Three-degree-of-freedom pectoral fin cooperative motion control and gait optimization method

Abstract

The invention discloses a three-degree-of-freedom pectoral fin cooperative motion control and gait optimization method, which comprises the following steps of: firstly, establishing a motion gait model of a three-degree-of-freedom rigid pectoral fin, and acquiring hydrodynamic feedback and attitude information of the pectoral fin under different input parameter combinations in real time by utilizing a multi-mode sensing system so as to construct a pectoral fin-environment interaction model; secondly, training a high-level strategy network by adopting a deep reinforcement learning algorithm, and optimizing a control signal cbase (t) by taking propulsive efficiency and attitude stability as reward functions; then, constructing a multi-layer hierarchical neural control network to decode cbase (t), outputting an incremental control signal delta c (t), and introducing a central mode generator network to generate a reference trajectory # imgabs0 # of each degree of freedom; finally, dynamic compensation of external disturbance and modeling errors is achieved based on a sliding mode control method of an extended state observer, delta c (t) is adjusted online through a performance evaluation index function J (t) to correct control parameters, pectoral fin motion is kept in the optimal propulsion and stable state all the time, closed-loop optimization is achieved, and the propulsion efficiency and attitude control capacity of the robotic fish are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater robots, and relates to a three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method, and in particular to a rigid pectoral fin multi-degree-of-freedom motion trajectory control and gait optimization. Background Art

[0002] Bionic robot fish is a new type of underwater robot with advantages such as high maneuverability, high concealment and low noise. It is widely used in underwater resource exploration, underwater equipment inspection, underwater biological observation and underwater archaeology. Compared with traditional propulsion methods, bionic fish can achieve fine control and efficient propulsion in complex waters through flexible fin movement, among which the pectoral fin plays an important role in attitude adjustment, steering control and stability maintenance. The pectoral fin is an important part of the mesoaxial fin propulsion system, especially in manta rays, kite fish and other fish, which show highly flexible control ability; studies have shown that the flapping movement of the pectoral fin can not only provide part of the propulsion force, but also assist the fish body to complete the attitude control such as pitch, roll and yaw; although some research has made some progress in the rigid pectoral fin control of single-degree-of-freedom or two-dimensional plane motion, its movement freedom is limited, and it is difficult to meet the needs of high-degree-of-freedom attitude adjustment and multi-task control.

[0003] Most current pectoral fin control methods are based on single-axis symmetrical flapping or two-dimensional trajectory generation, and a complete three-degree-of-freedom rigid pectoral fin flapping model and control method have not yet been established; especially in bionic structures, the control method of three-degree-of-freedom coordinated flapping of the pectoral fins, such as forward and backward flapping, up and down flapping, and swaying, is realized through three servo drive units, and related research and literature are rarely published; in existing patent technologies, there is no systematic solution for the coordinated control mechanism and gait optimization strategy for three-degree-of-freedom rigid pectoral fins; in addition, the coordinated control of multi-degree-of-freedom pectoral fin movements not only faces the problem of kinematic coupling, but also involves complex rhythm generation, parameter synchronization, and motion efficiency optimization. Existing methods make it difficult to achieve rhythm matching, phase coordination, and gait optimization between multi-degree-of-freedom flapping, thereby limiting their application potential in high-performance bionic propulsion.

[0004] In view of this, there is an urgent need for a collaborative motion control and gait optimization method suitable for a rigid pectoral fin three-degree-of-freedom flapping system. Through system modeling, rhythmic control and optimization solution of the three-degree-of-freedom drive model, the unification of pectoral fin propulsion efficiency and posture stability can be achieved, filling the gap in existing research on three-degree-of-freedom pectoral fin flapping control and rhythm optimization. Summary of the invention

[0005] In response to the problems in the technical background, the present invention provides a three-degree-of-freedom pectoral fin collaborative motion control and gait optimization method, which can realize multi-degree-of-freedom motion trajectory control and gait optimization of rigid pectoral fins, and is mainly used to improve the propulsion efficiency, posture stability and disturbance robustness of robot fish in complex water environments.

[0006] The present invention provides a three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method, which comprises the following steps: (1) referring to the typical motion behavior of the pectoral fin of a real fish during underwater swimming, a basic motion gait model of a three-degree-of-freedom rigid pectoral fin is established, including forward and backward wing-flapping motion, up and down wing-flapping motion and wing-swaying motion, and a periodic function is used to model the three-degree-of-freedom pectoral fin kinematic model equation, with the generalized coordinate vector q(t) = [θ ro (t), θ fl (t), θ s (t)] T Describes the pectoral fin posture, θ ro (t) is the angular displacement of the wing flapping motion, θ fl (t) is the angular displacement of the wing flapping motion, θ s (t) is the angular displacement of the wing motion, t is time, and the control signal vector c(t) is defined as the complete control parameter set of the pectoral fin; (2) a multimodal sensing system is used to collect the hydrodynamic feedback and attitude information of the pectoral fin under different control input parameter combinations in real time. The sensing system includes a distributed pressure sensor and an inertial measurement unit to collect thrust F T (t), lift F L (t), lateral force F A (t) and attitude angle θ imu (t); (3) Based on real-time perception feedback data, a pectoral fin-environment interaction model is constructed, and a deep reinforcement learning algorithm is used to train the high-level strategy network to optimize the basic control signal c base (t), taking propulsion efficiency, attitude stability and lateral force suppression as the multi-objective reward function; (4) constructing a multi-layer hierarchical neural control network to base (t) is decoded and the incremental control signal Δc(t) is output. The first layer is used to extract the dynamic characteristics of the environment and the strategy mode, and the second layer outputs the amplitude, frequency, phase difference and bias of each degree of freedom. (5) The central pattern generator network (CPG) is introduced, which adopts a coupled nonlinear oscillator structure. According to the control signal c(t) = c base (t) +Δc(t) generates the rhythmic angular displacement reference trajectory of each degree of freedom , and through the phase difference Constructing the synergistic rhythmic relationship between degrees of freedom, is the current oscillator phase of the central pattern generator network, is the selected reference oscillator phase of the central pattern generator network, and t is time; (6) Adopt a sliding mode control method based on an Extended State Observer (ESO), and use the sliding mode surface to construct a disturbance compensation control law u i (t), and dynamically compensate for external disturbances and modeling errors by estimating the disturbance term z i3 (t), is the difference between the desired trajectory and the actual trajectory of the pectoral fin, is the derivative of the difference between the desired trajectory and the actual trajectory of the pectoral fin, is a positive real adjustment parameter, and t is time; (7) During continuous operation, dynamically evaluate the current gait output effect according to the performance evaluation index function J(t). If it deviates from the threshold ε, online adjust the incremental control signal Δc(t) based on the deviation direction to correct the control parameters, and keep the pectoral fin movement always in the optimal propulsion and stable state to achieve closed-loop optimization, improving the propulsion efficiency and attitude control ability of the robotic fish.

