Stability analysis of quasi-periodic hopping of a passive one-legged robot with compliant hip joint

Aimed at improving energy efficiency of legged robots, flexible elements like springs are introduced to realize temporary energy storage. To achieve the excellent locomotion performance of animals, it is necessary to introduce the torsional spring at the revolute joint into the robot. This paper focuses on a simplified one-legged robot with compliant hip joint, and studies the influence of the torsional spring on the stability of robot quasi-periodic hopping. Firstly, the dynamics differential equations of stance phase and flight phase are established and solved by numerical and analytical methods respectively. Then Poincare map of one whole hopping cycle is built through the unity of four sub-maps. In condition of completely passive hopping of the robot, fixed points are searched through cell mapping and orthogonal table methods. Finally, quasi-periodic solution is obtained, and its stability is analyzed. The analysis results show that the introduced flexible element in revolute joint deteriorates the stability of robot hopping.