Improving Robustness of Computed-Torque Schemes via LMI-Based Nonlinear Feedback

This paper is concerned with a novel computed-torque technique for trajectory tracking, which enhances robustness by replacing some of the system nonlinearities in the inner-loop feedback by the signals of the desired trajectory. This substitution leads to a nonlinear error system whose stabilization is achieved via a nonlinear outer-loop feedback in the form of parallel distributed compensation, whose gains are solved in terms of linear matrix inequalities derived from the direct Lyapunov method and exact convex modelling of nonlinearities. The proposal makes use of a recently appeared factorization which explicitly allows extracting the error signal in the difference of identical expressions that depend on a different set of variables. Simulations suggest that the magnitude of the computed-torque signal can be significantly reduced when compared with ordinary schemes while augmenting robustness by employing user-generated signals instead of measurements where appropriate.