Sea-turtle-imitating amphibious robot path tracking method based on model predictive control

Abstract

The invention discloses a sea-turtle-imitating amphibious robot path tracking method based on model predictive control, which comprises the following steps of: firstly, establishing a sea-turtle-imitating amphibious robot multi-rigid-body dynamic simplified model containing a water flow dynamic coefficient, and simplifying a control dimension in combination with biological motion characteristics; analyzing and quantifying water flow dynamic parameters through computational fluid mechanics simulation in combination with a steady-state dragging test, a rotating arm test and an unsteady planar motion mechanism; constructing a robot model and an underwater environment in a dynamic simulator; a model predictive control-fuzzy logic cascade controller is designed, an upper layer generates reference force and torque through rolling horizon optimization, and a lower layer maps the reference force and torque into an actuator instruction based on a fuzzy rule; and finally, verifying and evaluating the robustness and tracking precision of the controller in a simulation environment. The method effectively deals with nonlinear water flow dynamic effect, parameter uncertainty and unmodeled environment interference, and has high control precision and strong robustness through U-shaped and 8-shaped path verification.

Description

TECHNICAL FIELD

[0001] The present application relates to amphibious robot technology, in particular to a turtle-imitating amphibious robot path tracking method based on model predictive control. BACKGROUND

[0002] In aquatic environments, turtle species exhibit superior complex path tracking capabilities due to their unique hydrodynamic morphology and flexible three-dimensional movement mechanisms. This survival strategy not only helps to avoid predators and efficiently forage, but also enables long-distance migration. This biological intelligence provides inspiration for the development of bionic robot systems, with high-precision path tracking control technology being a key challenge for autonomous underwater operations.

[0003] The basis for precise control lies in establishing an accurate hydrodynamic model. Small deviations in hydrodynamic coefficients can cause nonlinear error accumulation in kinematic equations, significantly weakening the robustness of path tracking control. Although traditional modeling methods using empirical formulas have advantages in terms of computational efficiency, they are difficult to meet the modeling needs of turtle robots due to their unique carapace curvature and the resulting complex vortex structure, which deviates from existing hydrodynamic coefficient databases. Experimental fluid mechanics methods such as towing tank tests can obtain high-fidelity data, but are limited by equipment dependency and high costs, limiting their practical application. In contrast, the computational fluid dynamics (CFD) method solves the Navier-Stokes equation numerically to achieve parameterized analysis of hydrodynamic responses under different conditions, thereby facilitating the establishment of high-fidelity hydrodynamic models.

[0004] The scientific community has invested significant effort in developing robust control strategies to address complex fluid dynamics and parameter uncertainties in aquatic environments. The widely used PID controller has difficulty in parameter calibration, making it difficult to ensure accuracy. Fuzzy logic controllers (FLC) perform better in nonlinear systems by handling uncertainties, but their effectiveness still depends on experience. Sliding mode controllers are not sensitive to environmental disturbances, but are constrained by oscillation effects when switching inputs. In contrast, the model predictive control (MPC) framework explicitly integrates kinematic constraints through the rear-view optimization method, effectively addressing parameter uncertainties, operator experience deficiencies, and control output fluctuations.

[0005] It should be noted that the information disclosed in the above background section is only for understanding the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0006] The main purpose of the present application is to overcome the defects in the above background art, and to provide a turtle-imitating amphibious robot path tracking method based on model predictive control.

[0007] To achieve the above object, the present invention adopts the following technical solutions: A path tracking method for a turtle-like amphibious robot based on model predictive control includes the following steps: S1. Establish a multi-rigid-body dynamic model of a turtle-like amphibious robot, derive simplified dynamic equations including hydrodynamic coefficients, and simplify the control dimension based on biological motion characteristics; S2. Quantify hydrodynamic parameters through computational fluid dynamics simulations combined with steady-state drag tests, rotating arm tests, and unsteady planar motion mechanism analysis; S3, building the robot model and underwater environment in the dynamics simulator; S4. Design model predictive control-fuzzy logic cascade controller: The upper-level model predictive controller generates reference forces and torques through rolling horizon optimization; The lower-level fuzzy logic controller adaptively maps the reference force and torque into actuator commands based on fuzzy rules; S5. Conduct path tracking control verification in a simulation environment to evaluate controller robustness and tracking accuracy.

[0008] Furthermore, the establishment of the simplified kinetic model in step S1 specifically includes: The robot's dual symmetry about the longitudinal-transverse plane and the longitudinal-vertical plane is used to ignore the coupling effect of longitudinal, transverse and yaw motions; Based on the bionic motion characteristics, the active control dimensions are limited to longitudinal propulsion force and yaw moment; Integrate added mass effects, linear damping terms, and nonlinear fluid resistance terms into the dynamic equations.

[0009] Furthermore, the quantification of the hydrodynamic parameters in step S2 specifically includes: The velocity-dependent damping factor was identified through drag tests, and the drag data at different flow rates were correlated and fitted with polynomial coefficients; Identify the resistance to rotational motion through the rotating arm test and fit the relationship between yaw moment and angular velocity; Inertial effects are identified through analysis of unsteady planar motion mechanisms, and acceleration-related hydrodynamic coefficients are extracted using Fourier analysis. The superposition grid technology is used to analyze the transient flow field, and data transmission between grids is realized through multi-region calculation domains.

