A Novel Fractional Fixed-Time Sliding Mode Control Method for Spherical Robot Linear Motion Speed Control

This paper studies the linear motion speed control problem of an underactuated spherical robot under unknown disturbances. A novel fractional fixed-time terminal sliding mode control with a nonlinear disturbance observer is proposed for the spherical robot to achieve fast stabilization and robust control performance. First, a novel fixed-time terminal sliding surface is proposed by adding a fractional differential operator in the traditional integer order fixed-time terminal sliding surface. A nonlinear disturbance observer is designed to estimate the unknown disturbances. Then a fractional hierarchical sliding mode speed controller is designed based on the novel fractional fixed-time terminal sliding surface and the nonlinear disturbance observer. Through the Lyapunov stability theorem, the boundedness of each sliding surface is achieved, and the stability of the whole system is guaranteed. The effectiveness of the proposed controller has been verified via simulation work. The simulation results show the fractional sliding mode controller has a shorter settling time and lower overshoot compared to an integer order sliding controller. When subjected to the abrupt changes of rolling friction, the fractional hierarchical sliding mode controller shows stronger robustness than the integer order one.