H∞ Control for Systems with Mechanical Constraints Based on Orthogonal Decomposition

Abstract

In this paper, we study H∞ control for systems with explicit mechanical constraints and a lack of state information, such as walking robots. This paper proposes an H∞ control design scheme based on solving an optimization problem with linear matrix inequality constraints. Our method is based on the orthogonal decomposition of the state variables and the use of two linear controllers and a Luenberger observer, tuned to achieve the desired properties of the closed-loop system. The method takes into account static linear additive disturbance, which appears due to the uncertainties associated with the mechanical constraints. We propose a dynamics linearization procedure for systems with mechanical constraints, taking into account the inevitable lack of information about the environment; this procedure allows a nonlinear system to be transformed into a form suitable for the application of the proposed control design method. The method is tested on a constrained underactuated three-link robot and a flat quadruped robot, showing the desired behavior in both cases.