  The feet of robots are typically used to design locomotion strategies, such
as balancing, walking, and running. However, they also have great potential to
perform manipulation tasks. In this paper, we propose a model predictive
control (MPC) framework for a quadrupedal robot to dynamically balance on a
ball and simultaneously manipulate it to follow various trajectories such as
straight lines, sinusoids, circles and in-place turning. We numerically
validate our controller on the Mini Cheetah robot using different gaits
including trotting, bounding, and pronking on the ball.
