Efficient motion control method for multi-degree-of-freedom bionic pectoral fin

Abstract

The invention discloses an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin, and the method comprises the steps: collecting the swimming feature data of the fish pectoral fin through a visual sensor, so as to fit the basic motion law of the pectoral fin; secondly, adjusting amplitude, frequency and phase difference of the pectoral fin by a central mode generator, controlling spanwise and chordwise movement of the pectoral fin, simulating spanwise and chordwise movement of the pectoral fin under different parameters by calculating fluid mechanics numerical values, and extracting thrust, resistance, lift force and lateral force to construct a hydrodynamic proxy model; by combining with a multi-objective optimization method, with maximum thrust and minimum resistance and lift / lateral force as objectives, optimizing to obtain an optimal combination of parameters of pectoral fin spanwise and chordwise fluctuations; finally, PID and a nonlinear mapping method are used for a pectoral fin control system, and the efficient motion law of the pectoral fin is achieved through dynamic control. The motion stability and swimming efficiency of the robotic fish are improved while it is ensured that the pectoral fins provide enough propulsive force, and the robotic fish has efficient and stable operation capacity.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater robots, and relates to an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin, in particular to the wave equations and control of the spanwise and chordwise directions of a rigid-flexible coupled pectoral fin. Background Art

[0002] A bionic robotic fish is a new type of underwater robot with high maneuverability, high concealment, and low noise, and is widely used in underwater resource exploration, underwater equipment inspection, underwater biological observation, underwater archaeology, etc.; the bionic pectoral fin plays a key role in the propulsion and pose adjustment of the robotic fish, and can significantly improve the swimming performance and stability of the robotic fish; therefore, researchers hope to imitate the swimming mechanism of the pectoral fin to achieve efficient undulation of the pectoral fin, so as to balance swimming efficiency and stability.

[0003] Existing research shows that whether it is the BCF or MPF propulsion mode, the pectoral fin plays a key role in the turning, stability, and attitude fine-tuning of fish, and its flexible control also provides important assistance for the movement of the robotic fish. Among them, the pectoral fin adjusts the pose of the robotic fish and maintains the stability of the movement through three-dimensional undulation of the fin surface.

[0004] Based on this, the fin-body integrated propulsion mechanism is the basis for realizing the efficient swimming of the robotic fish. However, most current research on pectoral fins focuses on the movement of rigid pectoral fins, and there is less research on the multi-degree-of-freedom movement of rigid-flexible coupled pectoral fins; among them, there are no relevant literature reports on the research of the rigid-flexible coupled pectoral fin mechanism composed of a rigid fin root - elastic fin rays - flexible fin membrane, the active and passive undulation of the fin surface, and the fin-body integrated propulsion mechanism; therefore, the present invention proposes a wave control method for a multi-degree-of-freedom bionic pectoral fin, which controls the pectoral fin with morphological bionics, functional bionics, and structural bionics according to the principles of bionics, so as to better realize the control of thrust, resistance, lift, and lateral force, and obtain a more stable swimming attitude and higher propulsion efficiency. Summary of the Invention

[0005] Aiming at the problems in the technical background, the present invention provides an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin, which can realize the efficient undulation motion of the pectoral fin in the spanwise and chordwise directions, and improve the swimming efficiency and stability of the robotic fish.

[0006] The present invention provides an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin. The method includes the following steps: (1) Collect the swimming gait of a real fish pectoral fin through a vision sensor, obtain the pectoral fin motion characteristic data, and fit the basic motion law of the pectoral fin based on the characteristic data. The basic motion law of the pectoral fin consists of a spanwise fluctuation and a chordwise fluctuation equation. The spanwise fluctuation and chordwise fluctuation equations are jointly determined by the wave amplitude envelope coefficient, the fluctuation amplitude, the fluctuation offset, the fluctuation phase difference, the wavelength multiple, and the generalized coordinate system representing the pectoral fin pose; (2) Adjust the parameters of the pectoral fin motion control equation through a central pattern generator (CPG). The CPG network consists of multiple mutually coupled neural oscillation units. Each unit calculates and adjusts the amplitude, frequency, and phase difference of the pectoral fin in real time to control the spanwise and chordwise fluctuation motions of the pectoral fin; (3) Use computational fluid dynamics (CFD) numerical simulation to simulate the motion process of the pectoral fin under different spanwise and chordwise fluctuation parameters, extract simulation data including thrust, drag, lift, and lateral force, and construct a hydrodynamic surrogate model based on the simulation data; (4) Based on the hydrodynamic surrogate model and the multi-objective optimization method, with the maximization of thrust, the minimization of drag, and the minimization of the fluctuation ranges of lift and lateral force as the objective functions, optimize to obtain the optimal combination of spanwise and chordwise fluctuation parameters of the pectoral fin; (5) Apply the optimized fluctuation parameters to the bionic pectoral fin control system through a PID controller and a non-linear mapping method to realize the efficient motion law of the pectoral fin in real time and improve the propulsion efficiency and motion stability of the robotic fish.

