Motion Planning for Kinematic systems

TL;DR

This paper develops a comprehensive motion planning theory for kinematic systems using subriemannian geometry, with detailed analysis of the ball with trailer case, advancing the mathematical framework for complex robotic systems.

Contribution

It summarizes and improves a general motion planning theory for kinematic systems, including detailed treatment of the ball with trailer case, based on subriemannian geometry.

Findings

Provides a unified geometric framework for motion planning.

Develops detailed solutions for the ball with trailer system.

Enhances understanding of complex kinematic distributions.

Abstract

In this paper, we present a general theory of motion planning for kinematic systems. This theory has been developed for long by one of the authors in a previous series of papers. It is mostly based upon concepts from subriemannian geometry. Here, we summarize the results of the theory, and we improve on, by developping in details an intricated case: the ball with a trailer, which corresponds to a distribution with flag of type 2,3,5,6. This paper is dedicated to Bernard Bonnard for his 60th birthday.