    -35.2
    (a): D01–D10 D09
    0.8
    (a): D01–D10 D10
    -17.1
  • FastWAM
    (a): D01–D10 D01
    データなし
    (a): D01–D10 D02
    データなし
    (a): D01–D10 D03
    データなし
    (a): D01–D10 D04
    データなし
    (a): D01–D10 D05
    データなし
    (a): D01–D10 D06
    データなし
    (a): D01–D10 D07
    データなし
    (a): D01–D10 D08
    データなし
    (a): D01–D10 D09
    データなし
    (a): D01–D10 D10
    データなし
  • S_{0,\mathrm{live}}
    (a): D01–D10 D01
    97.8
    (a): D01–D10 D02
    97.8
    (a): D01–D10 D03
    97.8
    (a): D01–D10 D04
    97.8
    (a): D01–D10 D05
    97.8
    (a): D01–D10 D06
    97.8
    (a): D01–D10 D07
    97.8
    (a): D01–D10 D08
    97.8
    (a): D01–D10 D09
    97.8
    (a): D01–D10 D10
    97.8
  • S_{0,\mathrm{freeze}}
    (a): D01–D10 D01
    92.5
    (a): D01–D10 D02
    83.1
    (a): D01–D10 D03
    52.5
    (a): D01–D10 D04
    91.9
    (a): D01–D10 D05
    81.9
    (a): D01–D10 D06
    94.3
    (a): D01–D10 D07
    91.9
    (a): D01–D10 D08
    91.9
    (a): D01–D10 D09
    91.9
    (a): D01–D10 D10
    91.9
  • S_{1,\mathrm{live}}
    (a): D01–D10 D01
    20.7
    (a): D01–D10 D02
    17.3
    (a): D01–D10 D03
    17.6
    (a): D01–D10 D04
    92.1
    (a): D01–D10 D05
    18.3
    (a): D01–D10 D06
    94.1
    (a): D01–D10 D07
    16.6
    (a): D01–D10 D08
    89.7
    (a): D01–D10 D09
    94.9
    (a): D01–D10 D10
    96.0
  • S_{1,\mathrm{freeze}}
    (a): D01–D10 D01
    23.8
    (a): D01–D10 D02
    13.1
    (a): D01–D10 D03
    6.3
    (a): D01–D10 D04
    91.3
    (a): D01–D10 D05
    36.3
    (a): D01–D10 D06
    92.9
    (a): D01–D10 D07
    30.6
    (a): D01–D10 D08
    90.6
    (a): D01–D10 D09
    90.0
    (a): D01–D10 D10
    91.9
  • \mathbf{G_{\mathrm{feedback}}}
    (a): D01–D10 D01
    -8.3
    (a): D01–D10 D02
    -10.4
    (a): D01–D10 D03
    -33.9
    (a): D01–D10 D04
    -5.0
    (a): D01–D10 D05
    -33.9
    (a): D01–D10 D06
    -2.2
    (a): D01–D10 D07
    -19.9
    (a): D01–D10 D08
    -6.8
    (a): D01–D10 D09
    -1.0
    (a): D01–D10 D10
    -1.8
  • Cosmos Policy
    (a): D01–D10 D01
    データなし
    (a): D01–D10 D02
    データなし
    (a): D01–D10 D03
    データなし
    (a): D01–D10 D04
    データなし
    (a): D01–D10 D05
    データなし
    (a): D01–D10 D06
    データなし
    (a): D01–D10 D07
    データなし
    (a): D01–D10 D08
    データなし
    (a): D01–D10 D09
    データなし
    (a): D01–D10 D10
    データなし
  • S_{0,\mathrm{live}}
    (a): D01–D10 D01
    97.5
    (a): D01–D10 D02
    97.5
    (a): D01–D10 D03
    97.5
    (a): D01–D10 D04
    97.5
    (a): D01–D10 D05
    97.5
    (a): D01–D10 D06
    97.5
    (a): D01–D10 D07
    97.5
    (a): D01–D10 D08
    97.5
    (a): D01–D10 D09
    97.5
    (a): D01–D10 D10
    97.5
  • S_{0,\mathrm{freeze}}
    (a): D01–D10 D01
    93.1
    (a): D01–D10 D02
    93.8
    (a): D01–D10 D03
    74.4
    (a): D01–D10 D04
    95.6
    (a): D01–D10 D05
    82.5
    (a): D01–D10 D06
    94.3
    (a): D01–D10 D07
    91.9
    (a): D01–D10 D08
    91.9
    (a): D01–D10 D09
    91.9
    (a): D01–D10 D10
    91.9
  • S_{1,\mathrm{live}}
    (a): D01–D10 D01
    21.7
    (a): D01–D10 D02
    26.9
    (a): D01–D10 D03
    21.4
    (a): D01–D10 D04
    95.8
    (a): D01–D10 D05
    9.0
    (a): D01–D10 D06
    97.4
    (a): D01–D10 D07
    75.8
    (a): D01–D10 D08
    80.8
    (a): D01–D10 D09
    97.5
    (a): D01–D10 D10
    91.7
  • S_{1,\mathrm{freeze}}
    (a): D01–D10 D01
    15.0
    (a): D01–D10 D02
    20.0
    (a): D01–D10 D03
    15.6
    (a): D01–D10 D04
    94.4
    (a): D01–D10 D05
    50.0
    (a): D01–D10 D06
    96.4
    (a): D01–D10 D07
    85.6
    (a): D01–D10 D08
    90.0
    (a): D01–D10 D09
    92.5
    (a): D01–D10 D10
    90.0
  • \mathbf{G_{\mathrm{feedback}}}
    (a): D01–D10 D01
    2.3
    (a): D01–D10 D02
    3.2
    (a): D01–D10 D03
    -17.4
    (a): D01–D10 D04
    -0.4
    (a): D01–D10 D05
    -56.1
    (a): D01–D10 D06
    -2.2
    (a): D01–D10 D07
    -15.4
    (a): D01–D10 D08
    -14.8
    (a): D01–D10 D09
    -0.6
    (a): D01–D10 D10
    -4.0
Table 11: Complete feedback-utilization results (continued). Panel (b): D11–D20.
  • OpenVLA-OFT
    (b): D11–D20 D11
    データなし
    (b): D11–D20 D12
    データなし
    (b): D11–D20 D13
    データなし
    (b): D11–D20 D14
    データなし
    (b): D11–D20 D15
    データなし
    (b): D11–D20 D16
    データなし
    (b): D11–D20 D17
    データなし
    (b): D11–D20 D18
    データなし
    (b): D11–D20 D19
    データなし
    (b): D11–D20 D20
    データなし
  • S_{0,\mathrm{live}}
    (b): D11–D20 D11
    97.1
    (b): D11–D20 D12
    97.1
    (b): D11–D20 D13
    97.1
    (b): D11–D20 D14
    97.1
    (b): D11–D20 D15
    97.1
    (b): D11–D20 D16
    97.1
    (b): D11–D20 D17
