Robust Model Predictive Control with Control Barrier Function for Nonholonomic Robots with Obstacle Avoidance

In this paper, we propose a Robust Model Predictive Control combined with Control Barrier Function (RMPC-CBF) for a nonholonomic robot with obstacle avoidance subject to additive input disturbances. Both Input-to-State Stability (ISS) and Input-to-State Safety (ISSf) are provided to theoretically guarantee the system's stability and safety. CBF-based safety conditions are formulated as constraints inside a robust MPC strategy. Robust satisfaction of the constraints is ensured by tightening the state constraint set. With admissible disturbances under a certain bound, ISS and robust recursive feasibility are guaranteed by computing the terminal region and state constraint set. For obstacle avoidance, Input-to-State Safe Control Barrier Function (ISSf-CBF) is chosen to provide robust set safety for the dynamic systems under input disturbances, which always guarantees that states stay inside or close to the safe set. With the proposed method, the future state prediction is taken into consideration and optimal performance is accomplished via MPC, and the system's safety is ensured via CBF. Numerical simulation results confirm the effectiveness and validity of the proposed approach.