An adaptive variable structure model following control design for robot manipulators

An adaptive variable structure model-following control (AVSMFC) design is proposed for trajectory tracking in a nonlinear robot system which ensures the stability of the intersection of the surfaces without necessarily stabilizing each individual one. The approach avoids the difficulties linked to the strict positive realness requirement in traditional AMFC by taking advantage of the inherent positive definiteness of the manipulator´s inertia matrix, and is easily extendible to a higher number of links. The controller does not require any knowledge of a nonlinear robotic system and does not necessarily need the occurrence of a sliding mode at each individually stable discontinuity surface. It thus greatly reduces the complexity of design. In the closed loop, the joint angles asymptotically converge to the reference trajectory with a prescribed transient response. Chattering is eliminated by restricting the state of the system to slide within a boundary layer rather than along the intersection of the surfaces