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

Real-time Trajectory Optimization and Control for Ball Bumping with Quadruped Robots