The coordinated movement of biological collectives, such as schools of fish or flocks of birds, demonstrates remarkable capabilities in energy efficiency, high adaptability, and robust mobility. These natural phenomena provide profound inspiration for the engineering of artificial systems, particularly in the challenging domain of underwater operations. Underwater bionic robot clusters, designed to emulate such collective behaviors, hold significant potential for applications including environmental monitoring, resource exploration, and infrastructure inspection. A paramount challenge in the practical deployment of these robotic swarms is the efficient management of on-board energy, which directly limits mission endurance and operational scope. Consequently, investigating energy-saving strategies inspired by biological collectives has become a critical research frontier. This review synthesizes the current state of key technologies enabling energy efficiency in underwater bionic robot clusters, focusing on three interconnected pillars: the hydrodynamic principles of biological energy saving, fluid field sensing for bionic robots, and energy-aware cluster control strategies. We analyze existing approaches, highlight prevailing challenges, and discuss promising future directions for achieving truly autonomous and energy-efficient underwater bionic collectives.
1. Hydrodynamic Principles of Energy Saving in Biological Collectives
The fundamental hypothesis that collective movement reduces individual energy expenditure was first formally proposed by Weihs in the context of fish schooling. The core idea is that individuals within a group can exploit favorable hydrodynamic interactions generated by their neighbors, such as reduced pressure zones or beneficial vortex structures, thereby lowering their cost of locomotion. Research in this area has progressed through two primary methodologies: direct observation of living organisms and sophisticated numerical simulation.
1.1 Insights from Biological Observations
Empirical studies on live animals provide direct evidence of energy savings in collective motion. Researchers have measured metabolic rates, tail-beat frequencies, and oxygen consumption to quantify this effect. Key findings consistently show that individuals positioned behind leaders exhibit reduced kinematic effort and lower metabolic costs.
| Species Studied | Key Observational Metric | Evidence of Energy Saving |
|---|---|---|
| Pacific Mackerel | Tail-beat frequency | Lower frequency observed in fish within a school compared to solitary swimmers. |
| Sea Bass | Tail-beat frequency & Oxygen consumption | Rear fish in a school showed significantly lower tail-beat frequency and oxygen consumption than leading fish. |
| Mullet | Metabolic rate & Positioning | Individuals with higher aerobic capacity positioned themselves at the front, suggesting rear positions are metabolically advantageous. |
| Manta Ray | Kinematic pattern | Observation of intermittent “burst-and-glide” propulsion strategy, indicating an inherent energy-saving behavior. |
These observations confirm that biological collectives inherently utilize spatial positioning to minimize locomotive costs, a principle that directly informs the design of formation strategies for underwater bionic robot clusters.
1.2 Insights from Numerical Simulation
Computational Fluid Dynamics (CFD) simulations offer a powerful tool to dissect the complex flow fields generated by collective motion and quantify hydrodynamic interactions. These studies allow researchers to systematically vary parameters like spacing, alignment, and phase difference to identify optimal configurations.
| Simulation Focus | Key Methodology | Principal Finding on Energy Efficiency |
|---|---|---|
| Vortex Exploitation | CFD coupled with Deep Reinforcement Learning | Simulated swimmers learned to actively exploit low-pressure vortex cores shed by upstream individuals, significantly increasing propulsion efficiency. |
| Spatial Arrangement | CFD of 2-3 foil configurations | Identified optimal lateral (D) and longitudinal (S) distances where hydrodynamic interactions passively assist body undulation, reducing energy cost. The relationship can be modeled as finding the minimum of a cost function $C_{total}(S, D)$. |
| Flexible Body Dynamics | Lattice Boltzmann-Immersed Boundary Method | Revealed the vortex shedding patterns and thrust generation mechanisms of a bio-inspired manta ray model, providing a basis for energy-efficient gait optimization in flexible bionic robots. |
Numerical models often describe the interaction force $\vec{F}_{hydro}$ on a follower robot due to the vortex field $\vec{\omega}$ of a leader as a function of relative position $\vec{r}$ and body orientation $\theta$:
$$
\vec{F}_{hydro} = \int_{Body} P(\vec{\omega}(\vec{r}, t), \theta) dA
$$
where $P$ represents the pressure distribution over the body surface area $A$. The goal is to find the relative state $(\vec{r}, \theta)$ that minimizes the opposing component of $\vec{F}_{hydro}$, effectively reducing drag.
2. Fluid Field Sensing for Underwater Bionic Robots
To exploit hydrodynamic benefits, an underwater bionic robot must first perceive its local flow environment. In nature, fish achieve this through a distributed sensory system called the lateral line, which detects minute water pressure and velocity gradients. Emulating this capability is essential for enabling reactive, energy-saving behaviors in robotic systems.
