Parameter Refinement of a Ballbot and Predictive Control for Reference Tracking with Linear Parameter-Varying Embedding

In this study, we implement a control method for stabilizing a ballbot that simultaneously follows a reference. We start the analysis by embedding the nonlinear dynamic model derived from first principles to a linear parameter-varying (LPV) formulation. Continuously, and as an extension of a past study, we refine the parameters of the nonlinear model, which significantly enhances its accuracy compared to the linear model. The crucial advantages of the LPV formulation are that it consists of a nonlinear predictor that can be used in model predictive control (LPV-MPC) by retaining the convexity of the quadratic optimization problem with linear constraints and further evades computational burdens that appear in other nonlinear MPC (NMPC) methods with only a slight loss in performance. The LPV-MPC control method can be solved efficiently as a quadratic program (QP) that provides timing that supports real-time implementation. We test the control designs for 1D non-smooth and 2D smooth references (e.g., Lissajous curves). Finally, theoretical guarantees such as stability and recursive feasibility are provided for a single-set point reference.