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Modeling of a carangiform-like robotic fish for both forward and backward swimming: Based on the fixed point

In this paper, a dynamic model is proposed for a carangiform-like robotic fish swimming both forwards and backwards. The robotic fish, which consists of a streamlined head, a flexible body and a caudal fin, is able to propel itself by generating a traveling propulsive wave traversing its body. We first modify the classical body wave function suggested by Lighthill to fit our robotic fish. Then we naturally define the point on fish's body which never undulates during swimming straight as “Fixed-point” and prove its existence and uniqueness. Using the property of the Fixed-point, we propose a model for our robotic fish and further investigate how the swimming speed is affected by the position of the unique Fixed-point. It is found that the robotic fish achieves its maximum speed of swimming forwards and backwards when the Fixed-point located on the head and the tail, respectively. Finally, we apply the proposed model combining with a CPG-based locomotion controller to the real robotic fish. Both simulations and experiments show that the proposed model is capable to predict the speed of the robotic fish.