[0010] Furthermore, step S3 specifically includes: The robot's hardware architecture is designed using a bionic propulsion system, including a central waterproof cabin and multiple three-degree-of-freedom flippers; Import a simplified robot model into the dynamics simulator and build an underwater environment to reduce parametric simulation distortion.

[0011] Further, the input generation of the model predictive controller in step S4 specifically comprises: Obtaining the desired position and heading angle by line-of-sight method; Decoupling the path following problem into thrust channel and torque channel: The thrust channel controls the longitudinal velocity by adjusting the fin oscillation frequency; The torque channel realizes the direction adjustment by cooperatively regulating the fin amplitude difference and tail rudder angle.

[0012] Further, the optimization process of the model predictive controller in step S4 specifically comprises: Solving the finite-time optimal control problem at discrete time points to generate the optimal control sequence within the prediction step; Adopting the moving horizon strategy to output the first element of the sequence as the current control action.

[0013] Further, the design of the fuzzy logic controller in step S4 specifically comprises: Building a fuzzy rule table to define the mapping relationship between the reference force / torque error and the actuator instruction; Processing the nonlinear and transient conditions through asymmetric response surface to balance the dynamic response and stability.

[0014] Further, the cooperation mechanism of the model predictive control-fuzzy logic cascade controller specifically comprises: The upper model predictive controller explicitly integrates the kinematic constraints to optimize the reference force / torque to cope with parameter uncertainty; The lower fuzzy logic controller compensates for the unmodeled fluid dynamics coupling and environmental disturbances through adaptive mapping.

[0015] Further, the path tracking verification in step S5 specifically comprises: Designing a U-shaped path containing straight lines and circular arcs to evaluate the straight line tracking and turning ability; Designing an 8-shaped path with bidirectional curvature change to evaluate the lateral error suppression and transient stability; Applying a random hydrodynamic disturbance model to test the anti-interference robustness of the controller.

[0016] A computer program product comprising a computer program which, when executed by a processor, implements the model predictive control-based sea-turtle-like amphibious robot path tracking method.

[0017] The present application has the following beneficial effects: The application provides a turtle-like amphibious robot path tracking method based on model predictive control, a high-fidelity fluid dynamics model is established through parameterization driven by computational fluid dynamics (CFD), and a hierarchical control framework integrating model predictive control (MPC) and fuzzy logic controller (FLC) is provided, the method effectively solves the problems of nonlinear fluid dynamics interaction, coefficient uncertainty and unmodeled environmental disturbance by combining the high-fidelity hydrodynamic model obtained through CFD numerical calculation and the stability of MPC-FLC cascade control.

[0018] The turtle-like amphibious robot platform established based on the application has reliable characteristics, the propulsion and steering of the turtle-like bionic prototype can be decoupled during movement, which provides a stable foundation for the path tracking algorithm of the robot, meanwhile, the simplified dynamics model based on the multi-rigid-body dynamics model parameterizes the influence of the water environment on the robot as hydrodynamic coefficients, and the control dimension is simplified through mechanical structure analysis and bionic prototype analysis, in addition, through integration of steady-state drag test, rotating arm simulation and PMM analysis, the corresponding hydrodynamic coefficients can be obtained through CFD simulation by using STAR-CCM+ software, and a high-fidelity hydrodynamic model is established, and a hydrodynamic environment model suitable for the turtle-like robot is also established in the dynamics simulator Webots, so that the model distortion problem in the general parameterized simulation process is reduced, and the running performance of the constructed path tracking framework can be more systematically evaluated.

[0019] The model predictive control framework of the application explicitly integrates kinematic constraints through receding horizon optimization, compared with the traditional PID control strategy and the sliding mode controller, the model predictive control framework can more effectively cope with problems such as parameter uncertainty, insufficient operator experience and control output oscillation, and a double-layer control strategy combining model predictive control and fuzzy logic control is proposed, the upper MPC optimizes the reference force and torque through the receding horizon optimization method, and the lower FLC adaptively maps the reference signal to the actuator instruction based on fuzzy rules, thereby effectively coping with nonlinear hydrodynamic interaction, parameter uncertainty and unmodeled environmental disturbance, in addition, the proposed control framework is compared through U-shaped path tracking simulation and 8-shaped path tracking, and higher control accuracy and more agile movement of the robot are realized.

[0020] Other beneficial effects in the embodiments of the application will be further described below. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is the coordinate system configuration of the amphibious robot system in the embodiments of the application.

[0022] Figure 2 is the dynamic model and joint configuration of the amphibious robot system in the embodiments of the application.

[0023] Figure 3 This is an analysis of the fluid dynamics characteristics of the bionic turtle robot in an embodiment of the present invention (based on CFD simulation): (a) flow field velocity distribution at an inflow velocity in the swing direction of 0.6 m / s; (b) velocity distribution around the bionic turtle at a calculation domain radius of 3.3 meters at an inflow velocity of 0.5 m / s; (c) flow field velocity distribution during pure pitch motion at 1 Hz; (d) relationship between pitch direction resistance and flow velocity; (e) relationship between yaw angular velocity and yaw moment; (f) time-dependent resistance and Fourier fitting results during pure pitch motion at 1 Hz.

