In this paper, we present a method of determining optimal gaits for shape actuated locomotion systems. This method is the synthesis of techniques for computing reduced equations for robotic locomotion systems and a numerical optimal control strategy. Symmetry reduction processes induce a form of locomotion system dynamics that reveals a cyclic-like coupling between group, shape, and momenta coordinates. This form allows one to focus on designing gaits, abandoning concern over shape dynamics. Using this vantage point we indicate how a numerical optimal control method based on Gaussian quadrature may be acclimatized to periodicity, thus providing optimal gaits. The method is demonstrated by means of its application to a snake-like serial-link structure or snake robot. This application provides scientific merit to hypotheses concerning observed locomotion phenomena amongst animals employing undulatory propulsive mechanisms.
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Hicks et al. (2005) studied this question.
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