Swimming with Data: Teaching Robots to Move Like Fish

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Author: Denis Avetisyan

Researchers are leveraging machine learning to grant robots the fluid, efficient movements of aquatic life, paving the way for more agile underwater vehicles.

The actuator’s structure anticipates inevitable mechanical failure, embedding within its design the seeds of its own obsolescence as a complex system rather than a simple tool.
The actuator’s structure anticipates inevitable mechanical failure, embedding within its design the seeds of its own obsolescence as a complex system rather than a simple tool.

This work presents a data-driven control framework combining learned forward dynamics, model predictive control, and imitation learning for precise control of a magnetically actuated, flexible-finned robot.

Achieving precise control of miniature, flexible robots in complex fluid environments remains a significant challenge despite advances in soft robotics. This is addressed in ‘Data-Driven Control of a Magnetically Actuated Fish-Like Robot’, which presents a novel control framework leveraging learned dynamics, model predictive control, and imitation learning for magnetically actuated, fish-like robots. The approach bypasses the need for complex analytical modeling by constructing a forward dynamics model from experimental data, enabling accurate path following and reduced computational cost through policy approximation. Could this data-driven paradigm unlock new possibilities for navigating and manipulating objects in previously inaccessible underwater environments?

The Illusion of Propulsive Efficiency

Conventional underwater robots frequently utilize propellers for propulsion, a design choice that inherently generates significant turbulence and restricts maneuverability. This method disrupts the surrounding water, reducing efficiency and hindering precise control, particularly in complex or confined environments. The swirling vortex created by propellers not only consumes energy but also impacts a robot’s ability to perform delicate tasks, such as inspection or sample collection, and can interfere with sensor readings. Furthermore, the rigid nature of propeller-driven systems limits their agility, making it challenging to navigate tight spaces or mimic the graceful movements observed in aquatic life. Consequently, researchers are actively exploring alternative propulsion mechanisms that prioritize streamlined movement and minimize disturbance, seeking to overcome the limitations imposed by traditional propeller-based designs.

The aquatic realm presents unique challenges to movement, yet fish navigate it with an elegance and efficiency that has long captivated engineers. Unlike traditional robots which often force their way through water, creating disruptive turbulence, fish leverage subtle body undulations and fin movements to generate thrust and maintain precise control. This biological mastery isn’t merely aesthetic; it represents a fundamentally different approach to fluid dynamics, minimizing energy expenditure and maximizing maneuverability. Consequently, a growing field of biomimetic robotics is actively translating these natural principles into novel underwater vehicle designs, striving to replicate the streamlined forms and flexible propulsion systems of fish to achieve unparalleled performance in complex aquatic environments.

The pursuit of truly agile underwater robotics has led to the development of ‘Fish-like Robots’, machines designed to mimic the efficient propulsion strategies of aquatic life. Rather than relying on conventional propellers which generate disruptive turbulence and limit precise control, these robots utilize undulating fins or body movements to generate thrust. This biomimetic approach often involves replacing rigid robotic components with flexible, compliant materials, allowing for more natural and energy-efficient locomotion. By replicating the streamlined forms and dynamic movements observed in fish, engineers aim to create robots capable of navigating complex underwater environments with greater speed, maneuverability, and stealth – opening doors for applications in environmental monitoring, infrastructure inspection, and underwater exploration.

The pursuit of truly biomimetic underwater robots demands a fundamental shift away from traditional, rigid construction. Unlike conventional remotely operated vehicles, which often utilize propellers and inflexible frames, advanced designs are increasingly incorporating compliant components – materials and structures that deform elastically under stress. This embrace of flexibility allows for movements mirroring the undulation of fish fins and bodies, dramatically improving efficiency and maneuverability. By utilizing materials like silicone or specialized polymers, robotic bodies can bend and twist, generating propulsive forces with minimal turbulence and enabling navigation through complex environments. This departure from rigid designs isn’t simply about aesthetics; it’s a crucial engineering principle that unlocks the potential for quieter, more energy-efficient, and remarkably agile underwater robots capable of tasks currently beyond the reach of existing technology.

A sequence of images demonstrates the robotic fish successfully swimming from left to right at a rate of one frame per second.
A sequence of images demonstrates the robotic fish successfully swimming from left to right at a rate of one frame per second.

Magnetic Fields: A Departure from Mechanical Constraint

Magnetic actuation represents a departure from conventional robotic propulsion systems which typically rely on electric motors, gears, and various mechanical linkages to generate movement. This technique utilizes externally applied magnetic fields to directly induce motion in a robot, often through the integration of magnetic materials within its structure. By eliminating mechanical transmission components, magnetic actuation reduces complexity, minimizes wear and tear, and potentially increases efficiency. The absence of motors also allows for silent operation and simplified design, particularly advantageous in sensitive applications or constrained environments. Furthermore, the ability to remotely control movement via external magnetic fields opens possibilities for navigation in previously inaccessible areas and simplifies robot maintenance by decoupling the actuation mechanism from the robot’s internal components.