[0024] Figure 4 This is a snapshot of a turtle-inspired robot in the Webots dynamics simulator in an embodiment of the present invention.

[0025] Figure 5 This is a block diagram of a turtle-inspired robot path tracking control in an embodiment of the present invention.

[0026] Figure 6 The input and output rules of the fuzzy inference system in the embodiment of the present invention are: (a) Input and With output The relationship between; (b) input and With output The relationship between them.

[0027] Figure 7 Performance evaluation of the path tracking controller in an embodiment of the present invention: (a) visualization of the U-shaped path compared to the actual motion; (b) time evolution of the lateral path tracking deviation.

[0028] Figure 8 It is the signal output of the MPC-FLC control strategy in the U-shaped trajectory tracking in the embodiment of the present invention.

[0029] Figure 9 Performance evaluation of the path tracking controller in an embodiment of the present invention: (a) Visual comparison of the figure-eight path and the actual motion; (b) Time evolution of the lateral path tracking deviation.

[0030] Figure 10 It is the signal output of the MPC-FLC control strategy in the embodiment of the present invention in the figure-8 trajectory tracking.

[0031] Figure 11 This is a flow chart of the path tracking method of the turtle-like amphibious robot based on model predictive control of the present invention. DETAILED DESCRIPTION

[0032] The embodiments of the present application will be described in detail below. It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present application and its applications.

[0033] The present application aims to solve the problems of nonlinear fluid dynamics interaction, coefficient uncertainty and unmodeled environmental disturbance in the path tracking of a turtle-like amphibious robot. A path tracking method for a turtle-like amphibious robot based on model predictive control is proposed. A high-fidelity fluid dynamics model is established through CFD-driven parameterization, and a hierarchical control framework integrating model predictive control (MPC) and fuzzy logic control (FLC) is constructed. This method relies on a reliable platform for decoupling propulsion and steering of the turtle-like robot, combines a simplified dynamic model, accurate acquisition of hydrodynamic parameters, and a Webots simulation environment. Through U-shaped and 8-shaped path verification, higher control accuracy and motion agility are achieved, and problems such as parameter uncertainty can be effectively addressed.

[0034] Referring to Figure 11 The present application provides a path tracking method for a turtle-like amphibious robot based on model predictive control, comprising the following steps: Step S1, a multi-rigid-body dynamics model of the turtle-like amphibious robot is established, a simplified dynamics equation containing hydrodynamic coefficients is derived, and the control dimension is simplified based on biological motion characteristics.

[0035] In some embodiments, the establishment of the simplified dynamics model in step S1 specifically includes: utilizing the double symmetry of the robot with respect to the longitudinal-horizontal plane and the longitudinal-vertical plane, ignoring the coupling effects of longitudinal, lateral and yaw motion; based on the bionic motion characteristics, limiting the active control dimension to longitudinal propulsion force and yaw moment; integrating the added mass effect, linear damping term and nonlinear fluid resistance term in the dynamics equation.

[0036] Step S2, through computational fluid dynamics simulation, combining steady-state drag test, rotating arm test and unsteady planar motion mechanism analysis, quantifying hydrodynamic parameters.

[0037] In some embodiments, the quantification of hydrodynamic parameters in step S2 specifically includes: identifying the speed-dependent damping factor through the drag test, correlating the resistance data at different flow rates and fitting the polynomial coefficients; identifying the rotational motion resistance through the rotating arm test, fitting the relationship between yaw moment and angular velocity; identifying the inertia effect through unsteady planar motion mechanism analysis, extracting the acceleration-dependent hydrodynamic coefficients using Fourier analysis; using the superposition grid technique to analyze the transient flow field, and realizing data transmission between grids through multi-zone calculation domain.

[0038] Step S3, constructing the robot model and underwater environment in the dynamics simulator.

[0039] In some embodiments, step S3 specifically comprises: designing a robotic hardware architecture with a biomimetic propulsion system, including a central waterproof cabin and multiple three-degree-of-freedom fins; importing a simplified model of the robot into a dynamics simulator and building an underwater environment to reduce parameterized simulation distortion.

[0040] Step S4, designing a model predictive control-fuzzy logic cascaded controller: the upper-layer model predictive controller generates reference forces and torques through rolling horizon optimization; the lower-layer fuzzy logic controller adaptively maps the reference forces and torques to actuator commands based on fuzzy rules.

[0041] In some embodiments, the input generation of the model predictive controller in step S4 specifically comprises: obtaining the desired position and heading angle through the line-of-sight method; decoupling the path tracking problem into thrust and torque channels: the thrust channel controls the longitudinal velocity by adjusting the fin oscillation frequency; the torque channel adjusts the direction by cooperatively regulating the fin amplitude difference and the tail rudder angle.

[0042] In some embodiments, the optimization process of the model predictive controller in step S4 specifically comprises: solving a finite-time optimal control problem at discrete time points to generate an optimal control sequence within a prediction step; using a moving horizon strategy, outputting the first element of the sequence as the current control action.

[0043] In some embodiments, the design of the fuzzy logic controller in step S4 specifically comprises: constructing a fuzzy rule table to define the mapping relationship between reference force / torque error and actuator command; processing nonlinear and transient conditions through an asymmetric response surface to balance dynamic response and stability.

