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

arXiv: https://arxiv.org/abs/2106.06330 · HTML: https://mlsanity.com/paper/2106.06330/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2021.

## Built on by (most cited first, 3 of 3)

- [Constrained Dynamic Movement Primitives for Safe Learning of Motor Skills](https://mlsanity.com/paper/2209.14461/) (2022)
- [Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning](https://mlsanity.com/paper/2207.08240/) (2022)
- [TRUST-UP: Trustworthy Reinforcement learning Using Safe Techniques for UAV Pursuit](https://mlsanity.com/paper/2411.17552/) (2024)

## Abstract (arXiv)

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.