In recent years, the development of underwater bionic robots has gained significant attention due to their potential applications in marine exploration, environmental monitoring, and industrial tasks. These robots mimic the efficient swimming mechanisms of aquatic animals, such as fish, to achieve high maneuverability and energy efficiency. However, controlling the motion of such bionic robots precisely remains a challenge, particularly due to the difficulty in tuning parameters of Central Pattern Generators (CPGs), which are inspired by biological neural circuits. This paper proposes an improved Particle Swarm Optimization (PSO) based approach to optimize CPG parameters for motion control in underwater bionic robots. By integrating CPG structures with PSO, we generate rhythmic control signals that enable accurate joint movements, enhancing the robot’s performance in real-world scenarios. The study includes simulations and prototype experiments to validate the effectiveness of the method, demonstrating its real-time capabilities and high control efficiency. This work lays a foundation for future advancements in high-mobility underwater bionic robots, offering a novel approach to motion control that leverages bio-inspired mechanisms and optimization algorithms.
The core of this research revolves around the use of CPGs, which are neural oscillators that produce rhythmic outputs for coordinated movements in bionic robots. Traditional CPG models often rely on manually tuned parameters, leading to suboptimal performance. To address this, we employ an improved PSO algorithm to automatically optimize CPG parameters, ensuring that the bionic robot’s motion closely resembles natural swimming patterns. The integration of these techniques not only improves control accuracy but also enhances adaptability to dynamic underwater environments. Throughout this paper, we emphasize the role of bionic robot design, highlighting how bio-inspired principles can be combined with computational optimization to achieve robust and efficient motion control. The following sections detail the theoretical background, control structure design, optimization process, and experimental validation, providing a comprehensive framework for developing advanced underwater bionic robots.
Theoretical Background on CPG and PSO
Central Pattern Generators (CPGs) are neural circuits found in biological systems that generate rhythmic signals for repetitive motions, such as walking or swimming. In the context of bionic robots, CPGs are modeled using oscillator networks to produce control signals for actuators. A typical CPG structure consists of interconnected neurons, each described by differential equations that govern their dynamic behavior. For instance, a neuron oscillator can be represented as:
$$
T_{\gamma} \dot{u_i} + u_i = – \sum_{j=1}^{N} \omega_{ij} y_j – \beta v_i + u_0 + \text{Feed}_i
$$
$$
T_{\alpha} \dot{v_i} + v_i = y_i
$$
$$
y_i = \max(u_i, 0)
$$
where \( u_i \) is the internal state of the neuron, \( v_i \) is the self-inhibition state, \( y_i \) is the output signal, \( \omega_{ij} \) represents the connection weight between neurons, \( T_{\gamma} \) and \( T_{\alpha} \) are time constants, \( \beta \) is the self-inhibition weight, \( u_0 \) is an external input, and \( \text{Feed}_i \) denotes feedback from sensors. This model allows the CPG to produce oscillatory outputs that drive the joints of a bionic robot, enabling rhythmic motions like undulation in fish-like swimming. The parameters \( T_{\gamma} \), \( T_{\alpha} \), \( \beta \), and \( \omega_{ij} \) critically influence the frequency, amplitude, and phase of the output signals, making their optimization essential for precise control in bionic robot applications.
Particle Swarm Optimization (PSO) is a population-based algorithm inspired by social behavior, such as bird flocking, and is widely used for solving optimization problems. In PSO, a swarm of particles moves through a search space, with each particle representing a potential solution. The position and velocity of each particle are updated iteratively based on its own experience and the swarm’s collective knowledge. The update equations are:
$$
v_i = \omega \cdot v_i + c_p \cdot \phi_1 (x_{p_i} – x_i) + c_g \cdot \phi_2 (x_q – x_i)
$$
$$
x_i = x_i + v_i
$$
where \( v_i \) and \( x_i \) are the velocity and position of particle \( i \), respectively, \( \omega \) is the inertia weight, \( c_p \) and \( c_g \) are acceleration coefficients, \( \phi_1 \) and \( \phi_2 \) are random numbers uniformly distributed in [0,1], \( x_{p_i} \) is the particle’s best position, and \( x_q \) is the global best position. PSO is particularly suitable for optimizing CPG parameters in bionic robots because it efficiently handles non-linear and multi-modal objective functions. By minimizing a cost function that measures the difference between desired and actual motion trajectories, PSO fine-tunes CPG parameters to enhance the performance of the bionic robot. This synergy between CPG and PSO enables adaptive and robust control, which is crucial for underwater environments where external disturbances are common.
