Trajectory tracking control method of under-actuated underwater robot

Abstract

The invention discloses a trajectory tracking control method of an underactuated underwater robot, and relates to a trajectory tracking control method of preset time bidirectional fuzzy brain emotion learning of the underactuated underwater robot with tunnel type error constraint. Errors are converted by utilizing a tunnel type performance function, and a bidirectional fuzzy brain emotion learning control strategy is adopted, so that the under-actuated underwater robot still has relatively high stability and robustness under the condition of ocean external disturbance and model uncertainty; compact preset performance constraints of the system during transient and steady states and stability of the system at a presettable time point are satisfied.

Description

Technical Field

[0001] The invention belongs to the technical field of three-dimensional trajectory tracking control, and in particular relates to a trajectory tracking control method of an underactuated underwater robot. Background Art

[0002] The ocean covers more than 70% of the Earth's surface and is a treasure trove of rich mineral and underwater biological resources. In this context, underwater robots (AUVs) have received increasing attention due to their key role in tasks such as ocean exploration, target detection, and deep-sea exploration. Among these underwater robots, underactuated underwater robots have attracted much attention because they reduce the number of actuators, effectively reduce energy consumption and system quality, and improve the propulsion efficiency of the remaining thrusters and the overall reliability of the system.

[0003] Trajectory tracking control is the basis for underactuated underwater robots to complete various underwater operations, and it is also a research hotspot in the field of motion control. However, the underactuated underwater robot system is highly nonlinear and strongly coupled, and the uncertain ocean current interference in the marine environment makes the control problem more complicated. Therefore, it is of great research value and practical significance to study how to design an effective controller to ensure that underactuated underwater robots can perform trajectory tracking tasks smoothly and reliably in complex marine environments. This can not only improve the performance of underwater robots, but also provide technical support for the exploration and utilization of marine resources.

[0004] In the field of trajectory tracking control of underactuated underwater robots, traditional control methods include PID control, sliding mode control, and adaptive backstepping control. PID control is popular because of its simplicity and low dependence on system models, but its performance is insufficient under strong interference and rapid environmental changes. Sliding mode control is favored for its fast response and robustness to parameter changes. It can maintain stability after the system state reaches the predetermined sliding surface, but it may produce chattering near the sliding surface, affecting the control accuracy and accelerating actuator wear. Adaptive backstepping control adjusts parameters in real time to adapt to external disturbances, but the calculation is large and the parameters are numerous, which increases the complexity of the design. In addition, the above control methods are developed based on system model information and the integration of various complex advanced technologies. The controller design process is complicated and has low practicality. With the development of intelligent control technology, many scholars have begun to study different intelligent algorithms to control underactuated underwater robot systems, such as fuzzy control, model predictive control, reinforcement learning control, neural network control, etc.

[0005] The brain emotion learning control algorithm is inspired by biological mechanisms, operates independently of the system model, and bypasses the traditional constraints of model information-dependent control strategies. The control algorithm adopts a dual-network architecture that reflects the process of the human brain processing sensory information and emotional responses. The first network represents the amygdala, which is responsible for generating the best emotional response to various stimuli and affecting memory; the second network imitates the orbitofrontal cortex and focuses on perception and emotion regulation learning. Therefore, the brain emotion learning control algorithm has good estimation ability and fast learning speed. The network not only effectively reduces the tracking error, but also reduces the dependence on the precise system model and reduces the complexity of the controller design. It has important research value in promoting the development of underactuated underwater robot technology.

[0006] Secondly, in the control field of underactuated underwater robots, error convergence is usually based on asymptotic convergence or finite-time convergence theory. The convergence speed of the system under the guidance of these theories is affected by the initial state, which makes it difficult to accurately predict the convergence time due to the uncertainty of the initial state during the execution of different tasks, thereby limiting the practicality of the control method. To solve this problem, the fixed-time control theory was proposed, aiming to make the convergence time independent of the initial conditions. However, the fixed-time control theory is limited by the selection of design parameters in design, and its convergence time expression provides an upper bound rather than an exact value, resulting in an overly conservative control strategy. Therefore, the preset time convergence theory came into being. This theory can accurately preset the system convergence time and is not limited by the initial conditions, thereby providing strong support for underactuated underwater robots to perform diverse trajectory tracking tasks and significantly improving the practicality and flexibility of the control strategy.