    97.1
    (b): D11–D20 D18
    97.1
    (b): D11–D20 D19
    97.1
    (b): D11–D20 D20
    97.1
  • S_{0,\mathrm{freeze}}
    (b): D11–D20 D11
    48.1
    (b): D11–D20 D12
    48.1
    (b): D11–D20 D13
    48.1
    (b): D11–D20 D14
    48.1
    (b): D11–D20 D15
    41.3
    (b): D11–D20 D16
    48.1
    (b): D11–D20 D17
    48.1
    (b): D11–D20 D18
    41.9
    (b): D11–D20 D19
    32.5
    (b): D11–D20 D20
    48.1
  • S_{1,\mathrm{live}}
    (b): D11–D20 D11
    84.6
    (b): D11–D20 D12
    79.6
    (b): D11–D20 D13
    70.1
    (b): D11–D20 D14
    70.4
    (b): D11–D20 D15
    91.7
    (b): D11–D20 D16
    93.8
    (b): D11–D20 D17
    93.3
    (b): D11–D20 D18
    18.3
    (b): D11–D20 D19
    62.9
    (b): D11–D20 D20
    95.4
  • S_{1,\mathrm{freeze}}
    (b): D11–D20 D11
    45.0
    (b): D11–D20 D12
    47.5
    (b): D11–D20 D13
    46.3
    (b): D11–D20 D14
    43.8
    (b): D11–D20 D15
    43.1
    (b): D11–D20 D16
    41.3
    (b): D11–D20 D17
    42.5
    (b): D11–D20 D18
    1.3
    (b): D11–D20 D19
    43.8
    (b): D11–D20 D20
    47.5
  • \mathbf{G_{\mathrm{feedback}}}
    (b): D11–D20 D11
    -9.4
    (b): D11–D20 D12
    -16.9
    (b): D11–D20 D13
    -25.1
    (b): D11–D20 D14
    -22.3
    (b): D11–D20 D15
    -7.3
    (b): D11–D20 D16
    3.5
    (b): D11–D20 D17
    1.8
    (b): D11–D20 D18
    -38.1
    (b): D11–D20 D19
    -45.4
    (b): D11–D20 D20
    -1.1
  • \pi_{0.5}
    (b): D11–D20 D11
    データなし
    (b): D11–D20 D12
    データなし
    (b): D11–D20 D13
    データなし
    (b): D11–D20 D14
    データなし
    (b): D11–D20 D15
    データなし
    (b): D11–D20 D16
    データなし
    (b): D11–D20 D17
    データなし
    (b): D11–D20 D18
    データなし
    (b): D11–D20 D19
    データなし
    (b): D11–D20 D20
    データなし
  • S_{0,\mathrm{live}}
    (b): D11–D20 D11
    93.3
    (b): D11–D20 D12
    93.3
    (b): D11–D20 D13
    93.3
    (b): D11–D20 D14
    93.3
    (b): D11–D20 D15
    93.3
    (b): D11–D20 D16
    93.3
    (b): D11–D20 D17
    93.3
    (b): D11–D20 D18
    93.3
    (b): D11–D20 D19
    93.3
    (b): D11–D20 D20
    93.3
  • S_{0,\mathrm{freeze}}
    (b): D11–D20 D11
    85.6
    (b): D11–D20 D12
    85.6
    (b): D11–D20 D13
    85.6
    (b): D11–D20 D14
    85.6
    (b): D11–D20 D15
    87.5
    (b): D11–D20 D16
    85.6
    (b): D11–D20 D17
    88.1
    (b): D11–D20 D18
    88.1
    (b): D11–D20 D19
    71.3
    (b): D11–D20 D20
    86.3
  • S_{1,\mathrm{live}}
    (b): D11–D20 D11
    86.3
    (b): D11–D20 D12
    87.5
    (b): D11–D20 D13
    83.7
    (b): D11–D20 D14
    83.3
    (b): D11–D20 D15
    90.4
    (b): D11–D20 D16
    92.9
    (b): D11–D20 D17
    87.6
    (b): D11–D20 D18
    65.3
    (b): D11–D20 D19
    78.3
    (b): D11–D20 D20
    94.2
  • S_{1,\mathrm{freeze}}
    (b): D11–D20 D11
    80.6
    (b): D11–D20 D12
    84.4
    (b): D11–D20 D13
    76.9
    (b): D11–D20 D14
    85.6
    (b): D11–D20 D15
    87.5
    (b): D11–D20 D16
    88.1
    (b): D11–D20 D17
    85.6
    (b): D11–D20 D18
    19.4
    (b): D11–D20 D19
    71.3
    (b): D11–D20 D20
    85.0
  • \mathbf{G_{\mathrm{feedback}}}
    (b): D11–D20 D11
    -2.1
    (b): D11–D20 D12
    -4.6
    (b): D11–D20 D13
    -0.9
    (b): D11–D20 D14
    -10.0
    (b): D11–D20 D15
    -2.9
    (b): D11–D20 D16
    -2.9
    (b): D11–D20 D17
    -3.2
    (b): D11–D20 D18
    40.7
    (b): D11–D20 D19
    -15.0
    (b): D11–D20 D20
    2.1
  • Anchor-Align
    (b): D11–D20 D11
    データなし
    (b): D11–D20 D12
    データなし
    (b): D11–D20 D13
    データなし
    (b): D11–D20 D14
    データなし
    (b): D11–D20 D15
    データなし
    (b): D11–D20 D16
    データなし
    (b): D11–D20 D17
    データなし
    (b): D11–D20 D18
    データなし
    (b): D11–D20 D19
    データなし
    (b): D11–D20 D20
    データなし
  • S_{0,\mathrm{live}}
    (b): D11–D20 D11
    91.3
    (b): D11–D20 D12
    91.3
    (b): D11–D20 D13
    91.3
    (b): D11–D20 D14
    91.3
    (b): D11–D20 D15
    91.3
    (b): D11–D20 D16
    91.3
    (b): D11–D20 D17
    91.3
    (b): D11–D20 D18
    91.3
    (b): D11–D20 D19
    91.3
    (b): D11–D20 D20
    91.3
  • S_{0,\mathrm{freeze}}
    (b): D11–D20 D11
    74.4
    (b): D11–D20 D12
    74.4
    (b): D11–D20 D13
    74.4
    (b): D11–D20 D14
    74.4
    (b): D11–D20 D15
    72.5
    (b): D11–D20 D16
    74.4
    (b): D11–D20 D17
    88.1
    (b): D11–D20 D18
    71.3
    (b): D11–D20 D19
    58.1
    (b): D11–D20 D20
    74.4
  • S_{1,\mathrm{live}}
    (b): D11–D20 D11
    73.3
    (b): D11–D20 D12
    81.3
    (b): D11–D20 D13
    79.6
    (b): D11–D20 D14
    79.6
    (b): D11–D20 D15
    90.8
    (b): D11–D20 D16
    92.1
    (b): D11–D20 D17
    85.9
    (b): D11–D20 D18
    21.9
    (b): D11–D20 D19
