Leader-Follower Formation Enabled by Pressure Sensing in Free-Swimming Undulatory Robotic Fish

Abstract

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 (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex> Bot/MUBot). The follower <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$200 \text{mm}(=1$</tex> body length) while swimming at speeds of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$155 \text{mm} / \mathrm{s}(=0.8$</tex> 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