[0007] As a further technical solution, the vision sensor is a high-speed camera with a shooting frequency greater than 500 frames per second. Taking the pectoral fin root as the coordinate origin, the fin surface as the xoy plane, the y-axis pointing outward along the fin surface, and determining the normal direction of the fin surface as the z-axis according to the right-hand screw rule to establish the generalized coordinate system of the pectoral fin pose.

[0008] As a further technical solution, both the spanwise fluctuation equation and the chordwise fluctuation equation are obtained by fitting the pectoral fin motion characteristic data using Fourier series. The specific equations are:

[0009] ;

[0010] where h y (y, t) is the spanwise fluctuation motion of the pectoral fin, y is the spanwise displacement length, c y0 , c y1 , c y2 are the constant term, the first-order term coefficient, and the second-order term coefficient of the spanwise wave amplitude envelope of the pectoral fin respectively, b y (t) is the fluctuation offset of the spanwise fluctuation curve, a y(t) is the amplitude of the spanwise fluctuation curve, is the phase difference of the spanwise fluctuation curve, k y is the wavelength multiple of the spanwise fluctuation curve; h x (x, t) is the chordwise fluctuation motion of the pectoral fin, x is the chordwise displacement length, c x0 , c x1 , c x2 are the constant term, the first-order coefficient, and the second-order coefficient of the chordwise wave amplitude envelope curve of the pectoral fin, b x (t) is the fluctuation offset of the chordwise fluctuation curve, a x (t) is the amplitude of the chordwise fluctuation curve, is the phase difference of the chordwise fluctuation curve, k x is the wavelength multiple of the chordwise fluctuation curve, t is the fluctuation time.

[0011] As a further technical solution, the central pattern generator equation is:

[0012] ;

[0013] where the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, b i and a i are the fluctuation offset and amplitude, is the phase difference of the chordwise fluctuation curve, k bi and k ai are the convergence rates of the fluctuation offset and amplitude, B i and A i are the extreme values of the fluctuation offset and amplitude, R i is the time ratio between the recovery stage and the outward swing stage in the swing period, ω i is the swing frequency; the parameters of the control equation are adjusted through CPG to control the pectoral fin to move according to the spanwise fluctuation equation and the chordwise fluctuation equation.

[0014] As a further technical solution, the CFD numerical simulation specifically includes steps of pectoral fin geometric modeling, mesh generation, boundary condition setting, solver setting, and post-processing analysis; real-time flow field calculation is performed using simulation software, and hydrodynamic coefficient data of the pectoral fin under different fluctuation conditions is output. The hydrodynamic surrogate model is constructed by the neural network method, and the model expression is:

[0015] ;

[0016] where, C d is the drag coefficient, C l is the lift coefficient, C a is the side force coefficient; F d 、F l 、Fa are respectively the nonlinear models between the pectoral fin undulation parameters and C d 、C l 、C a respectively.

[0017] As a further technical solution, based on the hydrodynamic surrogate model and the multi-objective optimization method, study and optimize the efficient undulation law of the pectoral fin with large thrust, small resistance, small lift and small lateral force under different spanwise and chordwise undulation parameters; the expression of the multi-objective optimization method is:

[0018] ;

[0019] where J1 represents the maximization of propulsion efficiency, that is, the ratio of the propulsion force generated by the pectoral fin undulation to the energy consumption; J2 represents the maximization of stability, ensuring that the pectoral fin undulation can maintain the stability of the trajectory under different environments; the constraint conditions for multi-objective optimization are:

[0020] ;

[0021] where the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, and the subscripts max and min represent the maximum and minimum values of the parameters respectively. The parameters in the constraint conditions depend on the pectoral fin undulation equation, and the range is limited by its mechanical structure.

[0022] As a further technical solution, the parameters of the PID controller are optimized in real time through fuzzy control, which specifically includes the following steps: (a) Obtain the error e(t) and the error change rate e c (t) between the real-time pectoral fin motion state and the target motion state, and perform normalization processing; (b) Fuzzify the normalized error and error change rate and input them into the fuzzy inference system; (c) According to the preset fuzzy rule base, determine the proportional coefficient adjustment amount Δk p 、the integral coefficient adjustment amount Δk i 、the differential coefficient adjustment amount Δk d through fuzzy inference; (d) Use the centroid method to defuzzify to obtain the accurate PID controller parameter adjustment value, and update the PID controller parameters in real time dynamically; (e) Convert the control output of the PID controller into the pectoral fin flapping parameter adjustment value through the nonlinear mapping method, including the fluctuation amplitude adjustment value ΔA, the fluctuation offset adjustment value ΔB, the fluctuation phase difference adjustment value 、the fluctuation frequency adjustment value Δω, where the fluctuation amplitude adjustment value 、the fluctuation offset adjustment value 、the fluctuation phase difference adjustment value 、the fluctuation frequency adjustment value , α, β, γ, and κ are non-linear mapping coefficients respectively, to ensure that the pectoral fin moves precisely according to the optimal undulation parameters, improving the propulsion efficiency and motion stability of the robotic fish.