[0007] As a further technical solution, with the center of the three-degree-of-freedom movement of the pectoral fin as the origin, define a local coordinate system {P} for the pectoral fin movement: the x-axis points in the forward direction of the robotic fish, the y-axis is in the left-right direction of the robotic fish, and the z-axis is perpendicular to the ventral-dorsal direction of the fish body to form a right-handed coordinate system, and establish a generalized coordinate system for the pose of the pectoral fin; the coordination of the three-degree-of-freedom movement determines the overall movement effect of the pectoral fin, and can realize the basic movement gaits of the pectoral fin, including figure-eight and elliptical curves; the kinematic model equation of the pectoral fin movement is:

[0008] ;

[0009] where θ ro (t) is the angular displacement of the forward and backward flapping movement, θ fl (t) is the angular displacement of the up and down flapping movement, θ s (t) is the angular displacement of the rocking movement, A ro is the amplitude of the forward and backward flapping movement, A fl is the amplitude of the up and down flapping movement, A s is the amplitude of the rocking movement, b ro is the offset of the forward and backward flapping movement, b fl is the offset of the up and down flapping movement, b s is the offset of the rocking movement, ω ro is the frequency of the forward and backward flapping movement, ω fl is the frequency of the up and down flapping movement, ω s is the frequency of the rocking movement, δ ro is the phase difference of the forward and backward flapping movement, δ fl is the phase difference of the up and down flapping movement, δs is the phase difference of the pectoral fin flapping motion, and t is the time; when 2ω ro = ω fl , δ ro = π / 2, δ fl = 0, the basic motion gait of the pectoral fin is an "8"-shaped trajectory. When ω ro = ω fl , δ ro = π / 2, δ fl = 0, the basic motion gait of the pectoral fin is a "0"-shaped trajectory;

[0010] The control signal vector c(t) of the three-degree-of-freedom model of the pectoral fin contains the following parameters:

[0011] c(t) = [A ro (t), A fl (t), A s (t), b ro (t), b fl (t), b s (t), ω ro (t), ω fl (t), ω s (t), δ ro (t), δ fl (t), δ s (t)] T , where A ro (t) is the amplitude of the forward and backward flapping motion of the pectoral fin at time t, A fl (t) is the amplitude of the up and down flapping motion of the pectoral fin at time t, A s (t) is the amplitude of the rocking motion of the pectoral fin at time t, b ro (t) is the offset of the forward and backward flapping motion of the pectoral fin at time t, b fl (t) is the offset of the up and down flapping motion of the pectoral fin at time t, b s (t) is the offset of the rocking motion of the pectoral fin at time t, ω ro (t) is the frequency of the forward and backward flapping motion of the pectoral fin at time t, ω fl (t) is the frequency of the up and down flapping motion of the pectoral fin at time t, ω s (t) is the frequency of the rocking motion of the pectoral fin at time t, δ ro (t) is the phase difference of the forward and backward flapping motion of the pectoral fin at time t, δ fl (t) is the phase difference of the up and down flapping motion of the pectoral fin at time t, δ s (t) is the phase difference of the rocking motion of the pectoral fin at time t.

[0012] As a further technical solution, the data sampling frequency of the multimodal perception system is: the sampling frequency of the pressure sensor ≥ 100 Hz, the sampling frequency of the inertial measurement unit ≥ 200 Hz, and the attitude angle θ imu (t), thrust F T (t), lift F L (t), lateral force F A (t) are recorded synchronously to construct a high-precision feedback closed loop and achieve a fast response to complex dynamic environments.

[0013] As a further technical solution, during the high-level policy training process, a sliding window strategy is adopted to evaluate convergence and stability, and the policy network parameters are updated in combination with historical feedback; the form of the reward function R(t) is:

[0014] ;

[0015] In the formula, F T (t) is the thrust, P(t) is the power consumption, F L (t) is the lift, F A (t) is the lateral force, Var(F L (t)) and Var(F A (t)) respectively represent the fluctuation ranges of the lift and the lateral force, θ imu (t) is the real-time attitude angle, θ ref is the target attitude angle, w 1 , w 2 , w 3 and w 4 are the weighting coefficients of the reward function.

[0016] As a further technical solution, the first layer of the multi-layer hierarchical neural network is a structure based on Graph Neural Networks (GNN) or Long Short-Term Memory (LSTM), which is used to identify the environmental state transition trend; the second layer is a feedforward neural network or a convolutional neural network, which is used to output the incremental control signal Δc(t) for adjusting the three-degree-of-freedom motion.

[0017] As a further technical solution, the neural oscillator of the central pattern generator network adopts an amplitude-phase coupling model, and its expression is:

[0018] ;

[0019] In the formula, is the phase of the i-th oscillator, ω i is the local frequency, κ ij is the coupling strength, is the target phase difference, A i is the current amplitude of the oscillator, A target is the target value amplitude of the oscillator, α i is the amplitude adjustment rate, b i is the bias output, b target is the target value of the bias, β i is the bias adjustment rate, ω i is the frequency output, ω target is the target value of the frequency, γ i is the bias adjustment rate, δ i is the phase difference, δ target is the target value of the phase difference, is the phase difference adjustment rate; dynamically adjust the oscillator amplitude A i , frequency ω i , bias b i and the oscillator phase , ensuring the coupling fluctuation and rhythm continuity between degrees of freedom.

[0020] As a further technical solution, the disturbance compensation control law u i (t) output by the sliding mode controller is converted into the angular acceleration α i through the equivalent moment of inertia J i (t), and then integrated to obtain the target angular velocity ω ref,i (t), which is used for servo drive control:

[0021] ;

[0022] In the formula, ω 0 is the initial angular velocity (which can be set as the velocity at the end of the previous cycle), and t is the time.

[0023] As a further technical solution, the performance evaluation index function J(t) is defined as:

[0024] ;

[0025] In the formula, F T (t) is the thrust, is the target thrust, F L (t) is the lift force, F A (t) is the lateral force, Var(F L (t)) and Var(F A (t)) respectively represent the fluctuation ranges of the lift force and the lateral force, θ imu (t) is the real-time attitude angle, θ ref is the target attitude angle, w 1 , w 2 , w 3 and w 4is the weighting coefficient of the reward function, and t is the time; when the performance evaluation index function J(t) > ε, it indicates that the current gait performance deviates greatly, and the feedback adjustment of each control component in the incremental control signal Δc(t) needs to be triggered, including:

[0026] ;

[0027] where i ∈ {ro, fl, s} respectively represent the three degrees of freedom of the pectoral fin's forward and backward flapping, up and down flapping, and rocking, t is the time, and η A , η ω , η b , η δ are the step adjustment factors of each parameter. The adjusted incremental control signal Δc(t) will be used to update the control signal c(t) = c base (t) + Δc(t), driving the central pattern generator network to generate a new displacement reference trajectory .

[0028] As a further technical solution, in the "8"-shaped trajectory movement, the parameter range of the control signal includes: the amplitude A ro of the forward and backward flapping movement ∈ [-90°, 90°], the frequency ω ro of the forward and backward flapping movement ∈ [1 Hz, 4 Hz], the bias b ro of the forward and backward flapping movement ∈ [-45°, 45°], the phase difference δ ro of the forward and backward flapping movement ∈ [-180°, 180°], the amplitude A fl of the up and down flapping movement ∈ [-65°, 65°], the frequency ω fl of the up and down flapping movement ∈ [1 Hz, 8 Hz], the bias b fl of the up and down flapping movement ∈ [-30°, 30°], the phase difference δ fl of the up and down flapping movement ∈ [-180°, 180°]; the amplitude A s of the rocking movement ∈ [-180°, 180°], the frequency ω s of the rocking movement ∈ [1 Hz, 4 Hz], the bias b s of the rocking movement ∈ [-180°, 180°], the phase difference δ s of the rocking movement ∈ [-180°, 180°]; in the "0"-shaped trajectory movement, the amplitude A ro of the forward and backward flapping movement ∈ [-90°, 90°], the frequency ω ro of the forward and backward flapping movement ∈ [1 Hz, 4 Hz], the bias b ro∈ [-45°, 45°], the phase difference δ of the front and rear flapping motion ro ∈ [-180°, 180°], the amplitude A of the up and down flapping motion fl ∈ [-65°, 65°], the frequency ω of the up and down flapping motion fl ∈ [1 Hz, 8 Hz], the bias b of the up and down flapping motion fl ∈ [-30°, 30°], the phase difference δ of the up and down flapping motion fl ∈ [-180°, 180°]; the amplitude A of the wing-rocking motion s ∈ [-180°, 180°], the frequency ω of the wing-rocking motion s ∈ [1 Hz, 4 Hz], the bias b of the wing-rocking motion s ∈ [-180°, 180°], the phase difference δ of the wing-rocking motion s ∈ [-180°, 180°]; when the pectoral fin moves in two trajectories of "8" shape and "0" shape, it needs to be adaptively optimized according to the task requirements and hydrodynamic feedback to achieve the joint optimization of the propulsion efficiency and attitude control ability of the robotic fish.

