Nonlinear optimal control of the 6-DOF parallel Stewart robotic platform

Abstract A new nonlinear optimal control method is proposed for solving the problem of control and stabilization of the 6-DOF parallel Stewart robotic platform. This parallel robotic platform is proven to be differentially flat. The dynamic model of this robotic system undergoes first approximate linearization around a temporary operating point that is updated at each iteration of the control algorithm. The linearization takes place through first-order Taylor series expansion and through the computation of the Jacobian matrices of the system's state-space description. For the approximately linearized model of the parallel robotic platform an H-infinity feedback controller is designed. Actually, the H-infinity controller stands for the solution of the optimal control problem for the parallel robotic platform's dynamic model under uncertainty and external perturbations. For the computation of the feedback gain of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control algorithm are proven through Lyapunov analysis. First, it shown that the control scheme achieves the H-infinity tracking performance which signifies elevated robustness for the control loop of the 6-DOF robotic platform against model uncertainties and external perturbations. Next,it is also shown that the control loop of the parallel robotic platform is globally asymptotically stable. The proposed control method achieves fast and accurate tracking of setpoints under moderate variations of the control inputs.