  This paper studies jumping for wheeled-bipedal robots, a motion that takes
full advantage of the benefits from the hybrid wheeled and legged design
features. A comprehensive hierarchical scheme for motion planning and control
of jumping with wheeled-bipedal robots is developed. Underactuation of the
wheeled-bipedal dynamics is the main difficulty to be addressed, especially in
the planning problem. To tackle this issue, a novel wheeled-spring-loaded
inverted pendulum (W-SLIP) model is proposed to characterize the essential
dynamics of wheeled-bipedal robots during jumping. Relying on a
differential-flatness-like property of the W-SLIP model, a tractable quadratic
programming based solution is devised for planning jumping motions for
wheeled-bipedal robots. Combined with a kinematic planning scheme accounting
for the flight phase motion, a complete planning scheme for the W-SLIP model is
developed. To enable accurate tracking of the planned trajectories, a linear
quadratic regulator based wheel controller and a task-space whole-body
controller for the other joints are blended through disturbance observers. The
overall planning and control scheme is validated using V-REP simulations of a
prototype wheeled-bipedal robot.