[0029] As a further technical solution, the weights w 1 、w 2 、w 3 and w 4 of each performance index in the reward function can be dynamically adjusted according to the environmental complexity and task objectives to adapt to strategy modes such as energy consumption efficiency priority, attitude stability priority or propulsion speed priority; the weights of each performance index in the performance evaluation index function are adaptively adjusted according to the environmental complexity and task requirements, including but not limited to: energy consumption efficiency, attitude stability and propulsion speed.

[0030] The additional aspects and advantages of the present invention will be partly given in the following description, partly become obvious from the following description, or be understood through the practice of the present invention.

[0031] The beneficial effects of the present invention are as follows:

[0032] (1) The optimized three-degree-of-freedom pectoral fin mechanism has biogenicity in three dimensions of morphology, structure and function.

[0033] (2) The multi-modal perception system adopted can collect the hydrodynamic feedback and attitude information of the pectoral fin under different combinations of control input parameters in real time.

[0034] (3) Based on the real-time perception feedback data, a pectoral fin-environment interaction model is constructed, and a deep reinforcement learning algorithm is used to train the high-level policy network. The control signal is optimized with the propulsion efficiency, attitude stability, and lateral force suppression as the multi-objective reward function. At the same time, a multi-layer hierarchical neural control network is constructed to decode the control signal and output the incremental control signal Δc(t).

[0035] (4) The present invention adopts a sliding mode control method based on an Extended State Observer (ESO). During the continuous operation process, the current gait output effect is dynamically evaluated according to the performance evaluation index function J(t). If it deviates from the threshold ε, the incremental control signal Δc(t) is adjusted online based on the deviation direction to correct the control parameters, realizing the precise adjustment and stable control of the pectoral fin motion parameters, and significantly improving the practical application performance and environmental adaptability of the bionic pectoral fin robot.

[0036] (5) According to the method of the present invention, the pectoral fin motion is always in the optimal propulsion and stable state to achieve closed-loop optimization, improving the propulsion efficiency and attitude control ability of the robotic fish. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flowchart of the three-degree-of-freedom pectoral fin cooperative motion control and its gait optimization method according to the embodiment of the present invention.

[0038] Figure 2 It is a motion displacement diagram of the "8"-shaped basic motion gait of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0039] Figure 3 It is a motion displacement diagram of the "0"-shaped basic motion gait of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0040] Figure 4 It is a schematic diagram of the description of the generalized coordinate system of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0041] Figure 5 It is a schematic diagram of the actual motion of the "8"-shaped and "0"-shaped trajectories of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0042] Figure 6 It is a schematic diagram of the layout and acquisition of the three-degree-of-freedom pectoral fin sensing system in the example of the present invention.

[0043] Figure 7 It is a flowchart of the optimization of the deep reinforcement learning algorithm during the motion of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0044] Figure 8 It is a structure diagram of the multi-layer hierarchical neural control network during the motion of the three-degree-of-freedom pectoral fin in the example of the present invention.

[0045] Fig. 9 It is the flow chart of generating motion control signals by the three - degree - of - freedom pectoral fin CPG network in the embodiment of the present invention.

[0046] Fig.10 It is the schematic diagram of smooth switching between the "8" - shaped and "0" - shaped trajectories of the three - degree - of - freedom pectoral fin in the embodiment of the present invention.

[0047] Fig.11 It is the block diagram of sliding - mode control based on an extended state observer in the coordinated motion of the three - degree - of - freedom pectoral fin in the embodiment of the present invention.

[0048] Fig.12 It is the overall control block diagram of the coordinated motion control and gait optimization method of the three - degree - of - freedom pectoral fin in the embodiment of the present invention. Specific implementation manners

[0049] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them; based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0050] Please refer to the attached Figures 1 to 12 , an embodiment of the present invention provides a method for coordinated motion control and gait optimization of a three - degree - of - freedom pectoral fin. The method includes the following steps: (1) Referring to the typical motion behaviors of real fish pectoral fins during underwater swimming, a basic motion gait model of a three - degree - of - freedom rigid pectoral fin is established, including forward - backward flapping motion, up - down flapping motion and yawing motion, and a kinematic model equation of the three - degree - of - freedom pectoral fin is modeled using a periodic function, with the generalized coordinate vector q(t)=[θ ro (t), θ fl (t), θ s (t)] T describing the pectoral fin attitude, θ ro (t) being the angular displacement of the forward - backward flapping motion, θ fl (t) being the angular displacement of the up - down flapping motion, θ s (t) being the angular displacement of the yawing motion, t being time, and defining the control signal vector c(t) as the complete control parameter set of the pectoral fin; (2) Using a multi - modal perception system to collect the hydrodynamic feedback and attitude information of the pectoral fin under different combinations of control input parameters in real time. The perception system includes distributed pressure sensors and inertial measurement units, which collect the thrust F T (t), lift F L (t), lateral force F A (t) and attitude angle θ imu(t); (3) Based on the real-time perception feedback data, construct a pectoral fin-environment interaction model, and use a deep reinforcement learning algorithm to train a high-level policy network to optimize the basic control signal c base (t), with propulsion efficiency, attitude stability, and lateral force suppression as multi-objective reward functions; (4) Construct a multi-layer hierarchical neural control network to decode the basic control signal c base (t) and output an incremental control signal Δc(t), where the first layer is used to extract environmental dynamic features and policy patterns, and the second layer outputs adjustment quantities such as amplitude, frequency, phase difference, and bias for each degree of freedom; (5) Introduce a Central Pattern Generator (CPG) network, adopt a coupled nonlinear oscillator structure, and generate a rhythmic angular displacement reference trajectory for each degree of freedom according to the control signal c(t) = c base (t) + Δc(t) , and construct a cooperative rhythmic relationship between degrees of freedom through the phase difference , where is the current oscillator phase of the central pattern generator network, is the selected reference oscillator phase of the central pattern generator network, and t is time; (6) Adopt a sliding mode control method based on an Extended State Observer (ESO), use the sliding mode surface to construct a disturbance compensation control law u i (t), and realize dynamic compensation for external disturbances and modeling errors by estimating the disturbance term z i3 (t), is the difference between the desired trajectory and the actual trajectory of the pectoral fin, is the derivative of the difference between the desired trajectory and the actual trajectory of the pectoral fin, is a positive real adjustment parameter, and t is time; (7) During the continuous operation process, dynamically evaluate the current gait output effect according to the performance evaluation index function J(t). If it deviates from the threshold ε, then online adjust the incremental control signal Δc(t) based on the deviation direction to correct the control parameters, and keep the pectoral fin movement always in the optimal propulsion and stable state to achieve closed-loop optimization, improving the propulsion efficiency and attitude control ability of the robotic fish.

