Search and optimization of the periodic gait of leg locomotion systems

The task of reproducing artificial legged locomotion presents lots of challenges, most of them related to the system dynamics, which is non-linear, hybrid and under actuated. Recently the scope of legged locomotion changed from static stability to dynamical stability, in which the dynamics of the system plays an important role in the development of control algorithms that have as a main goal the construction of a stable limit cycle. This article projects a periodic control for trot without the air phase for a quadruped though the multiple shooting method with Hermite-Simpson direct collocation. The algorithm was first tested in a monopod where the control for hopping and forward hopping was searched, such that the optimization occurred after finding the periodic gait and for each case the stability of the control was determined through the Floquet Multipliers from Poincare's map. The quadruped system could not be wholly analyzed because the search for the periodic gait failed for the initial estimation, leaving this analysis for future researches.