[0023] As a further technical solution, the multi-degree-of-freedom bionic pectoral fin is made of rigid fin rays, elastic fin rays, and flexible fin membranes. The fin rays are made of PLA rigid material with a hardness not less than 60D, the fin rays are made of super-elastic shape memory alloy plates, and the fin membranes are made of silicone material with a hardness less than 5. The motion control program of the multi-degree-of-freedom bionic pectoral fin is stored in the master-slave controllers of the Raspberry Pi and FPGA.

[0024] As a further technical solution, a medium for storing programs and data stores computer programs and data. When the computer programs are executed by the master-slave controllers of the Raspberry Pi and FPGA, the undulation control of the multi-degree-of-freedom bionic pectoral fin is realized.

[0025] As a further technical solution, a rigid-flexible coupled bionic pectoral fin includes a bionic pectoral fin mechanism, a controller, and a motion control method. It is characterized in that the master-slave controller is configured to execute an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin.

[0026] The additional aspects and advantages of the present invention will be partly given in the following description, partly will become obvious from the following description, or be understood through the practice of the present invention.

[0027] The beneficial effects of the present invention are as follows:

[0028] (1) The multi-degree-of-freedom rigid-flexible coupled pectoral fin structure is made of rigid fin rays, elastic fin rays, and flexible fin membranes, having the characteristics of morphological bionics and structural bionics.

[0029] (2) By measuring the swimming mechanism of the real fish pectoral fin with a vision sensor, analyzing the pectoral fin motion characteristic data and fitting to obtain the basic undulation law of the pectoral fin, the pectoral fin has bionic characteristics in terms of motion function; and by adjusting the parameters of the CPG regulation control equation, the input can be smoothed when adjusting the parameters, avoiding the chattering caused by parameter switching.

[0030] (3) Using computational fluid dynamics numerical simulation to construct a pectoral fin hydrodynamic surrogate model, reducing the calculation cost; based on the hydrodynamic surrogate model and the multi-objective optimization method of non-dominated sorting genetic algorithm II (NSGA-II), studying and optimizing the efficient undulation curves with large thrust, small resistance, small lift, and small lateral force of the pectoral fin under different spanwise and chordwise undulation parameters, realizing the optimal combination selection of the spanwise and chordwise undulation parameters of the pectoral fin.

[0031] (4) The present invention adopts a method combining a PID controller and fuzzy control, and uses a non-linear mapping method to precisely adjust the motion parameters of the pectoral fin, achieving precise adjustment and stable control of the pectoral fin motion parameters, and significantly improving the actual application performance and environmental adaptability of the bionic pectoral fin robot.

[0032] (5) According to the method of the present invention, on the premise of ensuring the pectoral fin propulsion speed, the stability of the robotic fish movement can be taken into account, improving the swimming efficiency and performance of the robotic fish, and enabling it to have the ability to operate stably. Brief Description of the Drawings

[0033] Figure 1 It is a flowchart of the high-efficiency motion control method for the multi-degree-of-freedom bionic pectoral fin according to the embodiment of the present invention.

[0034] Figure 2 It is a three-dimensional structure diagram of the multi-degree-of-freedom bionic pectoral fin in the embodiment of the present invention.

[0035] Figure 3 It is a schematic diagram of the control signal position when the multi-degree-of-freedom bionic pectoral fin has no bias in spanwise undulation in the embodiment of the present invention.

[0036] Figure 4 It is a schematic diagram of the control signal position when the multi-degree-of-freedom bionic pectoral fin has a bias in spanwise undulation in the embodiment of the present invention.

[0037] Figure 5 It is a schematic diagram of the control signal position when the multi-degree-of-freedom bionic pectoral fin has no bias in chordwise undulation in the embodiment of the present invention.

[0038] Figure 6 It is a schematic diagram of the control signal position when the multi-degree-of-freedom bionic pectoral fin has a bias in chordwise undulation in the embodiment of the present invention.

[0039] Figure 7 It is a schematic diagram of the spatial grid division and computational domain of the multi-degree-of-freedom bionic pectoral fin model in the embodiment of the present invention.

[0040] Figure 8 It is a flowchart of constructing the hydrodynamic model of the multi-degree-of-freedom bionic pectoral fin in the embodiment of the present invention.

[0041] Figure 9 It is a simulation flowchart of the high-efficiency undulation optimization method for the multi-degree-of-freedom bionic pectoral fin in the embodiment of the present invention.

