A Data-Driven Gait Design Method for a Turtle-Inspired Amphibious Robot

Abstract

A data-driven gait design method for a turtle-inspired amphibious robot includes: constructing a physical platform, designing a CAD model and fabricating a prototype, using flexible materials to create turtle fins, and monitoring motion power consumption with a power meter; collecting multi-source mechanical data, obtaining hydrodynamic data through computational fluid dynamics simulation, measuring three-dimensional interaction forces in particulate media using a three-dimensional sensor, evaluating and optimizing various materials; performing kinematic modeling and power consumption mapping, determining D-H parameters based on the CAD model and geometric parameters to build a single-limb model, defining the workspace using Monte Carlo methods, traversing core parameters to collect power consumption, and establishing a parameter-power consumption mapping using a backpropagation neural network; optimizing parameters using Bayesian methods, modeling in a dynamic simulation environment, aiming for maximum speed and minimum power consumption, fitting the objective function using a Gaussian process surrogate model, and iteratively obtaining the optimal parameters; generating single-limb trajectories based on the optimal parameters, and adjusting limb phase differences to generate a coordinated gait for the entire robot. This method integrates multi-source data to improve gait adaptability and performance.

Description

Technical Field

[0001] This invention relates to amphibious robot technology, and in particular to a data-driven method for designing the gait of a turtle-inspired amphibious robot. Background Technology

[0002] Efficient and adaptive gait design for biomimetic legged robots is a key prerequisite for achieving precise movement in complex terrains, especially in dynamic, unstructured environments such as the water-land interface. However, existing methods face significant challenges: simply mimicking the movement characteristics of organisms makes it difficult to extract universal movement laws, while design methods based on precise mathematical equations, such as central pattern generators and specific flapping wing motion equations, suffer from insufficient versatility. Especially when drastic environmental changes require significant adjustments to movement patterns, the pre-set equations often fail to adapt or even become ineffective.

[0003] The development of neural network technology has provided a powerful tool for mining complex patterns from data and is expected to overcome the limitations of pre-set models. However, neural network methods themselves have two major limitations: dependence on large-scale, high-quality data and lack of interpretable physical mechanism constraints within the model.

[0004] When using optimization algorithms to search for optimal gait parameters in a dynamics simulator, traditional methods such as genetic algorithms are prone to getting stuck in local optima.

[0005] It should be noted that the information disclosed in the background section above is only for understanding the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a data-driven method for designing the gait of a turtle-like amphibious robot.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A data-driven method for designing the gait of a turtle-inspired amphibious robot includes the following steps:

[0009] S1. Constructing a robot physical platform: Design a CAD model of a turtle-like amphibious robot and make a physical prototype. Use flexible materials to make biomimetic turtle fins and use a power meter to monitor the power consumption of the robot in real time during its movement.

[0010] S2. Multi-source mechanical data acquisition: Hydrodynamic data of turtle fins are acquired through computational fluid dynamics simulation, and three-dimensional interaction force data of turtle fin movement are measured in particulate media through three-dimensional mechanical sensors; the influence of various materials on mechanical properties is evaluated and the material with the best comprehensive performance is selected.

[0011] S3. Kinematic Modeling and Power Consumption Mapping: Based on the robot CAD model and actual geometric parameters, determine the DH parameters, establish a single biomimetic turtle fin kinematic model, and use the Monte Carlo method to determine the workspace; by traversing the core gait parameter combinations and collecting the power consumption data of the physical prototype, use a backpropagation neural network to establish a nonlinear mapping model from gait parameters to power consumption.

[0012] S4. Bayesian optimization of gait parameters: A robot interaction model is built in a dynamic simulation environment. The optimization objectives are to maximize the movement speed and minimize the power consumption. The normalized objective function is input into the Bayesian optimization algorithm. The objective function is fitted using a Gaussian process surrogate model. The optimal combination of gait parameters is obtained by iterative convergence through the balancing exploration and utilization of the acquisition function.

[0013] S5. Gait Coordination: Generate single-limb motion trajectories based on optimal gait parameters, and generate a fully coordinated gait by adjusting the phase difference between limbs.

[0014] Further, step S2 specifically includes:

[0015] Import the turtle fin CAD model into computational fluid dynamics software to simulate the lift and drag characteristics under a set flow velocity with varying angle of attack.

[0016] Fabricate a single-unit testing device identical to the robot drive mechanism, fix it to a three-dimensional force sensor, and place it in a granular medium container;

[0017] The control and testing device executes a typical land gait, and collects three-dimensional data of longitudinal force, lateral force, and support force;

[0018] The turtle fins were made of various flexible and rigid materials, and repeated experiments were conducted in fluid environments and particulate media to compare the mechanical responses and select the best material.

[0019] Furthermore, establishing the power consumption mapping model in step S3 includes:

[0020] The kinematic model is established based on the robot CAD model and the DH parameters determined by the actual geometric parameters. A large number of angle combinations are randomly generated within the joint motion range. The workspace is visualized using the Monte Carlo method to define the feasible domain of gait parameters.

[0021] The system samples the core gait parameter combination, records the steady-state motion power of the physical prototype, and plots the parameter-power consumption response surface.