    68.8
    (b): D11–D20 D20
    88.3
  • S_{1,\mathrm{freeze}}
    (b): D11–D20 D11
    71.3
    (b): D11–D20 D12
    75.6
    (b): D11–D20 D13
    71.3
    (b): D11–D20 D14
    76.9
    (b): D11–D20 D15
    83.1
    (b): D11–D20 D16
    82.5
    (b): D11–D20 D17
    73.8
    (b): D11–D20 D18
    12.5
    (b): D11–D20 D19
    60.6
    (b): D11–D20 D20
    79.4
  • \mathbf{G_{\mathrm{feedback}}}
    (b): D11–D20 D11
    -14.8
    (b): D11–D20 D12
    -11.3
    (b): D11–D20 D13
    -8.5
    (b): D11–D20 D14
    -14.2
    (b): D11–D20 D15
    -11.0
    (b): D11–D20 D16
    -7.3
    (b): D11–D20 D17
    9.0
    (b): D11–D20 D18
    -10.7
    (b): D11–D20 D19
    -25.0
    (b): D11–D20 D20
    -7.9
  • FastWAM
    (b): D11–D20 D11
    データなし
    (b): D11–D20 D12
    データなし
    (b): D11–D20 D13
    データなし
    (b): D11–D20 D14
    データなし
    (b): D11–D20 D15
    データなし
    (b): D11–D20 D16
    データなし
    (b): D11–D20 D17
    データなし
    (b): D11–D20 D18
    データなし
    (b): D11–D20 D19
    データなし
    (b): D11–D20 D20
    データなし
  • S_{0,\mathrm{live}}
    (b): D11–D20 D11
    97.8
    (b): D11–D20 D12
    97.8
    (b): D11–D20 D13
    97.8
    (b): D11–D20 D14
    97.8
    (b): D11–D20 D15
    97.8
    (b): D11–D20 D16
    97.8
    (b): D11–D20 D17
    97.8
    (b): D11–D20 D18
    97.8
    (b): D11–D20 D19
    97.8
    (b): D11–D20 D20
    97.8
  • S_{0,\mathrm{freeze}}
    (b): D11–D20 D11
    91.9
    (b): D11–D20 D12
    91.9
    (b): D11–D20 D13
    91.9
    (b): D11–D20 D14
    91.9
    (b): D11–D20 D15
    80.6
    (b): D11–D20 D16
    91.9
    (b): D11–D20 D17
    91.3
    (b): D11–D20 D18
    83.8
    (b): D11–D20 D19
    58.8
    (b): D11–D20 D20
    91.9
  • S_{1,\mathrm{live}}
    (b): D11–D20 D11
    94.2
    (b): D11–D20 D12
    88.9
    (b): D11–D20 D13
    83.8
    (b): D11–D20 D14
    86.5
    (b): D11–D20 D15
    93.4
    (b): D11–D20 D16
    89.7
    (b): D11–D20 D17
    94.8
    (b): D11–D20 D18
    38.2
    (b): D11–D20 D19
    81.2
    (b): D11–D20 D20
    93.2
  • S_{1,\mathrm{freeze}}
    (b): D11–D20 D11
    86.3
    (b): D11–D20 D12
    89.4
    (b): D11–D20 D13
    77.5
    (b): D11–D20 D14
    84.4
    (b): D11–D20 D15
    88.8
    (b): D11–D20 D16
    90.0
    (b): D11–D20 D17
    94.4
    (b): D11–D20 D18
    19.4
    (b): D11–D20 D19
    61.3
    (b): D11–D20 D20
    90.6
  • \mathbf{G_{\mathrm{feedback}}}
    (b): D11–D20 D11
    2.0
    (b): D11–D20 D12
    -6.3
    (b): D11–D20 D13
    0.4
    (b): D11–D20 D14
    -3.8
    (b): D11–D20 D15
    -12.5
    (b): D11–D20 D16
    -6.2
    (b): D11–D20 D17
    -6.1
    (b): D11–D20 D18
    4.9
    (b): D11–D20 D19
    -19.1
    (b): D11–D20 D20
    -3.3
  • Cosmos Policy
    (b): D11–D20 D11
    データなし
    (b): D11–D20 D12
    データなし
    (b): D11–D20 D13
    データなし
    (b): D11–D20 D14
    データなし
    (b): D11–D20 D15
    データなし
    (b): D11–D20 D16
    データなし
    (b): D11–D20 D17
    データなし
    (b): D11–D20 D18
    データなし
    (b): D11–D20 D19
    データなし
    (b): D11–D20 D20
    データなし
  • S_{0,\mathrm{live}}
    (b): D11–D20 D11
    97.5
    (b): D11–D20 D12
    97.5
    (b): D11–D20 D13
    97.5
    (b): D11–D20 D14
    97.5
    (b): D11–D20 D15
    97.5
    (b): D11–D20 D16
    97.5
    (b): D11–D20 D17
    97.5
    (b): D11–D20 D18
    97.5
    (b): D11–D20 D19
    97.5
    (b): D11–D20 D20
    97.5
  • S_{0,\mathrm{freeze}}
    (b): D11–D20 D11
    91.9
    (b): D11–D20 D12
    91.9
    (b): D11–D20 D13
    91.9
    (b): D11–D20 D14
    91.9
    (b): D11–D20 D15
    83.1
    (b): D11–D20 D16
    91.9
    (b): D11–D20 D17
    97.5
    (b): D11–D20 D18
    84.4
    (b): D11–D20 D19
    71.3
    (b): D11–D20 D20
    91.9
  • S_{1,\mathrm{live}}
    (b): D11–D20 D11
    90.8
    (b): D11–D20 D12
    87.5
    (b): D11–D20 D13
    81.7
    (b): D11–D20 D14
    70.8
    (b): D11–D20 D15
    92.5
    (b): D11–D20 D16
    93.3
    (b): D11–D20 D17
    87.4
    (b): D11–D20 D18
    32.5
    (b): D11–D20 D19
    93.3
    (b): D11–D20 D20
    95.8
  • S_{1,\mathrm{freeze}}
    (b): D11–D20 D11
    88.8
    (b): D11–D20 D12
    95.0
    (b): D11–D20 D13
    81.3
    (b): D11–D20 D14
    82.5
    (b): D11–D20 D15
    95.6
    (b): D11–D20 D16
    92.5
    (b): D11–D20 D17
    90.6
    (b): D11–D20 D18
    3.8
    (b): D11–D20 D19
    76.3
    (b): D11–D20 D20
    95.6
  • \mathbf{G_{\mathrm{feedback}}}
    (b): D11–D20 D11
    -3.5
    (b): D11–D20 D12
    -13.1
    (b): D11–D20 D13
    -5.2
    (b): D11–D20 D14
    -17.3
    (b): D11–D20 D15
    -17.5
    (b): D11–D20 D16
    -4.8
    (b): D11–D20 D17
    -3.3
    (b): D11–D20 D18
    15.7
    (b): D11–D20 D19
    -9.2
    (b): D11–D20 D20
    -5.4

