Stochastic adaptive optimal control of under-actuated robots using neural networks

Stochastic adaptive optimal control of robotic manipulators with a passive joint which has neither an actuator nor a brake is investigated. Firstly, the under-actuated system is decomposed into two subsystems with the first n−1n−1 joints subsystem fully actuated while the second one unactuated. Secondly, a reference model for the first subsystem is derived by using the Linear Quadratic Regulator (LQR) optimization approach which guarantees the motion tracking and achieves the minimized moving accelerations. Instead of leaving the unactuated joint dynamics uncontrolled, the reference trajectory for the last joint is designed to indirectly affect the movements such that the desired trajectory can be achieved. Radial Basis Function neural networks (RBFNNs) have been employed to design the adaptive reference control and to construct a reference trajectory generator for the last joint. The stability and the optimal tracking performance in finite time have been rigorously established by theoretic analysis. Simulation studies show the effectiveness of the proposed control approach.