[0044] In some embodiments, the cooperation mechanism of the model predictive control-fuzzy logic cascaded controller specifically comprises: the upper-layer model predictive controller explicitly integrates kinematic constraints and optimizes reference forces / torques to cope with parameter uncertainties; the lower-layer fuzzy logic controller compensates for unmodeled fluid dynamics coupling and environmental disturbances through adaptive mapping.

[0045] Step S5, carrying out path tracking control verification in a simulation environment to evaluate the robustness and tracking accuracy of the controller.

[0046] In some embodiments, the path tracking verification in step S5 specifically comprises: designing a U-shaped path containing straight lines and circular arcs to evaluate straight line tracking and turning ability; designing an 8-shaped path with bidirectional curvature variation to evaluate lateral error suppression and transient stability; applying a random water dynamic disturbance model to test the anti-interference robustness of the controller.

[0047] The main technical advantages of the present application are that: by bionics design, the biological characteristics of decoupling of propulsion and steering during turtle movement are fully utilized to provide a stable basis for path tracking; combined with the high-precision modeling method of computational fluid dynamics (CFD), the steady-state drag test, the rotating arm test and the unsteady planar motion mechanism analysis are integrated, the water dynamic parameters are quantified systematically, and the vortex modeling deviation caused by the curvature of the carapace and the high-cost limitations of experimental fluid mechanics of traditional empirical formula are overcome; innovatively, model predictive control (MPC) and fuzzy logic control (FLC) cascade architecture are adopted, wherein the upper MPC explicitly handles kinematic constraints and generates reference forces / torques through rolling time domain optimization, effectively dealing with parameter uncertainty and control oscillation problems, and the lower FLC adaptively maps actuator commands based on fuzzy rules to compensate for nonlinear fluid coupling and unmodeled environmental disturbances in real time; relying on the dynamics simulator to build a high-fidelity hydrodynamic environment, the parameterized simulation distortion is greatly reduced, and through the comparison and verification of U-shaped and 8-shaped paths, it is proved that this method has higher control accuracy, stronger anti-interference robustness and more agile dynamic response capability in complex trajectory tracking.

[0048] The specific embodiments of the present application, algorithm examples and experimental verification are further described below.

[0049] A sea turtle inspired amphibious robot path tracking method based on model predictive control mainly includes the following aspects: a multi-rigid-body dynamics model of the sea turtle inspired amphibious robot is established, and a simplified dynamics model with hydrodynamic coefficients is derived; a grid calculation model of the robot is built in STAR-CCM+, and steady-state drag test, rotating arm test and unsteady planar motion mechanism (PMM) analysis are carried out; the CAD model of the robot is imported into the dynamics simulator webots, and a simulation pool environment is built; a fuzzy rule table is designed; a model predictive control-fuzzy logic cascade controller is established; U-shaped path tracking control and 8-shaped path tracking control simulation are carried out in the dynamics simulator. The sea turtle inspired amphibious robot path tracking method based on model predictive control proposes a double-layer control strategy, which combines model predictive control and fuzzy logic control. The upper MPC realizes the optimization of the reference force and torque through rolling time domain optimization, and the lower FLC adaptively maps these reference values to actuator commands based on fuzzy rules, effectively dealing with water dynamic nonlinear coupling, coefficient uncertainty and unmodeled environmental disturbances.

[0050] The present application provides a sea turtle inspired amphibious robot path tracking method based on model predictive control, which comprises the following steps: S1, a sea turtle inspired amphibious robot coordinate system is established, and the spatial configuration relative to the global coordinate system is given. According to the established ship dynamics method, the dynamic behavior of the system can be represented in the robot fixed coordinate system as:

[0051]

[0052] where, and correspond to the rigid body inertia matrix and the Coriolis- centripetal matrix, respectively, while and are used to describe the hydrodynamic added mass effect. and represent the viscous damping force and the hydrostatic restoring force, respectively, where represents the generalized control input vector.

[0053] Considering the robot's double symmetry with respect to the longitudinal-lateral (xoy) and planar longitudinal-vertical (xoz) planes, the coupling between the longitudinal, lateral and yaw motions can be neglected. Based on the biological observation of the tortoise's motion pattern and the engineering simplification objective, it is determined that only the longitudinal and yaw motions need to be actively controlled during planar motion. Following this biomechanical principle and combining the latest research findings, the simplified dynamics model for planar navigation is expressed as follows:

[0054]

[0055] where, , and quantify the added mass effect, while , and correspond to the linear damping coefficients. The quadratic damping terms , and capture the nonlinear hydrodynamic drag. The control input quantities and control the propulsion and yaw moments, respectively (refer to Figure 5 ). denotes the total mass of the robot, is the vertical axis moment of inertia.

[0056] S2, the established dynamics equations are expressed in the matrix form and Key fluid-structure interaction components are integrated, which respectively capture hydrodynamic inertial and viscous dissipation characteristics. To construct a high-fidelity parametric model, these uncertain hydrodynamic parameters are systematically identified using computational fluid dynamics simulations. The invention focuses on quantifying three major hydrodynamic dependencies: 1) velocity-dependent damping factors, 2) rotational motion resistance, and 3) inertial effects induced by acceleration. The parameter identification process combines two complementary computational frameworks: steady-state hydrodynamic simulations including tow tank and rotating arm tests, and unsteady-state hydrodynamic simulations using standardized PMM test protocols. The invention uses STAR-CCM+ software for CFD simulations.

