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Swimming, turning, and whip-sweeping propulsion for carangiform locomotion of a fish robot are investigated by means of a 4-link planar tail and an autonomous underwater vehicle (AUV)-like model. It is observed that excellent acceleration occurs when a whip sweeping behavior has been applied to the fish tail. The forward speed can even increases twice to the nominal swimming via the simulation study. The efficient movement is thus incorporated to the fish robot for agile movement. The robot's swimming patterns realize the effect in terms of the forward swimming, turning swimming, acceleration increasing, descended swimming, ascended swimming, depth regulating, and self-stabilization. Verification is accomplished by incorporating the 4-link planar tail, AUV-like model, and a two degree-of-freedom (DOF) barycenter mechanism. The four-link planar tail and 2-DOF barycenter mechanism act, respectively, as the thrust generator and stabilizing actuator for the fish robot. Sliding mode control (SMC) has been applied for three-dimensional (3D) trajectory tracking. Simulation results illustrate satisfactory performances of the fish robot in terms of the fish-like behaviors and maneuverability, which are due to the consequence of the mimicked predator-fish behaviors and performance robustness of the SMC for trajectory tracking under ocean current perturbations and modeling uncertainties.

This study develops a 6-DOF mathematical model for a robotic fish that considers surge, sway, heave, roll, pitch, and yaw. The model considers the conditions of a fish swimming in ocean current perturbations similar to the ocean current perturbations of the slender-body autonomous underwater vehicles. For swimming and turning behaviors, a nonlinear, dynamic, carangiform locomotion model is derived by using a planar four-link model. A 2-DOF barycenter mechanism is proposed to provide body stabilization and to serve as an actuating device for active control design. A barycenter control scheme is developed to change the center of gravity of the robot fish body by moving balancing masses along two axes. The projected torque on x and y axes propel pitch and roll angles to the desired settings. A Stabilizing controller, fish-tail mechanism, rigid body dynamics, and kinematics are incorporated to enable the fish robot to move in three dimensional space. Simulation results have demonstrated maneuverability and control system performance of the developed controller which is proposed to conduct path tracking of the robot fish as it swims under current perturbations.

Nonlinear equations of motion for fish-robot have been derived based on three basic motion behaviors, swimming, orientating, and driving. By incorporating the fish-tail mechanism, 2-DOF barycenter mechanism, and autonomous underwater vehicle-like dynamics model, the fish robot motion and maneuverability are considered in north-east-down frame. A sliding mode controller for swimming, orientating, and tracking control of a fish robot in three-dimensional motion is designed. Simulation results demonstrate excellent maneuverability and tracking performance of the fish-robot in three-dimensional swimming, which shows effectiveness of the controller against modeling uncertainty and ocean's current turbulence.

Two-DOF barycenter mechanism and its control are proposed. The mechanism by means of the moved balancing masses along two axes changes the center of gravity of fish's body. The projected torques on x and y axes propel pitch and roll angles to the desired values. Merging the pitching and rolling models with fish-tail and rigid-body models, the fish robot motion and maneuverability can be achieved in three dimensions. The 3-D motion has been derived based on three basic behaviors as swimming, orientating, and stabilizing. Lastly, simulation results of the barycenter stabilization system and the robot motion are given and feasibility of the realization is discussed.

Derivation of the mathematical model for a robot fish considering forward motion and yaw angle kinematics is presented. This model also includes details of the hydrodynamic force by considering the condition of fish swimming underwater. The nonlinear dynamical model in Carangi form locomotion type is derived by use of Lagrange's equation, which concerning about 4 links of fish robot equivalent model similar to the 4-link planar robot manipulator. Computer simulations conduct both in terms of open-loop response and animation motion of the fish robot swimming. These results indicate feasibility of the model for the robot with swimming speed 0.48 m/s and yaw swing angle ±12 degree. The model derived will be served as a basis for further investigation of control design for the complicated object.