Compliant control of a two-link flexible manipulator by constraint Hamiltonian system

Abstract

Two essential tasks of robotic manipulators are characterized by position-to-position movement and contact with external environment. The contact usually results in the generation of external forces in the end-effector of the manipulator, which always modify the dynamic behavior. Consequently, issues of appropriate modeling techniques and effective compliant control strategies arise. In this paper, a new approach employing the framework of constraint Hamiltonian system is proposed for the compliant control of a two-link flexible manipulator with surface constraints. Two non-linear controllers consisting of force part and position part are derived from a constrained Hamiltonian system, followed by the formulation of corresponding linear feedback controllers that satisfy the Lyapunov stability of the total Hamiltonian system which possesses the non-linear controllers. The compliant control strategy is accomplished by steering the end-effector of the flexible manipulator onto the constraint surface with the linear controllers, and subsequently by executing imposed desired motion with the non-linear controllers. Computer simulations are undertaken in order to demonstrate the analytical formulation and the effectiveness of the proposed control methodology.