The control of routine fish maneuvers: Connecting midline kinematics to turn outcomes

Effects of caudal fin stiffness on optimized forward swimming and turning maneuver in a robotic swimmer

In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (μBots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aμBot equipped with each caudal fin (andμBot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofμBot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10-4Pa m4(∼10.6 Hz) and stiffness >10-4Pa m4(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10-4Pa m4, with theμBot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theμBots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inμBot swimming.

Energetic benefits in coordinated circular swimming motion of two swimmers

The coordinated movement of multiple swimmers is a crucial component of fish schools. Fish swimming in different formations, such as tandem, side-by-side, diamond, and phalanx, can achieve significant energetic advantages. However, the energetic benefits of nonstraight swimming behaviors, such as the collective motion of a milling pattern, are not well understood. To fill in this gap, we consider two swimmers in circular tracks, controlled by a PID approach to reach stable configurations. Our study finds that the optimal phase is affected by circumferential effects, and that substantial energy savings can result from both propulsion and turning. We also explore the radial effect in terms of energetic benefits. In a milling pattern, the inner swimmers can easily gain a certain energetic benefit (-8%), while their peers on the outside must be close enough to the inner swimmer with a proper phase to gain the energetic benefit (-14%). When the radial spacing becomes larger or is in an unmatched phase, the swimming of the outer swimmers becomes more laborious (+16%). Our results indicate that swimmers who maintain a matched phase and minimum radial effect obtain the highest energetic benefits (-26%). These findings highlight the energetic benefits of swimmers, even in a milling pattern, where the position difference dominates the extent of benefit.

Testing the effects of body depth on fish maneuverability via robophysical models

Fish show a wide diversity of body shapes which affect many aspects of their biology, including swimming and feeding performance, and defense from predators. Deep laterally compressed bodies are particularly common, and have evolved multiple times in different families. Functional hypotheses that explain these trends include predator defense and increased maneuverability. While there is strong evidence that increasing body depth helps fish avoid gape-limited predators, the evidence that body shape increases a fish's maneuverability is ambiguous. We used a two-pronged approach to explore the effects of body shape on the control of maneuvers using both live fish and a robotic model that allowed us to independently vary body shape. We captured ventral video of two tetra species (Gymnocorymbus ternetziandAphyocharax anisitsi) performing a wide range of maneuvers to confirm that both species of live fish utilize fundamentally similar body deformations to execute a turn, despite their different body depths. Both species use a propagating 'pulse' of midline curvature that is qualitatively similar to prior studies and displayed similar trends in the relationships between body kinematics and performance. We then tested the robotic model's maneuverability, defined as the total heading change and maximum centripetal acceleration generated during a single pulse, at a range of different input kinematics across three body shapes. We found that deepening bodies increase the robot's ability to change direction and centripetal acceleration, though centripetal acceleration exhibits diminishing returns beyond a certain body depth. By using a robotic model, we were able to isolate the effects of body shape on maneuverability and clarify this confounded relationship. Studying the functional morphology of complex traits such as body shape and their interaction with complex behavior like maneuverability benefits from both the broad view provided by comprehensive comparative studies, and the control of variables enabled by robophysical experiments.

Comparing the turn performance of different motor control schemes in multilink fish-inspired robots

Fish robots have many possible applications in exploration, industry, research, and continue to increase in design complexity, control, and the behaviors they can complete. Maneuverability is an important metric of fish robot performance, with several strategies being implemented. By far the most common control scheme for fish robot maneuvers is an offset control scheme, wherein the robot's steady swimming is controlled by sinusoidal function and turns are generated biasing bending to one side or another. An early bio-inspired turn control scheme is based on the C-start escape response observed in live fish. We developed a control scheme that is based on the kinematics of routine maneuvers in live fish that we call the 'pulse', which is a pattern of increasing and decreasing curvature that propagates down the body. This pattern of curvature is consistent across a wide range of turn types and can be described with a limited number of variables. We compared the performance of turns using each of these three control schemes across a range of durations and bending amplitudes. We found that C-start and offset turns had the highest heading changes for a given set of inputs, whereas the bio-inspired pulse turns had the highest linear accelerations for a given set of inputs. However, pulses shift the conceptualization of swimming away from it being a continuous behavior towards it being an intermittent behavior that is built by combining individual bending events. Our bio-inspired pulse control scheme has the potential to increase the behavioral flexibility of bio-inspired robotic fish and solve some of the problems associated with integrating different swimming behaviors, despite lower maximal turning performance.