This paper introduces the equations of motion of modular 2D snake robots in the vertical plane. In particular, the kinematics of pedal wave motion (undulation in vertical plane) of modular snake robots is presented and using the Euler-Lagrange method, the equations of motion of the robot are obtained. Moreover, using the well-known Spring-Damper contact model, external contact forces are taken into account and pedal wave locomotion on uneven terrain is modelled and simulated. Enabled by the dynamical model of the robot, an adaptive controller based on external force feedback in gait parameter space is proposed and implemented, resulting in the robot to successfully climbing over a stair-type obstacle without any prior knowledge about the environment.

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