Path-planning and Control of Underactuated Manipulators by Nonlinear Discrete-time Approaches

Planar, horizontal manipulators with passive joints are a special challenge within the class of underactuated systems, because a linearization about an equilibrium leads to a model which is not completely controllable. Hence, for rest-to-rest motions linear control approaches are not applicable. The control problem is ill-conditioned close to an equilibrium, even if using a nonlinear model. Therefore, continuous-time controllers, which guarantee that the system approaches an equilibrium asymptotically, usually don't lead to satisfactory behavior. The presented discrete-time path-planning and control approaches avoid this problem by ensuring convergence to an equilibrium in a finite-time interval. Besides path-planning approaches, which provide good convergence properties and a systematic calculation of the transition time, two feedback controllers are presented and verified.