A Fixed-Time Composite Control With Variable Exponent Coefficients for Stewart Parallel Mechanism Tracking in Task Space

Abstract

To improve tracking control performance in the task space of the Stewart parallel mechanism (SPM) with uncertainties of modeling errors and external disturbances in our developed rust removal sandblasting robot for the surface roughness processing of a bridge's steel box girder, a fixed-time composite control with variable exponent coefficients (VEC-FxTCC) approach for multi-input multi-output (MIMO) nonlinear robotic systems is developed. Firstly, by devising only one regulation term with a variable exponent coefficient (VEC) function in the system's Lyapunov differential inclusion, a novel VEC fixed-time stability theorem for the MIMO nonlinear dynamic system is proposed and proven. Secondly, based on the proposed theorem, VEC-FxTCC is formed by designing and combining a VEC fixed-time disturbance observer (VEC-FxTDOB) and a VEC fixed-time super-twisting control (VEC-FxTSTC), in order to achieve fast, steady, and uniformly bounded-time convergence for SPM's end-effector tracking, while avoiding singularity. Finally, the effectiveness of the proposed VEC-FxTCC approach is validated through the simulations and the rust removal sandblasting robot prototype experiments.