Nonlinear Tracking Control with Reduced Complexity of Serial Robots: A Robust Fuzzy Descriptor Approach

Abstract

This paper presents a nonlinear tracking control approach for a two-degree-of-freedom serial manipulator. The design goal is to achieve a guaranteed $$\mathcal {H}_{\infty }$$ tracking performance while keeping the designed controller as simple as possible for real-time implementation. To this end, the descriptor Takagi–Sugeno fuzzy modeling is used to describe the nonlinear dynamics of the robot. Then, based on Lyapunov stability theory, we propose conditions to design fuzzy controllers for trajectory tracking purposes. The control design procedure is reformulated as an optimization problem under linear matrix inequality constraints which can be effectively solved with semidefinite programming technique. Numerical experiments carried out with the Simscape Multibody™ library of MATLAB® clearly demonstrate the effectiveness of the proposed approach in terms of tracking control and numerical simplicity.