[0022] A backpropagation neural network with hidden layers is used to train the model with core gait parameters as input and power consumption as output. After obtaining a high-precision nonlinear mapping model, it is integrated into the dynamics simulator.

[0023] Furthermore, the core gait parameters include:

[0024] The trajectory amplitude parameters that determine the force exerted by the turtle fins and the degree of swaying;

[0025] Gait period parameters that determine the movement speed of turtle fins.

[0026] Furthermore, the dynamics simulator adopts a simplified contact dynamics model, and its contact parameters are calibrated based on the three-dimensional force curve measured in step S2 to approximate the nonlinear viscoelastic characteristics of real silicone materials.

[0027] Furthermore, the Bayesian optimization in step S4 specifically includes:

[0028] Virtual sensors are configured in the dynamics simulator to acquire the robot's motion speed;

[0029] Using the parameter range defined in step S3 as the search space, the normalized speed and power consumption are used as the objective function;

[0030] A probabilistic proxy model of the objective function is established through a Gaussian process, and the sampling function is used to guide the parameter space sampling.

[0031] Iteratively update the surrogate model and evaluate new sampling points until the objective function converges to the optimal solution.

[0032] Furthermore, the gait coordination in step S5 includes:

[0033] Generate the periodic trajectory of the single-limb end effector based on the optimal core parameters;

[0034] By setting the phase difference of movement between different limbs, quadrupedal coordination gait patterns are constructed, including walking gait, symmetrical gait, jumping gait and swimming gait.

[0035] Furthermore, the method integrates the following data sources:

[0036] Real-time power consumption data collected from the motion of the physical prototype;

[0037] Three-dimensional interaction force data between turtle fins and medium measured by a mechanical platform;

[0038] Hydrodynamic laws revealed by computational fluid dynamics simulations;

[0039] Among them, Bayesian optimization is used to achieve the above-mentioned multi-source data-driven gait parameter collaborative optimization.

[0040] Furthermore, the flexible material is a silicone-based composite material, which is reinforced by an embedded skeleton to achieve a balance between terrain-adaptive deformation and load-bearing capacity.

[0041] A computer program product includes a computer program that, when executed by a processor, implements the data-driven gait design method for a turtle-inspired amphibious robot.

[0042] The present invention has the following beneficial effects:

[0043] This invention proposes a data-driven gait design method for a turtle-inspired amphibious robot. By fusing motion data from a real prototype, measured data of biomimetic turtle fins on a mechanical platform, and fluid dynamics data obtained from finite element simulations, and employing a Bayesian optimization strategy, a highly adaptive gait is generated through synergistic optimization of energy consumption and motion performance. Applying this method, the amphibious biomimetic turtle robot can effectively integrate the aforementioned multi-source data to achieve synergistic optimization of energy consumption and motion performance, generating a highly adaptive gait.

[0044] The turtle-inspired amphibious robot gait design method of this invention further enhances the convenience and adaptability of amphibious robot gait design by integrating the reliability of real prototype motion data, the physical background of measured data of biomimetic turtle fins on a mechanical platform, and the inspiration from fluid dynamics in finite element simulation. Specifically, this technical solution has several advantages: it deeply integrates multi-source physical data, innovatively combining measured power consumption data of physical prototypes, three-dimensional interaction force data obtained from biomimetic turtle fins on a dedicated mechanical platform, and hydrodynamic laws revealed by computational fluid dynamics simulation, providing a solid physical background support for gait design and significantly enhancing the reliability and environmental adaptability of the design results.

[0045] Meanwhile, the algorithm design of this invention considers the influence of the turtle fin material on propulsion performance, achieving coordinated optimization of software and hardware design. This not only optimizes gait performance but also avoids control signal distortion or excessive hardware wear caused by neglecting hardware characteristics such as material stiffness and friction coefficient, thus extending the service life of the hardware. In addition, the gait design process fully considers the influence of the mechanical properties of the biomimetic turtle fin itself interacting with the medium, revealing the mechanical characteristics from the perspective of fluid dynamics simulation and particle-medium interaction experiments, and applying the discovered mechanical laws to the gait design.

[0046] This method also abandons the traditional complex and potentially distorted multi-rigid-body dynamics power consumption modeling, and innovatively adopts a BP neural network based on physical prototype measured data to establish an accurate mapping model from gait parameters to power consumption. This model is seamlessly integrated into the dynamics simulation environment, providing highly reliable power consumption prediction for Bayesian optimization.

[0047] In this invention, precise kinematic modeling and Monte Carlo workspace analysis are performed based on the DH parameters determined by the robot CAD model and actual geometric parameters. This strictly defines the physical feasible range of the gait design parameters and ensures that the gait parameters generated by the Bayesian optimization process are physically realizable.

[0048] To address the complex nonlinear relationship between gait parameters and motion performance, this invention optimizes motion speed and power consumption in a dynamics simulator using a Bayesian optimization algorithm. This algorithm efficiently finds the global optimal solution in the parameter space, reducing distortion caused by inaccurate simple multi-rigid-body dynamics modeling and improving the effectiveness and efficiency of gait design algorithms.

