Rolling manipulation with a single control

Underactuated manipulation is the process of controlling several object degrees-of-freedom with fewer robot actuators. Underactuated manipulation allows us to build dextrous robots with only a few actuators. In this paper we explore the possibility of useful dynamic manipulation with only a single actuator. Our case study is a ball rolling in an asymmetrical bowl which can be accelerated along one linear degree-of-freedom. For a real physical system we show that it is possible to control the equilibrium orientation of the ball on the three-dimensional manifold SO(3) using the single input. We built an experimental demonstration of this system and constructed a motion planner to find a sequence of motions of the bowl to accomplish a desired reorientation.