[0057] S3, Turtles achieve efficient locomotion in unsteady media by means of flexible three-degree-of-freedom flippers, while maintaining body stability with low center of gravity and intermittent ground contact. These biological principles provide inspiration for the mechanical design of a biomimetic robotic system. The experimental platform employs a biomimetic propulsion system, with a compact overall size of only 430 mm in total length, and a net mass of 10.48 kg achieved through optimized structural design.

[0058] The hardware architecture consists of two major subsystems: a central carapace structure and three three-degree-of-freedom biomimetic flipper mechanisms. The central carapace is a waterproof cabin made of a carbon fiber support frame, housing all electronic components. The main control system is equipped with a Raspberry Pi 4B single-board computer with 4 GB of memory, enabling wireless communication only when floating on water and moving on land, while underwater propulsion is achieved through pre-programmed instructions.

[0059] A nine-axis inertial measurement unit (IMU) MPU-9250 is used to monitor three-axis acceleration and angular velocity (X, Y, Z directions) with a sampling frequency of 100 Hz, enabling quantitative analysis of disturbance dynamics during motion. The drive system is equipped with twelve custom GXYipin waterproof servo motors, each with a maximum output torque of 130 kg·cm. The wireless cable electronic architecture supports autonomous mobility and real-time data transmission capabilities.

[0060] Based on the above robot design, the simplified model is imported into the dynamics simulator Webots.

[0061] S4, When performing a path tracking task, the robot obtains the desired position X d , Y d and the desired heading angle using the line-of-sight (LOS) method Figure 5). The invention proposes a hierarchical model predictive control-fuzzy logic controller (MPC-FLC) architecture. In this framework, the MPC serves as the upper controller to generate the reference force and torque, while the fuzzy logic controller deployed at the lower level maps these reference quantities to the specific actuator commands. This two-layer framework ensures optimal path tracking through predictive optimization, while coping with dynamic uncertainties with the help of adaptive signal allocation.

[0062] Model predictive control provides a systematic framework for regulating nonlinear multivariable systems through finite-time horizon optimization. At each discrete time point , the algorithm computes the optimal control sequence by solving a finite-time optimal control problem over prediction steps. The implemented control action is the first element of this sequence, embodying the hallmark moving horizon strategy in predictive control.

[0063] To tackle the key technical challenges in the field of biomimetic turtle robot motion control, the invention proposes a dual-module control architecture based on fuzzy logic control. The system complexity mainly stems from three core issues: 1) the inherent nonlinear fluid dynamics of the mechanical structure; 2) the uncertainty of fluid dynamics coefficients; 3) the unmeasurability of ocean environment disturbances. Notably, the strong nonlinear relationship between three-dimensional fin movement and dynamic response has not been accurately modeled. This hierarchical control framework aims to achieve path tracking goals. The upper model predictive controller decouples the output into two independent channels: the thrust channel for speed regulation by adjusting the oscillation frequency of the front and rear fins, and the torque channel for direction adjustment by regulating the amplitude difference of the front and rear fins in coordination with the tail fin rudder angle. At the lower control level, a fuzzy logic compensation mechanism is employed to cope with system modeling uncertainties.

[0064] S5, a U-shaped path composed of two straight lines and a semicircular arc, is suitable for evaluating the robot's straight path tracking and turning ability. The invention designs a U-shaped trajectory, which includes a 5-meter-long straight line and a semicircular arc with a radius of 2.5 meters. For this trajectory, three controllers - PID controller, sliding mode controller, and the proposed MPC-FLC strategy - are compared and evaluated. To investigate the robustness of the controller, random hydrodynamic disturbances are applied to the robot system, with the modeling expression as follows:

[0065]

[0066] where represents a normally distributed noise signal with a mean of 0 and a variance of 1.

[0067] The figure-8 path has the characteristics of bidirectional turning and continuous curvature variation, and is a strict benchmark for evaluating the lateral error suppression capability and transient stability of a controller. The figure-8 path is mathematically defined by a parametric equation as follows:

[0068]

[0069] wherein represents a rotation angle.

[0070] A turtle-like amphibious robot path tracking method based on model predictive control mainly includes the following steps: S1, the spatial pose coordinates of the robot are defined as , represents three-axis coordinates, represents the corresponding attitude angle, and the body coordinate system OB-XBYBZB The movement speed of the robot is defined as , represents three-axis velocity, represents the corresponding angular velocity. Specifically, Figure 1 The coordinate system configuration of the amphibious robot system in the embodiment of the application is shown, and the local body attached reference frame and the global inertial coordinate system OE-XEYEZE are described in detail. Based on the legged robot, the autonomous underwater vehicle (AUV) and the bionic underwater robot (BUR), the full body dynamic model of the turtle-like amphibious robot is specifically shown as Figure 2 . Figure 2 The dynamic model and joint configuration of the amphibious robot system in the embodiment of the application are shown, wherein represents the center of the robot body, represents the center of gravity of the robot. f 0s 、f 1s 、f 2s 、f 3s are respectively the contact force vectors of the four fin-shaped limbs, P 0 、P 1 、P 2 、P 3 are respectively the position vectors of the four fin ends, O-XsYsZs is the global inertial coordinate system, and g represents gravity.

