Adaptive bias RBF neural network control for a robotic manipulator

Considering the bias of the dynamics which is a global trend of the dynamical equation of a robot manipulator because of the gravity or the constant payloads, two kinds of adaptive bias radial basis function neural network (RBFNN) control schemes, which are the local bias scheme and the global bias scheme, are proposed to remedy the negative influence of the bias of the dynamics. Such slight modifications lead to the following two attractive features: 1) both of two schemes can improve the approximation accuracy of the RBFNN for the dynamics with significant bias, and then enhance the control performance correspondingly; 2) when the inputs deviate from the approximation domain of the RBFNN because of the large payloads, the controller with the local bias or global bias degrades to the PID controller to push the states back. It improves the robustness of the adaptive RBFNN controller further. We also propose a simpler controller structure that reduces the dimension of the input vectors from 4n to 3n, where n is the degree of freedom of the manipulator. It exponentially decreases the computation cost of the RBFNNs. Uniform ultimate boundedness of the closed-loop system is proved by the Lyapunov stability theory. Finally, simulation results demonstrate the effectiveness of the proposed two schemes.