Safe Control Design through Risk-Tunable Control Barrier Functions

TL;DR

This paper introduces a risk-tunable control barrier function framework for safe control of uncertain nonlinear systems, balancing safety guarantees with sample complexity via chance-constrained optimization.

Contribution

It proposes a novel uncertain control barrier function approach combined with scenario optimization to provide probabilistic safety guarantees with adjustable risk levels.

Findings

Successfully applied to quadcopter obstacle avoidance

Provides probabilistic safety guarantees up to a user-defined risk bound

Balances safety and sample complexity effectively

Abstract

We consider the problem of designing controllers to guarantee safety in a class of nonlinear systems under uncertainties in the system dynamics and/or the environment. We define a class of uncertain control barrier functions (CBFs), and formulate the safe control design problem as a chance-constrained optimization problem with uncertain CBF constraints. We leverage the scenario approach for chance constrained optimization to develop a risk-tunable control design that provably guarantees the satisfaction of CBF safety constraints up to a user-defined probabilistic risk bound, and provides a trade-off between the sample complexity and risk tolerance. We demonstrate the performance of this approach through simulations on a quadcopter navigation problem with obstacle avoidance constraints.