Data-Driven Control of a Magnetically Actuated Fish-Like Robot

Akiyuki Koyama; Hiroaki Kawashima

cs.ROMar 5, 2026

Data-Driven Control of a Magnetically Actuated Fish-Like Robot

Authors: Akiyuki Koyama, Hiroaki Kawashima

Organizations: Graduate School of Information Science, University of Hyogo, Japan

Abstract

Magnetically actuated fish-like robots offer promising solutions for underwater exploration due to their miniaturization and agility; however, precise control remains a significant challenge because of nonlinear fluid dynamics, flexible fin hysteresis, and the variable-duration control steps inherent to the actuation mechanism. This paper proposes a comprehensive data-driven control framework to address these complexities without relying on analytical modeling. Our methodology comprises three core components: 1) developing a forward dynamics model (FDM) using a neural network trained on real-world experimental data to capture state transitions under varying time steps; 2) integrating this FDM into a gradient-based model predictive control (G-MPC) architecture to optimize control inputs for path following; and 3) applying imitation learning to approximate the G-MPC policy, thereby reducing the computational cost for real-time implementation. We validate the approach through simulations utilizing the identified dynamics model. The results demonstrate that the G-MPC framework achieves accurate path convergence with minimal root mean square error (RMSE), and the imitation learning controller (ILC) effectively replicates this performance. This study highlights the potential of data-driven control strategies for the precise navigation of miniature, fish-like soft robots.

Figures & tables

Panel of Figure 1 — Figure 1: Robot structure (left: cross section, right: size)

Panel of Figure 3 — Figure 3: Robotic fish swimming sequence (1 image per second; from left to right)

Figure 4: The architecture of control strategy

Panel of Figure 5 — Figure 5: World coordinate (left) and robot-oriented local coordinate (right)

Panel of Figure 6 — Algorithm 1 Gradient-Based Model Predictive Control (G-MPC)

Parameter	Value
Number of layers	3
Number of units per layer	8
Activation function	ReLU
Optimizer	AdamW
Learning rate	0.001
Batch size	8

Table 1: FDM parameters

Parameter	Value
Prediction horizon ( $H$ )	10
Optimization iterations ( $N$ )	1000
Look-ahead distance ( $L_{\text{lookahead}}$ )	50.0 mm
Learning rate	0.005
Action dimension	2
Loss weight (x, y, yaw)	(5.0, 5.0, 1.0)

Table 2: G-MPC parameters

Panel of Figure 7 — Figure 7: G-MPC path-following results from different start positions (top left: above path, top right: on path, bottom: below path). Red line: connection of the output positions after each control step. Black dashed line: target path. Orange cross: reference point each control step. Green square: start position.

Parameter	Value
Number of layers	2
Number of units per layer	8
Learning rate	0.1
Batch size	32
Number of epochs	1000
Optimizer	AdamW

Table 3: Imitation learning parameters

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Complex tasks for underwater robots remain limited by the capabilities of their controllers. Learning a better one for a soft, underactuated robotic fish trades simulator cost against fidelity. We show that an intentionally low-fidelity simulator is enough: a stateless, quasi-steady fluid model with no wake and no added-mass history suffices to learn a general, closed-loop controller that transfers to hardware without tuning. Our platform is a soft, single-motor, tendon-driven fish whose policy observes only what the hardware can measure. A staged pipeline grounds the simulator in two independent identifications, fixing the tail dynamics and a stateless fluid model; the policy then acts through a band-limited rhythmic trajectory generator rather than commanding the tail directly. Deployed unchanged in an outdoor pool, a single policy performs closed-loop target reaching, disturbance rejection, and out-of-distribution target acquisition and tracking. The transfer rests on the constraint rather than the fidelity: the generator cannot leave the band over which the fluid was identified. This raises the question of how much of the physics can reside in the controller rather than in the simulator.

Abstract

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