Smooth Feedback Motion Planning with Reduced Curvature

• URL: http://arxiv.org/abs/2604.01614v1
• Date: Thu, 02 Apr 2026 04:48:55 GMT
• Title: Smooth Feedback Motion Planning with Reduced Curvature
• Abstract summary: Existing algorithms produce paths with unnecessary bending, leading to slower motion and higher control effort.<n>A novel geometric algorithm constructs a maximal star-shaped chain of simplexes around the goal.<n> 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%.
• Score: 2.227314660022684
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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