[0051] The following further describes specific embodiments of the present invention.

[0052] Refer to Figure 1 , this method is based on the motion modeling of biological pectoral fin flapping behavior, combines multi-modal perception systems, deep reinforcement learning strategies, hierarchical neural network controllers, CPG networks, ESO, and sliding mode control and other modules to achieve fine, rhythmic, and robust closed-loop control and adaptive optimization of bionic pectoral fins.

[0053] S1. Referring to the research results on the pectoral fin motion gait of real fish during swimming, the basic motion gaits of the rigid pectoral fin include the "8"-shaped and "0"-shaped trajectories. At the same time, the pectoral fin motion behavior of biological fish is systematically analyzed, and referring to its typical flapping-wing motion mechanism, the basic three-degree-of-freedom motion mode of the rigid pectoral fin is extracted: forward and backward flapping motion, up and down flapping motion, and wing-rocking motion. The motion of each degree of freedom can be modeled by a periodic function and form effective propulsion through specific phase relationships. Based on this, the kinematic model of the three degrees of freedom of the pectoral fin is:

[0054] ;

[0055] In the formula, θ ro (t) is the angular displacement of the forward and backward flapping motion, θ fl (t) is the angular displacement of the up and down flapping motion, θ s (t) is the angular displacement of the wing-rocking motion, A ro is the amplitude of the forward and backward flapping motion, A fl is the amplitude of the up and down flapping motion, A s is the amplitude of the wing-rocking motion, b ro is the offset of the forward and backward flapping motion, b fl is the offset of the up and down flapping motion, b s is the offset of the wing-rocking motion, ω ro is the frequency of the forward and backward flapping motion, ω fl is the frequency of the up and down flapping motion, ω s is the frequency of the wing-rocking motion, δ ro is the phase difference of the forward and backward flapping motion, δ fl is the phase difference of the up and down flapping motion, δ s is the phase difference of the wing-rocking motion, t is time; Refer to Figure 2 , when 2ω ro = ω fl , δ ro = π / 2, δ fl = 0, the basic motion gait composed of the forward and backward flapping and up and down flapping of the pectoral fin is the "8"-shaped trajectory; Refer to Figure 3 , when ω ro = ω fl , δ ro = π / 2, δ fl = 0, the basic motion gait composed of the forward and backward flapping and up and down flapping of the pectoral fin is the "0"-shaped trajectory.

[0056] Furthermore, referring to Figure 4, To uniformly express the three - degree - of - freedom motion state of the pectoral fin in space, a generalized coordinate system is introduced to describe it. As a rigid planar structure, the actual motion of the pectoral fin occurs within the local fish - body coordinate system. First, with the center of the three - degree - of - freedom motion of the pectoral fin as the origin, a local coordinate system {P} for the pectoral fin motion is defined: the x - axis points in the forward direction of the robotic fish, the y - axis is in the left - right direction of the robotic fish, and the z - axis is perpendicular to the ventral - dorsal direction of the fish body, forming a right - hand coordinate system. The motion of the pectoral fin is relative to this local coordinate system.

[0057] Specifically, define the generalized coordinate vector q(t) as a set of state variables describing the current posture of the pectoral fin, including the angular displacement θ ro (t) of the forward - backward flapping motion, the angular displacement θ fl (t) of the up - down flapping motion, and the angular displacement θ s (t) of the wing - rocking motion. It is expressed as: q(t)=[θ ro (t), θ fl (t), θ s (t)] T 。

[0058] Specifically, this generalized coordinate vector can be used as the core input of the controller and optimizer, connecting the perception, control, and execution modules. By tracking the changes of q(t) in real - time, the system can achieve dynamic modeling and control planning of the complex motion behavior of the pectoral fin, realizing the efficient propulsion and attitude adjustment of the robotic fish.

[0059] Furthermore, to establish an input - output mapping relationship for subsequent optimization and control, define the control - signal vector c(t) as a set of control parameters for the pectoral fin motion, used to drive the three - degree - of - freedom motion of the pectoral fin. The specific form of c(t) is: c(t)=[A ro (t), A fl (t), A s (t), b ro (t), b fl (t), b s (t), ω ro (t), ω fl (t), ω s (t), δ ro (t),δ fl (t), δ s (t)] T ,where A ro (t) is the amplitude of the forward - backward flapping motion of the pectoral fin at time t, A fl (t) is the amplitude of the up - down flapping motion of the pectoral fin at time t, A s (t) is the amplitude of the wing - rocking motion of the pectoral fin at time t, b ro (t) is the offset of the forward - backward flapping motion of the pectoral fin at time t, b fl(t) is the offset of the pectoral fin's up-and-down flapping motion at time t, b s (t) is the offset of the pectoral fin's pitching motion at time t, ω ro (t) is the frequency of the pectoral fin's front-and-back flapping motion at time t, ω fl (t) is the frequency of the pectoral fin's up-and-down flapping motion at time t, ω s (t) is the frequency of the pectoral fin's pitching motion at time t, δ ro (t) is the phase difference of the pectoral fin's front-and-back flapping motion at time t, δ fl (t) is the phase difference of the pectoral fin's up-and-down flapping motion at time t, δ s (t) is the phase difference of the pectoral fin's pitching motion at time t; the control signal c(t) serves as the interface signal between the neural control network and the output of the reinforcement learning strategy, is used to describe the desired pectoral fin motion pattern, and is further generated by the controller to generate an execution instruction to drive the pectoral fin to achieve the target motion behavior.

[0060] Specifically, the control signal c(t) can be further divided into the combined relationship between the basic control signal c base (t) output by the strategy and the incremental control signal Δc(t) adjusted by the neural network. Its mathematical expression is: c(t) = c base (t) + Δc(t), where c base (t) represents the basic control signal directly generated by the reinforcement learning strategy, and Δc(t) is the dynamic incremental control signal output by the multi-layer neural control network according to the environmental feedback; the two work together to form the final control signal that drives the pectoral fin to execute, realizing the efficient decoupling and coordination between the strategy layer and the execution layer.

[0061] Specifically, refer to Figure 5 , based on the established kinematic model, use simulation tools to visually simulate the pectoral fin motion trajectories under different fluctuation parameters. The simulation results show that the model can accurately describe the three-dimensional coordinated motion and gait structure coordination of the fish pectoral fin, and can provide an accurate reference for subsequent rhythm control and optimization learning.

[0062] S2. To implement the closed-loop adjustment mechanism for the three-degree-of-freedom motion modeling and control of the pectoral fin, a multi-modal perception system is introduced into the pectoral fin system of the robotic fish to collect the hydrodynamic feedback data and motion attitude information of the pectoral fin under different control input parameters (amplitude A, frequency ω, offset b, phase difference δ, etc.) in real time; refer to Figure 6, the perception system mainly consists of pressure sensors and inertial measurement units. Adopting a right-angled isosceles triangle layout strategy, three pressure sensors are respectively installed at the near root, the central area of the leading edge, and the end edge of the pectoral fin to record the normal pressure distribution generated during the interaction between the pectoral fin and the fluid, and then calculate hydrodynamic characteristics such as thrust, lateral force, and lift. This layout can maximize the coverage of the main working surface of the pectoral fin, improve the information content and identification ability of sensor data, and the sensor layout positions on the front and back sides of the pectoral fin are mirror-symmetrical about the fin surface; the inertial measurement unit module is installed at the base of the pectoral fin or the connection structure to continuously obtain the triaxial angular velocity, linear acceleration, and spatial attitude angle change data of the pectoral fin.

