CBFs-Based Model Predictive Control for Obstacle Avoidance With Tilt Angle Limitation for Ball-Balancing Robots

This study investigates an automatic navigation method for one type of underactuated system, ball-balancing robot (ballbot), in complex environments with both dynamic obstacles and complex-shaped obstacles. To ensure safe operations, which means that ballbot has to avoid obstacles and maintain tilt angles in a desired range, Nonlinear Model Predictive Control (NMPC) is formulated to predict the position and behavior of the ballbot, followed by the optimization problem assisted by Control Barrier Function (CBF) constraints to drive the ballbot in the safe trajectory. Instead of directly implementing tilt angle limitations on the main NMPC, another Quadratic Programming Optimizer based on CBF is designed outside the main controller to reduce the constraint complexity of optimization. An elliptic-bounded generation method is used to simplify the object boundary, especially concave obstacles definition in NMPC constraints, while Extended State Observer is used for observing, compensating the uncertainty terms, and estimating the velocities of the ballbot. In general, by combining this CBF-based NMPC and Quadratic Programming, this research addresses simultaneously high-quality observer, tracking control, balancing control, complex motion planning and safe-angle constraints for the 3D-ballbot system. The effectiveness of our proposed method is determined by simulations in complicated tracking scenarios with static, dynamic and complex-shaped objects.