A.3 Complete Recovery Intervention Results

Figure 8 and Table 12 provide the recovery gains and success rates for Hold, Retry, and Restore (Reset).

Figure 8: Recovery-intervention gains, \Delta_{I}=S_{I}-S_{\mathrm{continue}} (percentage points), for Hold, Retry, and Restore (labeled Reset in the figure). Positive values indicate improvement over Continue, while negative values indicate degradation.
Table 12: Success rates (%) under Hold, Retry, and Restore (Reset) interventions across all dynamic perturbations. Both panels retain the same intervention and model order.
  • Model
    D01
    D02
    D03
    D04
    D05
    D06
    D07
    D08
    D09
    D10
  • Hold
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    48.1
    48.8
    46.3
    47.5
    49.4
    55.7
    48.8
    48.8
    48.8
    48.8
  • \pi_{0.5}
    93.8
    92.5
    92.5
    90.6
    91.3
    97.9
    93.1
    93.1
    93.1
    93.1
  • Anchor-Align
    89.4
    90.0
    89.4
    91.9
    88.8
    92.1
    89.4
    89.4
    89.4
    89.4
  • FastWAM
    92.5
    93.1
    90.0
    92.5
    92.5
    96.4
    95.6
    95.6
    95.6
    95.6
  • Cosmos Policy
    98.1
    98.1
    96.3
    98.1
    98.1
    99.3
    98.1
    98.1
    98.1
    98.1
  • Retry
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    0.0
    0.0
    0.6
    48.8
    0.0
    53.6
    48.8
    48.8
    48.8
    48.8
  • \pi_{0.5}
    0.0
    7.5
    18.1
    98.8
    16.9
    95.7
    98.8
    99.4
    98.8
    99.4
  • Anchor-Align
    0.6
    1.9
    17.5
    90.6
    9.4
    89.3
    90.6
    90.6
    90.6
    90.6
  • FastWAM
    1.9
    4.4
    16.9
    98.8
    12.5
    92.9
    98.8
    99.4
    98.8
    99.4
  • Cosmos Policy
    0.0
    5.6
    20.6
    99.4
    15.0
    97.1
    99.4
    100.0
    99.4
    100.0
  • Reset
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    0.6
    11.3
    0.6
    34.4
    0.0
    43.6
    13.1
    30.6
    44.4
    45.6
  • \pi_{0.5}
    49.4
    80.6
    20.0
    91.9
    20.6
    97.1
    15.0
    65.0
    92.5
    93.8
  • Anchor-Align
    15.6
    32.5
    17.5
    89.4
    13.8
    79.3
    12.5
    33.1
    90.0
    80.6
  • FastWAM
    23.8
    15.6
    17.5
    93.1
    17.5
    90.0
    20.0
    84.4
    92.5
    91.3
  • Cosmos Policy
    20.0
    21.9
    24.4
    97.5
    19.4
    99.3
    73.8
    84.4
    99.4
    97.5
  • (b) D11–D20
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • Model
    D11
    D12
    D13
    D14
    D15
    D16
    D17
    D18
    D19
    D20
  • Hold
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    48.8
    48.8
    48.8
    48.8
    48.8
    48.8
    48.8
    48.8
    48.1
    48.8
  • \pi_{0.5}
    93.1
    93.1
    93.1
    93.1
    89.4
    93.1
    94.4
    91.9
    89.4
    93.1
  • Anchor-Align
    89.4
    89.4
    89.4
    89.4
    88.8
    89.4
    92.5
    91.3
    86.3
    89.4
  • FastWAM
    95.6
    95.6
    95.6
    95.6
    95.6
    95.6
    95.0
    93.8
    91.9
    95.6
  • Cosmos Policy
    98.1
    98.1
    98.1
    98.1
    98.1
    98.1
    98.1
    98.8
    99.4
    98.1
  • Retry
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    48.8
    48.8
    16.3
    3.1
    0.0
    3.1
    6.9
    0.0
    1.9
    48.8
  • \pi_{0.5}
    99.4
    99.4
    21.9
    12.5
    1.3
    12.5
    1.9
    0.0
    11.9
    99.4
  • Anchor-Align
    90.6
    90.6
    13.1
    9.4
    0.0
    10.0
    3.8
    0.0
    17.5
    90.6
  • FastWAM
    99.4
    99.4
    16.9
    11.9
    1.3
    20.6
    4.4
    0.0
    8.1
    99.4
  • Cosmos Policy
    100.0
    100.0
    13.1
    6.9
    1.3
    13.1
    1.9
    0.6
    9.4
    100.0
  • Reset
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
    データなし
  • OpenVLA-OFT
    48.8
    48.1
    48.1
    43.8
    45.0
    43.1
    46.3
    15.0
    49.4
    47.5
  • \pi_{0.5}
    87.5
    88.8
    86.3
    90.0
    91.3
    88.8
    88.8
    56.9
    96.3
    90.0
  • Anchor-Align
    78.8
    77.5
    79.4
    83.1
    90.0
    86.3
    83.1
    29.4
    90.0
    90.0
  • FastWAM
    91.3
    87.5
    86.9
    86.3
    91.3
    88.8
    92.5
    38.1
    92.5
    93.8
  • Cosmos Policy
    95.6
    91.3
    83.8
    84.4
    96.9
    90.6
    93.1
    23.1
    98.8
    97.5

A.4 Complete Robustness Composition Results

Table 13 lists all evaluated pairwise and three-way compositions, grouped by static and dynamic intervention types.

