Detection and Stabilization of Hybrid Periodic Orbits of Passive Running Robots

In this paper a new algorithm to detect hybrid periodic orbits of autonomous hybrid dynamical system is developed. Conventional Newton algorithm is modified so that it suits to the analysis of Poincaré return map of hybrid dynamical systems that include multiple phases (modes) and discrete jumps. Then, the algorithm is applied to a specific example; planar one-legged robot model having a springy leg and a compliant hip joint. With the algorithm, passive running gaits of the one-legged robot are automatically detected for various parameter sets and initial conditions. The analysis of the characteristic multiplier of the return map revealed the stability and the bifurcation of the passive running gaits. Two kinds of controllers that achieve orbital stabilization are presented. A similarity is found between the detection algorithm and the stabilizing controller. The algorithm can be applied to any kinds of the robots (e.g. walking robot).