[0063] Furthermore, during the data acquisition process, by setting gait input parameters (such as amplitude A, frequency ω, bias b, phase difference δ, etc.) to drive the pectoral fin to perform periodic motion, and using the perception system to record the hydrodynamic and attitude data of the pectoral fin under each input condition in real time; for each control cycle T, the sampling frequency is set to f c = 500 Hz to obtain high-resolution data; the above data includes the hydrodynamic forces on the pectoral fin, the attitude angles and angular velocities in the three-axis directions.

[0064] Specifically, the calculation of hydrodynamic forces is based on the pressure integration method. Let the normal pressure distribution function on the surface of the pectoral fin be p n (x, y, t), and the time is t. Then the thrust F T 、lift F L and lateral force F A expressions can be respectively expressed as:

[0065] ;

[0066] In the formula, α(x, y) represents the angle between the normal of the surface element of the pectoral fin and the propulsion direction, β(x, y) represents the angle between the normal and the lateral direction, S is the force-bearing surface area of the pectoral fin, and x and y are the force-bearing directions of the pectoral fin respectively.

[0067] Specifically, the attitude data is obtained by fusing the gyroscope and accelerometer in the inertial measurement unit to obtain the actual attitude angle θ imu (t); all sensor data is timestamped and synchronized with the controller signal, so that the pectoral fin attitude q(t), the control signal c(t), and the thrust F T (t), lift F L (t), lateral force F A (t) in the feedback force value maintain a one-to-one correspondence, providing continuous and high-precision input for subsequent gait optimization and control strategy learning.

[0068] Specifically, the data collected by the perception system can not only be used to evaluate the execution effect of the three-degree-of-freedom motion of the pectoral fin, but also provide a basis for the parameter adjustment of the subsequent control strategy and the construction of the reward function of the optimization algorithm; by comparing the perception data with the generalized coordinate output in real time, the control error can be effectively monitored, supporting the update of the state-action mapping of reinforcement learning, so as to realize the dynamic adaptive control of the pectoral fin motion mode; and it is used to optimize the controller parameters and construct a hydrodynamic feedback mapping model, providing an input basis for the reward and punishment mechanism in reinforcement learning, and used for error correction between the actual motion and the ideal gait in the subsequent closed-loop control link.

[0069] S3. Refer to Figure 7 , on the basis of completing the three-degree-of-freedom motion modeling of the pectoral fin and the acquisition of perception data, a deep reinforcement learning algorithm is further introduced to realize the online optimization training of the basic motion gait of the pectoral fin; the optimization goal not only focuses on the improvement of the propulsion efficiency, but also takes into account the attitude stability and lift control to ensure that the bionic fish has good motion performance in a complex underwater environment.

[0070] Furthermore, the reinforcement learning framework takes the real-time feedback data provided by the perception system as the input of the environmental state, and combines the action output generated by the neurodynamics model to form a complete state-action space; the pectoral fin attitude angle vector q(t) and attitude angle change q̇(t) represented by the generalized coordinates are used as state features, combined with the basic control signal c base (t) and the feedback hydrodynamic values of thrust F T (t), lift F L (t), and lateral force F A (t) to construct an interaction model between the pectoral fin and the environment.

[0071] Specifically, the Deep Deterministic Policy Gradient (DDPG) algorithm is used for policy training. Its policy network outputs high-level control parameters of three degrees of freedom, including continuous variables such as amplitude A, frequency ω, bias b, and phase difference δ, and maps them to actual control instructions through the action network to guide the pectoral fin to complete a complete gait cycle.

[0072] Specifically, to achieve a balance among propulsion efficiency, attitude stability, and lift constraint, the following reward function R(t) is constructed:

[0073] ;

[0074] In the formula, F T (t) is the thrust, P(t) is the power consumption, F L (t) is the lift, F A (t) is the lateral force, Var(F L(t)) and Var(F A (t)) represent the fluctuation ranges of the lift and the lateral force respectively, and θ imu (t) is the real-time attitude angle, and θ ref is the target attitude angle, and w 1 , w 2 , w 3 and w 4 are the weighting coefficients of the reward function, and t is the time; while encouraging the propulsion efficiency, this reward function suppresses the attitude fluctuations and the lift instability.

[0075] In each training iteration, the agent samples trajectories by continuously interacting with the environment, performs policy evaluation and policy update, and gradually forms an efficient and stable motion pattern; the finally output high-level control policy is defined as the basic control signal c base (t). This control policy contains the basic control parameters of the three degrees of freedom of the pectoral fin, and its structural form is: c base (t) = [A rob (t), A flb (t), A sb (t), b rob (t), b flb (t), b sb (t), ω rob (t), ω flb (t), ω sb (t), δ rob (t), δ flb (t), δ sb (t)] T , where A rob (t) is the basic amplitude of the pectoral fin flapping back and forth at time t, A flb (t) is the basic amplitude of the pectoral fin flapping up and down at time t, A sb (t) is the basic amplitude of the pectoral fin rocking at time t, b rob (t) is the basic offset of the pectoral fin flapping back and forth at time t, b flb (t) is the basic offset of the pectoral fin flapping up and down at time t, b sb (t) is the basic offset of the pectoral fin rocking at time t, ω rob (t) is the basic frequency of the pectoral fin flapping back and forth at time t, ω flb (t) is the basic frequency of the pectoral fin flapping up and down at time t, ω sb (t) is the basic frequency of the pectoral fin rocking at time t, δ rob (t) is the basic phase difference of the pectoral fin flapping back and forth at time t, δ flb (t) is the basic phase difference of the pectoral fin flapping up and down at time t, δ sb(t) is the basic phase difference of the pectoral fin flapping motion at time t; the above parameters serve as the input reference for the decoding and adjustment of the incremental control signal Δc(t) in the subsequent neural network module.

[0076] S4. Refer to Figure 8 , based on the basic control signal c base (t) output by reinforcement learning, a multi-layer hierarchical neural control network structure is designed to generate the incremental control signal Δc(t) for executable pectoral fin motion; this neural network control system consists of a policy parsing layer and a degree-of-freedom decoding layer, and by decoupling the policy parameters layer by layer, while maintaining the flexibility of high-degree-of-freedom control, the coordinated control between the three degrees of freedom of the pectoral fin is achieved.

[0077] Furthermore, the first-layer policy parsing network takes the current basic control signal c base (t), the generalized coordinate state q(t), and the feedback attitude error θ imu (t) - θ ref (t) as inputs, extracts the current environmental state features through a feedforward neural network, and dynamically selects the appropriate basic gait pattern type (such as high-thrust type, stable type, or energy-saving type). The intermediate variable output by this layer is the policy mode vector s(t), which is used to guide the refinement process of the lower-layer control.

[0078] Furthermore, the second-layer degree-of-freedom parameter decoding network takes the policy mode vector s(t) and the basic control signal c base (t) as inputs, uses a convolutional network to extract multi-scale information, embeds an LSTM network structure to model the temporal dynamic characteristics of the pectoral fin, and outputs the refined adjustment incremental control signal Δc(t).

