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In this paper we extend a non-smooth 3D mathematical model of a snake robot to also include external obstacles to enable obstacle aided locomotion. The model is based on the framework of non-smooth dynamics and convex analysis. This framework enables us to systematically and easily incorporate unilateral contact forces (from the obstacles and the ground) and isotropic friction forces based on Coulomb's law. The obstacles are shaped as vertical cylinders and we describe the contact between adoi:10.1109/robio.2006.340097 dblp:conf/robio/TransethLGP06a fatcat:cym3qcwlyjdwjbtte7zt6wjzly