Smooth trajectory planning for XYnR~ planar underactuated robots

We consider the trajectory planning problem for the class of XYnR~ planar underactuated robots, having the first two (rotational or prismatic) joints actuated and the last n rotational joints passive. Under the assumption that each passive link is attached at the center of percussion of the previous passive link, the dynamic model assumes a simplified form and we show how to recursively design a dynamic feedback that completely linearizes the system equations. This result allows to plan smooth rest-to-rest motions using polynomial interpolation. As an example, we report the numerical results obtained for trajectory planning of an RR2R~ robot.