[0042] Figure 10 It is a high-efficiency motion control block diagram of the multi-degree-of-freedom bionic pectoral fin in the embodiment of the present invention. Detailed Embodiment

[0043] In order to make the purpose, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0044] Please refer to the attached Figures 1 to 10 The embodiment of the present invention provides an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin, the method comprising the following steps: (1) collecting the swimming gait of the pectoral fin of a real fish through a visual sensor, obtaining the pectoral fin motion characteristic data, and fitting the basic motion law of the pectoral fin based on the characteristic data, wherein the basic motion law of the pectoral fin is composed of spanwise wave and chordwise wave equations, and the spanwise wave and chordwise wave equations are jointly determined by the amplitude envelope coefficient, the wave amplitude, the wave offset, the wave phase difference, the wavelength multiple, and the generalized coordinate system characterizing the pectoral fin posture; (2) adjusting the pectoral fin motion control equation parameters through CPG, the CPG network is composed of a plurality of mutually coupled neural oscillating units, each unit calculates and adjusts the amplitude, frequency and phase difference of the pectoral fin in real time, and controls the spanwise and chordwise wave motion of the pectoral fin; (3) using CFD numerical simulation, the motion process of the pectoral fin under different spanwise and chordwise wave parameter conditions, extracting simulation data including thrust, drag, lift and lateral force, and constructing a hydrodynamic proxy model based on the simulation data; (4) Based on the hydrodynamic proxy model and multi-objective optimization method, the optimal spanwise and chordwise fluctuation parameter combinations of the pectoral fins are optimized with thrust maximization, drag minimization, and lift and lateral force fluctuation range minimization as objective functions; (5) The optimized fluctuation parameters are applied to the bionic pectoral fin control system through a PID controller and a nonlinear mapping method, and real-time dynamic control is used to realize the efficient movement law of the pectoral fins, thereby improving the propulsion efficiency and movement stability of the robotic fish.

[0045] The specific embodiments of the present invention are further described below.

[0046] S1. The rigid-flexible coupled pectoral fin is made of rigid fin rays, elastic fin rays and flexible fin membrane. The fin rays are made of PLA hard material with a hardness of not less than 60D, the fin rays are made of superelastic shape memory alloy plates, and the fin membrane is made of silicone material with a hardness of less than 5; the fin root is connected to the fish body, the fin rays are installed in the barrier of the fin root, the fin membrane and the fin rays are bonded together with Nanjing University 703 silicone rubber, and the fin ray bending movement is driven by the shape memory alloy actuator to drive the fin membrane to fluctuate; the pectoral fin root is taken as the coordinate origin, the fin surface is the xoy plane, the y-axis points outward along the fin surface, and the normal direction of the fin surface is determined as the z-axis according to the right-hand screw rule to establish the pectoral fin generalized coordinate system, such as Figure 2 shown.

[0047] S2. First, use a vision sensor, namely a high-speed camera, to collect real fish pectoral fin motion data. Select a high-speed camera with a shooting frequency exceeding 500 frames per second for high-speed image capture to ensure the accuracy and integrity of the motion feature data collection. During the shooting process, place the fish in a transparent water tank or experimental pool to minimize environmental interference and stably capture the complete motion gait of the fish pectoral fin in the normal swimming state. The image data obtained by shooting with the high-speed camera will be preliminarily processed using image processing techniques such as background removal, image segmentation, edge extraction, and skeleton extraction to extract the pectoral fin contour and skeleton motion information. Based on the motion feature data, use numerical analysis methods such as the least squares method or curve fitting technology to obtain an analytical formula describing the basic motion law of the pectoral fin, which is composed of the spanwise wave equation and the chordwise wave equation.

[0048] Furthermore, the spanwise wave represents the wave propagation characteristic of the pectoral fin from the root to the fin tip, while the chordwise wave describes the motion pattern from the leading edge to the trailing edge of the pectoral fin. Both of these wave equations are jointly determined by the wave amplitude envelope coefficient, wave amplitude, wave offset, wave phase difference, wavelength multiple, and the generalized coordinate system parameters used to determine the three-dimensional motion posture of the pectoral fin. The expressions of the spanwise wave and chordwise wave equations are as follows:

[0049] ;

[0050] Among them, h y (y, t) is the spanwise wave motion of the pectoral fin, y is the spanwise displacement length, c y0 , c y1 , c y2 are the constant term, first-order coefficient, and second-order coefficient of the spanwise wave amplitude envelope of the pectoral fin respectively, b y (t) is the wave offset of the spanwise wave curve, a y (t) is the wave amplitude of the spanwise wave curve, is the wave phase difference of the spanwise wave curve, k y is the wavelength multiple of the spanwise wave curve; h x (x, t) is the chordwise wave motion of the pectoral fin, x is the chordwise displacement length, c x0 , c x1 , c x2 are the constant term, first-order coefficient, and second-order coefficient of the chordwise wave amplitude envelope of the pectoral fin respectively, b x (t) is the wave offset of the chordwise wave curve, a x (t) is the wave amplitude of the chordwise wave curve, is the wave phase difference of the chordwise wave curve, k x is the wavelength multiple of the chordwise wave curve, and t is the wave time.

[0051] S3. To achieve precise and smooth motion control of the bionic pectoral fin, a CPG network is used to control the motion of the pectoral fin. The CPG network consists of multiple mutually coupled neural oscillation units, and each unit corresponds to a specific degree of freedom of motion of the pectoral fin, calculating and adjusting the amplitude, frequency, and phase difference of the pectoral fin in real time, so as to achieve coordinated control of the spanwise and chordwise wave motions of the pectoral fin.