CPG-Based Control Structure for Bionic Robot
The motion control of an underwater bionic robot relies on a CPG-based structure that generates coordinated signals for multiple joints. Inspired by the undulatory movements of fish, the robot’s body is modeled as a series of linked segments, each controlled by a CPG unit. The kinematic model of the bionic robot is derived from a traveling wave equation that describes the body’s lateral displacement:
$$
Y_{\text{body}}(x,t) = (c_1 x + c_2 x^2) \sin(kx – \omega t)
$$
where \( Y_{\text{body}} \) is the lateral displacement along the body length \( x \), \( c_1 \) and \( c_2 \) are amplitude coefficients, \( k \) is the wave number, \( \omega \) is the angular frequency, and \( t \) is time. This equation captures the propagating wave pattern typical of fish swimming, which the bionic robot aims to emulate. To implement this in a robotic system, the body is divided into multiple links, and the joint angles are computed to approximate the desired wave form. For a bionic robot with three joints, the CPG structure consists of three neuron oscillators, each producing output signals that control the corresponding joint angles. The joint angle \( \theta_i \) for the \( i \)-th joint is given by:
$$
\theta_i = s_i (y_i^e – y_i^f)
$$
where \( s_i \) is a scaling factor, and \( y_i^e \) and \( y_i^f \) are the outputs of extensor and flexor neurons, respectively. The CPG network ensures phase synchronization between joints, enabling smooth and efficient locomotion. The design of this control module is critical for achieving naturalistic swimming in the bionic robot, as it allows for adjustments in swimming speed and direction through parameter modulation.
The CPG control module for a multi-joint bionic robot typically includes interconnected neuron oscillators, as shown in the figure above. Each oscillator comprises extensor and flexor neurons with mutual inhibition, and the connections between oscillators determine the phase relationships. The dynamics of the CPG are described by a set of coupled differential equations, which can be optimized using PSO to minimize the error between the robot’s actual motion and the desired traveling wave. This approach ensures that the bionic robot exhibits stable and adaptive swimming patterns, even in the presence of external disturbances. By leveraging CPG principles, the control structure provides a bio-inspired framework for robust motion generation in underwater bionic robots, highlighting the importance of neural oscillators in achieving coordinated multi-joint movements.
PSO-Based Optimization of CPG Parameters
Optimizing CPG parameters is essential for achieving precise motion control in bionic robots. The PSO algorithm is employed to tune parameters such as time constants \( T_{\gamma} \) and \( T_{\alpha} \), connection weights \( \omega_{ij} \), self-inhibition weight \( \beta \), and scaling factors \( s_i \). The objective function for optimization is defined as the integral of the absolute error between the desired traveling wave and the actual body wave of the bionic robot over a time period \( T \):
$$
f_{\omega} = \int_0^T |e(t)| dt
$$
where \( e(t) \) is the difference at time \( t \), computed as:
$$
e(t) = \sum_{i=1}^{3} \int_{x_{i-1}(t)}^{x_i(t)} |Y_{\text{body}}(x,t) – Y_{\text{link}_i}(x,t)| dx
$$
Here, \( Y_{\text{body}}(x,t) \) is the desired wave from the kinematic model, and \( Y_{\text{link}_i}(x,t) \) represents the wave form of the \( i \)-th link of the bionic robot, derived from the joint angles and link positions. The positions \( x_i(t) \) and \( y_i(t) \) of each link are calculated recursively based on the joint angles and link lengths. For example, for the first link, \( x_0(t) = 0 \) and \( y_0(t) = 0 \), and for subsequent links:
$$
x_i(t) = x_{i-1}(t) + l_i \cos(\theta_i(t))
$$
$$
y_i(t) = y_{i-1}(t) + l_i \sin(\theta_i(t))
$$
where \( l_i \) is the length of the \( i \)-th link. The PSO algorithm minimizes \( f_{\omega} \) by adjusting the CPG parameters, ensuring that the bionic robot’s motion closely matches the desired undulatory pattern. The optimization process involves initializing a swarm of particles with random positions and velocities, evaluating the objective function for each particle, and iteratively updating the positions based on personal and global best values. This results in an optimized set of CPG parameters that enhance the swimming performance of the bionic robot.
To illustrate the optimization results, the following table summarizes the optimized CPG parameters obtained from PSO for a bionic robot with three joints. These parameters were used in simulations and experiments to generate control signals for the robot’s motion.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| \( T_{\gamma} \) | 2.99985 | \( T_{\alpha} \) | 0.429918 |
| \( \beta \) | 9.84874 | \( \omega_{ef} \) | 3.02762 |
| \( \omega_{12}^e \) | 3.45688 | \( \omega_{12}^f \) | 5.8351 |
| \( \omega_{13}^e \) | 3.83181 | \( \omega_{13}^f \) | 7.7661 |
| \( \omega_{21}^e \) | 5.3505 | \( \omega_{21}^f \) | 2.80495 |
| \( \omega_{23}^e \) | 6.55237 | \( \omega_{23}^f \) | 3.11608 |
| \( \omega_{31}^e \) | 5.19203 | \( \omega_{31}^f \) | 4.93922 |
| \( \omega_{32}^e \) | 3.58118 | \( \omega_{32}^f \) | 2.53456 |
| \( s_1 \) | 0.645567 | \( s_2 \) | 2.73989 |
| \( s_3 \) | 2.3313 | – | – |
The optimization process typically converges within a few iterations, as shown by the decrease in the objective function value over time. For instance, in our experiments, the average objective function value reduced to 0.83254 after 50 trials, indicating effective parameter tuning. This optimized CPG structure enables the bionic robot to generate stable and efficient swimming motions, demonstrating the utility of PSO in enhancing the control of underwater bionic robots.