[0007] In addition, when performing trajectory tracking control, in order to meet performance requirements, physical limitations and safety issues, the tracking accuracy of the trajectory becomes particularly critical. The preset performance control method has attracted attention because it can constrain the system error, thereby improving the tracking accuracy in transient and steady states. At present, with the complexity of task requirements, the transient performance requirements of underactuated underwater robots have also increased. However, the existing preset performance control methods mostly use symmetrical performance boundaries, which leads to a funnel-shaped constraint error boundary. Therefore, the performance boundary in the transient stage is relatively loose, and the system error may produce a large overshoot in the transient state, affecting the accuracy of trajectory tracking. In order to solve this problem, it is necessary to improve the curve shape of the preset performance boundary and tighten the transient error feasibility interval to significantly improve the control accuracy of the preset performance control method.

[0008] Therefore, through the above analysis, although there have been many studies on trajectory tracking control of underactuated underwater robots and many effective methods have been proposed, most controllers rely on detailed model information and do not limit the system error to a preset interval. In addition, these controllers are usually based on asymptotic convergence or finite time convergence, which makes the control reliability and practicality low. Summary of the invention

[0009] In view of the above-mentioned deficiencies in the prior art, the trajectory tracking control method of an underactuated underwater robot provided by the present invention solves the problems of the influence of external disturbances and model uncertainties on the system stability of the underactuated underwater robot during the trajectory tracking process, the problem of the controller relying on detailed model information resulting in an overly complex design, the problem of the system error convergence time being difficult to directly control, and the problem of transient error boundary interval redundancy in the existing preset performance control.

[0010] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: a trajectory tracking control method of an underactuated underwater robot, comprising the following steps:

[0011] S1. Use practical preset time control theory and its proof lemma to construct a five-degree-of-freedom kinematic and dynamic model of an underactuated underwater robot;

[0012] S2. Based on the constructed five-DOF kinematic and dynamic models, the tracking error of the underactuated underwater robot is determined by the line-of-sight method;

[0013] S3, constructing a tunnel-type performance function, and performing error conversion with the tracking error of the underactuated underwater robot, thereby determining the preset performance constraints;

[0014] S4. Designing a preset time virtual control law according to the determined preset performance constraints;

[0015] S5, constructing a bidirectional fuzzy brain emotion learning control network for outputting an approximate ideal control law of an underactuated underwater robot, and using the surge, pitch and yaw directions of the underactuated underwater robot obtained based on a preset time virtual control law as inputs of the bidirectional fuzzy brain emotion learning control network;

[0016] S6. Adaptively compensate the output control law of the bidirectional fuzzy brain emotion learning control network to obtain the actual control law, and use the actual control law to perform trajectory tracking control on the under-actuated underwater robot.

[0017] Furthermore, in step S1, the five-degree-of-freedom kinematics and dynamics model of the underactuated underwater robot constructed is expressed as:

[0018]

[0019] in:

[0020]

[0021] g(η)=[0 0 0ρg▽GM L sin(θ)0] T

[0022] Where J(η) represents the rotation matrix between the earth coordinate system and the underwater robot body coordinate system, M represents the mass inertia matrix, represents the hydrodynamic damping coefficient matrix, represents the Coriolis force and centripetal force matrix of the underwater robot, g(η) represents the vector of buoyancy and gravity, x, y, z represent the real displacement of the underactuated autonomous underwater robot, represents the yaw angle, θ represents the pitch angle, represents the first-order derivative of η, u,ν,w,q,r represent x,y,z,θ, The true speed in the direction, express The first-order derivative of , τ represents the control input, F = [ω u ,ω v ,ω w ,ω q ,ω r ] T represents the time-varying position ocean disturbance, ω u ,ω v ,ω w ,ω q ,ω r Represent x, y, z, θ, The ocean disturbance in the direction, ρ represents water density, g represents gravitational acceleration, ▽ represents displacement, M L Indicates the longitudinal metacentric height, m 11 、m 22 、m 33 、m 55 and m 66 Denote the equivalent mass along the x-axis, along the y-axis, along the z-axis, around the y-axis, and around the z-axis, respectively. 11 ,d 22 ,d 33 ,d 55 and d 66 They represent the linear damping coefficients along the x-axis, along the y-axis, along the z-axis, and the rotational damping coefficients around the y-axis and around the z-axis, respectively.

