Fish use their lateral lines to sense flows and pressure gradients, enabling them to detect nearby objects and organisms. Towards replicating this capability, we demonstrated successful leader-follower formation swimming using flow pressure sensing in our undulatory robotic fish ($\mu$Bot/MUBot). The follower$\mu$Bot is equipped at its head with bilateral pressure sensors to detect signals excited by both its own and the leader's movements. First, using experiments with static formations between an undulating leader and a stationary follower, we determined the formation that resulted in strong pressure variations measured by the follower. This formation was then selected as the desired formation in free swimming for obtaining an expert policy. Next, a long short-term memory neural network was used as the control policy that maps the pressure signals along with the robot motor commands and the Euler angles (measured by the onboard IMU) to the steering command. The policy was trained to imitate the expert policy using behavior cloning and Dataset Aggregation (DAgger). The results show that with merely two bilateral pressure sensors and less than one hour of training data, the follower effectively tracked the leader within distances of up to$200 \text{mm}(=1$body length) while swimming at speeds of$155 \text{mm} / \mathrm{s}(=0.8$body lengths/s). This work highlights the potential of fish-inspired robots to effectively navigate fluid environments and achieve formation swimming through the use of flow pressure feedback. Video—https://youtu.be/DIDYGi9Td0I

Here we present the development of an autonomous modular swimming robot. This robot, named µBot 2.0, was upgraded from our previous robot platform µBot and features onboard computing, sensing, and power. Its compact size and modularity render the robot an ideal platform for studying bio-inspired robot swimming. The robot is equipped with a micro controller in its head that communicates with external computers through Bluetooth Low Energy (BLE) and sends motor commands to the body segments via Inter-Integrated Circuit (I2C) protocol. Each body segment has a customized printed circuit board (PCB) that receives commands and controls the electromagnetic actuator for generating body movements. The robot head is also equipped with an Inertial Measurement Unit (IMU) to measure its heading and a battery for power. In this work, a µBot 2.0 with three actuators was assembled and the swimming performance was tested. The robot actuators were activated via rhythmic motor input from a central pattern generator (CPG). Experimental results showed that the swimming speed was highly sensitive to the frequency of the motor input, with a maximum swimming speed of 130 mm/s (equivalent to 0.7 body length per second) at 6 Hz. The robot also had the capability to correct its heading with IMU feedback and follow desired paths using a line-of-sight (LOS) guidance law with an overhead camera. Our results demonstrate the effectiveness of the robot's design and its potential in a variety of aquatic applications.

In this work, we developed a mathematical model and a simulation platform for a fish-inspired robotic template, namely Magnetic, Modular, Undulatory Robot$(\mu \text{Bot})$. 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$\mu\text{Bots}$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.

Here we developed an experimental platform with a magnetic, modular, undulatory robot (μBot) for studying fish-inspired underwater locomotion. This platform will enable us to systematically explore the relationship between body morphology, swimming gaits, and swimming performance via reinforcement learning methods. The μBot was designed to be easily modifiable in morphology, compact in size, easy to be controlled and inexpensive. The experimental platform also included a towing tank and a motion tracking system for real-time measurement of the μBot kinematics. The swimming gaits of μBot were generated by a central pattern generator (CPG), which outputs voltage signals to μBot's magnetic actuators. The CPG parameters were learned experimentally using the parameter exploring policy gradient (PGPE) method to maximize swimming speed. In the experiments, two μBot designs with the same body morphology but different caudal-fin shapes were tested. Results showed that swimming gaits with back-propagating traveling waves can be learned experimentally via PGPE, while the shape of the caudal fins had moderate influences on the learned gaits and the swimming speed. Furthermore, robot swimming speed was sensitive to the undulating frequency and the voltage magnitude of the last three posterior actuators. In contrast, swimming gaits and speed were relatively invariant to the variances within the inter-module connection weights of CPG and the voltage applied to the anterior actuator.