The pectoral fins on most fish control pitching (up-and-down motion of the body), yawing (the side-to-side motion) and rolling. The pectoral fins can be held close to the body to increase speed by reducing drag, or they can be extended to increase drag and serve as a brake [Wilson and Wilson1985]. Many reef fishes use pectoral swimming to achieve very fine motion control, such as backwards motions, by keeping their bodies still and using their pectoral fins like oars. Through functional modeling, we successfully synthesize a full range of pectoral motor control in artificial fishes.
To model the pectoral fins, we equip the artificial fish with five additional parameterized motor skills, namely, the ascend-MC, descend-MC, balance-MC, brake-MC and backward-MC. The artificial fish is neutrally buoyant in the virtual water and the pair of pectoral fins enable it to navigate freely in its 3D world. The pectoral fins function in a similar, albeit simplified, manner to those of real fishes. For our purposes, the detailed movement of the pectoral fins is of less interest than the movement of the fish body. To simplify the fish model and its numerical solution, we do not simulate the elasticity and dynamics of the pectoral fins. However, we do approximate the dynamic forces that the pectoral fins exert on the body of the fish to control locomotion.
Figure: The pectoral fin geometry.
The pectoral fins (Fig. ) work by applying reaction forces to nodes in the midsection of the fish body, i.e. nodes (see Fig. ). The fins are analogous to the airfoils of an airplane. Pitch and yaw control stems from changing their orientations relative to the body. Assuming that a fin has an area A, surface normal and the fish has a velocity relative to the water (Fig. ), the fin force is
(cf. Eq. ) and is distributed equally to the 6 midsection nodes on the side of the fin. When the leading edge of a fin is elevated (i.e. ), a lift force is imparted on the body and the fish ascends, and when it is lowered (i.e. ), a downward force is exerted and the fish descends. When the fin angles differ, the fish yaws and rolls.
The artificial fish can produce a braking effect by angling its fins to decrease its forward speed, i.e. . This motion control is useful, for instance, in maintaining schooling patterns. As we mentioned earlier, backward swimming motion in natural fishes is usually achieved by backwards oaring of the pectoral fins. In this case, eq. () is inadequate in producing the control. Nevertheless, for visualization purposes, we do simulate the pectoral oaring motions kinematically (details can be found in Section. ) while producing backward forces proportional to the rowing speed. The combination of the with the backward forces results in the retreating motion useful, for example, during mating behavior.
The parameterization of the pectoral fin motor controllers is simple:
( ) takes the desired angle of ascent (see Fig. ) and maps it into the fin orientation . Similarly, the descend-MC maps the desired angle of descent into . The balance-MC takes the desired angle of rolling, defined by the angle between the fish's local z-axis (see Fig. ) and the plane formed by and the world z-axis (pointing upwards), and maps it into two fin orientation angles, one for the left fin and the other for the right fin. The brake-MC takes a constant as its parameter and the backward-MC takes the desired speed of retreating and maps it to rowing speed.
Figure: The local coordinate system of a fish.
|Xiaoyuan Tu||January 1996|