Passive running of planar 1/2/4-legged robots

In this paper, we report on passive running of planar one-legged, biped, and quadruped robots. The topic includes the analysis of passive running gaits and their orbital stabilization. For one-legged robot, two stabilizing controllers that asymptotically stabilize periodic passive gaits are derived. In particular, the second controller is based on "energy-preserving principle" and its original form generates interesting quasi-periodic running gaits, which can be seen in Hamiltonian system. The controller is extend to a planar biped robot with torso, which does not have any passive running gaits. Combining simple attitude controller at stance phase generates stable periodic running gaits. For a planar quadruped robot, with an advanced gait searching algorithm, some fundamental proterties of the passive running gaits, such as stability or symmetry, are observed.