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 dexterous 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. We show that the state of the ball relative to the bowl is controllable by this single controlled acceleration. In particular, it is possible to control the equilibrium orientation of the ball on the three-dimensional manifold SO(3) using this single input. We have built an experimental demonstration of this system and we have constructed a motion planner to find a sequence of motions of the bowl to accomplish a desired reorientation. KEY WORDS—nonholonomic and underactuated systems, rolling manipulation, global controllability, motion planning