A Motion Control Method for a Bionic Manta Ray Robot

Abstract

The present invention discloses a motion control method for a biomimetic manta ray robot, comprising: (1) selecting a plurality of feature points on the flexible pectoral fins of the biomimetic manta ray robot and establishing a mathematical model for describing the motion of the feature points; (2) improving the CPG controller by introducing an amplitude adjustment parameter a and a frequency adjustment parameter ω to improve the CPG controller; (3) designing a CPG controller parameter tuning method based on the perturbation method; (4) coupling the improved CPG controller with the biomimetic manta ray robot; (5) using the improved CPG controller as the underlying motion controller for controlling the flapping of the pectoral fins, and using a fuzzy controller as the high-level decision-making controller to build a hierarchical control architecture based on the CPG model, and using a fuzzy algorithm to control the input parameters a and ω of the CPG controller to achieve closed-loop control of the motion speed of the manta ray robot. By using the present invention, the controller can still quickly converge after being disturbed and continue to generate a periodic signal of a given pattern.

Description

Technical Field

[0001] The present invention belongs to the field of underwater robots, and particularly relates to a motion control method for a bionic manta ray robot. Background Technique

[0002] In recent years, in order to further develop marine resources and deeply explore the ocean, many scholars have started research on underwater robot technology, and more and more underwater robots have been applied to challenging underwater tasks. At the same time, the diversification of task requirements and the complexity of the detection environment have put forward higher requirements for the performance of underwater robots in all aspects. At present, torpedo-shaped or open-frame underwater robots powered by propeller thrusters have the disadvantages of low propulsion efficiency, poor flexibility, and high noise, and there is no proper solution strategy. Therefore, the research on new underwater robots is imminent.

[0003] Bionics, as a new discipline, has injected vitality into the development of robot technology. Many scholars have begun to study the bionic principles of underwater biological structures and behaviors, trying to get inspiration and guidance from them. The flapping-wing motion mode of manta rays has been favored by researchers for its advantages such as good stability, strong maneuverability, and high propulsion efficiency. The research on bionic manta ray robots has become the focus of current research on underwater bionic robots.

[0004] For example, the Chinese patent document with the publication number CN110304223A discloses a bionic manta ray robot, including a head cabin, a central cabin, a pair of pectoral fins, and a tail fin cabin. The pectoral fins include a crank-rocker mechanism and a bevel gear mechanism, and the wave-like propulsion of the manta ray is realized through the coordinated periodic motion of the crank-rocker mechanism; the complex closed motion trajectory tracking of the end of the manta ray pectoral fin is realized through the cooperation of the bevel gear mechanism and the crank-rocker mechanism.

[0005] It should be noted that the current main research on bionic manta rays focuses on the explanation of motion principles, the improvement of propulsion efficiency, and the design of bionic structures. The research on how to effectively control bionic manta ray robots has not been fully carried out. Technical difficulties in the research process include system modeling in complex fluid environments, generation of stable and adjustable periodic oscillation signals, switching and smooth transition of multi-modal motions, and multi-degree-of-freedom cooperative control.

[0006] With the continuous in - depth research on neurobiology, bionic control methods from the perspective of rhythmic movement have received extensive attention from scholars. The Central Pattern Generator (CPG) has been applied to simulate the underlying controller of rhythmic movement due to its characteristics such as model parameterization, self - organization, and self - adaptability, which provides ideas for the research of bionic manta ray robots. Due to the high - dimensional, non - linear, and strongly coupled characteristics of CPG, only numerical methods can be used to analyze the parameters in the model. It is very difficult to quantitatively analyze the relationship between model parameters and system performance, and only the experimental trial - and - error method can be used for parameter tuning, lacking systematicness and theory.

[0007] The difficulty in dynamic modeling of bionic manta ray robots is another reason restricting their development. Since the movement of manta rays in water involves the hydrodynamic model in the fluid environment, it is currently difficult to accurately establish the dynamic model during their movement, with great modeling uncertainty. Therefore, it is also difficult to control the movement of manta rays through the dynamic model. Summary of the Invention

[0008] The present invention provides a motion control method for a bionic manta ray robot, which can still quickly converge after being disturbed and continue to generate periodic signals of a given pattern. When changing oscillation characteristics such as amplitude and angular frequency, it can utilize the asymptotic convergence characteristics of the limit cycle to achieve a smooth transition within a finite time and control the bionic manta ray robot to output environment - adaptive behaviors.

