Around the World: Unified Learned Locomotion on a 270 g Continuous-Rotation Quadruped

Can a single learned policy running onboard a sub-kilogram quadruped exploit continuous-rotation legs to unify upright and inverted walking, posture conditioning, and landing recovery?

Sub-kilogram quadrupeds largely rely on open-loop or off-board control; bounded revolute joints cannot reach antipodal supporting configurations, and sim-to-real transfer is complicated by low mass, servo dynamics, backlash, lightweight links, limited onboard compute, and varying foot geometry.

Prior miniature platforms such as MiNI-Q and Q8bot have mainly used precomputed trajectories or open-loop control; bounded-joint quadrupeds use behavior families and separate recovery controllers such as Walk These Ways, AllGaits, and ANYmal recovery, which cannot represent antipodal postures or require state machines and specialized policies.

The paper trains a compact 128x128 ELU PPO policy in 4096 parallel Isaac Gym environments using toroidal joint-space posture references on T^8, a gravity-conditioned mirror transformation that maps the same command to upright or inverted poses, periodic sin/cos joint encoding, coordinated posture and release curricula, and randomized foot-shape contact geometry. The identified servo model and cross-engine validation in MuJoCo and Isaac Lab support deployment on an ESP32-S3/C3 stack with SIMD inference at 50 Hz.

On hardware, forward-velocity RMSE at a 0.15 m/s command was 0.037 +/- 0.004 m/s upright and 0.050 +/- 0.003 m/s inverted over N=5 per orientation, roughly 25% and 33% error. A 25 s posture-change trial maintained mean forward-velocity RMSE around 0.04 m/s over five repetitions. Release recovery succeeded in 24 of 30 trials (80%): upright pitch 4/6, inverted pitch 4/6, upright roll 5/6, inverted roll 6/6, throw 5/6. Foot-geometry transfer walked in all 16 geometry-surface cells; rounded feet had lowest error per surface (0.041-0.065 m/s), unseen shapes had median RMSE 0.087 and range 0.055-0.136 m/s. The fitted actuator model reduced trajectory RMSE from about 0.49 rad for nominal PD to 0.029 rad at the hip and 0.025 rad at the knee, and 0.019 rad on a held-out servo. The deployed 128x128 policy used 150.3 kB RAM, 846.7 kB flash, and 594.33 microseconds inference, about 3% of the 20 ms period. Training took about eight hours on one NVIDIA RTX 4090 at around 70k environment steps per second for 20k iterations. In simulation ablations, the unified baseline achieved tracked/commanded velocity 0.98 upright and 1.00 inverted; removing the gravity-conditioned reference cut inverted tracking to 0.02, and removing toroidal encoding cut it to 0.21.

Reported limitations include evaluation on one robot assembly, four indoor surfaces, selected postures, and 20-30 cm releases; cross-unit variability, outdoor terrain, and large initial angular velocities are uncharacterized. Tracking error is large relative to the 0.15 m/s command, and failures include actuator overcurrent shutoff, battery-contact dislodgement, and belt slippage. Small trial counts (N=5 or 6 per condition, N=3 per foot cell) and single-run simulation ablations limit statistical confidence; no matched sphere-only hardware policy is evaluated, and no code release is reported.