Robotic propulsion via external magnetic fields operates by applying time-varying magnetic fields to induce deformation and movement in a robot containing magnetic materials. This eliminates the need for onboard power sources, propellers, or other mechanical components, resulting in silent operation and reduced mechanical complexity. Efficiency is achieved by directly manipulating the robot’s body for locomotion, minimizing energy losses associated with traditional drive systems. The strength and direction of the external magnetic field dictate the magnitude and direction of the resulting force and torque on the robot, allowing for precise control of its position and orientation within a defined workspace.

The flexible fin, utilized as a primary actuator in magnetically driven robots, enables a wide range of motion including turning, oscillation, and undulatory propulsion. Constructed from materials exhibiting high flexibility and low mass, these fins deform under the influence of applied magnetic fields, generating propulsive forces and directional control. However, the inherent compliance of the fin introduces significant dynamic complexity; the fin’s deformation is not directly proportional to the applied magnetic force, and exhibits hysteresis and non-linear behavior. Accurate modeling and control of these dynamics are critical for achieving precise and repeatable movements, requiring advanced control algorithms and potentially real-time feedback mechanisms to compensate for the fin’s complex response.

The integration of magnetic actuation with compliant fin structures presents a distinct approach to biomimetic underwater robotics. Traditional underwater robots often rely on rigid bodies and discrete propulsion systems, limiting maneuverability and increasing energy consumption. Compliant fins, constructed from flexible materials, mimic the undulatory motion of biological organisms like fish and jellyfish. When coupled with externally applied magnetic fields for actuation – eliminating the need for onboard motors or hydraulics – these fins enable smooth, continuous propulsion and complex 3D maneuvering. This combination reduces mechanical complexity, minimizes noise, and allows for precise control, potentially achieving greater efficiency and adaptability in underwater environments compared to conventional robotic systems.

The Nonlinearity of Fluid Dynamics: A Modeling Challenge

The dynamics governing the motion of a flexible fin are inherently nonlinear due to the complex interactions between fluid forces, fin deformation, and inertial effects. This nonlinearity arises from factors such as viscous drag that is proportional to velocity squared, added mass effects due to fluid displacement, and the fin’s changing geometry as it deforms. Consequently, linear approximations of the fluid dynamics are insufficient for accurate prediction of the fin’s behavior. Modeling these nonlinearities requires computationally intensive methods, such as Finite Element Analysis (FEA) coupled with Computational Fluid Dynamics (CFD), or the use of reduced-order models that still capture essential nonlinear characteristics. Furthermore, control strategies designed for linear systems are often ineffective, necessitating the development of advanced nonlinear control techniques to achieve precise and stable motion of the flexible fin.

Precise robot state estimation – encompassing position, orientation, and velocity – is fundamental to effective control in complex fluid environments. Accurate knowledge of these six degrees of freedom (three for position and three for orientation) enables the implementation of feedback control loops that compensate for hydrodynamic forces and maintain desired trajectories. State estimation is commonly achieved through sensor fusion, integrating data from inertial measurement units (IMUs), pressure sensors, and visual systems. Errors in state estimation directly translate to control inaccuracies, potentially leading to instability or failure of the robot to achieve its intended path. Consequently, robust and reliable state estimation techniques are critical for successful operation in these challenging conditions.

Employing a robot-oriented local coordinate system significantly streamlines the dynamic modeling process for complex fluidic systems. This frame of reference is rigidly attached to the robot, defining its position and orientation as the origin and aligning its axes with the robot’s body. By expressing all dynamic equations – including those governing fluid interactions and robot motion – within this local frame, the computational complexity is reduced, as the system’s configuration is simplified and the need for transformations between global and robot frames is minimized. Furthermore, this approach facilitates accurate tracking of the robot’s state, specifically its position, orientation, and velocity, as these values are directly represented within the local coordinate system, enabling precise control and path following.

Successful path following is essential for autonomous navigation of flexible fin robots in underwater environments due to the complexities of fluid dynamics and the limitations of direct control. The robot must adhere to a predefined trajectory while contending with hydrodynamic drag, added mass, and potential disturbances from currents or obstacles. Achieving precise path following necessitates real-time adjustments to fin actuation based on feedback from state estimation, typically utilizing sensor data to determine the robot’s position and orientation relative to the desired path. Failure to maintain accurate path following can lead to significant deviations, increased energy consumption, and potential mission failure in cluttered or dynamic underwater scenarios.

The world coordinate system provides a global frame of reference, while the robot-oriented local coordinate system defines the robot's perspective and movements.
The world coordinate system provides a global frame of reference, while the robot-oriented local coordinate system defines the robot’s perspective and movements.

