Moving Obstacle Collision Avoidance via Chance‐Constrained Model Predictive Control With Control Barrier Function

ABSTRACT Model predictive control (MPC) with control barrier function (CBF) is a promising solution to address the moving obstacle collision avoidance (MOCA) problem. Unlike MPC with distance constraints (MPC‐DC), MPC‐CBF approach can achieve comparable early obstacle‐avoidance behavior with a shorter prediction horizon. However, the existing MPC‐CBF method is deterministic and fails to account for perception uncertainties. This paper proposes a generalized MPC‐CBF approach for environments with stochastic obstacle‐measurement uncertainties, which maintains the advantages of the deterministic method for addressing the MOCA problem. Specifically, the chance‐constrained MPC‐CBF (CC‐MPC‐CBF) technique is introduced to ensure that a user‐defined collision avoidance probability is met by utilizing probabilistic CBFs. However, due to the potential empty intersection between the reachable set and the safe region confined by CBF constraints, the CC‐MPC‐CBF problem can pose challenges in achieving feasibility. To address this issue, we propose a sequential implementation approach that first solves a standard MPC optimization problem, followed by a predictive safety filter optimization. The safety filter is handled using a novel iterative convex optimization algorithm. This sequential approach improves feasibility compared to the CC‐MPC‐CBF optimization, although it may degrade the nominal stability properties of the MPC controller. We apply our proposed algorithm to a 2‐D integrator system for MOCA, and we showcase its resilience to obstacle measurement uncertainties and favorable feasibility properties.