[0009] A motion control method for a bionic manta ray robot includes:

[0010] (1) Select several characteristic points on the flexible pectoral fins of the bionic manta ray robot, establish a mathematical model describing the movement of the characteristic points, and describe the flapping characteristics of the flexible pectoral fins by analyzing the movement laws of the characteristic points;

[0011] (2) Improve the CPG controller, introduce the amplitude adjustment parameter a and the frequency adjustment parameter ω to improve the CPG controller, and adjust the characteristics of the oscillation signal output by the CPG controller through the above parameters;

[0012] (3) Design a parameter tuning method for the CPG controller based on the perturbation method;

[0013] (4) Couple the improved CPG controller with the bionic manta ray robot, so that the improved CPG controller can generate stable and pattern - adjustable periodic oscillation signals in the absence of periodic input signals;

[0014] (5) Using an improved CPG controller as the underlying motion controller for controlling the pectoral fin flapping, and a fuzzy controller as the high-level decision-making controller, a hierarchical control architecture based on the CPG model is built. The fuzzy algorithm is used to control the input parameters a and ω of the CPG controller to achieve closed-loop control of the movement speed of the manta ray robot.

[0015] The core of the present invention is to design CPG as the underlying motion controller to control the movement of the bionic manta ray robot, and to propose a method for tuning the parameters of the CPG controller. Using a fuzzy controller as the high-level decision-making device, without establishing the dynamic model of the manta ray robot, the movement speed v is controlled to enable it to track the expected value v. d 。

[0016] In step (1), the flapping characteristics of the flexible pectoral fin are described by analyzing the motion law of the characteristic points, specifically as follows:

[0017] The flapping contour of the pectoral fin is fitted by a quadratic curve, and the flapping curve expressions of the three fin lines at any time are established.

[0018]

[0019] In the formula, Z represents the vertical displacement of different fin lines during flapping; A consists of the flapping amplitude coefficient a(t) of the flexible pectoral fin, A T =(a1(t) a2(t) a3(t)); X represents the position coordinates of different fin lines along the spanwise direction; M represents the coordinate range of different fin lines along the x-axis, which is determined by the curve length integral formula; L represents the lengths of different fin lines.

[0020] By measuring the actual displacements of the characteristic points of the biological manta ray, the functional expression of the flapping amplitude coefficient a(t) as a function of time is obtained by function fitting; thus, the displacements of each characteristic point in the vertical direction at any time are obtained. By analyzing the displacements of the characteristic points, the flapping periodic law of the pectoral fin of the manta ray robot is obtained.

[0021] The mathematical expression of the improved CPG controller is as follows:

[0022]

[0023] In the formula, x is the output signal of the improved CPG controller, and the state variable is the first derivative of x with respect to time, and the state variable is the second derivative of x with respect to time, ε is the nonlinear strength coefficient, a is the amplitude adjustment parameter, and ω is the frequency adjustment parameter.

[0024] In step (3), the method for tuning the parameters of the CPG controller based on the perturbation method is specifically as follows:

[0025] The multi-scale singular perturbation method is used to obtain the analytical solution of the output signal of the CPG controller, and then the quantitative relationship between the controller parameters and the output signal is analyzed to realize the effective control of the bionic manta ray robot by the CPG controller.

[0026] The process of obtaining the analytical solution of the output signal of the CPG controller by using the multi-scale singular perturbation method is as follows:

[0027] Introduce two time scales \(T_0 = t\) and \(T_1=\varepsilon t\), and expand the approximate solution series as shown in Equation (3):

[0028] \(x(t,\varepsilon)=x_0(T_0,T_1)+\varepsilon x_1(T_0,T_1)\quad(3)\)

[0029] Take the first derivative of \(x(t)\) with respect to time \(t\) as shown in Equation (4):

[0030]

[0031] In the formula, \(D_0\) and \(D_1\) are differential operators.

