Model Predictive Control for Trajectory Tracking of the Spherical Robot Based on the Koopman Theory

To improve the trajectory tracking ability of the high nonlinear spherical robot, this paper proposes a model predictive trajectory tracker that considers the kino-dynamic model (KDMPC). Utilizing data identification algorithm based on the Koopman theory, we derived an equivalent linear approximated dynamic model. The kinematic model is linearized by the Taylor expansion. Consequently, the nonlinear kino-dynamic model predictive trajectory planning problem can be transformed into a quadratic programming (QP) problem, enabling real-time online solving. Experiment results with a physical spherical robot demonstrate that the obtained linear kino-dynamic model can achieve accurate trajectory predictions, meeting precision requirements. The KDMPC tracker, proposed in the paper, outperforms traditional trajectory trackers that only consider the kinematic model (KMPC) in terms of tracking accuracy and attitude stability. This work enhances the moving capabilities and increases the application potential of the spherical robot.