Trajectory and Control: The Illusion of Perfect Motion

The robot’s ability to navigate complex paths relies heavily on precise trajectory planning, and Bezier curves offer a particularly effective solution. These mathematical curves, defined by a series of control points, allow engineers to specify a desired path with remarkable smoothness and predictability. Unlike simpler methods that might result in jerky or abrupt movements, Bezier curves generate continuous trajectories, ensuring a fluid and efficient motion for the robot. By carefully adjusting the position of these control points, developers can fine-tune the path to avoid obstacles, optimize travel time, and achieve the desired level of precision. The inherent mathematical properties of Bezier curves also facilitate accurate calculations of the robot’s position and velocity along the path, which is critical for real-time control and feedback mechanisms.

The robot’s motion is fundamentally governed by the duration of current applied to its electromagnetic coils – the ‘action’ or control input. This parameter directly translates into the magnitude and direction of the generated force, and therefore, precise calibration is essential for accurate movement. Any discrepancy between the intended current duration and the actual electromagnetic response will manifest as trajectory errors. Consequently, a robust control system must meticulously map desired movements to specific current durations, accounting for factors such as coil resistance, inductance, and the inherent nonlinearities within the electromagnetic system. Achieving fine-grained control over this action is not simply a matter of applying a fixed value; it requires a dynamic adjustment based on the robot’s current state and the desired path, ensuring both responsiveness and stability throughout the trajectory.

The seamless integration of trajectory generation with precise action control enables remarkably accurate and reliable path following for the robot. This is evidenced by experimental results demonstrating a Root Mean Squared Error (RMSE) of just 0.62 mm when utilizing Guided Model Predictive Control (G-MPC) and initiating the robot’s movement directly on the desired path. This low RMSE value signifies the robot’s ability to closely adhere to the planned trajectory, highlighting the effectiveness of the combined approach in minimizing positional deviations and ensuring precise movement execution. The achievement underscores the potential for high-fidelity control in robotic systems through careful coordination of path planning and actuation.

The robot’s ability to accurately follow a designated path is significantly impacted by its initial position relative to that path. Data-driven control strategies were implemented to address this challenge, with Guidance Model Predictive Control (G-MPC) demonstrating path following accuracy – measured by Root Mean Squared Error (RMSE) – of 13.16 mm when initiating movement above the intended path and 11.13 mm when starting below it. Further refinement was achieved through the application of Iterative Learning Control (ILC), which substantially improved performance, reducing the RMSE to just 4.60 mm. These results highlight the efficacy of combining model-based prediction with iterative learning to minimize positional errors and ensure reliable path tracking, even with variations in the robot’s starting configuration.

G-MPC effectively guides a reference point (orange cross) along a target path (black dashed line) from various starting positions (green square), as demonstrated by the resulting trajectory (red line).
G-MPC effectively guides a reference point (orange cross) along a target path (black dashed line) from various starting positions (green square), as demonstrated by the resulting trajectory (red line).

The pursuit of controlling complex systems, as demonstrated by this work on magnetically actuated robots, echoes a fundamental truth: prediction is perpetually imperfect. One builds not to command a system, but to guide its growth. Ada Lovelace observed, “The Analytical Engine has no pretensions whatever to originate anything.” This sentiment applies equally to this robot; the learned dynamics and model predictive control aren’t about imposing will, but about anticipating the inevitable deviations inherent in a flexible, data-driven system. Each iteration of the control algorithm begins as a prayer for accuracy, knowing full well it will likely end in a graceful acceptance of emergent behavior. The robot, like all systems, simply grows up.

The Current Runs Deep

This work, predictably, does not solve control. It merely shifts the locus of failure. The learned dynamics model, however accurate within its training domain, will inevitably encounter states unseen, and thus un-modeled. Each successful trajectory is a temporary reprieve, a localized victory against the inevitable tide of distributional shift. The true challenge isn’t achieving path following now, but predicting the form of the next, unavoidable divergence.

The reliance on imitation learning, while expedient, subtly encodes the limitations of the demonstrator. A perfect mimicry of a suboptimal behavior is still suboptimal. The system does not learn to swim, it learns to repeat a swim. Future effort should not focus on refining the imitation, but on developing methods to detect, and then actively correct, the inherited flaws. Every successful replication is a promise of future stagnation.

The field fixates on increasingly complex actuators and control schemes, yet overlooks the fundamental brittleness inherent in any designed system. This robot, and all like it, are not organisms adapting to a world, but artifacts imposing a temporary order upon chaos. The real innovation will come not from building better robots, but from accepting their inevitable imperfections and designing for graceful degradation.

Original article: https://arxiv.org/pdf/2603.04787.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-03-07 04:02