Robust Tracking Control of a Three-DOF Planar Under-actuated Manipulator

A manipulator with free joints is a class of under-actuated mechanisms. Control of such systems is one of major topics in robotics and control engineering. In this paper, we develop a nonlinear feedback controller to force a three-dof planar under-actuated manipulator affected by smooth, bounded uncertainties to globally asymptotically track a reference trajectory. This under-actuated manipulator moving in a horizontal plane has two prismatic actuated joints and one revolute free joint. The control development is based on some coordinate transformations, Lyapunov´s direct method and popular integrator backstepping technique. Numerical simulations are presented that demonstrate the effectiveness of the controller.