[0023] Furthermore, in the five-degree-of-freedom kinematics and dynamics model of the underactuated underwater robot, there are:

[0024] and

[0025] Also, the position, velocity, and acceleration in the x, y, and z directions, as well as their first- and second-order derivatives, are bounded.

[0026] Furthermore, in step S2, the tracking error of the underactuated underwater robot includes position error, pitch angle error and yaw angle error, and the corresponding derivative forms are expressed as follows:

[0027]

[0028] in:

[0029]

[0030] In the formula, and They represent the position error ρ determined by the line-of-sight method respectively. e , pitch angle error θ e and yaw error The corresponding derivative, (x d ,y d ,z d ) represents the desired time-varying 3D trajectory, It means (x d ,y d ,z d ) corresponds to the first-order derivative.

[0031] Furthermore, in step S3, the constructed tunnel-type performance constraint is expressed as:

[0032]

[0033] In the formula, represents the upper bound of the error constraint, represents the lower bound of the error constraint, represents the decision parameter of the initial error constraint boundary value, and Both represent positive adjustment parameters, which are used to adjust the final upper and lower bounds of the system error in the steady-state stage. represents the initial value of the error, Express decision The convergence speed parameter, express The preselected convergence time of

[0034] When the tunnel-type performance function is converted into the tracking error of the underactuated underwater robot, the tracking error satisfies:

[0035]

[0036] In the formula, z u =ρ e ,z q =θ e , ρ e ,θ e and Respectively represent the position error, pitch angle error and yaw angle error in the tracking error;

[0037] The formula for error conversion is:

[0038]

[0039] In the formula, It represents the position error, pitch angle error and yaw angle error after the error conversion formula. Represents the original position error, pitch angle error, and yaw angle error.

[0040] Furthermore, in step S4, the designed preset time virtual control law is expressed as:

[0041]

[0042] In the formula, u c ,q c and r represent the preset time virtual control laws for surge, pitch and yaw directions, respectively, κ(t) represents the time-varying scaling function, represents the first-order derivative of κ(t), and They represent the position error, pitch angle error and yaw angle error after the error conversion formula, respectively, 2u ,k 2q ,k 2r ,k 1u ≥2,k 1q ≥2,k 1r ≥2 indicates a positive constant, θ indicates the pitch angle, ρ e ,θ e and They represent the position error, pitch angle error and yaw angle error in the tracking error respectively.

[0043] Furthermore, in step S5, the constructed bidirectional fuzzy brain emotion learning control network includes a sensory input layer, a wavelet sensory cortex, an amygdala space, an orbitofrontal cortex space, and an output space;

[0044] The sensory input of the sensory input layer is represented as in, represents the nth input node of the underwater robot, and the derived virtual control rate u c ,q c ,r c Subtract the actual speed u, q, r to get the error It is represented as the input of the bidirectional fuzzy brain emotion learning control network acting on the surge, pitch and yaw directions of the underactuated underwater robot, and its fuzzy inference rules are expressed as:

[0045] when for for for When

[0046] when for for for When

[0047] In the formula, Defined as the nth underwater robot j , mth k The fuzzy rules of the layer input, and Represent the output of the amygdala network space and the orbitofrontal cortex network space, respectively. represents the characteristic signal output value in the sensory cortex, represents the network weights in the amygdala space, The network weights representing the orbitofrontal cortical space;

[0048] In the wavelet sensory cortex, the sensory input of each layer is fuzzy quantized by a wavelet function, which is expressed as:

[0049]

[0050] In the formula, Indicates that the mth k The nth layer j The wavelet function corresponding to the input is and They represent the center vector and width vector that determine the activation degree of the wavelet function respectively;

[0051] In the wavelet sensory cortex, when the input signal in the sensory cortex is subjected to time-frequency analysis by the wavelet function, the maximum value of the characteristic signal is identified. and pass it on to the amygdala space as a key feature;

