Motion planning and stabilization of nonholonomic systems using gradient flow approximations

TL;DR

This paper introduces a unified control approach using oscillating inputs and gradient flow approximations for trajectory tracking and stabilization of nonholonomic systems, with theoretical analysis and practical applications.

Contribution

It presents a novel control design scheme that employs oscillating inputs and gradient-like dynamics for nonholonomic systems, expanding existing methods.

Findings

Characterizes asymptotic behavior of solutions under general conditions

Demonstrates effectiveness in nonholonomic trajectory tracking

Shows applicability to obstacle avoidance scenarios

Abstract

Nonlinear control-affine systems with time-varying vector fields are considered in the paper. We propose a unified control design scheme with oscillating inputs for solving the trajectory tracking and stabilization problems. This methodology is based on the approximation of a gradient like dynamics by trajectories of the designed closed-loop system. As an intermediate outcome, we characterize the asymptotic behavior of solutions of the considered class of nonlinear control systems with oscillating inputs under rather general assumptions on the generating potential function. These results are applied to examples of nonholonomic trajectory tracking and obstacle avoidance.