Abstract: Conventional digital fish animations primarily rely on keyframe interpolation, cyclic frame playback and rigid-body kinematics, which suffer from unnatural motion characteristics, insufficient fluid–body coupling and fixed behavioral patterns. To address these limitations, this paper proposes a biomimetic motion simulation framework for AI fish based on bionic kinematic modeling, real-time hydrodynamic simulation and deep reinforcement learning (DRL). The proposed system achieves high-fidelity digital simulation of fish locomotion, including body undulation, multi-fin coordination, water damping adaptation and swarm intelligent behaviors. This study systematically elaborates the technical principles, core algorithms, engineering difficulties and optimization strategies of the biomimetic AI fish system, and discusses its application prospects and future development trends.

1. Introduction
Fish have evolved sophisticated underwater locomotion mechanisms featuring high efficiency, low energy consumption and high maneuverability through long-term natural selection. Fish swimming is essentially a compound motion dominated by flexible body undulation propulsion, assisted by multi-fin attitude regulation and dynamic water environment adaptation. Traditional computer graphics (CG) based fish simulation methods adopt predefined trajectory animation, which fails to reproduce realistic biological motion characteristics. Such conventional approaches suffer from rigid body deformation, physically inconsistent fin movement, missing inertial damping effects and repetitive swarm behaviors.
Different from traditional animation techniques, the biomimetic AI fish system integrates biomechanics, hydrodynamics and reinforcement learning to realize real-time motion solving and environment interaction, rather than fixed-frame looping playback. The proposed system achieves physically consistent, non-repetitive and autonomous bionic motion, which can be widely applied in digital waterscape visualization, underwater bionic robot simulation and virtual biological modeling.
2. Multi-Segment Flexible Bionic Motion Modeling
Fish propulsion mainly originates from the flexible undulation of the spinal trunk, which is fundamentally different from rigid-body motion. To reproduce realistic swimming kinematics, this work adopts a multi-joint segmented flexible dynamic model. The fish body is discretized into continuous motion units, including the head, anterior trunk, mid-trunk, caudal peduncle and caudal fin. Series joint constraints are applied to generate smooth and natural body undulation.
2.1 Rhythmic Undulation Modeling
Based on the locomotion characteristics of bony fish, a bio-inspired traveling wave model is constructed to describe body lateral displacement. The model adopts a sine attenuation function to simulate torque transmission and amplitude amplification from the head to the tail. The head maintains minor amplitude and high stability, while the posterior trunk and tail generate progressively larger oscillation amplitudes, which conforms to the natural “stable head and oscillating tail” swimming pattern. Furthermore, a motion damping coefficient is introduced to simulate muscle-driven start-stop transition, effectively eliminating the unnatural instantaneous acceleration and halt phenomena in traditional animations.
2.2 Adaptive Motion State Fitting
By dynamically adjusting kinematic parameters, the proposed model adapts to multiple realistic swimming modes. Steady cruising is realized via low-frequency and low-amplitude undulation; sprint motion adopts high-frequency and high-amplitude trunk oscillation; deceleration and hovering are achieved through attenuated undulation combined with subtle posture adjustment. All motion postures are algorithmically computed in real time without predefined frame constraints, reproducing the energy-saving intermittent swimming characteristics of natural fish.
3. Multi-Fin Coordinated Attitude Control Algorithm
Fish attitude maintenance, steering, ascending and diving depend on the cooperative motion of pectoral, dorsal, pelvic and caudal fins. Single caudal fin oscillation cannot support realistic and stable attitude regulation. Accordingly, the biomimetic AI fish system establishes an independent fin PID control framework with differentiated motion logic and functional weights for each fin.
Caudal fin: Serves as the primary power unit, governing propulsion velocity and overall movement direction, with its oscillation frequency tightly coupled with trunk undulation rhythm.
Pectoral fin: Functions as a fine-tuning unit, responsible for low-speed steering, hovering balance and motion braking by small-amplitude high-frequency oscillation to correct body offset.
Dorsal and pelvic fins: Act as stability units to suppress body rolling and sidesway, ensuring posture stability during high-speed locomotion.
The system dynamically adjusts fin motion parameters according to real-time locomotion states. During steering, the swing amplitude of the unilateral pectoral fin is increased and the caudal fin deflection angle is fine-tuned. During ascending and diving, fin inclination angles are synchronously modified to achieve full-dimensional precise attitude control. This method effectively solves the inherent defect of traditional digital fish models that rely merely on tail oscillation without effective attitude adjustment.
4. Hydrodynamic Real-Time Coupling Simulation
The physical consistency between fish motion and water environment determines the authenticity of virtual swimming animation. Traditional animations ignore fluid resistance, flow disturbance and inertial damping, resulting in unnatural floating, drifting and abrupt motion. In this work, a simplified Navier–Stokes fluid solver is integrated to realize bidirectional real-time coupling between fish kinematics and hydrodynamic environment.