[0032] Similarly, take the second derivative with respect to time \(t\), and simplify by omitting the high-order terms of \(\varepsilon\). The calculation result is shown in Equation (5):

[0033]

[0034] Substitute Equations (3), (4) and (5) into the mathematical expression of the improved CPG controller to get Equation (6):

[0035]

[0036] After expansion, omit the high-order terms of \(\varepsilon\), simplify and combine like terms to get Equation (7):

[0037] \(D_0\) 2 \(x_0+\omega\) 2 \(x_0+\varepsilon(D_0\) 2 \(x_1 + 2D_0D_1x_0+ax_0\) 3 \(D_0 - D_0x_0+\omega\) 2 \(x_1)=0\quad(7)\)

[0038] Let the coefficients of each power of \(\varepsilon\) be equal to zero to obtain the equation as shown in Equation (8):

[0039]

[0040] The initial condition of the first equality of the non-perturbative Equation (8) is determined by the initial state of the controller. Solve the differential equation to get:

[0041] \(x_0(T_0,T_1)=\zeta(T_1)\cos[\omega T_0+\beta_0]\quad(9)\)

[0042] where ζ is a function of the time scale T1, and β0 is the initial phase of the system, which is related to the initial conditions of the controller; substituting x0 into the second equation of Equation (8) gives Equation (10):

[0043]

[0044] If there is no divergent term in the form of tsint in the desired solution x1(T0, T1), then the resonance term needs to be eliminated Let the amplitude The following Equation (11) is obtained:

[0045]

[0046] Integrating both sides of the above equation gives the expression of ζ as shown in Equation (12):

[0047]

[0048] where ζ0 is the initial value of ζ at t = 0, which is related to the initial state x(0) of the controller related;

[0049] v is the perturbation amount. When ε → 0, ignoring its influence, the first-order approximate analytical solution of the improved CPG controller is obtained as shown in Equation (13):

[0050]

[0051] where β0 is the initial phase of the system, which is related to the initial state x(0) of the controller related.

[0052] In step (4), when coupling the improved CPG controller with the biomimetic manta ray robot, the CPG controller controls the pectoral fin flapping. Its output oscillation signal has a stable phase difference. The phase relationship between CPG units can be controlled by the initial phase β0, and a control network of multiple CPGs coupled with each other is established through the phase difference to achieve the coordinated control of multiple pectoral fin drive devices.

[0053] In step (5), select the frequency adjustment parameter ω in the input parameters of the improved CPG controller as the relevant variable for motion speed control, and select its increment Δω as the output variable of the fuzzy controller;

[0054] Select the difference e = v - v d between the actual moving speed v of the manta ray robot and the speed expectation value v d and the error change rate de as the input variables of the fuzzy controller.

[0055] According to the input variables and output variables of the fuzzy controller, determine the fuzzy control rule table for the speed v of the bionic manta ray robot; during the control process, select the defuzzification method based on the centroid method to convert the fuzzy linguistic variable obtained after fuzzy inference into an accurate output variable Δω, which is accumulated with ω at the previous moment and used as a control parameter to be input into the CPG controller to control the frequency of the oscillating signal output by the CPG, and then change the flapping frequency of the pectoral fins in the form of an increment, so that the actual speed v of the manta ray robot approaches the expected value v d 。

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] 1. The CPG controller based on the nonlinear oscillator used in the present invention utilizes the self-excited oscillation phenomenon of the nonlinear system to generate a stable periodic signal. On this basis, amplitude and frequency adjustment parameters are introduced. The improved CPG controller can still quickly converge after being disturbed and continue to generate periodic signals of a given pattern. When changing oscillation characteristics such as amplitude and angular frequency, it can utilize the asymptotic convergence characteristics of the limit cycle to achieve a smooth transition within a finite time.

[0058] 2. Aiming at the problems that the CPG controller model of biological neurons is complex and has numerous parameters that are difficult to tune, the CPG controller based on the nonlinear oscillator is introduced in the present invention, and the multi-scale perturbation method is used to approximately analyze the CPG controller to realize the quantitative tuning of the parameters of the CPG controller.