Table 13: Success rates (%) under pairwise and three-way perturbation compositions. Compositions are grouped by perturbation type.
  • Static + Static
    Composition
    データなし
    OpenVLA-OFT
    データなし
    \pi_{0.5}
    データなし
    Anchor-Align
    データなし
    FastWAM
    データなし
    Cosmos Policy
    データなし
  • P01
    Composition
    S11 + S15
    OpenVLA-OFT
    30.4
    \pi_{0.5}
    0.0
    Anchor-Align
    0.0
    FastWAM
    5.0
    Cosmos Policy
    50.8
  • P02
    Composition
    S09 + S13
    OpenVLA-OFT
    12.5
    \pi_{0.5}
    12.5
    Anchor-Align
    10.0
    FastWAM
    9.2
    Cosmos Policy
    12.9
  • P03
    Composition
    S19 + S21
    OpenVLA-OFT
    82.9
    \pi_{0.5}
    86.3
    Anchor-Align
    82.5
    FastWAM
    5.8
    Cosmos Policy
    85.4
  • P04
    Composition
    S08 + S22
    OpenVLA-OFT
    82.5
    \pi_{0.5}
    80.8
    Anchor-Align
    73.8
    FastWAM
    76.3
    Cosmos Policy
    80.4
  • Static + Dynamic
    Composition
    データなし
    OpenVLA-OFT
    データなし
    \pi_{0.5}
    データなし
    Anchor-Align
    データなし
    FastWAM
    データなし
    Cosmos Policy
    データなし
  • P05
    Composition
    S11 + D01
    OpenVLA-OFT
    7.9
    \pi_{0.5}
    56.3
    Anchor-Align
    14.6
    FastWAM
    15.8
    Cosmos Policy
    21.7
  • P06
    Composition
    S09 + D13
    OpenVLA-OFT
    12.5
    \pi_{0.5}
    12.1
    Anchor-Align
    11.3
    FastWAM
    11.7
    Cosmos Policy
    11.7
  • P07
    Composition
    S15 + D18
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    0.0
    Anchor-Align
    0.0
    FastWAM
    0.0
    Cosmos Policy
    0.4
  • Dynamic + Dynamic
    Composition
    データなし
    OpenVLA-OFT
    データなし
    \pi_{0.5}
    データなし
    Anchor-Align
    データなし
    FastWAM
    データなし
    Cosmos Policy
    データなし
  • P08
    Composition
    D02 + D18
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    22.9
    Anchor-Align
    0.8
    FastWAM
    0.0
    Cosmos Policy
    1.3
  • P09
    Composition
    D03 + D19
    OpenVLA-OFT
    60.0
    \pi_{0.5}
    73.8
    Anchor-Align
    67.5
    FastWAM
    73.8
    Cosmos Policy
    80.8
  • P10
    Composition
    D18 + D20
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    17.5
    Anchor-Align
    0.0
    FastWAM
    0.0
    Cosmos Policy
    2.9
  • Three-way Compositions
    Composition
    データなし
    OpenVLA-OFT
    データなし
    \pi_{0.5}
    データなし
    Anchor-Align
    データなし
    FastWAM
    データなし
    Cosmos Policy
    データなし
  • T01
    Composition
    S11 + S21 + D01
    OpenVLA-OFT
    7.1
    \pi_{0.5}
    56.7
    Anchor-Align
    14.6
    FastWAM
    14.6
    Cosmos Policy
    24.6
  • T02
    Composition
    S13 + S15 + D18
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    0.0
    Anchor-Align
    0.0
    FastWAM
    0.0
    Cosmos Policy
    0.0
  • T03
    Composition
    S09 + S22 + D13
    OpenVLA-OFT
    12.5
    \pi_{0.5}
    12.9
    Anchor-Align
    11.7
    FastWAM
    10.0
    Cosmos Policy
    12.1
  • T04
    Composition
    S13 + D02 + D18
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    8.3
    Anchor-Align
    0.0
    FastWAM
    0.0
    Cosmos Policy
    0.0
  • T05
    Composition
    S13 + S22 + D09
    OpenVLA-OFT
    80.8
    \pi_{0.5}
    86.7
    Anchor-Align
    75.0
    FastWAM
    75.0
    Cosmos Policy
    86.7
  • T06
    Composition
    S10 + S18 + D06
    OpenVLA-OFT
    83.8
    \pi_{0.5}
    87.1
    Anchor-Align
    73.3
    FastWAM
    80.4
    Cosmos Policy
    87.1
  • T07
    Composition
    S11 + S22 + D07
    OpenVLA-OFT
    81.3
    \pi_{0.5}
    31.7
    Anchor-Align
    12.9
    FastWAM
    23.8
    Cosmos Policy
    85.4
  • T08
    Composition
    S19 + S21 + D14
    OpenVLA-OFT
    84.6
    \pi_{0.5}
    85.0
    Anchor-Align
    81.3
    FastWAM
    6.3
    Cosmos Policy
    85.4
  • T09
    Composition
    S08 + S13 + D17
    OpenVLA-OFT
    69.6
    \pi_{0.5}
    80.0
    Anchor-Align
    52.5
    FastWAM
    76.3
    Cosmos Policy
    63.8
  • T10
    Composition
    S14 + S21 + D18
    OpenVLA-OFT
    0.0
    \pi_{0.5}
    21.7
    Anchor-Align
    0.0
    FastWAM
    0.0
    Cosmos Policy
    1.7

Appendix B Perturbation Design

The following panels illustrate all 22 static and 20 dynamic perturbations. Each row shows one perturbation using aligned views or consecutive frames; the complete definitions are given in Appendix C.

Figure 9: Static perturbations S01–S05. Each row contrasts BASE and the perturbed scene using the external and wrist views.
Figure 10: Static perturbations S06–S10.
Figure 11: Static perturbations S11–S14.
Figure 12: Static perturbations S15–S18.
Figure 13: Static perturbations S19–S22.
Figure 14: Dynamic perturbations D01–D05. Each row shows the temporal sequence around an intervention, using the views indicated in the panels.
Figure 15: Dynamic perturbations D06–D10.
Figure 16: Dynamic perturbations D11–D15.
Figure 17: Dynamic perturbations D16–D20.
Figure 18: Representative failure rollouts under perturbations; each row contains two five-frame sequences, read from left to right.

Appendix C Perturbation Catalogue

This section supplements the LIBERO-Pro2.0 results with definitions of all 22 static and 20 dynamic perturbations and the task partition used in the controlled eight-task studies. The examples in Appendix B illustrate these definitions; the nominal, unperturbed task is the BASE reference.

Design scope.

Perturbations cover object and scene geometry, appearance, sensing, temporal alignment, action execution, robot state, and language. Each type shares a semantic definition across suites; affected objects, magnitudes, directions, and event settings are specified per task. These parameter choices do not define additional perturbation types.

Task validity.

The original goal and success predicate are preserved. Geometry and state changes retain reachable, collision-free configurations and feasible task completion. Planar pose changes combine horizontal translation and yaw; pitch and roll are excluded from this category. Physical parameters such as mass, inertia, friction, stiffness, and damping are not varied. Grasp loss and robot displacement are represented by injected outcome states or bounded control interventions, rather than simulated impact or falling forces.

Initialization and runtime events.

