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.

Touchless underwater wall-distance sensing via active proprioception of a robotic flapper.

In this work, we explored a bioinspired method for underwater object sensing based on active proprioception. We investigated whether the fluid flows generated by a robotic flapper, while interacting with an underwater wall, can encode the distance information between the wall and the flapper, and how to decode this information using the proprioception within the flapper. Such touchless wall-distance sensing is enabled by the active motion of a flapping plate, which injects self-generated flow to the fluid environment, thus representing a form of active sensing. Specifically, we trained a long short-term memory (LSTM) neural network to predict the wall distance based on the force and torque measured at the base of the flapping plate. In addition, we varied the Rossby number (Ro, or the aspect ratio of the plate) and the dimensionless flapping amplitude (A∗) to investigate how the rotational effects and unsteadiness of self-generated flow respectively affect the accuracy of the wall-distance prediction. Our results show that the median prediction error is within 5% of the plate length for all the wall-distances investigated (up to 40 cm or approximately 2-3 plate lengths depending on theRo); therefore, confirming that the self-generated flow can enable underwater perception. In addition, we show that stronger rotational effects at lowerRolead to higher prediction accuracy, while flow unsteadiness (A∗) only has moderate effects. Lastly, analysis based on SHapley Additive exPlanations (SHAP) indicate that temporal features that are most prominent at stroke reversals likely promotes the wall-distance prediction.