Dynamic model based on Boltzmann-Hamel equation and adaptive sliding mode trajectory tracking control of spherical mobile robot

Spherical mobile robot has a compact structure, flexible mobility, and exceptional environmental adaptability, which gives it potential for applications in unmanned exploration. However, spherical mobile robot is a special non-chained nonholonomic system with under-actuation and strong coupling, which makes its dynamic model complex and trajectory tracking control very difficult to implement. In this paper, to achieve strong robustness and anti-interference of trajectory tracking control of spherical mobile robot, a comprehensive dynamic model is established using the Boltzmann-Hamel equation for a two-degree-of-freedom pendulum-driven spherical mobile robot and then simplified to improve controllability while preserving key motion characteristics. Comparative experiments with the dynamic model established with the Euler-Lagrange method were conducted to evaluate its superiority. Furthermore, to address the model uncertainty of the spherical mobile robot and the environment disturbances that may be encountered during motion, an adaptive sliding mode trajectory tracking control based on double power reaching law was proposed and proved to be stable by Lyapunov theorem. The effectiveness and robustness of the proposed controller were validated through both simulations and physical experiments.