Mathematical modelling and control of a nonholonomic spherical robot on a variable-slope inclined plane using terminal sliding mode control

Abstract

Motion analysis and control of a pendulum-driven spherical robot (PDSR) on an inclined plane with a variable slope is investigated. Firstly, the mathematical model of a PDSR on a variable-slope inclined plane is deduced applying a Lagrangian formulation. Afterwards, in the presence of an unknown external disturbance, the terminal sliding mode control (TSMC) technique is employed to stabilize the robot on the inclined plane, while the plane is still moving. In other words, the terminal sliding mode disturbance observer is used to estimate the unknown disturbance. Based on the disturbance estimation, the TSMC scheme is established to control the single-input and single-output nonlinear system with control singularity and an unknown nonsymmetric control input saturation. In fact, a compound disturbance is defined and estimated, which includes the external disturbance, the control singularity and the unknown input saturation. Simulations are then conducted to validate the proposed approach for motion control of a PDSR on a variable-slope inclined plane with an unknown external disturbance and nonsymmetric input limits.