Static perturbations are introduced at reset; altered scene or fault settings persist while normal robot and object motion remains possible. Dynamic perturbations are triggered at task-relevant phases, such as approach, grasp, transport, or placement. Trigger conditions, duration, and release rules are specified by each case. Restoring a sensor or control channel does not imply rolling back the complete scene. Experiment-specific freeze or waiting durations are distinct from these general mechanism definitions.

C.1 Category Definitions and Assignment Principle

We assign each perturbation to one category according to its primary intervention target. The categories organize perturbations by their dominant operational effect and are not mutually exclusive descriptions of every downstream consequence. Condition perturbations modify task-relevant object or receiver configurations, relative layouts, or geometric constraints on approach and placement. Environment perturbations modify object instances or scene context, including clutter, distractors, occlusion, visual-domain appearance, support-surface appearance, and external visual conditions such as camera motion or lighting changes. Observation perturbations modify the formation, quality, availability, or synchronization of the inputs delivered to the policy. Execution perturbations modify control timing or action execution. Robot perturbations modify robot initialization, calibration, or robot-related state and manipulation outcomes. Language perturbations modify instruction wording while preserving task semantics. Some perturbations may affect multiple aspects of task execution; each is assigned according to its primary intervention target. This mapping is used consistently to compute the category averages in Tables 1–3.

Table 14: Mapping of static and runtime perturbations to evaluation categories.
  • Condition
    Static perturbations
    S01–S05, S07–S09
    Runtime perturbations
    D01–D06
  • Environment
    Static perturbations
    S06, S10–S14, S22
    Runtime perturbations
    D07–D09
  • Observation
    Static perturbations
    S15–S16, S19
    Runtime perturbations
    D10–D13
  • Execution
    Static perturbations
    S20
    Runtime perturbations
    D14–D16
  • Robot
    Static perturbations
    S17–S18
    Runtime perturbations
    D17–D19
  • Language
    Static perturbations
    S21
    Runtime perturbations
    D20

C.2 Static Perturbations

Table 15 summarizes each initialization-time intervention and the constraints that preserve the manipulation task.

Table 15: Static perturbation definitions. Interventions are introduced at reset. Modified geometry or fault settings persist; initial-state changes do not prevent normal subsequent motion. Alternatives within a row are selected by the task configuration.
  • S01
    Perturbation
    Target planar pose
    Intervention
    Translate the target in the horizontal plane and rotate it in yaw.
    Constraint
    Preserve the target identity and intended goal.
  • S02
    Perturbation
    Receiver planar pose
    Intervention
    Translate or rotate the receiver to change the placement destination and approach.
    Constraint
    Preserve receiver identity and task goal.
  • S03
    Perturbation
    Receiver or support height
    Intervention
    Change receiver or support elevation using a support platform or a coupled layout adjustment.
    Constraint
    Retain a collision-free initial layout and feasible placement.
  • S04
    Perturbation
    Object position swap
    Intervention
    Swap the planar positions of two objects; use a safe layout offset when a direct swap is unsuitable.
    Constraint
    Keep object identities, task roles, and goal unchanged.
  • S05
    Perturbation
    Restricted approach or path
    Intervention
    Add geometry that constrains approach or transport.
    Constraint
    Retain valid inverse kinematics and a complete collision-free route.
  • S06
    Perturbation
    Instance replacement
    Intervention
    Replace the target with a same-class or unseen asset specified by the task configuration.
    Constraint
    Preserve semantic class and graspability.
  • S07
    Perturbation
    Functional-part geometry
    Intervention
    Change an opening, rim, or receiving region used for grasping or placement.
    Constraint
    Retain the intended functional role.
  • S08
    Perturbation
    Size or aspect ratio
    Intervention
    Apply uniform or anisotropic target scaling.
    Constraint
    Change geometric extent while preserving target identity.
  • S09
    Perturbation
    Opening clearance and pose
    Intervention
    Jointly change object/container geometry and the relative insertion configuration.
    Constraint
    Use collision geometry with full containment, positive clearance, and sufficient depth.
  • S10
    Perturbation
    Irrelevant clutter
    Intervention
    Add irrelevant objects or change their spatial density.
    Constraint
    Preserve target and receiver; support clutter without interpenetration.
  • S11
    Perturbation
    Similar distractors
    Intervention
    Add objects of the same class or similar color or shape.
    Constraint
    The intended target remains the same.
  • S12
    Perturbation
    Persistent occlusion
    Intervention
    Place and retain a foreground occluder between the camera and the target region.
    Constraint
    Keep the occlusion intervention active during the rollout.
  • S13
    Perturbation
    Object appearance
    Intervention
    Change target or receiver color, texture, reflectance, or visual surface state.
    Constraint
    Preserve task semantics; do not vary physical material parameters.
  • S14
    Perturbation
    Contrast or scene domain
    Intervention
    Change object-background contrast or the visual scene domain.
    Constraint
    Preserve the intended manipulation task.
  • S15
    Perturbation
    Camera extrinsics
    Intervention
    Apply fixed camera position/orientation offsets or cross-camera calibration offsets.
    Constraint
    Offsets are fixed for the episode; affected cameras are case-specific.
  • S16
    Perturbation
    Camera image formation
    Intervention
    Change field of view, resolution, cropping, or lens distortion.
    Constraint
    The configured imaging transformation remains active.
  • S17
    Perturbation
    Initial robot state
    Intervention
    Change initial joints, end-effector pose/orientation, or gripper opening.
    Constraint
    Modify initialization; the robot then executes normally.
  • S18
    Perturbation
    Robot calibration
    Intervention
    Offset the base, tool center point, joint zero, or grasp center.
    Constraint
    Keep the configured calibration error fixed.
  • S19
    Perturbation
    Observation quality
    Intervention
    Apply compression artifacts, noise, blur, exposure contamination, or missing depth.
    Constraint
    Affect only the configured observation channels.
  • S20
    Perturbation
    Fixed timing or action window
    Intervention
    Apply a fixed delay or change control rate, replanning rate, or the action execution window.
    Constraint
    Use the configured timing intervention; distinguish it from model defaults.
  • S21
    Perturbation
    Instruction paraphrase
    Intervention
    Replace the instruction with a semantic paraphrase.
    Constraint
    Preserve goal, referenced objects, and action order.
  • S22
    Perturbation
    Support texture
    Intervention
    Replace the visual texture of the work surface.
    Constraint
    Preserve collision geometry, friction, and initial object poses.

C.3 Dynamic Perturbations

Table 16 summarizes runtime interventions, including their trigger phases and event lifetimes.

