Symmetry based searching process for initial conditions of passive running

Symmetrical passive running of a simple spring model is commonly used to predict the locomotion of real animals and develop the design strategies for legged systems. If the initial conditions for running can be found automatically, we can expand the ranges of the model parameters freely. To achieve this objective, we derive an efficient searching procedure based on analysis of the symmetries. Using this process, the desired initial states of the passive running are obtained. Existence of the results reveals that the leg symmetries can be used to generate the symmetrical running. Moreover, the leg forces are associated with the running pattern, implying that we should choose suitable motion for the given model characteristics.