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Pectoral Fin Motor Controllers

 

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.

   figure897
Figure: The pectoral fin geometry.

The pectoral fins (Fig. gif) work by applying reaction forces to nodes in the midsection of the fish body, i.e. nodes tex2html_wrap_inline2932 (see Fig. gif). The fins are analogous to the airfoils of an airplane. Pitch and yaw control stems from changing their orientations tex2html_wrap_inline2934 relative to the body. Assuming that a fin has an area A, surface normal tex2html_wrap_inline2488 and the fish has a velocity tex2html_wrap_inline2490 relative to the water (Fig. gif), the fin force is

  equation907

(cf. Eq. gif) 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. tex2html_wrap_inline2944 ), a lift force is imparted on the body and the fish ascends, and when it is lowered (i.e. tex2html_wrap_inline2946 ), 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. tex2html_wrap_inline2948 . 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. (gif) is inadequate in producing the control. Nevertheless, for visualization purposes, we do simulate the pectoral oaring motions kinematically (details can be found in Section. gif) while producing backward forces proportional to the rowing speed. The combination of the tex2html_wrap_inline2918 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: The ascend-MC
( tex2html_wrap_inline2952 ) takes the desired angle of ascent tex2html_wrap_inline2954 (see Fig. gif) and maps it into the fin orientation tex2html_wrap_inline2956 . Similarly, the descend-MC maps the desired angle of descent into tex2html_wrap_inline2958 . The balance-MC takes the desired angle of rolling, defined by the angle between the fish's local z-axis tex2html_wrap_inline2960 (see Fig. gif) and the plane formed by tex2html_wrap_inline2962 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 tex2html_wrap_inline2948 as its parameter and the backward-MC takes the desired speed of retreating and maps it to rowing speed.

   figure930
Figure: The local coordinate system of a fish.


next up previous contents
Next: Modeling the Form and Appearance Up: Motor Controllers Previous: Muscle Motor Controllers
Xiaoyuan TuJanuary 1996