[0071] S2, to quantify the axial motion resistance characteristics, hydrodynamic experiments were carried out by simulating the towing conditions along the main translation axis. In these numerical studies, the bionic robot platform was kept in a static position within the controlled fluid domain, while the environmental flow rate was sequentially increased from the static state to 1 m / s. According to the standardized specifications of the International Towing Tank Conference (ITTC), the computational domain size was optimized to minimize the wall interference effects and ensure the solution accuracy.

[0072] Referring to Figure 3 , Figure 3 shows the bionic turtle robot fluid dynamics characteristic analysis (based on CFD simulation) in the embodiments of the application: (a) flow field velocity distribution under 0.6 m / s swing direction inflow velocity. (b) velocity distribution around the bionic turtle at a radius of 3.3 meters in the computational domain under 0.5 m / s inflow velocity. (c) flow field velocity distribution under 1 Hz pure heave motion. (d) relationship between heave direction resistance and flow rate. (e) relationship between yaw angular velocity and yaw moment. (f) time-dependent resistance and Fourier fitting results in 1 Hz pure heave motion.

[0073] Specifically, Figure 3 (a) of the application shows the vortex structure and velocity profile formed under lateral motion under 0.6 m / s lateral flow conditions. By systematically scanning different inflow velocities, the longitudinal resistance is recorded and correlated with the corresponding flow rate, as shown in (d) of the application. Subsequently, based on the force-velocity characteristic curve, the coefficients are extracted by polynomial regression analysis, and the velocity-dependent hydrodynamic parameters are determined. Figure 3

[0074] To determine the yaw angle-dependent hydrodynamic coefficients , the application performs a rotating arm test simulation by changing the computational domain radius R when the mechanical turtle rotates. Under the premise of keeping the constant inflow velocity at 0.5 meters per second, the computational domain radius is gradually expanded from 2.2 meters to 4.4 meters with a step size of 0.55 meters. Figure 3 (b) of the application shows the uniform distribution of the flow field around the mechanical turtle at a typical radius of 3.3 meters. As shown in (e) of the application, the influence of the rotation parameter on the flow field is quantified by least squares fitting of the torque and yaw angular velocity r. Figure 3

[0075] To simulate the unsteady motion in PMM testing, the application uses the superimposed grid technology to realize efficient flow field analysis under complex geometric structures through overlapping grid areas. By constructing a multi-zone computational domain including inner and outer zones, the data transmission between grids is effectively promoted. Given the inherent transient characteristics of PMM simulation, the application uses a time-dependent solver. Figure 3 (c) of the application shows the transient velocity field under a frequency f = 1 Hz in pure surge motion, and​​Figure 3 (f) shows the time-varying resistance at the same frequency. By performing Fourier analysis on the time-varying resistance data, the present invention obtains the fluid dynamics coefficient related to acceleration.

[0076] S3. Build a pool environment in the dynamics simulator. Figure 4 , shows a turtle-inspired robot in the Webots dynamics simulator in an embodiment of the present invention.

[0077] S4. A hierarchical model predictive control-fuzzy logic controller (MPC-FLC) architecture was established. The MPC, acting as the upper-level controller, generates reference forces and torques, while the lower-level fuzzy logic controller maps these reference quantities into actuator-specific commands. This two-layer framework ensures optimal path tracking through predictive optimization while addressing dynamic uncertainty through adaptive signal distribution. For a detailed block diagram of the turtle-inspired robot path tracking control, see Figure 5 The asymmetric surface of the fuzzy rule graph highlights the system's ability to handle nonlinear and transient states, thereby balancing response and stability under different operating conditions. Figure 6 , which shows the input and output rules of the fuzzy inference system in an embodiment of the present invention. (a) Input and With output (b) Input and With output The relationship between them.

[0078] S5. Starting from a stationary state, the proposed controller enables the turtle-like robot to converge smoothly to the target trajectory without overshoot. The robot then drives along the reference path with minimal deviation between the desired trajectory and the actual trajectory. Figure 7 , shows the performance evaluation of the path tracking controller in an embodiment of the present invention, including (a) visualization of the comparison between the U-shaped path and the actual motion; (b) time evolution of the lateral path tracking deviation. By quantitatively analyzing the lateral error defined as the shortest distance from the center of mass to the reference path, Figure 7 (b) shows the time series changes of the lateral errors of the three controllers. The SMC controller takes 317.4 seconds to complete the path with an average lateral error of 0.112 meters; the PID controller takes 244.0 seconds with an average error of 0.097 meters. In comparison, this control strategy performs better, completing the task in only 145.4 seconds, significantly reducing the lateral error to 0.0295 meters, and showing better tracking accuracy and efficiency. Specifically, the signal output of the MPC-FLC control strategy in the U-shaped trajectory tracking in the embodiment of the present invention can be found in Figure 8The smooth and stable control signal generated by the strategy is further demonstrated, verifying its reliable operation.