[0049] The gait optimized by this invention not only performs excellently in the simulation environment, but has also been fully verified through rigorous multi-terrain testing on a physical prototype, proving that the method has excellent simulation-to-real-world transfer capability.

[0050] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0051] Figure 1 The exhibition showcased a biomimetic prototype and CAD modeling of a turtle-inspired amphibious robot.

[0052] Figure 2 The simulation results of lift and drag of the biomimetic turtle fin are presented at an incoming flow velocity of 0.3 m / s.

[0053] Figure 3 A model diagram of a biomimetic turtle fin mechanical testing device is shown.

[0054] Figure 4 The exhibition showcases turtle fins made from different materials.

[0055] Figure 5 The mechanical testing device and the three-dimensional force curve of the turtle's fin in water were displayed.

[0056] Figure 6 A schematic diagram of the turtle fin's gait and a three-dimensional force curve are shown.

[0057] Figure 7 It showcases a visualized workspace in robot kinematics simulation.

[0058] Figure 8 An experimental data fitting surface is shown to demonstrate the relationship between robot motion energy consumption and gait period and wheel parameter α.

[0059] Figure 9 The iterative convergence process of the Bayesian optimization algorithm is demonstrated.

[0060] Figure 10 The example demonstrates the joint motion trajectory generated using three servos on one leg.

[0061] Figures 11A to 11D The temporal patterns of limb contact and movement phase decomposition in four gait types are shown respectively.

[0062] Figure 12 This presentation showcases a comparative analysis of robot motion in various terrain environments: simulation and physical prototype performance. The simulation environments, from left to right, represent a hard surface, a hard slope in a land-water transition zone, and an underwater environment.

[0063] Figure 13 The overall flow of the data-driven gait design method for turtle-inspired amphibious robots of this invention is demonstrated. Detailed Implementation

[0064] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0065] To address the shortcomings of traditional methods, a feasible solution is proposed. The motion space of the target robot prototype is determined based on its specific structural constraints, and a dataset is constructed through systematic parameter traversal experiments. Simultaneously, by combining a physical experimental platform or high-fidelity finite element simulation, the mechanical properties of the biomimetic turtle fin during interaction with different media are accurately measured, laying a solid physical foundation for gait design. This data-driven approach combined with physical modeling enables the effective modeling and optimization of key performance indicators that were previously difficult to quantify precisely. In particular, for power consumption data that is difficult to obtain accurately in a simulation environment, a dedicated dataset can be constructed by collecting operational data under different combinations of gait parameters on a real robot platform, and a high-precision fitting is performed using neural networks to establish a parameter-power consumption mapping model. Bayesian optimization, as a global optimization method based on a probabilistic model, is particularly suitable for handling black-box function optimization problems with high evaluation costs and multiple objectives, efficiently balancing exploration and utilization. This invention proposes a data-driven gait design method for a turtle-inspired amphibious robot: it integrates motion data from real prototypes, measured data of biomimetic turtle fins on a mechanical platform, and fluid dynamics data obtained from finite element simulations, and uses a Bayesian optimization strategy to achieve highly adaptive gait generation with coordinated optimization of energy consumption and motion performance.

[0066] See Figure 13 This invention provides a data-driven gait design method for a turtle-inspired amphibious robot, comprising the following steps:

[0067] Step S1: Construct the robot physical platform: Design a CAD model of the turtle-inspired amphibious robot and make a physical prototype. Use flexible materials to make biomimetic turtle fins and use a power meter to monitor the power consumption of the robot during its movement in real time.

[0068] In some embodiments, the flexible material is a silicone-based composite material, which is reinforced by an embedded skeleton to achieve a balance between terrain-adaptive deformation and load-bearing capacity.

[0069] Step S2, Multi-source mechanical data acquisition: Obtain hydrodynamic data of turtle fins through computational fluid dynamics simulation, and simultaneously measure the three-dimensional interaction force data of turtle fin movement in particulate media using a three-dimensional mechanical sensor; evaluate the influence of various materials on mechanical properties and select the material with the best comprehensive performance;

[0070] In some embodiments, step S2 specifically includes: importing the turtle fin CAD model into computational fluid dynamics software to simulate the lift and drag characteristics of the angle of attack change under a set flow velocity; fabricating a single test device identical to the robot drive mechanism, fixing it to a three-dimensional force sensor and placing it in a granular medium container; controlling the test device to perform a typical land gait and collecting three-dimensional data of longitudinal force, lateral force and support force; using various flexible / rigid materials to fabricate the turtle fin, and repeating the experiment in both fluid environment and granular medium to compare the mechanical response and select the optimal material.

[0071] Step S3, Kinematic Modeling and Power Consumption Mapping: Based on the robot CAD model and actual geometric parameters, determine the DH parameters, establish a single biomimetic turtle fin kinematic model, and use the Monte Carlo method to determine the workspace; by traversing the core gait parameter combinations and collecting the power consumption data of the physical prototype, use a backpropagation neural network to establish a nonlinear mapping model from gait parameters to power consumption.

