Lyapunov based dynamic controller designs for reach-and-avoid problems

TL;DR

This paper introduces a Lyapunov-based reactive control method for nonlinear systems to achieve obstacle avoidance and target stabilization, using local information and hybrid systems to ensure safety and path adherence.

Contribution

It presents a novel control design combining virtual dynamics with Lyapunov stability and hybrid systems framework for safe obstacle avoidance in nonlinear systems.

Findings

Successful numerical example with unicycle dynamics demonstrating effectiveness.

Guarantees system safety and path adherence through Lyapunov and invariance principles.

Framework accommodates discrete decision-making in obstacle avoidance.

Abstract

Safe obstacle avoidance and target set stabilization for nonlinear systems using reactive feedback control is under consideration. Based only on local information and by considering virtual dynamics, a safe path is generated online. The control law for the virtual dynamics is combined with a feedback controller for the dynamics of interest, where Lyapunov arguments and forward invariance are used to ensure that the state of the system remains in a vicinity of the path. To allow for discrete decisions in the avoidance controller design, the closed-loop dynamics are formulated using the hybrid systems framework. The results are illustrated by a numerical example for unicycle dynamics.