This paper addresses the optimal control and selection of gaits in a class of nonholonomic locomotion systems that exhibit group symmetries. We study optimal gaits for the snakeboard, a representative example of this class of systems. We employ Lagrangian reduction techniques to simplify the optimal control problem and describe a general framework and an algorithm to obtain numerical solutions to this problem. This work employs optimal control techniques to study the optimality of gaits and issues involving gait transitions. The general framework provided in this paper can easily be applied to other examples of biological and robotic locomotion.
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