[0072] In some embodiments, establishing the power consumption mapping model in step S3 includes: establishing a kinematic model based on the robot CAD model and the DH parameters determined by the actual geometric parameters; randomly generating a large number of angle combinations within the joint motion range; visualizing the workspace using the Monte Carlo method to define the feasible domain of gait parameters; systematically sampling core gait parameter combinations; recording the steady-state motion power of the physical prototype and plotting the parameter-power consumption response surface; and using a backpropagation neural network with hidden layers, training it with core gait parameters as input and power consumption as output to obtain a high-precision nonlinear mapping model, which is then integrated into the dynamics simulator.

[0073] In some embodiments, the core gait parameters include: trajectory amplitude parameters that determine the force applied by the turtle fins and the degree of swaying; and gait period parameters that determine the movement speed of the turtle fins.

[0074] In some embodiments, the dynamics simulator employs a simplified contact dynamics model, whose contact parameters are calibrated based on the three-dimensional force curve measured in step S2, in order to approximate the nonlinear viscoelastic characteristics of real silicone materials.

[0075] Step S4: Bayesian optimization of gait parameters: Build a robot interaction model in the dynamic simulation environment, with the optimization objectives of maximizing movement speed and minimizing power consumption. Input the normalized objective function into the Bayesian optimization algorithm; use a Gaussian process surrogate model to fit the objective function, and obtain the optimal combination of gait parameters by balancing exploration and utilization through the acquisition function and iteratively converging.

[0076] In some embodiments, the Bayesian optimization in step S4 specifically includes: configuring virtual sensors in the dynamics simulator to acquire the robot's motion speed; using the parameter range defined in step S3 as the search space, constructing the objective function from the normalized speed and power consumption; establishing a probabilistic surrogate model of the objective function through a Gaussian process, and using a sampling function to guide parameter space sampling; iteratively updating the surrogate model and evaluating new sampling points until the objective function converges to the optimal solution.

[0077] Step S5, Gait Coordination: Single-limb motion trajectories are generated based on optimal gait parameters, and the coordinated gait of the entire robot is generated by adjusting the phase difference between limb movements. In some embodiments, the robot is also deployed to a physical prototype in various terrain environments for motion performance verification.

[0078] In some embodiments, the gait coordination in step S5 includes: generating a periodic trajectory of a single limb end effector based on optimal core parameters; and constructing a quadrupedal coordinated gait pattern, including walking gait, symmetrical gait, jumping gait, and swimming gait, by setting the motion phase difference between different limbs.

[0079] In some embodiments, the method integrates the following data sources: real-time power consumption data collected from the motion of a physical prototype; three-dimensional interaction force data between the turtle fin and the medium measured by a mechanical platform; and hydrodynamic laws revealed by computational fluid dynamics simulation. Among these, Bayesian optimization is used to achieve collaborative optimization of gait parameters driven by the above multi-source data.

[0080] The main technical advantages of this invention are as follows: It constructs a multi-source physical data collaborative driving framework by deeply integrating measured power consumption data from physical prototypes, three-dimensional interactive force data obtained from biomimetic turtle fins on a mechanical platform, and hydrodynamic laws revealed by computational fluid dynamics simulations; it innovatively uses a BP neural network based on measured physical prototype data to establish an accurate mapping model from gait parameters to power consumption, replacing the traditional multi-rigid-body dynamics power consumption modeling which has a high risk of distortion; it combines kinematic modeling using the improved DH parameter method with Monte Carlo workspace analysis to strictly define the physical feasible domain of parameters, ensuring the feasibility of the optimization results; and it utilizes Bayesian optimization algorithms for high efficiency. This approach effectively addresses the multi-objective black-box optimization problem of motion speed and power consumption by exploring and utilizing Gaussian process surrogate models and acquisition functions to achieve global optimization in the parameter space. Simultaneously, it achieves hardware and software co-optimization, systematically examining the impact of the mechanical properties of the turtle fin material on propulsion performance. It integrates the mechanical laws revealed by fluid dynamics simulation and particulate media experiments into the gait design, avoiding control distortion or hardware wear caused by neglecting material stiffness and friction coefficient. Finally, it verifies the simulation-to-real-world transfer capability through multi-terrain testing of a physical prototype, significantly improving the amphibious robot's motion adaptability, design reliability, and hardware lifespan in dynamic unstructured environments.

[0081] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0082] A data-driven gait design method for a turtle-inspired amphibious robot mainly includes: designing a three-degree-of-freedom (DOF) biomimetic turtle amphibious robot model and building a robot prototype; calculating the lift and drag data of the biomimetic turtle fins in finite element simulation software; building a mechanical platform and measuring the three-dimensional mechanical data of the biomimetic turtle fins when performing common robot gaits; determining the workspace and range of common gait parameters of the three-DOF biomimetic turtle fins using mathematical calculation and numerical analysis software such as MATLAB's robot toolbox; constructing a mapping relationship between gait parameters and robot power consumption by traversing gait parameters, and fitting the mapping through a backpropagation neural network; building a simplified model of the three-DOF turtle-inspired robot in the dynamics simulator Webots, obtaining the simulated motion speed of the robot by setting sensors in the simulator, obtaining power consumption values ​​under different motion parameters through the trained backpropagation neural network model, optimizing gait parameters using a Bayesian optimization method with the goal of maximizing motion speed and minimizing power consumption, thereby obtaining the robot's typical gait; and testing the typical gait using the robot prototype in various terrains. The amphibious biomimetic turtle robot of the present invention integrates motion data from real prototypes, measured data of biomimetic turtle fins on a mechanical platform, and fluid dynamics data obtained from finite element simulation. Through a Bayesian optimization strategy, it achieves highly adaptive gait generation with coordinated optimization of energy consumption and motion performance.

