A Global Steering Method for Nonholonomic Systems

TL;DR

This paper introduces a globally convergent iterative steering algorithm for nonholonomic systems, utilizing algebraic lifting and sinusoidal controls for nilpotent systems, advancing motion planning techniques.

Contribution

It presents an explicit algebraic lifting method for nonholonomic systems and a sinusoidal control-based motion planning algorithm for nilpotent systems.

Findings

Proves global convergence under Lie Algebraic Rank Condition

Develops an algebraic lifting procedure for regularization

Introduces sinusoidal control laws for nilpotent systems

Abstract

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in [29] for chained-form systems.