面向nR平面机械手的基于工作空间纤维分解的完整运动规划

中文摘要 AI 辅助

我们提出一种工作空间纤维分解框架，用于在杂乱环境中运行的nR平面冗余机械手的运动规划。该方法不直接在完整的n维配置空间中规划，而是逐步构建低维非冗余子链的受障碍物约束的可达工作空间，并通过冗余方向纤维递归提升这些工作空间，从而得到一系列简化的规划流形，这些流形保留分支一致的可达性结构，同时避免显式构建完整配置空间障碍物几何。我们首先证明，对于仅平面位置的机械手，由最小非冗余子链诱导的受障碍物约束的可达工作空间，能精确表征相对于起始构型连通分量的可行性，从而在引入冗余自由度（DOF）之前实现早期不可行性检测。随后，我们提出一种增量纤维提升过程，该过程通过连续冗余链路传播可达工作空间结构，同时利用雅可比行列式连续性约束强制执行局部逆运动学分一致性。所得表示允许直接在递归构建的工作空间纤维流形上进行高效的简化空间规划。对冗余nR平面机械手的实验结果表明，所提出的构造在连续提升阶段保留了无碰撞连通性结构，同时相较于直接配置空间推理大幅降低了碰撞检测复杂度。

英文摘要

We propose a workspace-fibered decomposition framework for motion planning in nR planar redundant manipulators operating in cluttered environments. Rather than planning directly in the full n-dimensional configuration space, the method incrementally constructs obstacle-constrained reachable workspaces of lower-dimensional non-redundant sub-chains and recursively lifts them through redundant orientation fibers. This yields a sequence of reduced planning manifolds that preserve branch-consistent reachability structure while avoiding explicit construction of the full configuration-space obstacle geometry. We first establish that, for planar position-only manipulators, the obstacle-constrained reachable workspace induced by the minimal non-redundant sub-chain provides an exact characterization of feasibility with respect to the connected component of the start configuration, enabling early infeasibility detection prior to introducing redundant degrees of freedom (DOF). We then introduce an incremental fiber-lifting procedure that propagates reachable workspace structure through successive redundant links while enforcing local inverse-kinematic branch consistency using Jacobian determinant continuity constraints. The resulting representation admits efficient reduced-space planning directly on recursively-constructed workspace-fiber manifolds. Experimental results on redundant nR planar manipulators demonstrate that the proposed construction preserves collision-free connectivity structure across successive lifting stages while substantially reducing collision checking complexity relative to direct configuration space reasoning.

发表机构

• Robotics Research Center, IIIT Hyderabad（IIIT海得拉巴机器人研究中心）

机构由 AI 辅助整理，请以论文原文为准。