2.1 Artificial Lateral Line (ALL) Sensor Arrays
The development of Artificial Lateral Line systems focuses on creating arrays of miniature flow sensors distributed over the robot’s body. The design and placement of these sensors are critical for effective perception.
| Sensor Technology | Key Feature | Application in Bionic Robot |
|---|---|---|
| Micro-Pressure Sensor Array | Discrete sensors placed at hydrodynamic “sensitive points” (e.g., stagnation points). | Mapping steady-state pressure distribution for estimating ambient flow velocity and direction. |
| MEMS Hair Cell Sensors | Bio-inspired, flow-responsive micro-pillars that bend under drag forces. | Detecting oscillatory flow components and vortices, useful for sensing nearby moving objects or robot kinematics. |
| Distributed Flexible Sensor Skin | Integrated, large-area sensing surfaces conforming to complex robot morphology. | Essential for future flexible bionic robots to gain full-body flow awareness, akin to a real fish. |
2.2 Information Processing and State Estimation
Raw sensor signals must be processed to extract meaningful information for control. This involves mapping pressure/velocity fields $\mathcal{S}(t)$ from sensor arrays to useful state estimates $\mathcal{X}(t)$.
$$
\mathcal{X}(t) = f(\mathcal{S}(t-\Delta t:t), \mathcal{M})
$$
where $\mathcal{M}$ is a hydrodynamic model and $f$ is an estimation function. Applications include:
- Speed & State Estimation: Using pressure differentials to estimate the robot’s own swimming speed and gait performance.
- Neighbor Detection: Classifying the distinctive wake signatures of other bionic robots to determine their relative position, distance, and even motion state. This enables perception-based interaction without direct communication.
- Flow-aided Navigation: Identifying current direction to enable energy-saving “drift” or station-holding behaviors.
Machine learning techniques, particularly Convolutional Neural Networks (CNNs), are increasingly used to handle the high-dimensional, nonlinear mapping from complex, time-varying ALL data to robot states.
3. Energy-Aware Control for Bionic Robot Clusters
The final step is synthesizing perception and hydrodynamic principles into cooperative control laws that explicitly minimize energy consumption for the collective. This involves both low-level gait control for individual bionic robots and high-level coordination strategies for the cluster.
3.1 Single Robot Locomotion Control
Efficient individual motion is the foundation for an efficient cluster. Control methods must handle the often nonlinear and periodic dynamics of bio-inspired propulsion.
| Control Method | Control Inputs/Parameters | Advantage for Bionic Robot Efficiency |
|---|---|---|
| Central Pattern Generator (CPG) | Oscillator amplitudes, frequencies, and phase couplings. | Generates stable, rhythmic control signals enabling smooth gait transitions. Allows easy integration of sensory feedback to modulate effort based on flow conditions. The dynamics of a coupled oscillator $i$ can be modeled as: $$ \dot{\theta}_i = \omega_i + \sum_j w_{ij} \sin(\theta_j – \theta_i – \phi_{ij}) $$ |
| Model-Based Control | Joint angles/torques derived from dynamic model. | Potentially optimal if an accurate model exists. Often challenged by the complex, fluid-coupled dynamics of a soft-bodied bionic robot. |
| Sinusoidal Controller | Fixed amplitude, frequency, and phase offset. | Simple to implement but inflexible; cannot easily adapt to changing conditions or exploit hydrodynamic benefits. |
3.2 Multi-Robot Coordination Strategies
Cluster control strategies must manage formation geometry, collision avoidance, and collective task execution, all while considering energy costs.
Formation Control:
| Approach | Core Idea | Potential for Energy Integration |
|---|---|---|
| Leader-Follower | A designated leader tracks a path; followers maintain prescribed relative offsets. | Followers can be controlled to seek positions of minimal hydrodynamic drag in the leader’s wake, optimizing the cost function $J = \int (F_{drag} + k_p e^2) dt$, where $e$ is formation error. |
| Virtual Structure | The entire formation is treated as a single rigid body. | The structure’s path and orientation can be planned to minimize overall drag, though individual optimization is limited. |
| Behavior-Based & Consensus | Emergent formation from weighted combination of basic behaviors (e.g., attract to goal, repel from neighbors). | An “exploit flow” behavior can be added, where the velocity command $\vec{v}_i$ includes a term derived from the perceived flow field $\vec{u}_i$: $\vec{v}_i^{flow} = \alpha \cdot \vec{u}_i$ to ride favorable currents. |
Obstacle Avoidance: Energy-efficient swarming must incorporate collision avoidance.
| Method | Integration with Energy Saving |
|---|---|
| Artificial Potential Fields | Repulsive fields from obstacles must be balanced against attractive fields from energy-saving positions (e.g., in-wake positions), requiring careful potential function design. |
| Behavior-Based Splitting | The cluster can self-organize to split around obstacles, with sub-formations reforming optimally on the other side to resume energy-saving configurations. |
3.3 Control Strategies Based Explicitly on Energy-Saving Principles
A nascent but critical area involves control laws where energy minimization is the primary objective, often using bio-inspired rules or learning.