[0059] 3. Aiming at the problem that the CPG controller lacks decision-making ability, a fuzzy controller is introduced as a high-level decision maker, and a hierarchical control architecture based on the CPG controller is built to improve the environmental adaptability of the bionic manta ray robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a schematic diagram of selecting characteristic points on the flexible pectoral fin of the bionic manta ray robot of the present invention;

[0061] Figure 2 It is the phase plane diagram of the CPG controller;

[0062] Figure 3 It is the output signal of the CPG controller under different initial states;

[0063] Figure 4 It is the output signal and phase plane diagram of the CPG controller when being disturbed externally;

[0064] Figure 5 It is the fitting effect diagram of the approximate analytical solution of the perturbation method;

[0065] Figure 6 It is the schematic diagram of the CPG controller realizing the control of the pectoral fin flapping;

[0066] Figure 7 A network structure diagram showing the coordinated control of multiple pectoral fins by multiple CPG controllers;

[0067] Figure 8 This is a structural diagram of a hierarchical control architecture based on the CPG model;

[0068] Figure 9 It is the schematic diagram of fuzzy control process;

[0069] Figure 10 A schematic diagram of tracking a given speed during a simulation experiment of the present invention;

[0070] Figure 11 Schematic diagram of the output waveform change of the CPG controller during the simulation experiment of the present invention;

[0071] Figure 12 This is the limit cycle transformation diagram during the simulation experiment of the present invention. DETAILED DESCRIPTION

[0072] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0073] The control object of the present invention uses the biological manta ray as a bionic prototype. Through analysis of the biological characteristics of manta rays, it is known that they mainly rely on the flapping of their flexible pectoral fins to achieve free swimming. Therefore, establishing a kinematic model of pectoral fin flapping is the key to the subsequent motion control of the manta ray robot.

[0074] A bionic manta ray robot motion control method comprises the following steps:

[0075] Step 1: Kinematic Modeling

[0076] First, several feature points are selected on the flexible pectoral fin, and a mathematical model describing the motion of the feature points is established. The flapping characteristics of the flexible pectoral fin are studied by describing the motion laws of the feature points. The feature points are selected as follows: Figure 1 shown.

[0077] The flapping profile of the pectoral fin is fitted by a quadratic curve to establish the three fin lines K at any time. 12 K 10 , K 23 K 20 , K 31 K 30 The flapping curve expression is shown in formula (1.1)

[0078]

[0079] Where A is composed of the flapping amplitude coefficient a(t) of the flexible pectoral fin,T = (a1(t) a2(t) a3(t));

[0080] L - The length of different fin lines;

[0081] M - The coordinate range of different fin lines along the x-axis, determined by the curve length integral formula;

[0082] X - The position coordinate of different fin lines distributed along the spanwise direction;

[0083] Z - The vertical displacement of different fin lines during flapping.

[0084] By measuring the actual displacements of the characteristic points of the biological manta ray, the functional expression of the flapping amplitude coefficient a(t) as a function of time is obtained through function fitting. Thus, the displacements of each characteristic point in the vertical direction at any moment are obtained, and by analyzing the displacements of the characteristic points, the flapping periodic law of the pectoral fins of the manta ray robot is obtained.

[0085] Step 2: CPG controller based on an improved nonlinear oscillator

[0086] As can be seen from Step 1, the core problem of controlling the bionic manta ray robot is to generate a stable and mode-adjustable periodic oscillation signal to control the pectoral fins to generate multi-modal periodic flapping. The simple harmonic signal generated by the harmonic function has poor stability and is prone to divergence after being disturbed and cannot converge back to the original oscillation state. The CPG controller based on the nonlinear oscillator uses the self-excited oscillation characteristics of the nonlinear system to provide an effective method to solve this problem.

[0087] The CPG controller based on the van der pol oscillator is a nonlinear second-order system with nonlinear damping. The mathematical expression of the controller is shown in Equation (2.1)

[0088]

[0089] Let the state variable x1 = x, The equation is rewritten as the state space expression as shown in Equation (2.2)

[0090]

[0091] In the formula, x1 and x2 are state variables, and ε is the nonlinear strength coefficient.

[0092] Take ε = 0.1, and make the phase plane diagram of the CPG controller as Figure 2 shown. The output signals of the CPG controller under different initial states are as Figure 3 shown. In the figure, (a) is the initial state located inside the limit cycle, and (b) is the initial state located outside the limit cycle. As Figure 4As shown in the figure, in the figure, (a) is the output signal of the CPG controller when it is subjected to external disturbances, and (b) is the phase plane diagram of the CPG subjected to external disturbances.

