A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.