CMAC adaptive control of flexible-joint robots using backstepping with tuning functions

A neural network used in a direct-adaptive control scheme can achieve trajectory tracking of a (highly) flexible joint robot holding an unknown payload without need for many learning repetitions. A modification of the Lyapunov stable nonlinear control method known as backstepping with tuning functions is derived to achieve this. Specifically, the introduction of appropriate weightings of the different tuning-function terms results in high performance. Also, a robust redesign of the tuning function method is presented to account for the uniform approximation (modeling) error of the neural network. This computationally burdensome method is made practical by taking advantage of the efficient structure of the CMAC neural network. Simulations with a (highly) flexible-joint robot show immediate compensation for a payload with performance nearly recovered after five seconds.