Design and Implementation of the Bionic Robot
The underwater bionic robot designed for this study features a streamlined body inspired by fish morphology, reducing hydrodynamic drag and improving maneuverability. The robot comprises several key components: a head section housing sensors and control modules, multiple jointed segments for undulatory motion, and pectoral fins for stability and steering. The body is constructed from lightweight materials to enhance buoyancy and efficiency, with actuators embedded in each joint to enable precise angle adjustments. The control system integrates the CPG network with sensors, such as inertial measurement units (IMUs), to provide feedback for adaptive motion. This design allows the bionic robot to perform various swimming gaits, including cruising and turning, by modulating the CPG parameters.
The bionic robot’s propulsion mechanism is based on the traveling wave model, where the tail and body segments generate thrust through oscillatory movements. The CPG control signals drive the joints to produce these oscillations, with the frequency and amplitude adjusted via the optimized parameters. For example, increasing the frequency of the CPG outputs results in faster swimming speeds, while modifying the phase differences between joints enables directional changes. The robot’s pectoral fins are controlled separately to assist in depth control and stabilization, making the bionic robot highly versatile in underwater environments. The integration of CPG and PSO ensures that the robot can adapt to varying conditions, such as currents or obstacles, by dynamically adjusting its motion patterns.
In terms of hardware, the bionic robot includes a central processor for running the CPG algorithms and PSO optimization, power management systems for extended operation, and communication modules for data transmission. The use of modular components facilitates easy maintenance and upgrades, which is essential for long-term deployments. The design emphasizes bio-inspiration, not only in the external shape but also in the internal control architecture, mimicking the neural coordination seen in natural swimmers. This approach highlights the potential of bionic robots to achieve high levels of autonomy and efficiency in aquatic applications, from scientific research to industrial inspections.
Simulation and Experimental Validation
To validate the proposed method, both simulations and physical experiments were conducted on the bionic robot prototype. The simulations involved implementing the CPG control structure with the optimized parameters in a dynamic model of the robot, using software tools to simulate underwater conditions. The joint angle outputs from the CPG were fed into the kinematic model to generate the robot’s motion trajectories, which were compared against the desired traveling wave. The results showed that the optimized CPG produced signals that closely matched the reference, with minimal error in the body wave form. For instance, the output signals for the three joints exhibited stable oscillations with appropriate phase lags, enabling smooth undulatory motion in the bionic robot.
In the experimental setup, the bionic robot was tested in a water tank equipped with sensors to measure its position, velocity, and orientation. High-speed cameras captured the robot’s movements, and data from IMUs were used to compute the actual joint angles and body waves. The optimized CPG parameters were loaded into the robot’s controller, and tests were performed for various swimming scenarios, including straight-line swimming and turning maneuvers. The experimental results demonstrated that the bionic robot achieved higher swimming speeds and better trajectory tracking compared to non-optimized CPG controls. For example, the velocity of the robot increased steadily during acceleration phases and stabilized at a maximum value, as shown in the following table comparing optimized and non-optimized performance.
| Metric | Non-Optimized CPG | Optimized CPG with PSO |
|---|---|---|
| Average Speed (m/s) | 0.15 | 0.25 |
| Tracking Error (m) | 0.05 | 0.02 |
| Energy Consumption (J) | 120 | 90 |
The PSO optimization also improved the convergence speed of the CPG parameters, with the algorithm reaching an optimal solution within a few iterations. This efficiency is crucial for real-time applications where the bionic robot must adapt quickly to environmental changes. Overall, the simulations and experiments confirm that the improved PSO-based CPG control enhances the motion performance of the bionic robot, making it more reliable and effective for underwater tasks. The success of this approach underscores the importance of combining bio-inspired control with advanced optimization techniques in the development of autonomous bionic robots.
Conclusion
This paper presents a novel motion control method for underwater bionic robots based on an improved PSO algorithm applied to CPG parameter optimization. By leveraging the rhythmic signal generation of CPGs and the global search capabilities of PSO, the method achieves precise and adaptive control of the robot’s joint movements. The theoretical foundations, including the CPG oscillator models and PSO update equations, provide a robust framework for designing efficient control systems. The kinematic model of the bionic robot, derived from fish swimming mechanics, ensures that the motion patterns are biologically plausible and energy-efficient. Through simulations and experiments, we demonstrated that the optimized CPG parameters significantly enhance the robot’s swimming performance, including speed, accuracy, and stability.
The integration of CPG and PSO offers several advantages for bionic robots, such as real-time adaptability, reduced parameter tuning effort, and improved robustness against disturbances. This approach not only advances the state-of-the-art in underwater robotics but also opens up new possibilities for applications in exploration, monitoring, and intervention. Future work will focus on extending the method to more complex environments and multi-robot systems, as well as incorporating machine learning techniques for online adaptation. The insights gained from this study contribute to the ongoing development of intelligent bionic robots that emulate the elegance and efficiency of natural swimmers, paving the way for next-generation autonomous underwater vehicles.