Chance Constraint Robust Control with Control Barrier Functions

TL;DR

This paper introduces a robust control synthesis method using chance constraints and control barrier functions to ensure safety and stability in navigation tasks under noisy measurements.

Contribution

It develops a convex optimization-based approach combining chance constraints with control barrier functions for robust control in polygonal environments.

Findings

Controller is robust to measurement noise

Convex quadratic program efficiently synthesizes controllers

Simulation confirms safety and stability guarantees

Abstract

In this paper, we propose a novel approach to synthesize linear feedback controllers for navigating in polygonal environments using noisy measurements and a convex cell decomposition. Our method is based on formulating chance constraints for the convergence and collision avoidance condition. In particular, the stability and safety guarantees come from chance Control Barrier Function (CBF) constraints and chance Control Lyapunov Function (CLF) constraints, respectively. We use convex over-approximations to get upper bounds of the constraints, leading to a convex robust quadratic program for finding the controller. We apply and provide simulation results for equilibrium control and path control. The result shows that the controller is robust with the noise input.