基于凸集图的采样式可保证规划
Sampling-based Certified Planning with Graphs of Convex Sets
- Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究针对凸集图规划器的无碰撞验证缺陷，构建了可自验证的采样式规划器，在14自由度双臂任务中实现零无效答案，效率与正确性均优于参考规划器。
中文摘要 AI 辅助
凸集图上的规划器返回的轨迹在构造上是无碰撞的，前提是凸区域本身无碰撞。区域生成器仅概率性地保证该属性，而该类规划器中没有任何一个能验证该属性。我们首次量化了这种差距带来的代价：在一个缩放后的14自由度双臂库中，3.2%的界面样本处于碰撞状态，而基于搜索的GCS规划器（\textsc{GCSstar}）将这种体积误差转化为62%的答案误差——29个抓取放置查询中有18个返回的轨迹会让手臂穿过货架，深度达91毫米，却被报告为成功。修复该库无效；十倍严格的验收契约、平方和可保证区域以及均匀裕度，均在提供正确性之前破坏了规划所需的连通性。我们转而构建一个能验证自身答案的规划器：它对分解的重叠区域和共享面进行采样，用可容许的知情界剪枝，并通过一系列无分辨率参数的 clearance 证书球，持续验证每一轮搜索提出的一个候选方案；失败时用区域内局部绕行修复，并重新验证凸抛光。在全部29个任务查询的直接对比中，它返回0个无效答案，而参考规划器返回21个；它在0.11秒内得到第一个可保证答案，而参考规划器的未经验证答案耗时1.59秒；对于参考答案在物理上有效的每个查询，它都能精确复现参考最优解。
英文摘要
Planners on graphs of convex sets return trajectories that are collision-free by construction, provided the convex regions are collision-free. The region generator only promises that property probabilistically, and no planner in the family verifies it. We report the first measurement of what the gap costs. On a scaled 14-DOF bimanual library, $3.2\%$ of interface samples are in collision, and a search-based GCS planner (\gcsstar) turns that volume error into a $62\%$ answer error: $18$ of $29$ pick-and-place queries return trajectories that drive the arms through the shelves, up to $91$\,mm deep, reported as successes. Repairing the library does not work; a ten times stricter acceptance contract, sums-of-squares certified regions, and uniform margins each destroy the connectivity planning needs before they deliver soundness. We instead build a planner that certifies its answers. It samples the overlaps and shared faces of the decomposition, prunes with an admissible informed bound, and verifies the one candidate each search round proposes, continuously, by a chain of clearance certificate balls with no resolution parameter; failures are repaired with local in-region detours, and the convex polish is re-verified. Head-to-head on all $29$ task queries it delivers zero invalid answers against $21$ for the reference, reaches its first certified answer in $0.11$\,s against $1.59$\,s for the reference's unverified one, and reproduces the reference optimum exactly on every query whose reference answer is physically valid.
