# Longitudinal Model Identification and Controller Design for a Fish Robot with Control Fins via Experiments

## TL;DR

This paper develops a control system for a fish robot using experimental models to manage its movement and stability in water.

## Contribution

The novelty lies in deriving input-output models and designing PID controllers for a complex, nonlinear fish robot system through experiments.

## Key findings

- Surge velocity models showed high agreement rates of 75.25% and 81.23% at 0.2 m/s and 0.4 m/s, respectively.
- Pitch angle models had lower agreement rates of 68.02% and 34.24% at 0.2 m/s and 0.4 m/s, respectively.
- Pitch angle responses converged to 0° with oscillations in both simulations and experiments.

## Abstract

This paper presents an experimental longitudinal mode control approach for a biomimetic underwater robot. Input–output models for surge velocity and pitch angle were derived through experiments, considering the fish robot body with servo motors and control pins as a single system to solve the problem of fish robots, which are complex and nonlinear, and also contain uncertainty. Closed-loop control systems were designed using PID controllers based on these models, and their performance was verified through simulations and experiments. Surge velocity and pitch angle response models were developed for nominal surge velocities of 0.2 m/s and 0.4 m/s. The surge velocity response models exhibited high agreement rates of 75.25% and 81.23% between the identified linear models and experimental results at 0.2 m/s and 0.4 m/s, respectively. In contrast, the pitch angle response model showed lower agreement rates of 68.02% and 34.24% between the identified linear model and experimental results at 0.2 m/s and 0.4 m/s, respectively. The gain margin and phase margin of the surge controller were 28.7 dB and 116°, and 37.2 dB and 70.6°, respectively. For the pitch response model, the low-frequency gain of the transfer function was very small at −31 dB when the nominal surge velocity was 0.2 m/s; this gain increased to −8 dB when the nominal surge velocity was increased to 0.4 m/s. It was observed that the initial value responses of the pitch angle converged to 0° with some oscillations in both the simulations and experiments. Therefore, it is believed that by identifying a linear model and subsequently designing a controller based on it, the surge velocity of the fish robot can be effectively controlled while stabilizing its pitch angle.