Adaptive Control of Closed Kinematics Chains Based on Singularly Perturbed Formulation

The dynamics of parallel robots containing closed kinematics chains (CKCs) are usually described by differential-algebraic equations (DAEs). For the sake of control this type robot, the conventional control schemes usually rely on solving nonlinear algebraic constraint equations to obtain the dependent coordinates using the Newton-type iterations, this is not applicable to real-time implementation. In this paper, a novel adaptive control approach to the control of CKCs considering the inertia parameters uncertainties is proposed based on singularly perturbed model. This method transfers the control of the original DAEs to the control of an artificially created singularly perturbed system and can be conveniently implemented. The scheme is shown using Lyapunov theory that asymptotic trajectory tracking can be achieved. Simulation results of an illustrate example are given to demonstrate its efficacy.