[0052] The amygdala space is represented as:

[0053]

[0054] In the formula, represents the network weights in the amygdala space, Represents characteristic signals from the sensory cortex to the amygdala The connection weight of

[0055] The output of the orbitofrontal cortex space is represented as:

[0056]

[0057] In the formula, The network weights representing the orbitofrontal cortical space;

[0058] The output of the output space is expressed as:

[0059]

[0060] Furthermore, the bidirectional fuzzy mood learning control network adjusts and updates the weights of the amygdala space and the orbitofrontal cortex space, as well as the characteristic signals in the wavelet sensory cortex through a reward-based bidirectional adjustment mechanism, and the update formula is:

[0061]

[0062] In the formula, represents the updated network weights in the amygdala space, represents the network weights of the current amygdala space, represents the change in the network weights in the amygdala space during the update interval, represents the connection weights of the updated sensory cortex feature signals of the amygdala, represents the connection weight of the current amygdala sensory cortex feature signal, represents the change in the connection weights of the characteristic signal of the sensory cortex of the amygdala during the update interval, represents the updated network weights in the orbitofrontal cortex space, represents the network weights in the current orbitofrontal cortex space, represents the change in the network weights in orbitofrontal cortical space during the update interval, and Respectively represent the learning rates of the update algorithm in the amygdala space and orbitofrontal cortex space; represents the reward signal, and Represents the positive gain parameter.

[0063] Furthermore, in step S6, an adaptive compensator is constructed to adaptively compensate the output control law of the bidirectional fuzzy brain emotion learning control network;

[0064] The adaptive compensator is expressed as:

[0065]

[0066]

[0067] In the formula, and are all normal numbers, for The estimated value of and meet represents the residual between the output value of the bidirectional fuzzy brain emotion learning controller and the ideal controller, represents the actual adaptive law in the compensator, represents the error between the actual adaptive law in the compensator and the estimated value, represents the ideal controller output value, Represents the output value of the control network output space, represents the output value of the adaptive compensator, Represents the error between the virtual control rate and the actual speed, represents the derivative of the compensator adaptation rate estimate, represents the time-varying scaling transformation function, represents the estimated value of the adaptive law in the compensator;

[0068] The actual control law for:

[0069]

[0070] The beneficial effects of the present invention are:

[0071] 1. The design of most traditional underactuated underwater robot trajectory tracking controllers relies on complex system models, resulting in cumbersome design and calculation processes. This invention simplifies the controller design process, proposes a new adaptive intelligent control method based on a bidirectional fuzzy brain emotion learning algorithm, and designs an adaptive compensator to optimize control performance. This method does not need to rely on an accurate system model, and still has good control effects in an environment with uncertain external interference, which improves the feasibility of the controller in practical applications.

[0072] 2. Most of the existing preset performance controls use symmetrical performance boundaries, and the system error has a large feasible range in the transient stage, which leads to the possibility of error overshoot, so the error accuracy of the system in the transient stage cannot be effectively guaranteed. The present invention converts the error by combining a tunnel-type performance function, effectively narrowing the feasible range of the tracking error in the transient stage to reduce the overshoot, thereby ensuring the tracking performance of the system in the transient and steady states.

[0073] 3. In the existing underactuated underwater robot trajectory tracking technology, the tracking error is mostly in the form of asymptotic convergence or finite time convergence, and the error convergence time of this form cannot be accurately predicted and set in advance. The present invention is based on the practical preset time stability theory, so that the error convergence time can be preset in advance and is not affected by the initial state of the system, further improving the scope of application and reliability of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 This is a flow chart of the trajectory tracking control method of the under-actuated underwater robot provided by the present invention.

[0075] Figure 2 The present invention provides a bidirectional fuzzy brain emotion learning network structure.

[0076] Figure 3 The present invention provides a control process.

[0077] Figure 4 This is a three-dimensional trajectory tracking diagram of the under-actuated underwater robot provided by the present invention.

[0078] Figure 5 This is a planar trajectory tracking diagram of the underactuated underwater robot provided by the present invention.

[0079] Figure 6 This is a tracking error diagram of the underactuated underwater robot provided by the present invention.