[0083] Specifically, a gait design method for a 12-DOF (quadrupedal x 3-DOF / leg) biomimetic turtle amphibious robot includes the following steps:

[0084] S1. Design a CAD model of a biomimetic turtle amphibious robot and manufacture a prototype. Soft fins made of silicone can increase the adhesion between the biomimetic drive device and the medium. The robot's main control board is a Raspberry Pi 4B, and a power meter that monitors the robot's motion power consumption is installed at the connection point between the circuit system and the model aircraft's lithium battery.

[0085] S2. Import the CAD model of the biomimetic turtle fin into Fluent and analyze the changes in lift and drag after the angle of attack changes at a certain flow velocity, thus providing a basis for the swimming gait design of the turtle-inspired amphibious robot. Using the same drive structure and materials as the robot, a separate biomimetic drive device is fabricated and fixed to a three-dimensional mechanical sensor. The three-dimensional mechanical sensor is fixed in a cuboid container filled with particulate media. Mechanical sensor data of the biomimetic drive device under common motion parameter conditions are collected to provide a basis for the design of the robot's land-based gait.

[0086] S3. Based on the robot's CAD model, determine the improved DH parameters and complete the kinematic modeling of the biomimetic drive device. Determine the working range of each joint based on the actual working conditions of the robot prototype, and import the modeling results into the MATLAB robot toolbox. Use the Monte Carlo method to generate joint angles, thereby analyzing the workspace of the biomimetic drive device. Based on the obtained workspace, use a method of traversing motion parameters to obtain the power consumption data of the prototype. Plot surface graphs of core motion parameters and power consumption data to analyze data trends. Use a backpropagation neural network to fit the experimental data of core motion parameters and power consumption, obtain the trained model, and import it into a dynamics simulator to obtain high-fidelity robot power consumption data in a simulation environment.

[0087] S4. Based on the robot's CAD model, an interactive model of the robot is built in the Webots dynamics simulator. A GPS sensor is set up in the dynamics simulator to obtain the robot's movement speed through position difference. Using core motion parameters as the gait design objective, the motion parameters are changed, and the robot executes these gait parameters in the dynamics simulator to obtain the corresponding power consumption and movement speed data. With minimum power consumption and maximum movement speed as optimization objectives, the above data is normalized to obtain the value of the objective function. The calculated value of the objective function is input into a Bayesian optimization algorithm, and the optimized gait parameters are obtained through iteration to determine the optimal gait for a single biomimetic drive device.

[0088] S5. Referring to a biomimetic quadruped robot, by changing the timing of movements between different limbs, the designed gait can be obtained. The robot prototype adopted the above gait and tested its movement performance on various terrains.

[0089] Furthermore, the influence of the biomimetic turtle fin material on its mechanical properties was investigated. Four common materials—PLA, TPU95, Ecoflex 00-50, and Dragon Skin 30—were selected to fabricate the biomimetic turtle fin. The drive mechanism adopted the same gait as the robot, and three-dimensional mechanical data were collected in a water tank and in a granular medium. The correspondence between the finite element simulation results and the mechanical curves was analyzed, and the influence of the material on the movement of the drive mechanism in the granular medium was also analyzed.

[0090] A data-driven method for designing the gait of a turtle-inspired amphibious robot mainly includes the following steps:

[0091] S1. Design a CAD model of a turtle-inspired amphibious robot and build a physical prototype. (See reference...) Figure 1 (a) shows the biomimetic prototype; and (b) shows the CAD model of the turtle-inspired amphibious robot. Specifically, the biomimetic turtle fins are made of Ecoflex 00-50 silicone material to enhance the adhesion and friction characteristics of the drive unit with different media, such as water, particulate matter, and hard surfaces. The main controller is a Raspberry Pi 4B single-board computer, and a high-precision power meter with a range of 0-1080W and an accuracy of 0.66% is integrated into the circuit system. This power meter is installed between the model aircraft's lithium battery and the drive circuit to monitor the robot's motion power consumption in real time.

