Complete Motion Planning using Workspace-Fibered Decomposition for nR-Planar Manipulator

2026-08-02

AI Summary

This work addresses the challenge of complete motion planning for highly redundant nR planar manipulators in complex obstacle-rich environments by proposing a dimensionality-reduction planning approach based on workspace fibration decomposition. The method incrementally constructs the obstacle-constrained reachable workspace of minimal non-redundant subchains and recursively lifts it along redundant directions to form a low-dimensional planning manifold that preserves inverse kinematics branch consistency. Continuity constraints on the Jacobian determinant are introduced to ensure branch consistency and enable early detection of infeasible configurations. Experimental results demonstrate that the proposed approach effectively maintains collision-free connectivity while significantly reducing the computational complexity of collision checking, outperforming conventional methods that plan directly in the high-dimensional configuration space.

Abstract

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.

Problem

• motion planning
• redundant manipulator
• workspace decomposition
• configuration space
• collision avoidance

Innovation

• workspace-fibered decomposition
• redundant manipulator
• motion planning
• configuration space reduction
• inverse-kinematic consistency