Planning in high-dimensional shape space for a single-wheeled balancing mobile robot with arms

The ballbot with arms is an underactuated balancing mobile robot that moves on a single ball. Achieving desired motions in position space is a challenging task for such systems due to their unstable zero dynamics. This paper presents a novel approach that uses the dynamic constraint equations to plan shape trajectories, which when tracked will result in optimal tracking of desired position trajectories. The ballbot with arms has shape space of higher dimension than its position space and therefore, the procedure uses a user-defined weight matrix to choose between the infinite number of possible combinations of shape trajectories to achieve a particular desired trajectory in position space. Experimental results are shown on the real robot where different motions in position space are achieved by tracking motions of either the body lean angles, or the arm angles or combinations of both.