[0080] Figure 7 This is a control input diagram provided by the present invention. DETAILED DESCRIPTION

[0081] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0082] The embodiment of the present invention provides a trajectory tracking control method for an underactuated underwater robot, such as Figure 1 As shown, the following steps are included:

[0083] S1. Use practical preset time control theory and its proof lemma to construct a five-degree-of-freedom kinematic and dynamic model of an underactuated underwater robot;

[0084] S2. Based on the constructed five-DOF kinematic and dynamic models, the tracking error of the underactuated underwater robot is determined by the line-of-sight method;

[0085] S3, constructing a tunnel-type performance function, and performing error conversion with the tracking error of the underactuated underwater robot, thereby determining the preset performance constraints;

[0086] S4. Designing a preset time virtual control law according to the determined preset performance constraints;

[0087] S5, constructing a bidirectional fuzzy brain emotion learning control network for outputting an approximate ideal control law of an underactuated underwater robot, and using the surge, pitch and yaw directions of the underactuated underwater robot obtained based on a preset time virtual control law as inputs of the bidirectional fuzzy brain emotion learning control network;

[0088] S6. Adaptively compensate the output control law of the bidirectional fuzzy brain emotion learning control network to obtain the actual control law, and use the actual control law to perform trajectory tracking control on the under-actuated underwater robot.

[0089] In step S1 of the embodiment of the present invention, in the practical preset time control theory:

[0090] Consider the following nonlinear system:

[0091]

[0092] Where x∈R m , f:R + ×R m →R m represents a continuous nonlinear function, and f(0,t) = 0, x(t) = 0 is a solution of system (1). If there exists T c ∈R + , so that t ≥ T c When x(t)=0, the solution of (1) is stable for the preset time; if there exists T c ∈R + , so that t ≥ T c hour, If it holds, then the solution of (1) is stable with respect to the practical preset time.

[0093] In the relevant proof lemma:

[0094] Lemma 1. Assume a radially unconstrained positive definite Lyapunov function V(t), if It can make:

[0095]

[0096] holds, and when t ≥ T c hour, And when t→+∞, Then the system (1) is practically stable in preset time. κ(t) represents a new type of time-varying scaling function:

[0097]

[0098] Where n>0, and T c >0, and It has the following two characteristics

[0099] Property 1: On t∈[0,+∞), κ(t) is a continuous and increasing function, and

[0100] Property 2: On [0,+∞), κ(t)∈C n , which means that κ(t) is n-th order differentiable.

[0101] Lemma 2. For any and The following inequality holds:

[0102] 0<|x|-xtanh(x / ν)≤δν(4)

[0103] Among them, δ=0.2785 satisfies δ=e -(δ+1) .

[0104] Lemma 3. According to the style inequality, for any a∈R and b∈R, the inequality Established.

[0105] Based on the above practical preset time control theory and its proof lemma, the five-degree-of-freedom kinematics and dynamics model of the underactuated underwater robot constructed in step S1 is expressed as:

[0106]

[0107] in:

[0108]

[0109] g(η)=[0 0 0ρg▽GM L sin(θ)0] T

[0110] Where J(η) represents the rotation matrix between the earth coordinate system and the underwater robot body coordinate system, M represents the mass inertia matrix, and D(v) represents the hydrodynamic damping coefficient matrix. represents the Coriolis force and centripetal force matrix of the underwater robot, g(η) represents the vector of buoyancy and gravity, x, y, z represent the real displacement of the underactuated autonomous underwater robot, represents the yaw angle, θ represents the pitch angle, represents the first-order derivative of η, u,ν,w,q,r represent x,y,z,θ, The true speed in the direction, express The first-order derivative of , τ represents the control input, F = [ω u ,ω v ,ω w ,ω q ,ω r ] T represents the time-varying position ocean disturbance, ω u ,ω v ,ω w ,ω q ,ω r Represent x, y, z, θ, The ocean disturbance in the direction, ρ represents water density, g represents gravitational acceleration, ▽ represents displacement, M L Indicates the longitudinal metacentric height, m 11 、m 22 、m 33 、m 55 and m 66 Denote the equivalent mass along the x-axis, along the y-axis, along the z-axis, around the y-axis, and around the z-axis, respectively. 11 ,d 22 ,d 33 ,d 55 and d 66 They represent the linear damping coefficients along the x-axis, along the y-axis, along the z-axis, and the rotational damping coefficients around the y-axis and around the z-axis, respectively.

