Motion Planning and Trajectory Control of an Underactuated Three-Link Robot via Dynamic Feedback Linearization

We present a new method for motion planning and feedback control of three-link planar robot arms with a passive rotational third joint. These underactuated mechanical systems are shown to be fully linearizable and input-output decoupable by means of a nonlinear dynamic feedback, provided a physical singularity is avoided. The linearizing output is the position of the so-called center of percussion of the third link. Based on this result, one can plan smooth motions joining in finite time any initial and desired final state of the robot. Moreover, it is easy to design an exponentially stabilizing feedback along the planned trajectory. Simulation results are reported for a 3R robot.