A convex optimization based solution for the robotic manipulator control design problem subject to input saturation

Abstract

This paper proposes a state-feedback design procedure for robotic manipulator systems with saturating actuators, a solution which is based on convex optimization subject to constraints in the form of linear matrix inequalities. Our fundamental idea is to express the system dynamics in a novel differential-algebraic representation with state-derivative components. This approach allows us to provide a systematic control design framework with formal theoretical guarantees, such as the asymptotic stabilization of the manipulator attitude reference error within a prescribed exponential decay-rate. Our method is capable of dealing with the nonlinearities of a mechanical manipulator system, including the input saturation effect, without relying on any kind of linearization or approximation. A two-link planar robotic manipulator example is employed in order to illustrate the proposed approach.