Optimal trajectory tracking control of a robot manipulator

In order to find the optimal control law for the precise trajectory tracking of a robot manipulator, a perturbational control method is proposed based on a linearized manipulator dynamic model which can be obtained in a very compact and computationally efficient manner using the dual number algebra. Manipulator control can be decomposed into two parts: the nominal control and the corrective perturbational control. The nominal control is precomputed from the inverse dynamic model using the quantities of a desired trajectory. The perturbational control is obtained by applying the second-variational method on the linearized dynamic model. Simulation results for a PUMA-560 robot show that, by using this controller, the desired trajectory tracking performance of the robot can be achieved, even in the presence of large initial positional disturbances.