Minimum Energy-cost Walking Exploiting Natural Dynamics of Multiple Spring-Mass Model

The energy-efficient locomotion for a legged robot has been an important research topic. In this paper, we propose a dynamic model and the conditions to realize minimal-cost walking exploiting natural dynamics by analytical solving the dynamics of walking. The proposed dynamic model for walking consists of two springs and three masses, and the dynamics and condition for this model to realize the continuous and minimal cost walking is derived theoretically. Because the legged model is a hybrid model depending on the landing of feet, the transition conditions are proposed to realize continuous motion and while avoiding the energy dissipation caused by the ground collision. The initial states of the model determine the entire motion with proposed transition conditions. The whole two-dimensional dynamics of the proposed biped model is solved, and the results reveal that the stiffness of legs and the initial positions of the feet can adjust the period and velocity of natural dynamics driven walking. The generated walking model and dynamics are verified using simulations which show the total energy of the proposed walking model is conserved while the repetitive motion is realized.