LARC: Lazy Adaptive Reachability Certification of Robot Manipulator Trajectories

2026-08-30

AI Summary

为解决机器人轨迹中可能遗漏的碰撞问题，提出了一种基于自适应可达性的懒惰认证方法（LARC），通过仅细分不确定间距来减少计算量。

Abstract

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.

Problem

• collision detection
• trajectory planning
• robot manipulator
• reachability certification
• continuous-time clearance

Innovation

• Lazy Adaptive Reachability Certification
• Continuous-time Obstacle Clearance
• Piecewise-cubic Hermite Joint Trajectories
• Interval Bisection
• Computational Efficiency