Stabilization of a planar prismatic-prismatic-revolute manipulator based on an energy approach

The paper presents the control of an underactuated planar robot, with two prismatic and one revolute joints. We propose a controller based on an energy approach and the passivity properties of the system. The stabilization algorithm proposed is related to the works of J. Collado et al. (2000), I. Fantoni et al. (1999; 2000) and R. Lozano et al. (2000), in which the total energy of the systems is used in the control of underactuated manipulators. The passivity properties of the system are analyzed and we use an energy-based approach to establish the proposed control law. The control algorithm as well as the convergence analysis are based on Lyapunov theory and LaSalle´s invariance theorem. The performance of the proposed control law is shown in simulation