  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 HTSMC, an instruction
planning controller MPC, and a trajectory tracking framework 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. MPC 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 MPC's stability and
dynamic constraints. Finally, hardware experiments demonstrate the efficacy of
the HTSMC, MPC, and MHH.