[0052] Specifically, each neural oscillation unit in the CPG network performs real-time dynamic calculations through a bias equation, an amplitude equation, and a phase equation; the CPG network equations are:

[0053] ;

[0054] Among them, the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, b i and a i are the wave biases and amplitudes, is the wave phase difference of the chordwise wave curve, k bi is a constant for adjusting the convergence speed of the wave bias. By appropriately adjusting this constant, the response speed of the wave bias can be effectively controlled. k ai is a constant for adjusting the convergence speed of the wave amplitude. By appropriately adjusting this constant, the response speed of the wave amplitude can be effectively controlled. B i and A i are the extreme values of the wave bias and amplitude, R i is the time ratio between the recovery stage and the outward swing stage in the swing period, ω i is the swing frequency; by calculating the above equations in real time, the CPG network can dynamically and precisely adjust the bias, amplitude, phase difference, and frequency between each neural oscillation unit, so as to control the bionic pectoral fin to move according to the spanwise and chordwise wave parameters; by adjusting the parameters of the pectoral fin wave equation through the CPG, smooth output can be achieved during parameter adjustment or switching, so as to avoid the jump and chatter of the actual pectoral fin mechanism movement and ensure the compliance of the pectoral fin movement.

[0055] Furthermore, referring to Figure 3 , taking c y0 = 0, c y1 = -0.012, c y2 = 1.067, A y = 1.5, when there is no bias (B y = 0), the spanwise wave curve of the pectoral fin fluctuates symmetrically about the center line; referring to Figure 4 , when there is a bias (B y = 0.7), the spanwise wave curve of the pectoral fin fluctuates with a bend to one side; referring to Figure 5 , taking c x0 = 0, c x1 = -0.010, c x2= 1.333, A x When = 2, in the case of no bias (B x = 0), the chordwise fluctuation curve of the pectoral fin fluctuates symmetrically about the center line; refer to Figure 6 , when there is a bias (B x = 1.2), the chordwise fluctuation curve of the pectoral fin bends and fluctuates to one side; The CPG-based control method not only improves the flexibility and stability of the pectoral fin movement, but also can effectively respond to the real-time changes and disturbances of the environment, significantly improving the movement performance of the bionic robot fish in practical applications.

[0056] S4. Use the Computational Fluid Dynamics (CFD) method to analyze the hydrodynamic performance of the pectoral fin, and combine neural network technology to establish an efficient hydrodynamic surrogate model; The specific implementation steps are as follows: First, import the rigid-flexible coupled pectoral fin three-dimensional model constructed in Creo software into ICEM CFD software, create the model of the pectoral fin and its surrounding fluid domain, and mesh the geometric model of the pectoral fin and its surrounding flow field area. Among them, the surface of the pectoral fin uses a fine boundary layer mesh, and the far field area uses a gradually sparse unstructured mesh to ensure the balance between calculation accuracy and calculation efficiency; At the same time, reasonably set the boundary conditions in the CFD calculation model, specifically: the surface of the pectoral fin uses a no-slip wall boundary condition, the inlet uses a velocity inlet condition, the outlet uses a pressure outlet condition, and the side and upper and lower surfaces use symmetric or slip wall conditions; Second, based on commercial or open-source CFD solvers, set appropriate turbulence models (SST k-ω) and time discretization formats, use transient simulation methods, solve the spanwise and chordwise fluctuation signals of the pectoral fin through UDF file programming and substitute them into ANSYS Fluent software for finite element simulation, and real-time simulate the dynamic movement process of the pectoral fin under different combinations of spanwise and chordwise fluctuation parameters, and solve the flow field information when the pectoral fin fluctuates according to the target signal, such as hydrodynamic coefficients, force / moment, pressure distribution and vorticity and other data; Finally, extract the hydrodynamic performance data of the pectoral fin under each working condition through post-processing software, including the drag coefficient C d , the lift coefficient C l and the side force coefficient C a , to form a training data set.

[0057] Specifically, refer to Figure 7 , make a grid division of the space around the pectoral fin and perform finite element calculations to obtain the flow field.

[0058] Furthermore, refer to Figure 8 , based on the obtained data set of fluctuation parameters and output hydrodynamic coefficients, use the neural network method to establish a hydrodynamic surrogate model, and the model expression is:

[0059] ;

[0060] Among them, C d is the drag coefficient, C l is the lift coefficient, and C a is the side force coefficient; F d , F l , F a are respectively the nonlinear mapping relationships between the pectoral fin undulation parameters obtained through neural network training and the drag coefficient C d , the lift coefficient C l , and the side force coefficient C a , which are used to quickly and efficiently predict the hydrodynamic performance of the pectoral fin under any undulation parameters.

[0061] Specifically, the method for establishing the pectoral fin hydrodynamic surrogate model is not unique, mainly the construction ideas and processes.