[0092] S2. Conduct multi-dimensional analysis of the biomimetic turtle fin's mechanical properties. Import the biomimetic turtle fin CAD model into the computational fluid dynamics software Ansys Fluent to simulate and analyze the lift and drag characteristics of the fin as a function of the angle of attack under an incoming current velocity of 0.3 m / s. This analysis provides a theoretical basis for the optimized design of underwater swimming gait, particularly the selection of the angle of attack during the power stroke. For details, see... Figure 2 The simulation results of lift and drag of the biomimetic turtle fin are shown in the figure at an incoming flow velocity of 0.3 m / s. The definition of ψ relative to the flow direction is shown in the figure. A specific angle of attack of 15° can effectively balance lift and drag and optimize propulsion efficiency. Based on the CAD model of S1, a single biomimetic turtle fin test device with the same biomimetic drive mechanism as the robot's drive mechanism was fabricated, such as... Figure 3The diagram shows a model of a biomimetic turtle fin mechanical testing device. It mainly includes a guide rail 1, a water tank 2, a three-dimensional force sensor 3, a granular medium 4 (gravel), and a single biomimetic turtle fin testing device. The single biomimetic turtle fin testing device is fixed on a high-precision three-dimensional force sensor 3 with a range of 0-200N and an accuracy of 0.1N, and placed in an experimental container filled with typical granular medium gravel. The guide rail can assist in adjusting the motion path or position of the testing device. The testing device is controlled to execute a typical land movement gait intended for a robot, and three-dimensional force data, including longitudinal force, lateral force, and support force, are collected during its movement. These measured data directly reflect the physical interaction characteristics of the turtle fin with complex terrain, providing key input for the design of the movement gait. To evaluate the influence of materials on propulsion performance, various materials were selected to make the turtle fin, including (a) Ecoflex 00-50, (b) DragonSkin 30, (c) PLA, and (d) TPU 95. Specifically, for example... Figure 4 As shown. The above experiments were conducted in both fluid and particulate media environments. Figure 5 The mechanical testing apparatus and the three-dimensional force curves of the turtle fins in water are shown. (a) Photograph of the mechanical testing apparatus. (b) Longitudinal force of the turtle fins in water. (c) Lateral force of the turtle fins in water. (d) Support force of the turtle fins in water. The shaded area represents the standard error band. Figure 6 A schematic diagram of the turtle fin's gait and three-dimensional force curves are shown. (a) Schematic diagram of the turtle fin's gait. (b) Longitudinal force of the turtle fin in the granular medium. (c) Lateral force of the turtle fin in the granular medium. (d) Support force of the turtle fin in the granular medium. The shaded area represents the standard error band. The mechanical responses of different materials under the same state are analyzed and compared, and the material with the best overall performance is selected.

[0093] Although Figure 2 Computational fluid dynamics simulations primarily study the relationship between hydrodynamic lift / drag and angle of attack. However, due to limitations in simulating complex fluid-structure interactions with deformable materials, they essentially assume an idealized rigid fin structure. Similarly, the Webots dynamics simulator uses a simplified contact dynamics model to simulate the mechanical properties of the fins, but it cannot fully reproduce the nonlinear viscoelastic characteristics of silicon-based materials. The results show that material compliance has a significant impact on the force distribution curves.

[0094] In aquatic environments, TPU 95 material exhibits significant thrust lag and high drag during the upward stroke. In particulate media, due to enhanced terrain adaptability, the softer silicone material (Ecoflex 00-50) produces higher peak thrust than the rigid polylactic acid material. These experimental curves provide a reference for Webots' contact dynamics parameters, making them closer to real-world behavior, although the simulation still focuses on geometry and kinematic properties.

[0095] The choice of fin material requires striking a critical balance between aquatic efficiency, land traction, and mechanical durability: In terms of aquatic performance, TPU 95 fins generate higher fluid drag during the recovery phase of paddling (see...). Figure 6 This resulted in a slight decrease in swimming speed compared to the Ecoflex fins. The thrust performance of the turtle fins made of Ecoflex 00-50, DragonSkin 30, and PLA materials showed a similar trend. In terms of land-based performance, rigid materials (such as PLA) tended to slip on hard surfaces due to their low friction and poor surface adhesion. While TPU 95 offered better flexibility, it couldn't perfectly integrate with the rigid skeletal support structure (copper rods + carbon fiber), leading to structural buckling under stress. The Ecoflex 00-50, with its embedded skeleton reinforcement, achieved excellent grip through terrain-adaptive deformation while maintaining load-bearing capacity.

[0096] S3. Based on the actual geometric parameters of the robot prototype, a kinematic model of a single three-degree-of-freedom biomimetic turtle fin drive mechanism is established using the improved DH parameter method. The visualized workspace in the robot kinematics simulation is shown below. Figure 7 As shown, this model describes the mapping relationship between joint spatial angles and the pose of the fin end effector in Cartesian space. The kinematic model is implemented using the MATLAB Robotics Toolbox. A large number of joint angle combinations are randomly generated within the joint range of motion using the Monte Carlo method, and the corresponding end effector position point set is calculated, thereby visualizing and determining the workspace reachable by the turtle fin. This workspace defines the physically feasible region of the end effector trajectory in gait design.

[0097] A cycloidal trajectory is chosen to determine the core parameters of the robot's gait. In this context, x and y represent the coordinates of the trajectory points. The parameter α determines the magnitude of the downward force exerted by the turtle fins, which serve as the driving mechanism, and the degree of their forward and backward swinging, while the gait period T determines the fin's movement speed.

