In this study, the C-turning, pitching, and flapping propulsion of a robotic dolphin during locomotion were explored. Considering the swimming action required of a three-dimensional (3D) robotic dolphin in the ocean, we propose a maneuverability model that can be applied to the flapping motion to provide precise and stable movements and function as the driving role in locomotion. Additionally, an added tail joint allows for the turning movement with efficient parameters obtained by a fluid-structure coupling method. To obtain a mathematical model, several disturbance signals were considered, including systematic uncertainties of the parameters, the perpetually changing environment, the interference from obstacles with effective fuzzy rules, and a sliding mode of control. Furthermore, a combined strategy of environment recognition was used for the positional control of the robotic dolphin, incorporating sonar, path planning with an artificial potential field, and trajectory tracking. The simulation results show satisfactory performance of the 3D robotic dolphin with respect to flexible movement and trajectory tracking under the observed interference factors.