[0093] It can be seen from Figures 2 to 4 that the CPG controller based on the nonlinear oscillator has a unique limit cycle, can quickly converge to the limit cycle under various initial conditions, and generate a stable periodic oscillation signal. When it deviates from the limit cycle due to external disturbances, it can quickly converge back to the limit cycle and continue to generate periodic oscillation signals. The above results show that the CPG controller based on the nonlinear oscillator meets the requirements of pectoral fin drive for periodic signals. On this basis, the amplitude adjustment parameter α and the frequency adjustment parameter ω are introduced to improve the CPG controller, and the characteristics of the output oscillation signal of the controller are adjusted through the above parameters to meet the requirements of multi-modal and adjustable CPG signals for pectoral fin drive.

[0094] The mathematical expression of the improved CPG controller is shown in Equation (2.3)

[0095]

[0096] where ε is the nonlinear strength coefficient, a is the amplitude adjustment parameter, and ω is the frequency adjustment parameter.

[0097] Step 3: Parameter tuning method of CPG controller based on perturbation method

[0098] To couple the CPG controller with the controlled object, it is first necessary to quantitatively analyze the influence of the parameters of the CPG controller on the oscillation characteristics of the output signal. At present, the tuning of CPG parameters mostly uses the experimental trial-and-error method. In this invention, the multi-scale singular perturbation method is used to obtain the approximate analytical solution of the CPG controller, and then the quantitative relationship between the controller parameters and the output signal is analyzed to realize the effective control of the bionic manta ray robot by the CPG controller.

[0099] First, time variables T of different scales are introduced. The time scale T is affected by the small parameter ε according to the law of T n = ε n t. Considering the solution accuracy and real-time performance of the solution, the first-order approximate solution is obtained this time, and two time scales of T0 = t and T1 = εt are introduced. The approximate solution series is expanded as shown in Equation (3.1)

[0100] x(t,ε) = x0(T0,T1) + εx1(T0,T1) (3.1)

[0101] The first-order derivative of x(t) with respect to time t is shown in Equation (3.2)

[0102]

[0103] where D0 and D1 are differential operators,

[0104] Similarly, take the second derivative with respect to time \(t\), simplify by omitting the high-order terms of \(\varepsilon\), and the calculation results are shown in Equation (3.3).

[0105]

[0106] Substitute Equations (3.1), (3.2), and (3.3) into the mathematical expression (3.3) of the improved CPG controller to obtain Equation (3.4):

[0107]

[0108] After expansion, omit the high-order terms of \(\varepsilon\), simplify and combine like terms to obtain Equation (3.5):

[0109] D0 2 x0 + ω 2 x0 + ε(D0 2 x1 + 2D0D1x0 + ax0 3 D0 - D0x0 + ω 2 x1) = 0 (3.5) Let the coefficients of each power of \(\varepsilon\) be equal to zero to obtain the equation shown in Equation (3.6):

[0110]

[0111] The initial conditions of the non-perturbed Equation (3.3.6a) are determined by the initial state of the controller. Solving the differential equation (3.6a) gives:

[0112] x0(T0, T1) = ζ(T1)cos[ωT0 + β0] (3.7)

[0113] where \(\zeta\) is a function of the time scale \(T1\), and \(\beta0\) is the initial phase of the system, which is related to the initial conditions of the controller. Substitute \(x0\) into Equation (3.6b) to obtain Equation (3.8):

[0114]

[0115] If there is no divergent term in the form of \(t\sin t\) in the desired solution \(x1(T0, T1)\), then the resonance term needs to be eliminated Let the amplitude to obtain Equation (3.9) as follows:

[0116]

[0117] Integrate both sides of the above equation to obtain the expression of \(\zeta\) shown in Equation (3.10)

[0118]

[0119] where \(\zeta0\) is the initial value of \(\zeta\) at \(t = 0\), related to the initial state \(x(0)\) of the controller, is related to

[0120] v is the perturbation amount. When ε→0, its influence can be ignored, and the first-order approximate analytical solution of the improved CPG controller is obtained as shown in Equation (3.11).

