Rest-to-rest trajectory planning for planar underactuated cable-driven parallel robots

This paper studies the trajectory planning of underconstrained and underactuated planar cable-driven parallel robots in the case of rest-to-rest motions. For these manipulators, it is possible to control only a subset of the generalized coordinates describing the system. Furthermore, when an arbitrary motion is prescribed for a suitable subset of these coordinates, the lack of constraint on the others leads to the impossibility of bringing the system at rest in a prescribed time. As a consequence, the behavior of the system may not be stable, unless a suitable trajectory is planned. In this paper, a planar 3-DoFs robot suspended by two cables is studied, and a planning method for the trajectory of a reference point on the moving platform is proposed, so as to ensure that the assigned path is tracked accurately and the system is brought to a static condition in a prescribed time.