[0062] S5. Based on the established basic undulation law of the pectoral fin and the hydrodynamic surrogate model, use the multi-objective optimization method of non-dominated sorting genetic (NSGA-II) to optimize the optimal combination of spanwise and chordwise undulation parameters that make the pectoral fin have large thrust, small drag, small lift, and small side force, and achieve the efficient undulation law of the pectoral fin.

[0063] Specifically, the multi-objective optimization method is as follows:

[0064] ;

[0065] Among them, J1 represents the maximization of propulsion efficiency, that is, the ratio of the propulsion force generated by the pectoral fin undulation to the energy consumption; J2 represents the maximization of stability, ensuring that the pectoral fin undulation can maintain the stability of the trajectory under different environments.

[0066] Furthermore, the constraint conditions for multi-objective optimization are:

[0067] ;

[0068] Among them, the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, and the subscripts max and min represent the maximum and minimum values of the parameters respectively. The parameters in the constraint conditions depend on the pectoral fin undulation equation, and the range is limited by its mechanical structure.

[0069] Furthermore, referring to Figure 9 , the implementation process of the non-dominated sorting genetic algorithm (NSGA-II) is as follows: (1) Initialize the population: randomly generate multiple combinations of pectoral fin undulation parameters As the initial population, where the population size is N and each individual represents a combination of pectoral fin undulation parameters; (2) Objective function evaluation: Using the established hydrodynamic surrogate model, quickly calculate the corresponding optimization objectives (i.e., thrust, drag, lift, and lateral force) for the undulation parameter combinations of each individual in the initial population; (3) Non-dominated sorting and crowding distance calculation: According to the objective function values of each individual, perform non-dominated sorting to determine the non-dominated level to which the individual belongs. For solutions on the same non-dominated front, calculate the crowding distance index to maintain the diversity of the population; (4) Tournament selection based on crowding distance: Randomly select two individuals in the parent population for tournament selection, and preferentially select individuals with a lower non-dominated level (better performance); if the levels are the same, select individuals with a larger crowding distance to ensure population diversity; (5) Crossover and mutation operations: Perform crossover and mutation operations on the selected individuals. The crossover operation adopts strategies such as simulated binary crossover (SBX), and the mutation operation adopts polynomial mutation methods to generate a new generation of offspring population and increase the exploration ability of the solution space; (6) Population update: Combine the newly generated offspring population with the parent population to form a temporary population, perform non-dominated sorting and crowding distance calculation, and retain the top N optimal individuals as the population for the next generation; (7) Iterative calculation: Repeat the calculation process from step 2 to step 6 above until the preset maximum number of iterations is reached or the optimization process converges, that is, there is no obvious performance improvement in the population for consecutive multiple iterations; (8) Determination of the optimal solution: When the optimization terminates, obtain a set of Pareto optimal solution sets, and each optimal solution corresponds to a specific combination of pectoral fin undulation parameters; Through the above optimization steps, the precise optimization of the pectoral fin undulation characteristics is achieved, effectively improving the propulsion efficiency and motion stability of the bionic pectoral fin robot and significantly enhancing its actual application performance.

[0070] S6. Refer to Figure 10 , to achieve efficient and stable real-time dynamic motion control of the bionic pectoral fin under the optimized undulation parameters, a method combining a PID controller and fuzzy control is adopted, and the motion parameters of the pectoral fin are precisely adjusted using a non-linear mapping method. The specific implementation process is as follows: (1) Real-time error acquisition and normalization processing: During the actual motion of the bionic pectoral fin, real-time collect the current motion state (actual value) and the optimized target motion state (expected value) of the pectoral fin, and calculate the motion error e(t) and the error change rate e c (t) between them; Subsequently, perform normalization processing on the collected error values to ensure that the error data input into the fuzzy inference system is within a unified and stable numerical range, improving the stability and real-time performance of the control system; (2) Fuzzification processing: For the normalized error e(t) and the error change rate e c(t) is fuzzified, and its linguistic variables are defined as seven fuzzy levels: negative big (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), and positive big (PB) to adapt to different states and change trends that may occur in the actual control process; (3) Fuzzy inference and PID parameter optimization: A fuzzy inference rule base is established. This rule base comprehensively considers the response speed and stability of the control system and presets multiple fuzzy control rules; through the fuzzy levels of the input error and the error change rate, after fuzzy inference calculation, the adjustment amount Δk p of the proportional coefficient, the adjustment amount Δk i of the integral coefficient, and the adjustment amount Δk d of the differential coefficient are obtained as fuzzy outputs; (4) Defuzzification processing and real-time update of PID parameters: The centroid method is used to perform defuzzification processing on the Δk p , Δk i , and Δk d obtained by fuzzy inference to obtain clear and accurate PID controller parameter adjustment values; the proportional coefficient k p , integral coefficient k i , and differential coefficient k d of the PID controller are updated in real-time dynamically to ensure that the controller parameters can reflect the changes in the pectoral fin movement state in real-time and respond quickly and accurately to the target movement requirements; (5) PID control output and non-linear mapping: Based on the optimized and updated PID controller parameters, the control output c(t) between the pectoral fin movement state and the target state is calculated in real-time; finally, the control output of the PID controller is accurately converted into the real-time adjustment values of the pectoral fin fluctuation parameters through a non-linear mapping method, including the fluctuation amplitude adjustment amount ΔA, the fluctuation offset adjustment amount ΔB, the fluctuation phase difference adjustment amount and the fluctuation frequency adjustment amount Δω.

