Dynamic modeling and control of multi-axis manipulator based on the Udwadia–Kalaba theory

The high accuracy tracking control of multi-axis manipulator with uncertainty is always a difficult problem for control theorists and engineers. The Udwadia–Kalaba theory effectively characterizes the explicit dynamics equations of constrained mechanical systems. The Sliding Mode Control (SMC) law is implemented under the circumstance of uncertainties in manipulator model, fluctuations in parameters, and external disturbances. However, the existing SMC law has limitations in the convergence speed and chattering. A proposed SMC law combining nonlinear sliding mode hypersurface and double-power reaching law is presented on the basis of dynamic equation provided by the Udwadia–Kalaba theory, which can address the slow convergence speed of reaching law and chattering phenomenon of SMC dynamic response. Moreover, the superiority of the proposed SMC law is verified through a comparison with two compared SMC laws: one that integrates a linear sliding mode manifold with an exponential reaching law, and another that combines the linear sliding mode manifold with the double-power reaching law. Finally, taking the SCARA robot as an illustrative example, the proposed scheme is implemented to the constraint tracking control of the multi-axis manipulator. The results show that the system has stronger robustness and faster convergence speed, which verifies the convincingness of the proposed strategy.