[0079] Figure 9 Performance evaluation of the path tracking controller in the embodiment of the present application: (a) visualization comparison of the 8-shaped path and the actual motion. (b) Time evolution of lateral path tracking deviation. Figure 9 (a) of figure 1 demonstrates the path following performance of the turtle-inspired robot under three control strategies, all of which achieve the basic path tracking function. Figure 9 (b) of figure 1 quantifies the time-varying trend of the lateral error of each controller: the SMC controller completes the trajectory in 663.3 seconds with an average lateral error of 0.122 meters; the PID controller shortens the time to 518.1 seconds while maintaining an average error of 0.101 meters. It is worth noting that the MPC-FLC strategy proposed in the present application performs better, completing the task in only 429.1 seconds with a significantly reduced average error of 0.0393 meters, demonstrating superior tracking accuracy and operational efficiency.

[0080] The signal output of the MPC-FLC control strategy in the embodiment of the present application in the 8-shaped trajectory tracking is referred to Figure 10 , which further demonstrates the drive signal of the controller, achieving stable motion control by adjusting the propulsion speed and steering angle in real time.

[0081] In summary, the embodiment of the present application proposes a model predictive control-based turtle-inspired amphibious robot path tracking method, which establishes a high-fidelity fluid dynamics model through CFD-driven parameterization and proposes a hierarchical control framework integrating MPC and FLC. The turtle-inspired amphibious robot path tracking method of the present application combines the high-fidelity hydrodynamic model obtained through CFD numerical calculation and the stability of MPC-FLC cascade control, effectively solving the problems of nonlinear fluid dynamics interaction, coefficient uncertainty, and unmodeled environmental disturbances. Specifically, the above technical solution has the following advantages:

[0082] 1. The turtle-inspired amphibious robot platform is reliable, and the turtle as a bionic prototype can decouple propulsion and steering during motion, providing a stable foundation for the robot's path tracking algorithm; 2. The simplified dynamics model based on multi-rigid-body dynamics model parameterizes the influence of the water environment on the robot as hydrodynamic coefficients, and simplifies the control dimension through mechanical structure analysis and bionic prototype analysis; 3. Through integration of steady-state drag test, rotating arm simulation and PMM analysis, CFD simulation is performed using STAR-CCM+ software to obtain the corresponding hydrodynamic coefficients, establishing a high-fidelity hydrodynamic model; 4. The water dynamic environment model suitable for the turtle robot is established in the dynamic simulator Webots, which reduces the model distortion problem in the general parameterized simulation process and can more systematically evaluate the running performance of the constructed path tracking framework.

[0083] 5. The model predictive control framework adopted by the present application explicitly integrates kinematic constraints through receding horizon optimization, which can more effectively deal with parameter uncertainty, insufficient operator experience and control output oscillation compared with traditional PID control strategy and sliding mode controller. 6. The present application proposes a double-layer control strategy combining model predictive control and fuzzy logic control. The upper layer MPC optimizes the reference force and torque through the rolling horizon optimization method, and the lower layer FLC adaptively maps the above reference signal to the actuator instruction based on fuzzy rules, effectively dealing with nonlinear water dynamic interaction, parameter uncertainty and unmodeled environmental disturbance.

[0084] 7. The proposed control framework has undergone U-shaped path tracking simulation comparison and 8-shaped path tracking comparison, achieving higher control accuracy and more agile robot motion.

[0085] The embodiment of the present application also provides a storage medium for storing a computer program, which is executed to perform at least the method described above.

[0086] The embodiment of the present application also provides a control device, which comprises a processor and a storage medium for storing a computer program; wherein the processor is used to execute the computer program to perform at least the method described above.

[0087] The embodiment of the present application also provides a processor, which executes a computer program to perform at least the method described above.

[0088] The storage medium can be implemented by any type of nonvolatile storage device, or a combination thereof. The nonvolatile memory can be a Read Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable Programmable Read-Only Memory (EPROM), an Electrically Erasable Programmable Read-Only Memory (EEPROM), a Ferromagnetic Random Access Memory (FRAM), a Flash Memory, a magnetic surface storage, an optical disc or a Compact Disc Read-Only Memory (CD-ROM). The magnetic surface storage can be a magnetic disc memory or a magnetic tape memory. The storage medium described in the embodiments of the present application is intended to include, but is not limited to, these and any other suitable type of memory.

[0089] In several embodiments provided by the present application, it should be understood that the disclosed system and method can be implemented in other manners. The described device embodiments are merely schematic, and the division of the units is merely a logical function division. For example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed coupling or direct coupling or communication connection between the components can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0090] The units described as separate components can or can not be physically separate, and the components shown as units can or can not be physical units, i.e., can be located in one place or distributed on a plurality of network units; some or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0091] In addition, each functional unit in the embodiments of the present application 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 the form of hardware, or in the form of hardware plus software functional units.

[0092] Those skilled in the art can understand that all or part of the steps of the above-mentioned method embodiments can be completed by program instruction related hardware, and the foregoing program can be stored in a computer readable storage medium, and the program performs the steps of the above-mentioned method embodiments when executed; and the foregoing storage medium includes a mobile storage device, a read-only memory (ROM), a random access memory (RAM), a magnetic disc or an optical disc and various storage medium capable of storing program codes.

