Safety of Dynamical Systems with Multiple Non-Convex Unsafe Sets Using Control Barrier Functions

TL;DR

This paper introduces a computationally efficient control method using barrier functions to ensure safety in dynamical systems with multiple non-convex unsafe regions, avoiding undesired equilibria and applicable to real robot navigation.

Contribution

It proposes a novel optimization-based control approach that guarantees safety without creating undesired equilibria in complex unsafe environments.

Findings

The method effectively ensures safety in simulations.

It prevents undesired equilibria in safety-critical control.

Validated on a real robot navigation task.

Abstract

This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high computational complexity in case of general nonlinear systems. Leveraging control barrier functions, on the other hand, results in computationally efficient control algorithms. Nevertheless, when safety guarantees have to be enforced alongside stability objectives, undesired asymptotically stable equilibrium points have been shown to arise. We propose a computationally efficient optimization-based approach which allows us to ensure safety of dynamical systems without introducing undesired equilibria even in presence of multiple non-convex unsafe sets. The developed control algorithm is showcased in simulation and in a real robot navigation application.