A nonlinear H-infinity control approach for closed-chain robotic mechanisms

Abstract

The article proposes a nonlinear H-infinity (optimal) control approach to the problem of control of closed-chain robotic mechanisms. The dynamic model of the closed-chain robotic mechanism undergoes approximate linearization, round a local operating point. This local equilibrium is re-calculated at each iteration of the control program and consists of the present value of the state vector of the robotic mechanism and of the last value of the control input that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. The modelling error due to truncation of higher order terms from this expansion is compensated by the robustness of the control scheme. Next, an H-infinity feedback controller is designed. The feedback gain is computed after solving an algebraic Riccati equation at each iteration of the control algorithm. The control scheme provides solution to a mini-max differential game in which the disturbances and modelling errors try to maximize a quadratic cost functional, while the control input tries to minimize it. Through Lyapunov stability analysis it is proven that the control loop satisfies an H-infinity tracking performance criterion, which signifies elevated robustness to model uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.