[0079] Specifically, the expression of the incremental control signal Δc(t) is: Δc(t) = [ΔA ro (t), ΔA fl (t), ΔA s (t), Δb ro (t), Δb fl (t), Δb s (t), Δω ro (t), Δω fl (t), Δω s (t), Δδ ro (t), Δδ fl (t), Δδ s (t)] T , where ΔA ro (t) is the amplitude adjustment amount of the pectoral fin's forward and backward flapping motion at time t, ΔA fl (t) is the amplitude adjustment amount of the pectoral fin's up and down flapping motion at time t, ΔA s$(t)$ is the amplitude adjustment amount of the pectoral fin flapping motion at time $t$, $\Delta b$ ro $(t)$ is the offset adjustment amount of the pectoral fin forward and backward flapping motion at time $t$, $\Delta b$ fl $(t)$ is the offset adjustment amount of the pectoral fin up and down flapping motion at time $t$, $\Delta b$ s $(t)$ is the offset adjustment amount of the pectoral fin flapping motion at time $t$, $\Delta\omega$ ro $(t)$ is the frequency adjustment amount of the pectoral fin forward and backward flapping motion at time $t$, $\Delta\omega$ fl $(t)$ is the frequency adjustment amount of the pectoral fin up and down flapping motion at time $t$, $\Delta\omega$ s $(t)$ is the frequency adjustment amount of the pectoral fin flapping motion at time $t$, $\Delta\delta$ ro $(t)$ is the phase difference adjustment amount of the pectoral fin forward and backward flapping motion at time $t$, $\Delta\delta$ fl $(t)$ is the phase difference adjustment amount of the pectoral fin up and down flapping motion at time $t$, $\Delta\delta$ s $(t)$ is the phase difference adjustment amount of the pectoral fin flapping motion at time $t$, $t$ is time; the above control instruction is the dynamic adjustment amount output of the basic control signal $c$ in the high-level strategy base $(t)$, representing the incremental adjustment of the original policy parameters by the neural network according to the environmental feedback; this instruction will be added to the basic control signal $c$ base $(t)$ to obtain the final control signal $c(t)$, which is used as the input of the subsequent CPG to achieve fine dynamic control of the gait.

[0080] Specifically, the multi-layer neural network is completed through an end-to-end training mechanism, learning from historical perception data and real control effects to optimize the network weights; at the same time, it supports online dynamic adjustment, correcting the output instruction through error feedback to ensure high responsiveness and adaptability; the finally output control signal will be input into the CPG module as a rhythm reference signal to drive the pectoral fin to execute fine movements.

[0081] Specifically, the multi-layer neural control architecture realizes a complete mapping process from policy generation to parameter decoding and then to execution control, with high scalability and environmental adaptability, providing flexible and efficient motion control capabilities for the bionic fish in complex environments.

[0082] S5. Refer to Fig. 9 , to ensure the rhythmic, coordinated and continuous composite motion control of the pectoral fin in a three-degree-of-freedom space, the system introduces a CPG network downstream of the neural network control structure as a periodic motion signal generator; this network realizes the real-time collaborative output of multi-degree-of-freedom rhythm signals by coupling multiple non-linear neural oscillators.

[0083] Furthermore, each degree of freedom of the pectoral fin (fore-aft flapping motion, up-down flapping motion, and wing-rocking motion) corresponds to an independent CPG neural oscillation unit, and the basic form of the oscillator is the Matsuoka neuron model or the Hopf oscillator model. To adapt to the complete structure of the pectoral fin flapping control signal, the CPG module includes the dynamic generation and regulation of four types of parameters: amplitude, frequency, phase difference, and bias. Their state equations can be expressed as follows:

[0084] ;

[0085] where, is the phase of the i-th oscillator, ω i is the local frequency, κ ij is the coupling strength, is the target phase difference, A i is the current amplitude of the oscillator, A target is the target value amplitude of the oscillator, α i is the amplitude adjustment rate, b i is the bias output, b target is the target value of the bias, β i is the bias adjustment rate, ω i is the frequency output, ω target is the target value of the frequency, γ i is the bias adjustment rate, δ i is the phase difference, δ target is the target value of the phase difference, is the phase difference adjustment rate.

[0086] Furthermore, to achieve the coordinated control between multiple degrees of freedom, the system uses the parameters in the control signal c(t) as the reference input of the CPG network to drive each CPG unit to stably generate the required periodic output. The output expression of the CPG network is: , where the phase difference δ i (t) is not generated independently, but is dynamically constructed through the difference between the current oscillator phase of the CPG network and the phase of the selected reference oscillator of the CPG network, that is , t is time; this trajectory model reflects the coordinated regulation ability of the motion rhythm ( ), amplitude (A i ), bias (b i ), and phase difference (δ i ), ensuring the rhythm, stability, and flexibility of the pectoral fin movement. The output is used as the target motion trajectory of the i-th degree of freedom of the pectoral fin, and i can take the values ro, fl, s, representing the fore-aft flapping motion, up-down flapping motion, and wing-rocking motion respectively.

[0087] Meanwhile, the coupling mechanism ensures a predefined phase synchronization relationship among the three-channel outputs, thereby generating continuous coordinated motion gaits such as "0"-shaped and "8"-shaped gaits, and realizing natural switching between motion modes such as propulsion and turning; refer to Fig.10 , and the output of the CPG network has both compliance and robustness while ensuring the fluctuation rhythm.

[0088] S6. Refer to Fig.11 , to further improve the robustness and control stability of the bionic robotic fish in a dynamically complex underwater environment, after the output of the rhythm control layer, this system introduces a disturbance suppression strategy combining an Extended State Observer (ESO) and Sliding Mode Control (SMC) to perform online estimation and real-time compensation for external disturbances, hydrodynamic changes, and model uncertainties.

[0089] Furthermore, take the target trajectory output by the CPG as the reference input of the control system, define the reference pose as , and construct an error signal by combining the actual pose response q(t) of the pectoral fin:

[0090] ;

[0091] In the formula, is the derivative of the actual pose of the pectoral fin, is the derivative of the reference pose of the pectoral fin, is the difference between the desired trajectory and the actual trajectory of the pectoral fin, is the derivative of the difference between the desired trajectory and the actual trajectory of the pectoral fin, and t is time.

[0092] Furthermore, based on the above error, construct a sliding mode surface:

[0093] ;

[0094] In the formula, λ i is a positive real number adjustment parameter, and t is time.

[0095] Furthermore, construct an extended state observer to estimate the system disturbance term d i (t) and the unmodeled dynamics. The structure of the ESO is as follows:

[0096] ;

[0097] In the formula, y i is the actual measured output of the system (the current pose q i (t) of the pectoral fin), u i is the control input, and z i1For estimating the output, z i2 For estimating the speed, z i3 For estimating the disturbance term (including uncertainties, modeling errors, environmental disturbances, etc.), β 1 , β 2 , β 3 is the observation gain of the ESO, which can affect the estimation speed and stability.

[0098] Furthermore, the controller design adopts a typical sliding mode control law:

[0099] ;

[0100] In the formula, the first term is the disturbance suppression sliding mode term, and the second term is the compensation term estimated in real time by the ESO; is the sliding mode output, is the sign function of the sliding mode surface. When , , when , , when , , is the gain, is the system estimated disturbance term.

[0101] Furthermore, the disturbance compensation control quantity u i (t) output by the sliding mode controller is converted into the angular velocity ω i that can be executed by the driver through the equivalent moment of inertia J ref,i (t). This process includes mapping the control compensation signal to the angular acceleration α i (t), and its expression is: ; Then, the target angular velocity trajectory ω ref,i (t) required by the pectoral fin motor is generated through integration, and its expression is ; In the formula, J i is the equivalent moment of inertia of the drive mechanism system, ω 0 is the initial angular velocity (which can be set as the velocity at the end of the previous cycle), t is the time, and ω ref,i (t) is the desired angular velocity input executed by the drive motor, which is directly used to control the servo motor or actuator to drive the pectoral fin to achieve the target pose response.