[0111] In the above five-DOF kinematic and dynamic model of the underactuated underwater robot, there are:

[0112]

[0113] And the position x in the x, y, z directions d ,y d ,z d , velocity and acceleration, and their first- and second-order derivatives are bounded.

[0114] Specifically, since the underactuated underwater robot has a stable center restoring force, the pitch angle of the underactuated underwater robot is unlikely to exceed range, it is reasonable to assume that the pitch angle of the underactuated underwater robot must satisfy

[0115] In step S2 of the embodiment of the present invention, the tracking position error of the underactuated underwater robot in the body coordinate system can be expressed as:

[0116]

[0117] Among them, (x d ,y d ,z d ) represents the desired time-varying 3D trajectory.

[0118] Then, according to the line-of-sight method, the position error ρ e , pitch angle error θ e and yaw error It is expressed as:

[0119]

[0120] Furthermore, the following two relations can be derived from equations (5), (6) and (7):

[0121]

[0122]

[0123] Finally, according to the above analysis, the tracking error of the underactuated underwater robot includes position error, pitch angle error and yaw angle error, and its corresponding derivative form is expressed as:

[0124]

[0125] in:

[0126]

[0127] In the formula, and They represent the position error ρ determined by the line-of-sight method respectively. e , pitch angle error θ e and yaw error The corresponding derivative, (x d ,y d ,z d ) represents the desired time-varying 3D trajectory, It means (x d ,y d ,z d) corresponds to the first-order derivative.

[0128] In step S3 of the embodiment of the present invention, error conversion is performed through position error, pitch angle error, yaw angle error and tunnel-type preset performance to achieve preset performance constraints.

[0129] In this embodiment, constructing a tunnel-type performance constraint is expressed as:

[0130]

[0131]

[0132] In the formula, represents the upper bound of the error constraint, represents the lower bound of the error constraint, represents the decision parameter of the initial error constraint boundary value, and Both represent positive adjustment parameters, which are used to adjust the final upper and lower bounds of the system error in the steady-state stage. represents the initial value of the error, Express decision The convergence speed parameter, express The preselected convergence time of

[0133] When the tunnel-type performance function is converted into the tracking error of the underactuated underwater robot, the tracking error satisfies:

[0134]

[0135] In the formula, z u =ρ e ,z q =θ e , ρ e ,θ e and Respectively represent the position error, pitch angle error and yaw angle error in the tracking error;

[0136] The formula for error conversion is:

[0137]

[0138] In the formula, It represents the position error, pitch angle error and yaw angle error after the error conversion formula. Represents the original position error, pitch angle error, and yaw angle error.

[0139] In step S4 of the embodiment of the present invention, in the process of designing the preset time virtual control law, the Lyapunov function is constructed as follows:

[0140]

[0141] Reviewing the result of formula (10), in order to facilitate the subsequent derivation, the following symbolic definitions are given:

[0142]

[0143]

[0144]

[0145] Then, we can derive formula (16):

[0146]

[0147] Then the designed preset time virtual control law is expressed as:

[0148]

[0149] In the formula, u c ,q c and r represent the preset time virtual control laws for surge, pitch and yaw directions, respectively, κ(t) represents the time-varying scaling function,

[0150] represents the first-order derivative of κ(t), and They represent the position error, pitch angle error and yaw angle error after the error conversion formula, respectively, 2u ,k 2q ,k 2r ,k 1u ≥2,k 1q ≥2,k 1r ≥2 indicates a positive constant, θ indicates the pitch angle, ρ e ,θ e and They represent the position error, pitch angle error and yaw angle error in the tracking error respectively.

