We have developed an underwater robotic fish using a unique three-layer electrostatic film motor. In the robotic fish, the unique motor actuates a flexible caudal fin to propel the robot via an elaborate power transmission system. In the present study, we describe the major disadvantages of the previous prototype of the robotic fish and improvements of the prototype. In addition, we present experimental evaluations related to the control parameters and locomotion performance of the robotic fish. These control parameters include the frequency and initial phase of AC voltage, and the amplitude and period of frequency sweeping. A simple theoretical model concerning the power transmission system of the robotic fish is also analyzed to provide a possible explanation for the unique swimming control. By appropriately adjusting these control parameters, we achieve cruising, emerging, submerging, and turning of the robotic fish even though only the caudal fin is active. Finally, we show smooth human-operated turn-around motion similar to that seen in real fish. Based on these experimental results, we further clarify the relationships between the open-loop motor pattern and motion parameters.