This paper presents an averaged model of the velocity dynamics of an underwater snake robot, suited for stability analysis and motion planning purposes for general sinusoidal motion gait patterns. Averaging theory is applied in order to derive a model of the average velocity for a control-oriented model of an underwater snake robot that is influenced by added mass effects (reactive fluid forces) and linear drag forces (resistive fluid forces). Based on this model we show that the average velocity of an underwater snake robot during sinusoidal motion patterns converges exponentially to a steady-state velocity. An explicit analytical relation is given between the steady state velocity and the amplitude, the frequency, the phase shift and the offset of the joint motion for the case of a sinusoidal gait pattern. The results of the paper are general and constitute a powerful tool for achieving faster forward motion by selecting the most appropriate motion pattern and the best combination of the gait parameters. Simulation results are presented both for lateral undulation and eel-like motion.
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