← 研踪 PaperTrailarXiv:2608.29767 · v2
LARC: Lazy Adaptive Reachability Certification of Robot Manipulator Trajectories
首次提交 2026-08-30 20:53
版本更新 2026-11-08 15:28
雷达观测 2026-11-10 12:16
摘要
Discrete trajectory checks can miss collisions between sampled robot states. Reachability-based certification bounds motion between states, but uniform time partitions waste computation where clearance is large. We present lazy adaptive reachability certification (LARC), which checks a planned trajectory by bisecting only intervals with an inconclusive clearance test. For piecewise-cubic Hermite joint trajectories, the method bounds link occupancy using midpoint capsules inflated by exact componentwise speed maxima. Certified intervals covering the trajectory provide continuous-time external-obstacle clearance, subject to geometric containment, static obstacles, and a prescribed margin. On 160 AgileX PIPER trajectories from 80 start-goal pairs, LARC matched all decisions of the fixed-fine baseline at depth nine. It used 20328 interval evaluations (24.8% of baseline work), with a median paired speedup of 10.28x. A separate MoveIt/FCL audit checked 158051 states and detected collisions in 21 direct-interpolation controls, none of which LARC certified. The method reduced computation under a shared certificate model, but 27 of 139 sampled-clear trajectories remained uncertified. The sampled audit cannot independently prove continuous-time clearance.
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v2 · 2026-11-08 15:28 · 最新观测版本
LARC: Lazy Adaptive Reachability Certification of Robot Manipulator Trajectories
Discrete trajectory checks can miss collisions between sampled robot states. Reachability-based certification bounds motion between states, but uniform time partitions waste computation where clearance is large. We present lazy adaptive reachability certification (LARC), which checks a planned trajectory by bisecting only intervals with an inconclusive clearance test. For piecewise-cubic Hermite joint trajectories, the method bounds link occupancy using midpoint capsules inflated by exact componentwise speed maxima. Certified intervals covering the trajectory provide continuous-time external-obstacle clearance, subject to geometric containment, static obstacles, and a prescribed margin. On 160 AgileX PIPER trajectories from 80 start-goal pairs, LARC matched all decisions of the fixed-fine baseline at depth nine. It used 20328 interval evaluations (24.8% of baseline work), with a median paired speedup of 10.28x. A separate MoveIt/FCL audit checked 158051 states and detected collisions in 21 direct-interpolation controls, none of which LARC certified. The method reduced computation under a shared certificate model, but 27 of 139 sampled-clear trajectories remained uncertified. The sampled audit cannot independently prove continuous-time clearance.
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