[0121]

[0122] In the formula, ζ0 is the initial value of ζ at t = 0, and β0 is the initial phase of the system, which is related to the initial state x(0) of the controller and is related to

[0123] Take x(0) = 2 and ω = 1, substitute them into (3.7) to get ε0 = 2, β0 = 0. Take ε = 0.1, and the fitting result of the first-order approximate analytical solution of the improved CPG controller when the perturbation amount ε = 0.1 is obtained, as Figure 5 shown

[0124] From Figure 5 it can be seen that when ε = 0.1, the multi-scale perturbation method can analyze the improved CPG controller with high precision. In the present invention, the parameter ε of the improved CPG controller is set to 0.1, and on this basis, the parameter tuning method of the improved CPG controller is studied.

[0125] It can be seen from Equation (3.11) that is the convergence term, indicating that the influence of the initial state on the system will weaken with time. When t→∞, that is, after the oscillation signal reaches the steady state, the output signal of the improved CPG controller expressed by Equation (2.3) can be approximately analyzed by the following formula:

[0126]

[0127] It can be seen from Equation (3.12) that the amplitude A of the oscillation signal can be adjusted by the parameter a, and the two satisfy the relationship The oscillation frequency of the signal can be directly adjusted by ω, and the initial phase β0 of the oscillation signal is determined by the initial conditions and can be solved by Equation (3.7).

[0128] Step Four: Coupling of the Improved CPG Controller and the Bionic Manta Ray Robot

[0129] It can be seen from Step Three that the improved CPG controller can generate a stable and pattern-adjustable periodic oscillation signal in the absence of a periodic input signal, and can quantitatively adjust the oscillation amplitude and oscillation frequency of the oscillation signal according to the input parameters of the controller. Therefore, it can be used as the underlying motion controller for controlling the pectoral fin flapping. Next, the application of the CPG controller to realize the control of the pectoral fin flapping will be studied, as Figure 6 shown

[0130] When the CPG controller controls the pectoral fin flapping, the output oscillation signal has a stable phase difference. The initial phase β0 can control the phase relationship between CPG units. A control network with multiple CPGs coupled to each other is established through the phase difference to achieve the coordinated control of multiple pectoral fin drive devices. The control network structure is as Figure 7 shown. In the figure, is the oscillation phase difference between CPG-x and CPG-y, which can be adjusted by adjusting the initial phase β0 of each CPG control unit and satisfies the following relationship:

[0131]

[0132] Step Five: Fuzzy CPG Hierarchical Control Framework

[0133] The complexity of underwater dynamics modeling makes the relationship between CPG input parameters and the motion characteristics of the manta ray robot very complex, and it is difficult to establish the transfer function of the control system. Fuzzy control does not require the establishment of a control model of the system, which provides the possibility for the environmental adaptability control of the bionic manta ray robot.

[0134] The present invention uses an improved CPG strategy as the underlying motion controller and a fuzzy controller as the high-level decision-making controller to build a hierarchical control architecture based on the CPG model, and uses a fuzzy algorithm to control the input parameters a and ω of the CPG to achieve the closed-loop control of the motion speed of the manta ray robot. The structural diagram of the fuzzy CPG hierarchical control is as Figure 8 shown.

[0135] The swimming speed of the manta ray has the highest correlation with the pectoral fin flapping frequency. Therefore, ω in the input parameters of the improved CPG controller is selected as the relevant variable for motion speed control, and its increment Δω is selected as the output variable of the fuzzy controller.

[0136] To ensure the stability, accuracy, and rapidity requirements of the control system, the system error and the error change rate should be comprehensively considered. Therefore, the difference e = v - v d between the actual moving speed v of the manta ray robot and the speed set value v d and the error change rate de are selected as the input variables of the fuzzy controller, thus forming a two-dimensional fuzzy controller as Figure 9 shown.

[0137] After fuzzifying the input and output variables, the fuzzy control rule table for the speed v of the bionic manta ray robot is determined as shown in Table 1.

