Sliding Modes in Constrained Systems Control

Abstract—In this paper, a sliding-mode-based design frame-work for fully actuated mechanical multibody system is discussed. The framework is based on the possibility to represent complex motion as a collection of tasks and to find effective mapping of the system coordinates that allows decoupling task and constraint control so one is able to enforce concurrently, or in certain time succession, the task and the constraints. The approach seems nat-urally encompassing the control of motion systems in interaction, and it allows application to bilateral control, multilateral control, etc. Such an approach leads to a more natural interpretation of the system tasks, simpler controller design, and easier establish-ment of the systems hierarchy. It allows a unified mathematical treatment of task control in the presence of constraints required to be satisfied by the system coordinates. In order to show the applicability of the proposed techniques, simulation and experi-mental results for high-precision systems in microsystem assembly tasks and bilateral control systems are presented. Index Terms—Bilateral control, constrained multibody systems, force control, motion control, nonlinear systems, sliding-mode control (SMC). I