Planning for Optimal Feedback Control in the Volume of Free Space

TL;DR

This paper introduces a sampling-based, asymptotically optimal feedback planning method for robot navigation in obstacle-filled spaces, combining triangulation, collision detection, and fast marching techniques, with extensions for dynamic environments.

Contribution

The paper presents a novel feedback planning algorithm that is asymptotically optimal, integrates multiple computational techniques, and extends to dynamic obstacle scenarios.

Findings

The method is asymptotically optimal and converges theoretically.

Numerical experiments show the method is competitive with state-of-the-art planners.

Feedback functions enable direct robot navigation, unlike shortest path algorithms.

Abstract

The problem of optimal feedback planning among obstacles in d-dimensional configuration spaces is considered. We present a sampling-based, asymptotically optimal feedback planning method. Our method combines an incremental construction of the Delaunay triangulation, volumetric collision-detection module, and a modified Fast Marching Method to compute a converging sequence of feedback functions. The convergence and asymptotic runtime are proven theoretically and investigated during numerical experiments, in which the proposed method is compared with the state-of-the-art asymptotically optimal path planners. The results show that our method is competitive with the previous algorithms. Unlike the shortest trajectory computed by many path planning algorithms, the resulting feedback functions can be used directly for robot navigation in our case. Finally, we present a straightforward extension of our method that handles dynamic environments where obstacles can appear, disappear, or move.