Nonlinear Optimal Control of Parallel Robotic Manipulators

Control and stabilization of parallel robotic manipulators is a non-trivial problem because of nonlinearities and multivariable structure. In this article a nonlinear optimal control approach is proposed for the dynamic model of such robotic systems, using as a case-study the model of a ¿ve-link parallel robot. The dynamic model of the parallel robotic manipulator undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-in¿nity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller's feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis..