通过重塑工作空间解决机械臂避障重叠问题，提升实时规划安全性。
Reactive 3D Motion Planning for a Franka Arm via Star-World Workspace Reshaping
- 用星形代理替代重叠的膨胀障碍物，重构工作空间以支持实时控制。
- 在6个场景中5次成功到达目标，较基线提升1次成功率，单次更新耗时0.68–8.70毫秒。
- 适合需要高安全性的冗余机械臂实时避障场景，尤其关注动态环境下的可靠性。
安全膨胀会导致邻近障碍物重叠，违反多数调制型反应式规划器所依赖的互不相交假设。本文研究针对三自由度机械臂Franka Emika Panda的星-世界工作空间重塑方法。每次更新时，将相交的膨胀障碍物聚类并替换为星形代理，再评估基于动力学系统的末端执行器控制器。通过零空间人工势场项实现对机械臂本体的补充避障。在六个PyBullet场景中，对比了重塑与未重塑障碍物表示的性能，使用目标达成率、路径长度比和计算时间作为指标。初步12次试验表明，重塑方法在6个场景中有5次成功达目标，优于基线的4次；可解决经典的重叠墙问题，单次工作空间更新耗时0.68–8.70毫秒（含1至7个障碍物）。但该方法也导致路径变长，在两例中出现近平衡点，并因过度合并关闭了原本可通行的通道。结果表明，将星-世界理论保证从工作空间几何转移到通过逆运动学控制的冗余机械臂时，兼具潜力与实际局限。
原文摘要 · Abstract (English)
Safety inflation can cause nearby obstacles to overlap, violating the disjoint-obstacle assumptions used by many modulation-based reactive planners. We investigate Star-World workspace reshaping for three-dimensional reactive control of a Franka Emika Panda manipulator. At each update, intersecting inflated obstacles are clustered and replaced by star-shaped proxies before a dynamical-system-based end-effector controller is evaluated. A null-space artificial-potential-field term provides complementary arm-body avoidance. We compare reshaped and unreshaped obstacle representations in six PyBullet scenarios using goal attainment, path-length ratio, and computation time. In this preliminary 12-trial evaluation, reshaping reaches the goal in five of six scenarios, compared with four of six for the unreshaped baseline. It resolves the canonical overlapping-wall case and requires 0.68--8.70\,ms per workspace update for scenes containing one to seven obstacles. However, it also increases path length, produces near-equilibria in two cases, and closes a navigable corridor through over-aggressive merging. These results show both the promise and the practical limitations of transferring Star-World guarantees from workspace geometry to a redundant manipulator controlled through inverse kinematics.
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