Modeling and Control of a New Spherical Robot with Cable Transmission

This paper presents a new spherical robot with a cable transmission mechanism. Cable transmission mechanism replaces conventional gear train to eliminate the influence of gear backlash, reduce the robot mass, lower the costs on mechanical customization and can be arranged flexibly. By projection method, the 3D robot dynamic model with structural asymmetry is decoupled into balance subsystem and velocity subsystem, and the kinetics equations are established based on Newton-Euler's law. For the balance control, an adaptive law is designed to estimate the upper bound instead of the exact value of the uncertainty caused by the structural asymmetry online firstly, then a finite-time adaptive hierarchical sliding mode control (FAHSMC) strategy is proposed based on the estimation result to minimize the convergence time. For the velocity control, a hierarchical sliding mode controller (HSMC) and a tracking differentiator (TD)-based nonlinear disturbance observer are designed, leading to enhanced disturbance rejection capability and a reduced steady-state error. Simulations and experiments on a real spherical robot are conducted to demonstrate the efficacy of the proposed control strategies.