A robust optimal controller for constrained robot manipulators

A mixed optimal/robust control is proposed in this paper for the tracking constrained robotic systems under parametric uncertainties and external perturbations. The dynamic model of the constrained system is modified to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained one. The design objective is that under a prescribed disturbance norm level, an optimal control system is to be designed as well as a robust control to overcome the effect of uncertainties. The optimal control is based on the solution of a non-linear Ricatti equation, which by virtue of the skew symmetry property of the reduced dynamics of the constrained manipulators and an adequate choice of state variables becomes an algebraic equation that is easy to solve. The design of the robust control of the uncertain is then investigated using a continuous state feedback function. It will be shown by using Lyapunov stability theory that the present approach globally stabilizes asymptotically the uncertain constrained robotic system. Simulation results made on a 2-degree-of-freedom constrained manipulator are given to illustrate this approach.