[0098]

[0099] On the physical prototype, core gait parameter combinations were systematically sampled. For each set of parameters... With T, run the robot and record its steady-state motion power P using an onboard power meter. Plot the response surface of the parameter space versus the power. Figure 8 An experimental data fitting surface demonstrates the relationship between robot motion energy consumption and gait period and wheel parameter α. A nonlinear mapping model from core gait parameters to power consumption is constructed using a backpropagation neural network. This neural network consists of a 2-node input layer, a 15-node hidden layer, and a 1-node output layer, achieving high fitting accuracy on the training set with a mean squared error (MSE) of 3.833 and a coefficient of determination (COP). This provides high-fidelity power consumption prediction capabilities for subsequent simulation optimization.

[0100] S4. Based on the robot's CAD model and physical characteristics, a high-fidelity interactive model of the robot is built in an open-source multibody dynamics simulator. Virtual sensors are configured in the model to obtain the robot's motion speed. Core gait parameters are used as the basis for this process. Let T be the optimization variables, and within the parameter range defined in S3, apply the Bayesian optimization algorithm. This algorithm uses a Gaussian process as a surrogate model to fit the objective function and balances exploration and utilization by acquiring a function. The iterative process eventually converges to the maximum point of the objective function, obtaining the optimal combination of gait parameters. Figure 9 The iterative convergence process of the Bayesian optimization algorithm is demonstrated. The optimal combination of gait parameters is: And T=1.006.

[0101] S5. Based on the optimal core gait parameters obtained in S4, generate the desired trajectory of the end effector of a single turtle fin. For example... Figure 10 The diagram illustrates the joint motion trajectory generated using three servos on one leg as an example. By adjusting the motion phase difference between the robot's four limbs, a coordinated full-body gait pattern is generated. Figures 11A to 11D The time patterns of limb contact and movement phase decomposition in four gait types are shown respectively: walking gait with asynchronous forelimbs and hindlimbs; symmetrical gait with completely synchronized left and right limbs, forming a symmetrical stroke trajectory; jumping gait with brief pulse jumps of the forelimbs and delayed contact of the hindlimbs; and swimming gait with the forelimbs providing propulsion and the hindlimbs performing turning adjustments.

[0102] The optimized typical gait program was deployed to a physical prototype built with S1. Furthermore, the robot's motion performance was tested on various representative terrains, such as... Figure 12 As shown.

[0103] In summary, this invention proposes a data-driven gait design method for a turtle-inspired amphibious robot: it integrates motion data from real prototypes, measured data of biomimetic turtle fins on a mechanical platform, and fluid dynamics data obtained from finite element simulations, and uses a Bayesian optimization strategy to achieve highly adaptive gait generation with coordinated optimization of energy consumption and motion performance.

[0104] By applying this invention, an amphibious biomimetic turtle robot integrates motion data from a real prototype, measured data of biomimetic turtle fins on a mechanical platform, and fluid dynamics data obtained from finite element simulation. Through a Bayesian optimization strategy, it achieves highly adaptive gait generation with coordinated optimization of energy consumption and motion performance.

[0105] The turtle-inspired amphibious robot gait design method of this invention integrates the reliability of real prototype motion data, the physical background of measured data of biomimetic turtle fins on a mechanical platform, and the fluid dynamics inspiration obtained from finite element simulation, further improving the convenience and adaptability of amphibious robot gait design. Specifically, the above technical solution has the following advantages:

[0106] 1. Deeply integrates multi-source physical data, innovatively combining measured power consumption data from physical prototypes, three-dimensional interactive force data obtained from biomimetic turtle fins on a dedicated mechanical platform, and hydrodynamic laws revealed by computational fluid dynamics simulation, providing a solid physical background support for gait design and significantly improving the reliability and environmental adaptability of the design results;

[0107] 2. Before designing the algorithm, the impact of the turtle fin material on propulsion performance was investigated, achieving coordinated optimization of hardware and software design. This not only optimized gait performance but also avoided control signal distortion or excessive hardware wear caused by neglecting hardware characteristics such as material stiffness and friction coefficient, thus extending hardware lifespan.

[0108] 3. The gait design process fully considers the influence of the mechanical properties of the biomimetic turtle fin itself and the interaction with the medium. The mechanical characteristics are revealed from the perspective of fluid dynamics simulation and particle medium interaction experiments, and the discovered mechanical laws are applied to the gait design.

[0109] 4. Abandoning the traditional, complex, and potentially distorted multi-rigid-body dynamics power consumption modeling, this paper innovatively employs a BP neural network based on measured data from a physical prototype to establish an accurate mapping model from gait parameters to power consumption. This model is seamlessly integrated into the dynamics simulation environment, providing highly reliable power consumption predictions for Bayesian optimization.

[0110] 5. Based on the improved DH parameter method, precise kinematic modeling and Monte Carlo workspace analysis strictly define the physical feasible range of gait design parameters, ensuring that the gait parameters generated by the Bayesian optimization process are physically realizable;

[0111] 6. To address the complex nonlinear relationship between gait parameters and motion performance, Bayesian optimization algorithm is used in the dynamics simulator to optimize motion speed and power consumption. The algorithm efficiently finds the global optimal solution in the parameter space, reducing distortion caused by inaccurate simple multi-rigid-body dynamics modeling and improving the effectiveness and efficiency of gait design algorithm.

