  This paper studies real-time motion planning and control for ball bumping
motion with quadruped robots. To enable the quadruped to bump the flying ball
with different initializations, we develop a nonlinear trajectory
optimization-based planning scheme that jointly identifies the take-off time
and state to achieve accurate ball hitting during the flight phase. Such a
planning scheme employs a two-dimensional single rigid body model that achieves
a satisfactory balance between accuracy and efficiency for the highly
time-sensitive task. To precisely execute the planned motion, the tracking
controller needs to incorporate the strict time-state constraint imposed on the
take-off and ball-hitting events. To this end, we develop an improved model
predictive controller that respects the critical time-state constraints. The
proposed planning and control framework is validated with a real Aliengo robot.
Experiments show that the problem planning approach can be computed in
approximately 60ms on average, enabling successful accomplishment of the ball
bumping motion with various initializations in real time.
