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This paper reports the algorithm of trajectory planning and the strategy of four-leg coordination for quasi-static stair climbing in a quadruped robot. This development is based on the geometrical interactions between robot legs and the stair, starting from single-leg analysis, followed by two-leg collaboration, and then four-leg coordination. In addition, a brief study on the robot’s locomotion stability is also included. Finally, simulation and experimental testing were executed to evaluate the performance of the algorithm.<br />