Near-optimal neural-network robot control with adaptive gravity compensation

Adaptive nonlinear optimal control methods, as proposed in the literature, give rise to some questions around practical implementation in robotics, especially how to find a solution in a reasonable time and how to deal with gravity. This paper proposes a method to solve these problems by using a neural network with local basis-function domains, specifically the Cerebellar Model Articulation Controller (CMAC). The algorithm uses the local domains in order to keep track of the value of local cost-functionals. In this way, it can freeze the learning of the network’s weights in a feedforward-like component in the CMAC when the bias has been overcome identified by using an error-based cost-functional e.g. automatic gravity compensation in a robot. After the feedforward component has been established, the algorithm then starts to learn another set of weights which contribute to feedback-like terms in the CMAC and these weights get frozen when they no longer reduce a cost-functional that includes additional control effort e.g. in a robot the control effort beyond that needed to compensate for gravity is penalized. Lyapunov methods guarantee uniformly ultimately bounded signals and ensure weight drift and bursting do not occur. One advantage is that the training time for finding a near-optimal control does not increase over previous neural-adaptive methods. Another advantage is that penalizing the control effort in a search for optimization does result in any steady-state error due to gravity. Simulations show that the proposed method significantly outperforms a standard adaptive-CMAC control using e-modification, without increasing control effort or training time. An experimental flexible-joint robot verifies that the adaptive method significantly outperforms a linear quadratic regulator.