Model-Free Safety Critical Model Predictive Control for Mobile Robot in Dynamic Environments

Within the context of Nonlinear Model Predictive Control (NMPC) design for autonomous mobile robots, which face challenges such as parametric uncertainty and measurement inaccuracies, focusing on dynamic modelling and parameter identification becomes crucial. This paper presents a novel safety-critical control framework for a mobile robot system that utilises NMPC with a prediction model derived entirely from noisy measurement data. The Sparse Identification of Nonlinear Dynamics (SINDY) is employed to predict the system's state under actuation effects. Meanwhile, the Control Barrier Function (CBF) is integrated into the NMPC as a safety-critical constraint, ensuring obstacle avoidance even when the robot's planned path is significantly distant from these obstacles. The closed-loop system demonstrates Input-to-State Stability (ISS) with respect to the prediction error of the learned model. The proposed framework undergoes exhaustive analysis in three stages, training, prediction, and control, across varying noise levels in the state data. Additionally, validation in Matlab and Gazebo illustrates that the NMPC-SINDY-CBF approach enables smooth, accurate, collision-free movement, even with measurement noise and short prediction times. Our findings, supported by tests conducted with the Husky A200 robot, confirm the approach's applicability in real-time scenarios.