Fractional-Order Adaptive Integral Hierarchical Sliding Mode Control Method for High-Speed Linear Motion of Spherical Robot

The development of the spherical robot to meet the requirements of high-speed and high-precision tasks is of great importance. In this study, a fractional-order adaptive integral hierarchical sliding mode controller (F-AIHSMC) is proposed. F-AIHSMC enables the spherical robot to have better controlled performance when facing unknown disturbances and system chattering, which can seriously affect the high-speed and high-precision motion of the spherical robot. We establish the standard dynamic model of the spherical robot for high-speed linear motion first, and then use the feedforward compensation method to compensate the controllable influencing factors in the motion process. According to the standard dynamic model, the integral term and fractional calculus methods are integrated into the hierarchical sliding mode controller, and the adaptive method is used to evaluate and compensate unknown disturbances in the high-speed motion process. In order to verify the efficiency of the proposed F-AIHSMC, we test its control effect using the BYQ-GS spherical robot. The experimental results demonstrate that, compared with the classical hierarchical sliding mode controller and the adaptive hierarchical sliding mode controller, the F-AIHSMC has obvious advantages in response speed, convergence speed, stability and robustness when being applied to the control of high-speed linear motion of spherical robot. Moreover, the advantages of its control performance are more highlighted with the increase of the speed of the spherical robot.