Table 16: Dynamic perturbation definitions. Trigger phase and event lifetime are part of each case configuration. A restored sensor or control channel does not imply rollback of the complete scene. IDs match the paper visualizations.
  • D01
    Perturbation
    Target pose update
    Intervention
    Change target horizontal position or yaw, requiring updated localization and approach.
    Trigger and lifetime
    Approach/pre-grasp; retain the update as configured.
  • D02
    Perturbation
    Receiver pose update
    Intervention
    Move or rotate the receiver without changing the task goal.
    Trigger and lifetime
    Post-grasp/pre-place; retain the update as configured.
  • D03
    Perturbation
    Receiver occupation
    Intervention
    Introduce an occupying or blocking object near the receiving region.
    Trigger and lifetime
    Pre-place; occupation/release follows the case configuration.
  • D04
    Perturbation
    Temporary occlusion
    Intervention
    Insert an occluder between camera and target, then remove it.
    Trigger and lifetime
    Task phase; enter, hold for a window, then exit.
  • D05
    Perturbation
    Path obstacle
    Intervention
    Place an obstacle on the upcoming transport route while preserving an alternative collision-free path.
    Trigger and lifetime
    Transport; persistence follows the case configuration.
  • D06
    Perturbation
    Distractor rearrangement
    Intervention
    Move irrelevant objects or rearrange local clutter; exclude the target and receiver.
    Trigger and lifetime
    Task phase; apply the configured scene update.
  • D07
    Perturbation
    Camera motion
    Intervention
    Change camera position to represent shake, drift, or a persistent offset.
    Trigger and lifetime
    Task phase; transient or persistent, as configured.
  • D08
    Perturbation
    Camera dropout
    Intervention
    Invalidate a selected camera observation stream.
    Trigger and lifetime
    Task phase; restore the stream after the event.
  • D09
    Perturbation
    Lighting or exposure
    Intervention
    Change RGB illumination, shadow, or exposure.
    Trigger and lifetime
    Task phase; restore after the event window.
  • D10
    Perturbation
    Frame-stream fault
    Intervention
    Drop, repeat, or freeze configured RGB/depth frames.
    Trigger and lifetime
    Task phase; apply the fault during the configured window.
  • D11
    Perturbation
    Modality misalignment
    Intervention
    Offset timestamps or freeze a modality while other modalities may continue to update.
    Trigger and lifetime
    Task phase; configured modality and event window.
  • D12
    Perturbation
    Latency spike
    Intervention
    Temporarily delay observation delivery or inference results.
    Trigger and lifetime
    Task phase; restore normal timing after the spike.
  • D13
    Perturbation
    Arm–gripper desynchronization
    Intervention
    Apply different delays or timing variations to arm and gripper commands.
    Trigger and lifetime
    Task phase; configured timing window.
  • D14
    Perturbation
    Command loss or repetition
    Intervention
    Disrupt the action stream; the listed implementation repeats the previous action.
    Trigger and lifetime
    Task phase; short command-fault window.
  • D15
    Perturbation
    Stale action chunk
    Intervention
    Replay an old action chunk or interrupt replanning, temporarily executing outdated actions.
    Trigger and lifetime
    State change; configurable chunk length and stale duration.
  • D16
    Perturbation
    Bounded takeover
    Intervention
    Inject contact-free bounded actions or a reachable state offset, respecting joint/workspace limits.
    Trigger and lifetime
    Task phase; temporary intervention, then return control.
  • D17
    Perturbation
    Grasp failure result
    Intervention
    Hold the gripper open on the first grasp attempt while retaining the possibility of retrying.
    Trigger and lifetime
    Grasp attempt; release after about 0.07 m of retreat or window expiry.
  • D18
    Perturbation
    Reachable drop state
    Intervention
    Place the transported target at a reachable, collision-free recovery location; do not simulate falling forces.
    Trigger and lifetime
    Transport; inject a recoverable outcome state.
  • D19
    Perturbation
    Robot joint displacement
    Intervention
    Inject one reachable joint displacement without self-collision and within joint/workspace limits.
    Trigger and lifetime
    Robot in motion; one state displacement, not a force simulation.
  • D20
    Perturbation
    Instruction restatement
    Intervention
    Restate or clarify the instruction while preserving goal, objects, and required action order.
    Trigger and lifetime
    Task phase; apply the equivalent instruction update.

C.4 Training and Evaluation Task Partition

For the controlled eight-task studies, two BASE tasks per suite are reserved for evaluation; the remaining eight per suite form the training pool (Table 17). The exact evaluation instructions are listed in Table 18. These roles do not imply that the evaluated pretrained checkpoints have never encountered the evaluation tasks. Demonstration selection and trajectory counts are specified separately for each training experiment. Long task 8 with D06 is not applicable and is excluded from the corresponding dynamic-evaluation denominator.

