LARC通过智能分割轨迹区间，高效验证机器人运动避障安全性。
LARC: Lazy Adaptive Reachability Certification of Robot Manipulator Trajectories
- 仅对模糊区段进行二分检查，避免冗余计算。
- 在160条轨迹上节省75.2%计算量，平均提速10.28倍。
- 适合需要高效率避障验证的机器人路径规划场景。
离散状态检测可能遗漏机器人状态间的碰撞。基于可达性的认证可约束状态间运动，但均匀时间划分在间隙较大时浪费计算。本文提出懒惰自适应可达性认证（LARC），仅对清除测试不确定的区间进行二分检查。针对分段三次埃尔米特关节轨迹，该方法利用中点胶囊并结合精确分量速度最大值进行膨胀，以界定连杆占据空间。经认证的区间可提供连续时间外部障碍物安全距离，前提为几何包含、静态障碍物及预设裕量。在80组起止点的160条AgileX PIPER轨迹上，LARC在深度9时与固定精细基准一致。其仅需20328次区间评估（为基准的24.8%），中位数配对加速达10.28倍。独立的MoveIt/FCL审计检查了158051个状态，在21个直接插值控制中发现碰撞，但均未被LARC认证。该方法在共享证书模型下减少计算，但仍有27条采样清晰轨迹未被认证。采样审计无法独立证明连续时间清空。
原文摘要 · Abstract (English)
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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