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.