4.1 Flow Resistance Adaptation
Fluid resistance is calculated in real time based on fish contact area, swimming velocity and water density to adaptively correct trunk oscillation amplitude and propulsion speed. High-speed swimming corresponds to increased water damping and enhanced body deformation, while low-speed motion presents smoother and gentler undulation, which faithfully reproduces the inertial characteristics of underwater locomotion.
4.2 Dynamic Flow Disturbance Interaction
The system supports the simulation of still water, laminar flow and micro-turbulence scenes. Fish swimming disturbs the surrounding flow field and generates local water ripples and velocity variations, which in turn affect the posture and trajectory of adjacent individuals. This mutual interaction realizes physically realistic dynamic coupling between fish swarm and water flow.
5. Deep Learning-Based Intelligent Behavior System
Precise kinematic modeling ensures physically realistic motion, while intelligent algorithms achieve biologically reasonable behavior. Based on fish behavioral datasets, a deep reinforcement learning (DRL) model is trained to endow virtual AI fish with autonomous and natural biological decision-making capabilities.
5.1 Fundamental Autonomous Behaviors
The model integrates four basic behavioral modes: cruising, obstacle avoidance, boundary adaptation and posture adjustment. The AI fish can independently plan real-time swimming trajectories without cyclic repetition, achieving stochastic and natural biological motion characteristics.
5.2 Swarm Cooperative Behavior Optimization
Based on the optimized Boid swarm model, three behavioral rules including distance maintenance, velocity matching and centroid aggregation are implemented to realize natural swarm aggregation, dispersion, following and obstacle avoidance. Different from conventional synchronous and homogeneous swarm animation, the proposed method maintains individual motion diversity while ensuring overall swarm orderliness.
5.3 Human–Computer Interaction Mechanism
Equipped with multi-source signal perception modules, the system responds to external interactive instructions in real time, triggering velocity adjustment, steering, obstacle avoidance, color variation and swarm reorganization. The low-latency response capability supports large-screen immersive interaction and real-time interactive visualization scenarios.
6. Technical Challenges and Engineering Optimization
6.1 Balance Between Simulation Fidelity and Computational Cost
Full hydrodynamic solving and multi-joint dynamic iteration require massive computational resources, which limits real-time rendering on ordinary terminals. To solve this problem, a hierarchical simulation strategy is proposed. The visual layer retains high-precision body deformation and flow disturbance details, while the physical layer optimizes iterative computation through weighted interpolation. The proposed scheme balances visual fidelity and computational efficiency, supporting stable real-time operation on PCs, large display screens and mobile devices.
6.2 Multi-Species Motion Parameter Adaptation
Different fish species present distinct body structures and swimming habits, making generic models prone to morphological and kinematic distortion. This study establishes a parameterized fish template library, which configures exclusive stiffness coefficients, oscillation frequencies, fin control weights and resistance parameters for koi, goldfish, deep-sea fish and tropical fish. The system realizes rapid switching of bionic modes for various fish species.
6.3 Non-Repetitive Dynamic Optimization
By introducing random phase offset, micro-parameter perturbation and stochastic behavioral weights, each frame of body undulation, fin movement and swimming trajectory presents subtle differences. The proposed method completely eliminates the mechanical cyclic effect of traditional animation, achieving stable 24/7 non-repetitive high-fidelity dynamic simulation.
7. Application Scenarios
Integrating bionic kinematics, hydrodynamic coupling and intelligent behavioral decision, the proposed AI fish system provides high-precision technical solutions for multiple engineering and academic scenarios:
Digital waterscape visualization: Replaces traditional cyclic animation with physically consistent bionic motion, supporting high-end immersive waterscape display for commercial spaces and exhibitions.
Interactive light and shadow simulation: Adapts to low-latency human–computer interaction requirements, providing core technical support for cultural tourism projection and immersive light-art exhibitions.
Marine biological education and simulation: Provides standardized fish kinematic simulation models for classroom teaching and marine ecological visualization research.
Bionic robot virtual verification: Offers a high-fidelity underwater simulation platform for the design and pre-experiment of flexible bionic robots, reducing physical prototype trial-and-error costs.
8. Future Development Trends
Future research of biomimetic AI fish will focus on high-precision physical simulation, multi-modal intelligent perception and generalized bionic modeling. At the physical level, coupled simulation of turbulence, light refraction and underwater bubble effects will be integrated to improve environmental fidelity. At the intelligent level, machine vision and environmental perception will be introduced to realize autonomous path planning and adaptive attitude adjustment in complex scenes. At the modeling level, a unified aquatic bionic framework will be established to expand simulation capability to diversified aquatic organisms, including shrimps and jellyfish.
Conclusion
The biomimetic motion simulation AI fish is a comprehensive bionic simulation system integrating kinematics, hydrodynamics and artificial intelligence. Different from conventional visual animation techniques, the proposed framework reproduces the natural motion logic of aquatic organisms, achieving physical self-consistency and behavioral autonomy. It effectively solves the problems of unnatural motion and rigid behavior in traditional virtual creature simulation. With the continuous advancement of digital simulation technology, the biomimetic AI fish system will have broad application potential in digital cultural tourism, marine scientific research, bionic robot design and digital creative industries, providing a reliable technical foundation for virtual bionic biological simulation.