  In this paper, we study a wheeled robot with a prismatic extension joint.
This allows the robot to build up momentum to perform jumps over obstacles and
to swing up to the upright position after the loss of balance. We propose a
template model for the class of such two-wheeled jumping robots. This model can
be considered as the simplest wheeled-legged system. We provide an analytical
derivation of the system dynamics which we use inside a model predictive
controller (MPC). We study the behavior of the model and demonstrate highly
dynamic motions such as swing-up and jumping. Furthermore, these motions are
discovered through optimization from first principles. We evaluate the
controller on a variety of tasks and uneven terrains in a simulator.