Table 17: Task partition for the controlled eight-task studies. IDs are zero-based indices in the pinned release manifest. The training pool is the complement of the evaluation tasks within each suite; it does not specify which demonstrations were actually used in a training run.
  • Spatial
    Evaluation IDs
    0, 8
    Training-pool IDs
    1, 2, 3, 4, 5, 6, 7, 9
  • Object
    Evaluation IDs
    1, 8
    Training-pool IDs
    0, 2, 3, 4, 5, 6, 7, 9
  • Goal
    Evaluation IDs
    3, 6
    Training-pool IDs
    0, 1, 2, 4, 5, 7, 8, 9
  • Long
    Evaluation IDs
    5, 8
    Training-pool IDs
    0, 1, 2, 3, 4, 6, 7, 9
Table 18: The eight evaluation tasks. Instructions are taken directly from the BASE scene descriptions, with whitespace normalized.
  • Spatial
    ID
    0
    BASE task instruction
    Pick the akita black bowl between the plate and the ramekin and place it on the plate
  • Spatial
    ID
    8
    BASE task instruction
    Pick the akita black bowl next to the plate and place it on the plate
  • Object
    ID
    1
    BASE task instruction
    Pick the cream cheese and place it in the basket
  • Object
    ID
    8
    BASE task instruction
    Pick the chocolate pudding and place it in the basket
  • Goal
    ID
    3
    BASE task instruction
    Open the top layer of the drawer and put the bowl inside
  • Goal
    ID
    6
    BASE task instruction
    Put the cream cheese on the bowl
  • Long
    ID
    5
    BASE task instruction
    pick up the book and place it in the back compartment of the caddy
  • Long
    ID
    8
    BASE task instruction
    put both moka pots on the stove
Table 19: The 32 training tasks. Instructions are taken directly from the BASE scene descriptions, with whitespace normalized.
  • Spatial
    ID
    1
    BASE task instruction
    Pick the akita black bowl next to the ramekin and place it on the plate
  • Spatial
    ID
    2
    BASE task instruction
    Pick the akita black bowl from table center and place it on the plate
  • Spatial
    ID
    3
    BASE task instruction
    Pick the akita black bowl on the cookies box and place it on the plate
  • Spatial
    ID
    4
    BASE task instruction
    Pick the akita black bowl in the top layer of the wooden cabinet and place it on the plate
  • Spatial
    ID
    5
    BASE task instruction
    Pick the akita black bowl on the ramekin and place it on the plate
  • Spatial
    ID
    6
    BASE task instruction
    Pick the akita black bowl next to the cookies box and place it on the plate
  • Spatial
    ID
    7
    BASE task instruction
    Pick the akita black bowl on the stove and place it on the plate
  • Spatial
    ID
    9
    BASE task instruction
    Pick the akita black bowl on the wooden cabinet and place it on the plate
  • Object
    ID
    0
    BASE task instruction
    Pick the alphabet soup and place it in the basket
  • Object
    ID
    2
    BASE task instruction
    Pick the salad dressing and place it in the basket
  • Object
    ID
    3
    BASE task instruction
    Pick the bbq sauce and place it in the basket
  • Object
    ID
    4
    BASE task instruction
    Pick the ketchup and place it in the basket
  • Object
    ID
    5
    BASE task instruction
    Pick the tomato sauce and place it in the basket
  • Object
    ID
    6
    BASE task instruction
    Pick the butter and place it in the basket
  • Object
    ID
    7
    BASE task instruction
    Pick the milk and place it in the basket
  • Object
    ID
    9
    BASE task instruction
    Pick the orange juice and place it in the basket
  • Goal
    ID
    0
    BASE task instruction
    Open the middle layer of the drawer
  • Goal
    ID
    1
    BASE task instruction
    Put the bowl on the stove
  • Goal
    ID
    2
    BASE task instruction
    Put the wine bottle on the top of the drawer
  • Goal
    ID
    4
    BASE task instruction
    Put the bowl on the top of the drawer
  • Goal
    ID
    5
    BASE task instruction
    Push the plate to the front of the stove
  • Goal
    ID
    7
    BASE task instruction
    Turn on the stove
  • Goal
    ID
    8
    BASE task instruction
    Put the bowl on the plate
  • Goal
    ID
    9
    BASE task instruction
    Put the wine bottle on the rack
  • Long
    ID
    0
    BASE task instruction
    put both the alphabet soup and the tomato sauce in the basket
  • Long
    ID
    1
    BASE task instruction
    put both the cream cheese box and the butter in the basket
  • Long
    ID
    2
    BASE task instruction
    turn on the stove and put the moka pot on it
  • Long
    ID
    3
    BASE task instruction
    put the black bowl in the bottom drawer of the cabinet and close it
  • Long
    ID
    4
    BASE task instruction
    put the white mug on the left plate and put the yellow and white mug on the right plate
  • Long
    ID
    6
    BASE task instruction
    put the white mug on the plate and put the chocolate pudding to the right of the plate
  • Long
    ID
    7
    BASE task instruction
    put both the alphabet soup and the cream cheese box in the basket
  • Long
    ID
    9
    BASE task instruction
    put the yellow and white mug in the microwave and close it

C.5 Evaluation Protocol

We evaluate all policies from fixed checkpoints under identical benchmark settings. Each policy receives observation modalities matching its architecture, while environment settings, perturbation parameters, and task success criteria are held constant across all models. We retain each policy’s original action representation and prediction horizon unless explicitly altered in diagnostic ablation experiments. No privileged information about the perturbation is available to the policy in standard evaluation runs.

An episode is marked successful only if the agent fulfills the original task completion requirements within the evaluation time horizon. Episodes that end due to timeout or failed manipulation are counted as failures.

Our main evaluation metric is task success rate (SR). For model m and perturbation case c, we define

\mathrm{SR}_{m,c}=\frac{1}{|\mathcal{T}_{c}|}\sum_{t\in\mathcal{T}_{c}}\frac{1}{N_{t,c}}\sum_{r=1}^{N_{t,c}}\mathbb{I}\left[\mathrm{Success}(m,t,c,r)\right],
(1)

where \mathcal{T}_{c} is the set of tasks compatible with perturbation c, N_{t,c} denotes the total number of rollouts for task t under perturbation c, and \mathbb{I}[\cdot] represents the binary success indicator function.

Execution Horizon Configuration.

For RQ1-B, we investigate the effect of policy update frequency by varying the number of executed actions K before obtaining a new observation and generating the next action chunk, while keeping each policy’s prediction horizon H fixed. We consider four nominal execution ratios, K/H\in\{1/8,1/4,1/2,1\}. Since different policies use different prediction horizons, the corresponding values of K vary across models, as detailed in Table 20. For \pi_{0.5}, non-integer values are rounded to valid integer action steps.

Table 20: Executed action lengths K for different policies and nominal execution horizon ratios in RQ1-B. The prediction horizon H remains fixed for each policy.
  • OpenVLA-OFT
    \bm{H}
    8
    \bm{1/8H}
    1
    \bm{1/4H}
    2
    \bm{1/2H}
    4
    \bm{1H}
    8
  • \pi_{0.5}
    \bm{H}
    10
    \bm{1/8H}
    1
    \bm{1/4H}
    3
    \bm{1/2H}
    5
    \bm{1H}
    10
  • Anchor-Align
    \bm{H}
    8
    \bm{1/8H}
    1
    \bm{1/4H}
    2
    \bm{1/2H}
    4
    \bm{1H}
    8
  • FastWAM
    \bm{H}
    32
    \bm{1/8H}
    4
    \bm{1/4H}
    8
    \bm{1/2H}
    16
    \bm{1H}
    32
  • Cosmos Policy
    \bm{H}
    16
    \bm{1/8H}
    2
    \bm{1/4H}
    4
    \bm{1/2H}
    8
    \bm{1H}
    16

C.6 Training Setup

Training Data.

We fine-tune \pi_{0.5} using a mixture of perturbation-augmented demonstrations and original LIBERO demonstrations. For each of the ten perturbation cases across five static–dynamic families, we select two tasks from each of the four LIBERO suites, yielding eight training tasks per case. We collect ten demonstrations per task, resulting in 10\times 8\times 10=800 perturbation-augmented trajectories. To preserve the policy’s original manipulation capabilities, we additionally include standard LIBERO demonstrations. Specifically, we sample 20 demonstrations from each of the 40 original tasks across the four suites, yielding another 40\times 20=800 trajectories. The two datasets are mixed at a 1:1 ratio, resulting in a total of 1,600 training trajectories.

Fine-tuning Configuration.

We adopt Low-Rank Adaptation (LoRA) for parameter-efficient fine-tuning of \pi_{0.5}. The LoRA rank is set to 32 for the Gemma vision-language model (VLM) and 16 for the Gemma action head. We use an effective batch size of 144 and train for one epoch over the mixed dataset.