[0112] 7. The optimized gait not only performs well in the simulation environment, but is also fully verified through rigorous multi-terrain testing on the physical prototype, proving the excellent simulation-to-real-world transfer capability of this method.

[0113] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0114] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0115] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0116] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0117] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0118] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0119] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0120] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0121] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0122] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0123] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0124] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0125] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A data-driven gait design method for a turtle-inspired amphibious robot, characterized in that, Includes the following steps: S1. Constructing a robot physical platform: Design a CAD model of a turtle-like amphibious robot and make a physical prototype. Use flexible materials to make biomimetic turtle fins and use a power meter to monitor the power consumption of the robot in real time during its movement. S2. Multi-source mechanical data acquisition: Hydrodynamic data of turtle fins are acquired through computational fluid dynamics simulation, and three-dimensional interaction force data of turtle fin movement are measured in particulate media through three-dimensional mechanical sensors; the influence of various materials on mechanical properties is evaluated and the material with the best comprehensive performance is selected. S3. Kinematic Modeling and Power Consumption Mapping: Based on the robot CAD model and actual geometric parameters, determine the DH parameters, establish a single biomimetic turtle fin kinematic model, and use the Monte Carlo method to determine the workspace; by traversing the core gait parameter combinations and collecting the power consumption data of the physical prototype, use a backpropagation neural network to establish a nonlinear mapping model from gait parameters to power consumption. S4. Bayesian optimization of gait parameters: A robot interaction model is built in a dynamic simulation environment. The optimization objectives are to maximize the movement speed and minimize the power consumption. The normalized objective function is input into the Bayesian optimization algorithm. The objective function is fitted using a Gaussian process surrogate model. The optimal combination of gait parameters is obtained by iterative convergence through the balancing exploration and utilization of the acquisition function. S5. Gait Coordination: Generate single-limb motion trajectories based on optimal gait parameters, and generate a fully coordinated gait by adjusting the phase difference between limbs.

2. The method according to claim 1, characterized in that, Step S2 specifically includes: Import the turtle fin CAD model into computational fluid dynamics software to simulate the lift and drag characteristics under a set flow velocity with varying angle of attack. Fabricate a single-unit testing device identical to the robot drive mechanism, fix it to a three-dimensional force sensor, and place it in a granular medium container; The control and testing device executes a typical land gait, and collects three-dimensional data of longitudinal force, lateral force, and support force; The turtle fins were made of various flexible and rigid materials, and repeated experiments were conducted in fluid environments and particulate media to compare the mechanical responses and select the appropriate material.

3. The method according to claim 1 or 2, characterized in that, The step S3 of establishing the power consumption mapping model includes: The kinematic model is established based on the robot CAD model and the DH parameters determined by the actual geometric parameters. A large number of angle combinations are randomly generated within the joint motion range. The workspace is visualized using the Monte Carlo method to define the feasible domain of gait parameters. The system samples the core gait parameter combination, records the steady-state motion power of the physical prototype, and plots the parameter-power consumption response surface. A backpropagation neural network with hidden layers is used to train the model with core gait parameters as input and power consumption as output. After obtaining a high-precision nonlinear mapping model, it is integrated into the dynamics simulator.

4. The method according to claim 3, characterized in that, The core gait parameters include: The trajectory amplitude parameters that determine the force exerted by the turtle fins and the degree of swaying; Gait period parameters that determine the movement speed of turtle fins.

5. The method according to claim 3, characterized in that, The dynamics simulator adopts a simplified contact dynamics model, and its contact parameters are calibrated based on the three-dimensional force curve measured in step S2 to approximate the nonlinear viscoelastic characteristics of real silicone materials.

6. The method according to claim 3, characterized in that, The Bayesian optimization in step S4 specifically includes: Virtual sensors are configured in the dynamics simulator to acquire the robot's motion speed; Using the parameter range defined in step S3 as the search space, the normalized speed and power consumption are used as the objective function; A probabilistic proxy model of the objective function is established through a Gaussian process, and the sampling function is used to guide the parameter space sampling. Iteratively update the surrogate model and evaluate new sampling points until the objective function converges to the optimal solution.

7. The method according to claim 1, characterized in that, The gait coordination in step S5 includes: Generate the periodic trajectory of the single-limb end effector based on the optimal core parameters; By setting the phase difference of movement between different limbs, quadrupedal coordination gait patterns are constructed, including walking gait, symmetrical gait, jumping gait and swimming gait.

8. The method according to claim 1, characterized in that, The method integrates the following data sources: Real-time power consumption data collected from the motion of the physical prototype; Three-dimensional interaction force data between turtle fins and medium measured by a mechanical platform; Hydrodynamic laws revealed by computational fluid dynamics simulations; Among them, Bayesian optimization is used to achieve collaborative optimization of gait parameters driven by multiple data sources.

9. The method according to claim 1, characterized in that, The flexible material is a silicone-based composite material, which is reinforced by an embedded skeleton to achieve a balance between terrain-adaptive deformation and load-bearing capacity.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the data-driven gait design method for a turtle-like amphibious robot as described in any one of claims 1 to 9.

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