[0138] Table 1 Fuzzy Control Rule Table for Speed v

[0139]

[0140] Select an exact method based on the centroid method to convert the fuzzy linguistic variable obtained after fuzzy reasoning into an exact output Δω, which is accumulated with ω at the previous moment and input as a control parameter into the CPG controller to control the frequency of the oscillating signal output by the CPG, and then change the flapping frequency of the pectoral fin in the form of an increment, so that the speed v of the manta ray robot approaches the expected value v d 。

[0141] To verify the effectiveness of the present invention, a simulation experiment using Simulink is carried out to prove the effectiveness of the control method proposed by the present invention. The nonlinear coefficient ε of the improved CPG controller is set to 0.1, and only ω in the input parameters of the improved CPG controller is selected as the relevant variable for motion speed control, and the amplitude adjustment parameter a is set to 1.

[0142] The range of the domain of the error e in the fuzzy controller is [-10, 10], the range of the domain of the error de is [-20, 20], and the domain of the output variable Δω of the fuzzy controller is [-15, 15]. The relationship between the above input and output variables and the actual measured values can be determined by the quantization coefficients k1, k2, and k3 according to the actual system situation. In this simulation, k1 = 1, k2 = 0.75, and k3 = 0.01 are selected.

[0143] When the initial speed value is 9 and tracking a step signal with a value of 3, the simulation results are as Figures 10 to 12 shown. Among them, Figure 10 shows tracking the given speed, Figure 11 shows the change in the output waveform of the CPG controller, Figure 12 shows the limit cycle transformation. It can be seen from Figure 10 that a hierarchical control framework with an improved CPG strategy as the underlying motion controller and a fuzzy controller as the high-level decision-making controller can achieve fast tracking of the given speed by the bionic manta ray robot. It can be seen from Figure 11 that during the process of tracking the given speed, due to the control of the high-level decision-making controller on the CPG oscillation mode, the oscillation mode of the output signal of the CPG controller changes, and the change is stable. It can be seen from Figure 12 that during the process of tracking the given speed, the state variable of the improved CPG controller quickly converges from a stable limit cycle to another stable limit cycle and continues to generate a stable periodic oscillation signal.

[0144] The above-described embodiments have detailed the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not used to limit the present invention. Any modification, supplement, and equivalent replacement made within the scope of the principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A motion control method for a biomimetic manta ray robot, characterized in that, Including: (1) Select several feature points on the flexible pectoral fin of the biomimetic manta ray robot, establish a mathematical model to describe the motion of the feature points, and describe the flapping characteristics of the flexible pectoral fin by analyzing the motion law of the feature points; (2) Improve the CPG controller, introduce the amplitude adjustment parameter a and the frequency adjustment parameter ω to improve the CPG controller, and adjust the characteristics of the oscillation signal output by the CPG controller through the above parameters; (3) Design a CPG controller parameter tuning method based on the perturbation method; (4) Couple the improved CPG controller with the biomimetic manta ray robot, so that the improved CPG controller generates a stable and mode-adjustable periodic oscillation signal in the absence of a periodic input signal; (5) Use the improved CPG controller as the underlying motion controller for controlling the pectoral fin flapping, and use the fuzzy controller as the high-level decision-making controller to build a hierarchical control architecture based on the CPG model, and use the fuzzy algorithm to control the input parameters a and ω of the CPG controller to achieve closed-loop control of the motion speed of the manta ray robot.

2. The biomimetic manta ray robot motion control method according to claim 1, wherein, In step (1), the specific description of the flapping characteristics of the flexible pectoral fin by analyzing the motion law of the feature points is as follows: Fit the flapping contour of the pectoral fin by a quadratic curve, and establish the flapping curve expressions of the three fin lines at any time Wherein, Z represents the vertical displacement of different fin lines during flapping; A is composed of the flapping amplitude coefficient a(t) of the flexible pectoral fin, and A T = (a1(t) a2(t) a3(t)); X represents the position coordinates of different fin lines distributed along the spanwise direction; M represents the coordinate range of different fin lines along the x-axis, which is determined by the curve length integral formula; L represents the lengths of different fin lines; By measuring the actual displacement of the feature points of the biological manta ray, the functional expression of the flapping amplitude coefficient a(t) as a function of time is obtained by function fitting; thus, the displacement of each feature point in the vertical direction at any time is obtained; by analyzing the displacement of the feature points, the flapping periodic law of the pectoral fin of the manta ray robot is obtained.

