Stochastic neural network control of rigid robot manipulator with passive last joint

Stochastic adaptive control of a manipulator with a passive joint which has neither an actuator nor a holding brake is investigated. Aiming at shaping the controlled manipulators dynamics to be of minimized motion tracking errors and joint accelerations, we employ the linear quadratic regulation (LQR) optimization technique to obtain an optimal reference model. Adaptive neural network (NN) control has been developed to ensure the reference model can be matched in finite time, in the presence of various uncertainties and stochastic noise. In addition, due to the stochastic noise, we transform the system equation to the Ito stochastic differential equation (SDE) form and then use the Ito formula to deal with the stochastic terms of the systems. Simulation studies show the effectiveness of the planned trajectory and the feedback control laws.