An effective control method that achieves movement over a small ridge as an example of three-dimensional (3D) snake-like creeping locomotion is presented. The creeping robot is modeled as a continuum with zero thickness capable of generating bending moment at arbitrary points. Under a simplified contact condition, the optimal bending moment distribution in terms of a quadratic cost function of input can be obtained as a function of curvature by solving an isoperimetric problem. The solution is well suited to an articulated body consisting of finite number of links. The model is demonstrated through simulations and experiments using a prototype robot to be effective for traversing smooth 3D terrain.

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