Safe Control Design Through Risk-Tunable Control Barrier Functions

Abstract

We consider the problem of designing controllers to guarantee safety for 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 uncertain 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.