GPU-Accelerated Path-Dependent Marginal Information Gain for Autonomous Exploration

Can depth-buffer projection and depth-ordered GPU evaluation compute path-dependent marginal information gain accurately and fast enough to improve sampling-based exploration planners?

Sampling-based exploration planners typically evaluate viewpoint gain independently, so overlapping views along one branch are counted multiple times, overestimating path value and misranking branches. Exact marginal gain would require expensive ancestor voxel-set unions, which scale poorly with tree depth and map resolution.

RH-NBVP and AEP use absolute per-viewpoint volumetric raycasting. ERRT computes marginal gain with UFOMap but limits branches, samples states sparsely, and uses coarser octree depths. Exact voxel hash-map marginal gain merges ancestor voxel sets and does not scale well enough for real-time planning.

Each planning-tree node stores a depth buffer of the first occupied surface along sensor rays. During gain evaluation, candidate rays are projected into ancestor buffers using a pinhole model and inverse-depth interpolation; overlap segments are clipped and traversed in screen space, then excluded from the 3D raycast. The CPU builds the full tree without scoring, and the GPU evaluates nodes depth-by-depth, parallelizing all nodes and rays within the same depth level.

Accuracy: over 166,440 node evaluations, depth-buffer marginal gain had R²=0.9937 and slope 1.028 versus exact hash-map gain, overestimating by 5–10%, while absolute and single-parent gains reached 2.6× and 2× exact gain with depth. Runtime: on desktop, marginal GPU gain was 6–48× faster than CPU hash map at 0.2 m voxels and 12–118× faster at 0.1 m; Jetson speedups were 3–12× and 10–28×. For 10,000 nodes, desktop evaluation dropped from 16.30 s to 0.40 s at 0.2 m and from 181.57 s to 1.95 s at 0.1 m. Exploration: marginal gain improved E95 in five of six planner–environment cases; AEP improved in all three simulated scenes by 0.8–1.8 min in school, 1.3–2.3 min in large maze, and 0.2–1.1 min in multi-story, while RH-NBVP improved by 0.7 min in school and 3.8 min in large maze but not in multi-story. In real UAV tests, marginal gain reached 50%, 75%, and 95% coverage in 0.49±0.05, 0.92±0.10, and 2.17±0.44 min versus 0.54±0.08, 1.01±0.19, and 3.10±1.05 min with absolute gain, a 30% E95 reduction; termination time was 4.04±0.34 vs 4.58±0.46 min.

The depth-buffer approximation overestimates gain by 5–10% because each pixel represents a beam area rather than a single ray. Evaluation is sequential across tree depths, so some parallelism is lost, and GPU marginal gain remains slower than GPU absolute gain. It was tested in three simulated scenes and one small outdoor environment on a single UAV platform. It is integrated only into RH-NBVP and AEP, so generalization to other planners is future work. In one environment, RH-NBVP did not improve with marginal gain, suggesting sampling reach rather than gain formulation can limit performance.