Effects of Design and Hydrodynamic Parameters on Optimized Swimming for Simulated, Fish-inspired Robots

Abstract

In this work, we developed a mathematical model and a simulation platform for a fish-inspired robotic template, namely Magnetic, Modular, Undulatory Robot <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(\mu \text{Bot})$</tex> . Through this platform, we systematically explored the effects of robot design and fluid parameters on swimming performance via reinforcement learning. The mathematical model was composed of two interacting subsystems, the robotic dynamic model and the hydrodynamic model. The hydrodynamic model consisted of the reactive components (added-mass force and pressure forces) and the resistive components (drag and friction forces). These components were nondimensionalized for deriving key “control parameters” of the robot-fluid interaction. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu\text{Bots}$</tex> were actuated via magnetic actuators controlled with harmonic voltage signals, which were optimized via EM-based Policy Hyper Parameter Exploration (EPHE) to maximize forward swimming speed. By varying the control parameters, a total of 36 cases with different robot template variations (Number of Actuators (NoA) and stiffness) and hydrodynamic parameters were simulated and optimized via EPHE. Results showed that the wavelength of the optimized gaits (i.e., backward traveling wave along the body) was independent of template variations and hydrodynamic parameters. Higher NoA yielded higher speed but lower speed per body length, suggesting a diminishing gain from added actuators. Body and caudal-fin dynamics were dominated by the interaction among fluid added-mass, spring, and actuation torque, with negligible contribution from fluid resistive drag. In contrast, thrust was dominated by the pressure force acting on the caudal fin, as steady swimming resulted from a balance between resistive force and pressure force, with minor contributions from added-mass force and body drag forces. Therefore, added-mass force only indirectly affected the thrust generation and forward swimming speed via the caudal fin dynamics.