[0102] Furthermore, this mapping process ensures the dynamic response consistency between the control compensation signal and the actuator, improves the tracking accuracy and attitude robustness in a disturbance environment, and realizes the dynamic compensation response for actual disturbances.

[0103] S6. Refer to Fig.12, based on the hydrodynamic feedback information collected in real time by the multi-modal perception system, dynamically optimize the pectoral fin gait parameters, and construct a closed-loop control mechanism by fusing the basic control signal c base (t) and the incremental control signal Δc(t), so that the pectoral fin movement is always in the optimal gait interval of high efficiency and stability, ensuring the closed-loop adaptability and long-term stable operation of the pectoral fin control system.

[0104] Furthermore, in the control execution stage, the perception system continuously collects the hydrodynamic response thrust F T (t), lift F L (t), lateral force F A (t) and attitude angle θ imu (t) as well as the target pose and the actual pose q(t), thereby constructing a gait performance evaluation index function J(t), which is used to measure the difference between the actual motion effect and the expected target. Its structure can be expressed as:

[0105] ;

[0106] In the formula, is the thrust, is the target thrust, F L (t) is the lift, F A (t) is the lateral force, Var(F L (t)) represents the fluctuation degree of the lift, Var(F A (t)) represents the fluctuation degree of the lateral force, θ imu (t) is the real-time attitude angle, θ ref (t) is the target attitude angle, w 1 , w 2 , w 3 , w 4 are weight coefficients, and t is time; the system calculates the gait performance evaluation index function J(t) in real time and compares it with the set threshold ε. If J(t) > ε, it means that the current gait performance deviates greatly and the parameter fine-tuning mechanism needs to be triggered.

[0107] Furthermore, during the gait parameter fine-tuning process, the system retains the basic control signal c base (t) generated by the reinforcement learning strategy, and at the same time adjusts all four types of key control quantities in the incremental control signal Δc(t) according to the error direction, including the amplitude adjustment amount ΔA i (t), the frequency adjustment amount Δω i (t), the bias adjustment amount Δb i (t) and the phase difference adjustment amount Δδ i (t); based on the thrust error, attitude error and lateral force fluctuation as the adjustment basis, the system can construct the following adaptive adjustment law:

[0108] ;

[0109] wherein, i ∈ {ro, fl, s} respectively represent three degrees of freedom of the pectoral fin flapping forward and backward, flapping up and down, and rocking, t is time, and η A , η ω , η b , η δ are the step adjustment factors of each parameter. The adjusted incremental control signal Δc(t) will be used to update the control signal c(t) = c base (t) + Δc(t), driving the CPG network to generate a new displacement reference trajectory .

[0110] Furthermore, this feedback fusion process realizes fast local correction without affecting the stability of the main strategy, improves the adaptive ability of the robotic fish in dynamic disturbances and task switching, and finally realizes a closed-loop fusion control framework of strategy learning, neuromodulation, rhythm generation and feedback correction, so that the pectoral fin movement is always in a state of cooperative optimization with high propulsion efficiency and stable posture.

[0111] According to the method of the present invention, it is possible to take into account the stability of the movement of the robotic fish while ensuring the pectoral fin propulsion speed, improve the swimming efficiency and performance of the robotic fish, and enable it to have the ability to operate stably.

[0112] 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.

[0113] The above content is a further detailed description of the present invention in combination with specific / preferred embodiments, and cannot determine 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 is also intended to include these modifications and variations.

Claims

1. A three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method, characterized in that: The following steps are involved: S1. With reference to the typical motion behaviors of the pectoral fins of real fishes during underwater swimming, a basic motion gait model of the three-degree-of-freedom rigid pectoral fins is established, including forward and backward wing-flapping motion, up and down wing-flapping motion, and wing-swaying motion. The three-degree-of-freedom pectoral fin kinematic model equation is modeled using a periodic function, with the generalized coordinate vector q(t) = [θ ro (t), θ fl (t), θ s (t)] T Describes the pectoral fin posture, θ ro (t) is the angular displacement of the wing flapping motion, θ fl (t) is the angular displacement of the wing flapping motion, θ s (t) is the angular displacement of the wing movement, t is the time, and the control signal vector c(t) is defined as the complete control parameter set of the pectoral fin; S2, using a multi-modal perception system to collect hydrodynamic feedback and attitude information of the pectoral fin under different control input parameter combinations in real time, the perception system includes a distributed pressure sensor and an inertial measurement unit to collect thrust F T (t), lift F L (t), lateral force F A (t) and attitude angle θ imu (t); S3. Based on real-time perception feedback data, a pectoral fin-environment interaction model is constructed, and a deep reinforcement learning algorithm is used to train the high-level strategy network to optimize the basic control signal c base (t), with propulsion efficiency, attitude stability and lateral force suppression as the multi-objective reward function; S4, build a multi-layer hierarchical neural control network to control the basic control signal c base (t) is decoded and an incremental control signal Δc(t) is output, wherein the first layer is used to extract the dynamic characteristics of the environment and the strategy mode, and the second layer outputs the adjustment values ​​such as the amplitude, frequency, phase difference and bias of each degree of freedom; S5, introduce the central pattern generator network, adopt the coupled nonlinear oscillator structure, according to the control signal c(t) = c base (t) + Δc(t) generates the rhythmic angular displacement reference trajectory of each degree of freedom , and through the phase difference Constructing the synergistic rhythmic relationship between degrees of freedom, is the current oscillator phase of the central pattern generator network, The reference oscillator phase is selected for the central pattern generator network, where t is time; S6, adopt the sliding mode control method based on the extended state observer, using the sliding surface Construct disturbance compensation control law u i (t), by estimating the disturbance term z i3 (t) Realize dynamic compensation for external disturbances and modeling errors, is the difference between the expected trajectory and the actual trajectory of the pectoral fin, is the derivative of the difference between the desired and actual pectoral fin trajectory, is a positive real number adjustment parameter, t is time; S7. During continuous operation, the current gait output effect is dynamically evaluated according to the performance evaluation index function J(t). If it deviates from the threshold ε, the incremental control signal Δc(t) is adjusted online based on the deviation direction to correct the control parameters, so as to keep the pectoral fin movement in the optimal propulsion and stable state at all times to achieve closed-loop optimization and improve the propulsion efficiency and posture control ability of the robot fish.

