In this paper, we have determined an analytical solution for a zero-work gait for the MSU Synthetic Wheel Biped [1, 2] by choosing proper constraints. The new optimized gait ensures that the total energy of the system is the same at the beginning and the end of each step. This results in zero total work, regardless of the initial velocity of the leg or step length provided there are no losses due to friction. Furthermore, the correct choice of the gait constraints completely eliminates the ground impact forces during the foot transition. The previously developed nominal gait and the new optimized gait are implemented on a hardware prototype and a comparison of the energy consumption of these two different gait functions indicates a significant reduction in mechanical cost of transport.

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