3. The biomimetic manta ray robot motion control method according to claim 1, wherein In step (2), the mathematical expression for improving the CPG controller is as follows: where x is the output signal of the improved CPG controller, and the state variable is the first derivative of x with respect to time, and the state variable is the second derivative of x with respect to time, ε is the nonlinear strength coefficient, a is the amplitude adjustment parameter, and ω is the frequency adjustment parameter.

4. The biomimetic manta ray robot motion control method according to claim 1, characterized in that, In step (3), the specific CPG controller parameter tuning method based on the perturbation method is as follows: Adopt the multi-scale singular perturbation method to obtain the analytical solution of the output signal of the CPG controller, and then analyze the quantitative relationship between the controller parameters and the output signal to achieve effective control of the biomimetic manta ray robot by the CPG controller.

5. The biomimetic manta ray robot motion control method according to claim 4, wherein The process of adopting the multi-scale singular perturbation method to obtain the analytical solution of the output signal of the CPG controller is as follows: Introduce two time scales T0 = t and T1 = εt, expand the approximate solution series, see Equation (3): x(t,ε) = x0(T0,T1) + εx1(T0,T1) (3) Take the first derivative of x(t) with respect to time t, see Equation (4): where D0 and D1 are differential operators, Similarly, take the second derivative with respect to time t, and simplify by omitting the high-order terms of ε. The calculation result is shown in Equation (5): Substitute Equations (3), (4) and (5) into the mathematical expression of the improved CPG controller to get Equation (6): After expansion, omit the high-order terms of ε, simplify and combine like terms to get Equation (7): D0 2 x0 + ω 2 x0 + ε(D0 2 x1 + 2D0D1x0 + ax0 3 D0 - D0x0 + ω 2 x1) = 0 (7) Let the coefficients of each power of ε be equal to zero, and the obtained equation is shown in Equation (8): The initial condition of the first equality of the non-perturbative Equation (8) is determined by the initial state of the controller. Solve the differential equation to get: x0(T0,T1) = ζ(T1)cos[ωT0 + β0] (9) Where ζ is a function of the time scale T1, and β0 is the initial phase of the system, which is related to the initial conditions of the controller; substitute x0 into the second equality in Equation (8) to get Equation (10): If there is no divergent term in the form of \(t\sin t\) in the desired solution \(x_1(T_0, T_1)\), then the resonance terms need to be eliminated. Let the amplitude We obtain Equation (11) as follows: Integrate both sides of the above equation to get the expression of ζ as shown in Equation (12): where ζ0 is the initial value of ζ at t = 0, related to the initial state x(0) of the controller, and is related to; ε is the perturbation amount. When ε→0, its influence is ignored, and the first-order approximate analytical solution of the improved CPG controller is obtained as shown in Equation (13): where β0 is the initial phase of the system, which is related to the initial state x(0) of the controller and is relevant.

6. The biomimetic manta ray robot motion control method according to claim 1, wherein, In step (4), when coupling the improved CPG controller with the biomimetic manta ray robot, the CPG controller controls the pectoral fin flapping. Its output oscillation signal has a stable phase difference. The phase relationship between CPG units can be controlled by the initial phase β0. A control network of multiple coupled CPGs is established through the phase difference to achieve the coordinated control of multiple pectoral fin drive devices.

7. The biomimetic manta ray robot motion control method according to claim 1, wherein In step (5), the frequency adjustment parameter ω in the input parameters of the improved CPG controller is selected as the relevant variable for motion speed control, and its increment Δω is selected as the output variable of the fuzzy controller; Select the difference e = v - v between the actual moving speed v of the manta ray robot and the expected speed value v d and the error change rate de as the input variables of the fuzzy controller. d ​ 8. The biomimetic manta ray robot motion control method according to claim 7, wherein, According to the input variables and output variables of the fuzzy controller, determine the fuzzy control rule table for the speed v of the bionic manta ray robot; during the control process, select the defuzzification method based on the centroid method to convert the fuzzy linguistic variable obtained after fuzzy inference into an accurate output variable Δω, which is accumulated with ω at the previous moment and used as a control parameter to be input into the CPG controller to control the frequency of the oscillation signal output by the CPG, and then change the flapping frequency of the pectoral fins in the form of an increment, so that the actual speed v of the manta ray robot approaches the expected value v d .

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