Smooth Feedback Motion Planning with Reduced Curvature

TL;DR

This paper introduces a new method for feedback motion planning that significantly reduces path curvature and control effort, improving efficiency and robustness in low-dimensional robot navigation.

Contribution

It presents a heuristic and geometric algorithm to produce more direct, less bent paths within simplicial decompositions, with proven reductions in bending and effort.

Findings

Reduced path bending by an average of 91.40%

Decreased control effort by an average of 45.47%

Confirmed time efficiency and robustness through comparative analysis

Abstract

Feedback motion planning over cell decompositions provides a robust method for generating collision-free robot motion with formal guarantees. However, existing algorithms often produce paths with unnecessary bending, leading to slower motion and higher control effort. This paper presents a computationally efficient method to mitigate this issue for a given simplicial decomposition. A heuristic is introduced that systematically aligns and assigns local vector fields to produce more direct trajectories, complemented by a novel geometric algorithm that constructs a maximal star-shaped chain of simplexes around the goal. This creates a large ``funnel'' in which an optimal, direct-to-goal control law can be safely applied. Simulations demonstrate that our method generates measurably more direct paths, reducing total bending by an average of 91.40\% and LQR control effort by an average of 45.47\%. Furthermore, comparative analysis against sampling-based and optimization-based planners confirms the time efficacy and robustness of our approach. While the proposed algorithms work over any finite-dimensional simplicial complex embedded in the collision-free subset of the configuration space, the practical application focuses on low-dimensional ($d\le3$) configuration spaces, where simplicial decomposition is computationally tractable.