Smooth Feedback Motion Planning with Reduced Curvature

2026-04-02

AI Summary

This work addresses the issue of excessively tortuous trajectories commonly produced by existing feedback motion planners based on simplicial complex decomposition, which lead to slow motion and high energy consumption. The authors propose a novel approach that constructs a safe, goal-directed “funnel” region by heuristically aligning local vector fields and building a goal-centric maximal star-shaped simplicial chain. By integrating systematic vector field alignment with geometric star-chain construction, the method significantly enhances path smoothness and control efficiency while preserving formal safety guarantees. Experimental results demonstrate a 91.40% average reduction in total path curvature and a 45.47% decrease in LQR control energy cost. In low-dimensional configuration spaces, the planner outperforms sampling- and optimization-based alternatives in both computational efficiency and robustness.

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.

Problem

• feedback motion planning
• curvature reduction
• cell decomposition
• robot motion planning
• path smoothness

Innovation

• feedback motion planning
• simplicial decomposition
• curvature reduction
• star-shaped chain
• vector field alignment