[0071] Specifically, the non-linear mapping method is:

[0072]

[0073] where α, β, γ, and κ are non-linear mapping coefficients determined according to the pectoral fin mechanical structure, control accuracy requirements, and response characteristic experiments.

[0074] Further, the obtained real-time adjustment values ΔA, ΔB, , Δω is applied to the pectoral fin undulation control system to adjust the pectoral fin movement in real time dynamically, making it move precisely according to the optimized undulation parameters; the above feedback control and real-time adjustment strategies are continuously implemented to ensure the efficient and stable movement of the pectoral fin, and ultimately achieve the goal of improving the propulsion efficiency and movement stability of the robotic fish; through the above detailed implementation steps, the precise adjustment and stable control of the pectoral fin movement parameters are realized, significantly improving the actual application performance and environmental adaptability of the bionic pectoral fin robot.

[0075] Furthermore, the Raspberry Pi and the FPGA master-slave controller store all computer programs and data for controlling the pectoral fin movement, and the controller is configured to execute an efficient movement control method for the multi-degree-of-freedom bionic pectoral fin.

[0076] According to the method of the present invention, on the premise of ensuring the pectoral fin propulsion speed, the stability of the robotic fish movement can be taken into account, improving the swimming efficiency and performance of the robotic fish, and endowing it with the ability to operate stably.

[0077] The background part of the present invention may include background information about the problems or environment of the present invention, rather than necessarily describing the prior art. Therefore, the content included in the background art section is not an admission by the applicant of the prior art.

[0078] The above content is a further detailed description of the present invention in combination with specific / preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. An efficient motion control method for a multi-degree-of-freedom bionic pectoral fin, characterized in that, The method includes the following steps: (1) Collect the swimming gait of the real fish pectoral fin through a vision sensor, obtain the pectoral fin motion characteristic data, and fit the basic motion law of the pectoral fin based on the characteristic data. The basic motion law of the pectoral fin consists of spanwise fluctuation and chordwise fluctuation equations, and the spanwise fluctuation and chordwise fluctuation equations are jointly determined by the wave amplitude envelope coefficient, fluctuation amplitude, fluctuation offset, fluctuation phase difference, wavelength multiple, and the generalized coordinate system representing the pectoral fin pose; (2) Adjust the parameters of the pectoral fin motion control equation through a Central Pattern Generators (CPG). The CPG network consists of multiple mutually coupled neural oscillation units, and each unit calculates and adjusts the amplitude, frequency, and phase difference of the pectoral fin in real time to control the spanwise and chordwise fluctuation motions of the pectoral fin; (3) Adopt Computational Fluid Dynamics (CFD) numerical simulation for the motion process of the pectoral fin under different spanwise and chordwise fluctuation parameters, extract the simulation data including thrust, drag, lift, and lateral force, and construct a hydrodynamic surrogate model based on the simulation data; (4) Based on the hydrodynamic surrogate model and the multi-objective optimization method, with the maximization of thrust, the minimization of drag, and the minimization of the fluctuation ranges of lift and lateral force as the objective functions, optimize to obtain the optimal combination of spanwise and chordwise fluctuation parameters of the pectoral fin; (5) Apply the optimized fluctuation parameters to the bionic pectoral fin control system through a PID controller and a nonlinear mapping method to realize the efficient motion law of the pectoral fin in real-time dynamic control, and improve the propulsion efficiency and motion stability of the robotic fish.

2. The high-efficiency motion control method of a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that, The vision sensor is a high-speed camera with a shooting frequency greater than 500 frames per second; taking the pectoral fin root as the coordinate origin, the fin surface as the xoy plane, the y-axis pointing outward along the fin surface, and determining the normal direction of the fin surface as the z-axis according to the right-hand screw rule to establish the generalized coordinate system of the pectoral fin pose.

3. The efficient motion control method of a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that Both the spanwise fluctuation equation and the chordwise fluctuation equation are obtained by fitting the pectoral fin motion characteristic data using Fourier series. The specific equations are: ； Among them, h y (y, t) is the spanwise oscillatory motion of the pectoral fin, y is the spanwise displacement length, c y0 , c y1 , c y2 are respectively the constant term, the first-order coefficient, and the second-order coefficient of the spanwise amplitude envelope curve of the pectoral fin, b y (t) is the fluctuation offset of the spanwise oscillatory curve, a y (t) is the fluctuation amplitude of the spanwise oscillatory curve, is the fluctuation phase difference of the spanwise oscillatory curve, k y is the wavelength multiple of the spanwise oscillatory curve; h x (x, t) is the chordwise oscillatory motion of the pectoral fin, x is the chordwise displacement length, c x0 , c x1 , c x2 are respectively the constant term, the first-order coefficient, and the second-order coefficient of the chordwise amplitude envelope curve of the pectoral fin, b x (t) is the fluctuation offset of the chordwise oscillatory curve, a x (t) is the fluctuation amplitude of the chordwise oscillatory curve, is the fluctuation phase difference of the chordwise oscillatory curve, k x is the wavelength multiple of the chordwise oscillatory curve, and t is the oscillation time.

