Control of underactuated manipulation by real-time nonlinear optimization

Underactuated manipulation is the process of controlling a large number of object degrees-of-freedom with fewer robot degrees-of-freedom. The challenge is to derive motion planners and feedback controllers to control underactuated manipulation. In this paper we study the use of real-time nonlinear optimization for motion planning and feedback control of planar batting manipulation with a one-joint robot. We study two tasks: cyclic juggling of a disk, and control of a disk from one six-dimensional state to another by a sequence of three bats. We show analytically and experimentally that the juggling controller yields a stable limit cycle with a large basin of attraction. The experimental results for state-to-state control are less successful and indicate that more accurate modeling of the impact and flight dynamics are required.