| Strategy | Mechanism | Mathematical / Algorithmic Basis |
|---|---|---|
| Vortex Phase Matching | Followers synchronize their body undulation phase to constructively interact with vortices shed by the leader. | Control rule adjusts tail-beat phase $\phi_i$ relative to sensed vortex period $T_v$: $\Delta \phi_i = g(T_v, \text{position})$. This strategy was shown to reduce power consumption in robotic fish pairs. |
| Bio-Inspired Heuristics + Optimization | Using simple rules (e.g., “maintain a specific lateral offset”) as a seed for numerical optimization of spacing. | Algorithms like Multi-Island Genetic Algorithms optimize formation parameters (distances, phases) to minimize a total power objective $P_{total}$. |
| Reinforcement Learning (RL) | The bionic robot cluster learns energy-saving formations and gaits through trial and interaction with the fluid environment. | The RL agent (each robot or the collective) takes actions $a$ (e.g., change relative position, adjust gait) to maximize a reward $R = -(\beta \cdot P_{mechanical} + \gamma \cdot \text{tracking\_error})$. Deep RL has been used to discover novel vortex-exploiting swimming strategies in simulation. |
The Vicsek-like model, a cornerstone of swarm dynamics, can be energy-augmented. The standard velocity update is:
$$
\vec{v}_i(t+1) = v_0 \mathcal{R}_\eta \left\langle \vec{v}_j(t) \right\rangle_{j \in N_i}
$$
where $\mathcal{R}_\eta$ adds noise. An energy-aware version could modulate the preferred speed $v_0$ based on local flow conditions:
$$
v_0^i(t) = h( \| \vec{u}_i(t) \|, \angle(\vec{v}_i, \vec{u}_i) )
$$
effectively allowing the bionic robot to “surf” on favorable flows.
4. Key Challenges and Future Research Directions
Despite significant progress, the realization of autonomously energy-optimizing underwater bionic robot clusters faces several interconnected challenges.
4.1 Challenge 1: High-Fidelity Modeling of Flexible Collective Hydrodynamics
Most numerical studies focus on rigid foils or simple kinematics. Future work must advance high-fidelity simulation of flexible bionic robot clusters, capturing the two-way coupling between complex body deformation and the resulting unsteady flow field. This requires integrating nonlinear structural dynamics with high-resolution CFD. The goal is to establish a generalized map from cluster gait parameters $\vec{G}$ and spatial configuration $\vec{X}$ to an energy cost metric $E$:
$$
E = \mathcal{H}(\vec{G}, \vec{X}; \mathcal{F})
$$
where $\mathcal{H}$ is the complex hydrodynamic function and $\mathcal{F}$ represents fluid properties.
4.2 Challenge 2: Robust Perceptual Awareness in Dynamic, Cluttered Flows
Current ALL systems are often validated in controlled flows. For real-world deployment, bionic robot perception must be robust to turbulence, background currents, and noisy sensor data. Future directions include:
- Developing conformable, durable sensor skins for flexible bionic robot bodies.
- Fusing ALL data with other modalities (e.g., vision, sonar) for robust state estimation.
- Employing advanced machine learning (e.g., Recurrent Neural Networks, Transformers) to process spatiotemporal flow data and disambiguate self-generated flow from external disturbances and neighbor signatures.
4.3 Challenge 3: Synthesis of Distributed, Real-Time, Energy-Optimal Control
The ultimate challenge is creating a distributed control framework where each bionic robot, using only local perception and limited communication, can make real-time decisions that collectively converge to an energy-minimizing configuration. This requires:
- Developing Hybrid Control Architectures: Combining reactive, behavior-based layers (for fast obstacle avoidance) with higher-level planners that solve for energy-efficient paths and formations over longer horizons.
- Co-design of Perception and Control: Optimizing what sensory information is most critical for energy-saving decisions and designing control laws that are robust to perceptual uncertainties.
- Scalable and Adaptive Algorithms: Control strategies must scale to large numbers of bionic robots and adapt to changing group objectives and environmental conditions.
Promising pathways involve bio-inspired “smart” particle models enhanced with learned value functions, and decentralized model predictive control (MPC) schemes where each robot solves a local optimization that includes a model of anticipated hydrodynamic benefits from neighbors.
5. Conclusion
The pursuit of energy efficiency for underwater bionic robot clusters is a compelling interdisciplinary endeavor, merging insights from biology, fluid dynamics, robotics, and control theory. This review has outlined the foundational work in understanding biological energy-saving mechanisms, the development of artificial flow sensing, and the formulation of energy-aware control strategies. While notable advances have been made, key challenges remain in accurately modeling flexible collective hydrodynamics, achieving robust situational awareness in complex flows, and synthesizing decentralized real-time control that explicitly optimizes for energy. Overcoming these challenges will require continued close collaboration across disciplines. The successful development of such technologies will transform the capabilities of underwater bionic robot clusters, enabling longer missions, more complex cooperative tasks, and a greater degree of autonomy, ultimately unlocking their full potential for exploring and operating in the vast and energy-critical underwater domain.