4. The high-efficiency motion control method of a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that, The CPG network equation is: ； where the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, b i and a i are the fluctuation offset and amplitude, is the fluctuation phase difference of the chordwise fluctuation curve, k bi and k ai are the convergence rates of the fluctuation offset and amplitude, B i and A i are the extreme values of the fluctuation offset and amplitude, R i is the time ratio between the recovery stage and the outward swing stage in the swing period, ω i is the swing frequency; the parameters of the control equation are adjusted by CPG to control the pectoral fin to move according to the spanwise fluctuation equation and the chordwise fluctuation equation.

5. The high-efficiency motion control method of a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that, The CFD numerical simulation specifically includes steps of pectoral fin geometric modeling, mesh generation, boundary condition setting, solver setting, and post-processing analysis; using simulation software to perform real-time flow field calculation, outputting the hydrodynamic coefficient data of the pectoral fin under different fluctuation conditions, and constructing the hydrodynamic surrogate model through a neural network method. The model expression is ； Among them, C d is the drag coefficient, C l is the lift coefficient, C a is the side force coefficient; F d , F l , F a are respectively the nonlinear models between the pectoral fin undulation parameters and C d , C l , C a .

6. The efficient motion control method of a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that Based on the hydrodynamic surrogate model and the multi-objective optimization method, study and optimize the efficient fluctuation law of the pectoral fin with large thrust, small drag, small lift, and small lateral force under different spanwise and chordwise fluctuation parameters; the expression of the multi-objective optimization method is: ； Among them, J1 represents the maximization of propulsion efficiency, that is, the ratio of the propulsion force generated by the pectoral fin fluctuation to the energy consumption; J2 represents the maximization of stability, ensuring that the pectoral fin fluctuation can maintain the stability of the trajectory under different environments; the constraint conditions are: ； Among them, the subscript i takes x and y, representing the spanwise and chordwise parameters respectively, the subscripts max and min represent the maximum and minimum values of the parameters respectively, and the parameters in the constraint conditions depend on the pectoral fin oscillation equation, and the range is limited by its mechanical structure.

7. An efficient motion control method for a multi-degree-of-freedom bionic pectoral fin according to claim 1, characterized in that The parameters of the PID controller are optimized in real time through fuzzy control, which specifically includes the following steps: (a) Obtain the error e(t) and the error change rate e c (t) between the real-time pectoral fin motion state and the target motion state, and perform normalization processing; (b) Fuzzify the normalized error and error change rate and input them into the fuzzy inference system; (c) According to the preset fuzzy rule base, determine the proportional coefficient adjustment amount Δk p , integral coefficient adjustment amount Δk i , and derivative coefficient adjustment amount Δk d through fuzzy inference; (d) Use the centroid method to defuzzify to obtain the accurate PID controller parameter adjustment value and update the PID controller parameters in real time and dynamically; (e) Convert the control output of the PID controller into the pectoral fin flapping parameter adjustment value through a non-linear mapping method, including the fluctuation amplitude adjustment value ΔA, the fluctuation offset adjustment value ΔB, the fluctuation phase difference adjustment value , and the fluctuation frequency adjustment value Δω, where the fluctuation amplitude adjustment value ΔA = α·log(1 + |c(t)|), the fluctuation offset adjustment value ΔB = β·log(1 + |c(t)|), the fluctuation phase difference adjustment value Δϕ = γ·atan(c(t)), and the fluctuation frequency adjustment value Δω = κ·c(t) 2 , where α, β, γ, and κ are non-linear mapping coefficients respectively, to ensure that the pectoral fin moves precisely according to the optimal fluctuation parameters, improving the propulsion efficiency and motion stability of the robotic fish.

8. An efficient motion control method for a multi-degree-of-freedom bionic pectoral fin according to any one of claims 1 to 7, characterized in that, The multi-degree-of-freedom bionic pectoral fin is made of rigid fin rays, elastic fin rays and flexible fin membranes. The fin rays are made of 3D-printed PLA rigid material, the fin rays are made of super-elastic shape memory alloy plates, and the fin membranes are made of silicone materials; the motion control program of the multi-degree-of-freedom bionic pectoral fin is stored in the master-slave controllers of the Raspberry Pi and FPGA.

9. A rigid-flexible coupled bionic pectoral fin, comprising a bionic pectoral fin mechanism, a circuit controller and a pectoral fin motion control method, characterized in that, The master-slave controller is configured to execute an efficient motion control method for a multi-degree-of-freedom bionic pectoral fin according to any one of claims 1 to 8.

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