A wheelchair kinematic model was constructed to address the wheelchair control problem in table tennis for disabled individuals. The influence of slipping factors was considered, and a differential model of motion trajectory error was derived. A table tennis wheelchair self-correcting control model was designed based on the back-stepping method. Under the self-correcting control model, the state observer continuously observes the error of the motion trajectory and provides compensation to suppress disturbances including slippage, ensuring the stability of the table tennis wheelchair operation. The Lyapunov stability of the proposed self-correcting control model has been demonstrated. Through two sets of simulation experiments, the control effect of the self-correcting model on the linear and circular movement of the wheelchair, especially the suppression effect on slipping interference, was verified. The comparative experimental results show that under the control of the self-correcting model, the error variation of the wheelchair`s movement trajectory is significantly smaller than that of the PID method and PSO method.
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