Chance Constraint Robust Control with Control Barrier Functions

Path planning and control is a crucial task for the robot, especially when considering noise measurements. In this paper, we propose a novel approach to design linear feedback controllers for a robot navigating in polygonal environments with noisy measurements. The stability and safety guarantees of the controller come from the chance Control Barrier Function constraints and the chance Control Lyapunov Function constraints, respectively. The controller design problem is set up as a chance constraint-based robust optimization. We apply convex over-approximations to obtain upper bounds of constraints, which lead to a quadratic constraint quadratic program (QCQP). We provide simulation results for equilibrium control and path control. Numerical experiments demonstrate that the controller is robust with noise measurements.