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Like the terrestrial robots playing football, fishlike robots can play polo game in the water. The accurate trajectory control of autonomous robot fish based on local vision information plays an important role in the game. However, path planning approaches for fishlike robots were lacking in the literature. Here, we develop a tangent circle method, which is based on its inherent kinematic constraints, to plan an executable path for the robot fish. Two kinds of tangent circles are defined to represent the motion tendencies of robot fish, and are drawn accurately by control parameters. By means of the combination of tangent circles and their external or internal common tangent, the robot fish can accomplish a path from an initial pose to a final pose, at which the fish can forward push the ball to the goal. Furthermore, experimental results validate the effectiveness of this method.