Quadruped performing a hockey-style skating stop via foot pivot and lateral slipIn this paper, we propose an effective mechanical and algorithmic solution to enabling skating motion with passive wheels on state-of-the-art quadrupedal robots. The skating locomotion enables a hybrid combination of wheeled and legged mobility without the necessity of motorization at the feet, which simultaneously promote efficiency, speed, and mechanical simplicity. To realize these potential advantage of skating, we employ a bilevel optimization approach with an upper level optimization via Bayesian Optimization (BO) to search for the best mechanical design and a lower level Reinforcement Learning (RL) to find an optimal motor policy. The end results not only provide optimal mechanical and control designs but also show versatile locomotion behaviors such as hockey stop (a rapid braking maneuver by turning sideways to maximize friction) and self-aligning behavior (automatically adjusts its orientation to move more efficiently in the commanded direction), providing the first comprehensive study on quadrupedal robotic skating.