2. A three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: Taking the pectoral fin three-degree-of-freedom motion center as the origin, define the pectoral fin motion local coordinate system {P}: the x-axis points to the forward direction of the robot fish, the y-axis is the left and right direction of the robot fish, and the z-axis is perpendicular to the ventral and dorsal direction of the fish body to form a right-handed coordinate system, and establish the generalized coordinate system of the pectoral fin posture; the three-degree-of-freedom motion determines the overall motion effect of the pectoral fin, and can realize the basic motion gait of the pectoral fin, including the 8-shaped and elliptical curves; the pectoral fin kinematic model equation is: ； In the formula, θ ro (t) is the angular displacement of the wing flapping motion, θ fl (t) is the angular displacement of the wing flapping motion, θ s (t) is the angular displacement of the swing wing, A ro is the amplitude of the wing flapping motion, A fl is the amplitude of the wing flapping motion, A s is the swing wing motion amplitude, b ro is the front and rear flapping motion offset, b fl is the up and down wing-flapping motion offset, b s is the swing wing motion bias, ω ro is the frequency of flapping wings forward and backward, ω fl is the frequency of wing flapping up and down, ω s is the wing swing frequency, δ ro is the phase difference of the front and rear wing flapping motion, δ fl is the phase difference of the up and down wing movement, δ s is the phase difference of the swinging wing motion, t is the time; when 2ω ro = ω fl ,δ ro = π / 2, δ fl = 0, the basic movement gait of the pectoral fin is an "8"-shaped trajectory. ro = ω fl ,δ ro = π / 2, δ fl =0, the basic motion gait of the pectoral fin is a "0"-shaped trajectory; the control signal vector c(t) of the pectoral fin three-degree-of-freedom model includes the following parameters: c(t) = [A ro (t), A fl (t), A s (t), b ro (t), b fl (t), b s (t),ω ro (t),ω fl (t),ω s (t), δ ro (t), δ fl (t), δ s (t)] T , where A ro (t) is the amplitude of the pectoral fin flapping back and forth at time t, A fl (t) is the amplitude of the pectoral fin flapping up and down at time t, A s (t) is the amplitude of the pectoral fin swinging motion at time t, b ro (t) is the pectoral fin flapping motion offset at time t, b fl (t) is the pectoral fin flapping motion offset at time t, b s (t) is the pectoral fin swing motion bias at time t, ω ro (t) is the frequency of the pectoral fin flapping back and forth at time t, ω fl (t) is the frequency of the pectoral fin flapping up and down at time t, ω s (t) is the frequency of the pectoral fin flapping movement at time t, δ ro (t) is the phase difference of the pectoral fin flapping forward and backward at time t, δ fl (t) is the phase difference of the pectoral fin flapping up and down at time t, δ s (t) is the phase difference of the pectoral fin swinging motion at time t.

3. A three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The data sampling frequency of the multimodal perception system is: the pressure sensor sampling frequency ≥ 100 Hz, the inertial measurement unit sampling frequency ≥ 200 Hz, and the attitude angle θ is recorded synchronously imu (t), thrust F T (t), lift F L (t), lateral force F A (t) To build a high-precision feedback loop and achieve rapid response to complex dynamic environments.

4. A three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: During the high-level strategy training process, a sliding window strategy is used to evaluate convergence and stability, and the strategy network parameters are updated in combination with historical feedback; the form of the reward function R(t) is: ； In the formula, F T (t) is thrust, P(t) is power consumption, F L (t) is the lift, F A (t) is the lateral force, Var(F L (t)) and Var(F A (t)) represent the fluctuation range of lift and lateral force, θ imu (t) is the real-time attitude angle, θ ref is the target posture angle, w1, w2, w3 and w4 are the weighted coefficients of the reward function.

5. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The first layer of the multi-layer recursive neural network is a structure based on a graph neural network or a long short-term memory network, which is used to identify the trend of environmental state transition; the second layer is a feedforward neural network or a convolutional neural network, which is used to output an incremental control signal Δc(t) for adjusting three-degree-of-freedom motion.

6. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The neural oscillator of the central pattern generator network adopts an amplitude-phase coupling model, which is expressed as: ； In the formula, is the phase of the i-th oscillator, ω i is the local frequency, κ ij is the coupling strength, is the target phase difference, A i is the current amplitude of the oscillator, A target is the oscillator target value amplitude, α i is the amplitude adjustment rate, b i is the bias output, b target is the bias target value, β i is the bias adjustment rate, ω i is the frequency output, ω target is the frequency target value, γ i is the bias adjustment rate, δ i is the phase difference, δ target is the phase difference target value, The phase difference is used to adjust the rate; the oscillator amplitude A is dynamically adjusted through the state equation i , frequency ω i , bias b i and oscillator phase , ensuring the coupling fluctuation and rhythmic continuity between degrees of freedom.

7. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The sliding mode controller outputs the disturbance compensation control law u i (t) via equivalent moment of inertia J i Convert to angular acceleration α i (t), and then integrate to get the target angular velocity ω ref,i (t), for servo drive control: ； Where ω0 is the initial angular velocity and t is the time.

8. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The performance evaluation index function J(t) is defined as: ； In the formula, F T (t) is the thrust, is the target thrust, F L (t) is the lift, F A (t) is the lateral force, Var(F L (t)) and Var(F A (t)) represent the fluctuation range of lift and lateral force, θ imu (t) is the real-time attitude angle, θ ref is the target posture angle, w1, w2, w3 and w4 are the weight coefficients of the reward function, and t is the time; When the performance evaluation index function J(t) > ε, it means that the current gait performance deviation is large, and it is necessary to trigger the feedback adjustment of each control component in the incremental control signal Δc(t), including: ； In the formula, i ∈ {ro, fl, s} represents the three degrees of freedom of the pectoral fin flapping forward and backward, flapping up and down, and shaking the wing, t is time, η A , η ω , η b , η δ is the parameter step adjustment factor, and the adjusted incremental control signal Δc(t) will be used to update the control signal c(t) = c base (t) + Δc(t), driving the central pattern generator network to generate a new displacement reference trajectory .

9. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: In the "8"-shaped trajectory motion, the control signal parameter range includes: the amplitude A of the forward and backward flapping motion ro ∈ [-90°, 90°], the frequency of the forward and backward wingbeat motion ω ro ∈ [1 Hz, 4 Hz], the bias b of the forward and backward wing-flapping motion ro ∈ [-45°, 45°], the phase difference δ between the front and rear flapping motions ro ∈ [-180°, 180°], the amplitude of the up and down wing-flapping motion A fl ∈ [-65°, 65°], the frequency of the up and down wing-flapping motion ω fl ∈ [1 Hz, 8 Hz], the bias b of the up and down wing-flapping motion fl ∈ [-30°, 30°], the phase difference δ between the up and down wingbeat motion fl ∈ [-180°, 180°]; Amplitude of the wing motion A s ∈ [-180°,180°], the frequency of the wing movement ω s ∈ [1 Hz, 4 Hz], the bias b of the swinging wing motion s ∈ [-180°, 180°], the phase difference of the swinging wing motion δ s ∈ [-180°, 180°]; In the "0"-shaped trajectory motion, the amplitude A of the forward and backward wingbeat motion ro ∈[-90°, 90°], the frequency of the forward and backward wing-flapping motion ω ro ∈ [1 Hz, 4 Hz], the bias b of the forward and backward wing-flapping motion ro ∈ [-45°, 45°], the phase difference δ between the front and rear flapping motions ro ∈ [-180°, 180°], the amplitude of the up and down wing-flapping motion A fl ∈ [-65°, 65°], the frequency of the up and down wing-flapping motion ω fl ∈ [1 Hz, 8 Hz], the bias b of the up and down wing-flapping motion fl ∈ [-30°, 30°], the phase difference δ between the up and down wingbeat motion fl ∈ [-180°, 180°]; Amplitude of the wing motion A s ∈ [-180°,180°], the frequency of the wing movement ω s ∈ [1 Hz, 4 Hz], the bias b of the swinging wing motion s ∈ [-180°, 180°], the phase difference of the swinging wing motion δ s ∈ [-180°, 180°]; When the pectoral fin moves in the "8" and "0" trajectories, it is necessary to adaptively optimize according to the task requirements and hydrodynamic feedback to achieve the joint optimization of the propulsion efficiency and attitude control ability of the robot fish.

10. The three-degree-of-freedom pectoral fin coordinated motion control and gait optimization method according to claim 1, characterized in that: The weights w1, w2, w3 and w4 of each performance indicator in the reward function can be dynamically adjusted according to the environmental complexity and task objectives, and can adapt to strategy modes such as energy efficiency priority, posture stability priority or propulsion speed priority; the weights of each performance indicator in the performance evaluation indicator function are adaptively adjusted according to the environmental complexity and task requirements, including but not limited to: energy efficiency, posture stability and propulsion speed.

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