Smooth Robust Adaptive Sliding Mode Control of Manipulators With Guaranteed Transient Performance

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Abstract
A systematic way to combine adaptive control and sliding mode control (SMC) for trajectory tracking of robot manipulators in the presence of parametric uncertainties and uncertain nonlinearities is developed. Continuous sliding mode controllers without reaching transients and chattering problems are first developed by using a dynamic sliding mode. Transient performance is guaranteed and globally uniformly ultimately bounded (GUUB) stability is obtained. An adaptive scheme is also developed for comparison. With some modifications to the adaptation law, the control law is redesigned by combining the design methodologies of adaptive control and sliding mode control. The suggested controller preserves the advantages of both methods, namely, asymptotic stability of the adaptive system for parametric uncertainties and GUUB stability with guaranteed transient performance of sliding mode control for both parametric uncertainties and uncertain nonlinearities. The control law is continuous and the chattering problem of sliding mode control is avoided. A prior knowledge of bounds on parametric uncertainties and uncertain nonlinearities is assumed. Experimental results conducted on the UCB/NSK SCARA direct drive robot show that the combined method reduces the final tracking error to more than half of the smoothed SMC laws for a payload uncertainty of 6 kg, and validate the advantage of introducing parameter adaptation in the smoothed SMC laws.

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