[0093] Alternatively, the integrated unit of the present application can be stored in a computer readable storage medium if it is realized in the form of a software function module and sold or used as an independent product. Based on such understanding, the technical solutions of the embodiments of the present application can be embodied in the form of a software product, and the computer software product is stored in a storage medium, includes several instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the methods described in the embodiments of the present application. The foregoing storage medium includes a mobile storage device, a ROM, a RAM, a magnetic disc or an optical disc and various storage medium capable of storing program codes.

[0094] The methods disclosed in the several method embodiments of the present application can be combined arbitrarily without conflict to obtain new method embodiments.

[0095] The features disclosed in the several product embodiments of the present application can be combined arbitrarily without conflict to obtain new product embodiments.

[0096] The features disclosed in the several method or device embodiments of the present application can be combined arbitrarily without conflict to obtain new method embodiments or device embodiments.

[0097] The above is a further detailed description of the present application in combination with specific preferred embodiments, and the specific implementation of the present application cannot be limited to these descriptions. For those skilled in the art, without departing from the concept of the present application, a number of equivalent substitutions or obvious modifications can be made, and the performance or use is the same, which should be regarded as belonging to the protection scope of the present application.

Claims

1. A path tracking method for a turtle-like amphibious robot based on model predictive control, characterized in that: The following steps are involved: S1. Establish a multi-rigid-body dynamic model of a turtle-like amphibious robot, derive simplified dynamic equations including hydrodynamic coefficients, and simplify the control dimension based on biological motion characteristics; S2. Quantify hydrodynamic parameters through computational fluid dynamics simulations combined with steady-state drag tests, rotating arm tests, and unsteady planar motion mechanism analysis; S3, building the robot model and underwater environment in the dynamics simulator; S4. Design model predictive control-fuzzy logic cascade controller: The upper-level model predictive controller generates reference forces and torques through rolling horizon optimization; The lower-level fuzzy logic controller adaptively maps the reference force and torque into actuator commands based on fuzzy rules; S5. Conduct path tracking control verification in a simulation environment to evaluate controller robustness and tracking accuracy.

2. The path tracking method according to claim 1, wherein: The simplified establishment of the multi-rigid body dynamics model in step S1 specifically includes: The robot's dual symmetry about the longitudinal-transverse plane and the longitudinal-vertical plane is used to ignore the coupling effect of longitudinal, transverse and yaw motions; Based on the bionic motion characteristics, the active control dimensions are limited to longitudinal propulsion force and yaw moment; Integrate added mass effects, linear damping terms, and nonlinear fluid resistance terms into the dynamic equations.

3. The path tracking method according to claim 1, wherein: The quantification of the hydrodynamic parameters in step S2 specifically includes: The velocity-dependent damping factor was identified through drag tests, and the drag data at different flow rates were correlated and fitted with polynomial coefficients; Identify the resistance to rotational motion through the rotating arm test and fit the relationship between yaw moment and angular velocity; Inertial effects are identified through analysis of unsteady planar motion mechanisms, and acceleration-related hydrodynamic coefficients are extracted using Fourier analysis. The superposition grid technology is used to analyze the transient flow field, and data transmission between grids is realized through multi-region calculation domains.

4. The path tracking method according to claim 1, wherein: Step S3 specifically includes: The robot's hardware architecture is designed using a bionic propulsion system, including a central waterproof cabin and multiple three-degree-of-freedom flippers; Import a simplified robot model into the dynamics simulator and build an underwater environment to reduce parametric simulation distortion.

5. The path tracking method according to claim 1, wherein: The input generation of the model predictive controller in step S4 specifically includes: Obtain the desired position and heading angle through the line of sight method; Decouple the path tracking problem into thrust and torque channels: The thrust channel controls the longitudinal velocity by adjusting the flipper oscillation frequency; The torque channel achieves directional adjustment by coordinating the amplitude difference of the fins and the tail fin rudder angle.

6. The path tracking method according to claim 1 or 5, wherein: The optimization process of the model predictive controller in step S4 specifically includes: Solve the finite-time optimal control problem at discrete time points and generate the optimal control sequence within the prediction step size; A moving horizon strategy is adopted to output the first element of the sequence as the current control action.

7. The path tracking method according to claim 1, wherein: The design of the fuzzy logic controller in step S4 specifically includes: Construct a fuzzy rule table to define the mapping relationship between reference force / torque error and actuator instructions; Asymmetric response surfaces are used to handle nonlinear and transient conditions, balancing dynamic response and stability.

8. The path tracking method according to claim 1, wherein: The cooperation mechanism of the model predictive control-fuzzy logic cascade controller specifically includes: The upper-level model predictive controller explicitly integrates kinematic constraints and optimizes reference forces / torques to cope with parameter uncertainties; The lower-level fuzzy logic controller compensates for the unmodeled fluid dynamics coupling and environmental disturbances through adaptive mapping.

9. The path tracking method according to claim 1, wherein: The path tracking control verification in step S5 specifically includes: Design a U-shaped path containing straight segments and arcs to evaluate straight-line tracking and steering capabilities; Design a figure-8 path with bidirectional curvature changes to evaluate lateral error suppression and transient stability; A random hydrodynamic disturbance model is applied to test the anti-disturbance robustness of the controller.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the path tracking method of the turtle-like amphibious robot based on model predictive control as described in any one of claims 1 to 9 is implemented.

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