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

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.