[0151] In step S5 of the embodiment of the present invention, the constructed bidirectional fuzzy brain emotion learning control network includes a sensory input layer, a wavelet sensory cortex, an amygdala space, an orbitofrontal cortex space, and an output space;

[0152] The sensory input of the sensory input layer is represented as in, represents the nth input node of the underwater robot, and the derived virtual control rate u c ,q c ,r c Subtract the actual speed u, q, r to get the error It is represented as the input of the bidirectional fuzzy brain emotion learning control network acting on the surge, pitch and yaw directions of the underactuated underwater robot, and its fuzzy inference rules are expressed as:

[0153] when for for for When

[0154] when for for for When

[0155] In the formula, Defined as the nth underwater robot j , mth k The fuzzy rules of the layer input, and Represent the output of the amygdala network space and the orbitofrontal cortex network space, respectively. represents the characteristic signal output value in the sensory cortex, represents the network weights in the amygdala space, The network weights representing the orbitofrontal cortical space;

[0156] In the wavelet sensory cortex, a multi-layer structure is described, and the sensory input of each layer is fuzzy quantized by a wavelet function, which is expressed as:

[0157]

[0158] In the formula, Indicates that the mth k The nth layer j The wavelet function corresponding to the input is and They represent the center vector and width vector that determine the activation degree of the wavelet function, and Respectively represent when the wavelet membership function and the mth k The nth layer j The translation and expansion adjustments are made to the inputs when they are associated.

[0159] In the wavelet sensory cortex, when the input signal in the sensory cortex is analyzed in time and frequency by the wavelet function, the maximum value of the characteristic signal is identified. It is then transferred to the amygdala space as a key feature, and the maximum value is defined as the sensory cortex feature signal;

[0160]

[0161] The amygdala space is represented as:

[0162]

[0163] In the formula, represents the network weights in the amygdala space, Represents characteristic signals from the sensory cortex to the amygdala The connection weight of

[0164] The signal after wavelet sensory cortex conversion is sent to the orbitofrontal cortex space and processed in its space. The output of the orbitofrontal cortex space is defined as:

[0165]

[0166] In the formula, The network weights representing the orbitofrontal cortical space;

[0167] In the output space, the output of the bidirectional simulated brain emotion learning control network is the output value of the amygdala space minus the orbitofrontal cortex space, and its output is expressed as:

[0168]

[0169] In an embodiment of the present invention, the bidirectional fuzzy mood learning control network adjusts and updates the weights of the amygdala space and the orbitofrontal cortex space, as well as the characteristic signals in the wavelet sensory cortex through a reward-based bidirectional adjustment mechanism, and the reward mechanism includes a positive reward signal and a negative reward signal. The update formula is:

[0170]

[0171]

[0172]

[0173] In the formula, represents the updated network weights in the amygdala space, represents the network weights of the current amygdala space, represents the change in the network weights in the amygdala space during the update interval, represents the connection weights of the updated sensory cortex feature signals of the amygdala, represents the connection weight of the current amygdala sensory cortex feature signal, represents the change in the connection weights of the characteristic signal of the sensory cortex of the amygdala during the update interval, represents the updated network weights in the orbitofrontal cortex space, represents the network weights in the current orbitofrontal cortex space, represents the change in the network weights in orbitofrontal cortical space during the update interval, and Respectively represent the learning rates of the update algorithm in the amygdala space and orbitofrontal cortex space; Represents the reward signal:

[0174]

[0175] in, and Represents the positive gain parameter.

[0176] In step S6 of the embodiment of the present invention, an output control law of the bidirectional fuzzy brain emotion learning control network is adaptively compensated by constructing an adaptive compensator;

[0177] The adaptive compensator is expressed as:

[0178]

[0179]

[0180] In the formula, and are all normal numbers, for The estimated value of and meet represents the residual between the output value of the bidirectional fuzzy brain emotion learning controller and the ideal controller, represents the actual adaptive law in the compensator, represents the error between the actual adaptive law in the compensator and the estimated value, represents the ideal controller output value, Represents the output value of the control network output space, represents the output value of the adaptive compensator, Represents the error between the virtual control rate and the actual speed, represents the derivative of the compensator adaptation rate estimate, represents the time-varying scaling transformation function, represents the estimated value of the adaptive law in the compensator;

[0181] Finally, the actual control law is the sum of the output of the bidirectional fuzzy mood learning control network and the output of the adaptive compensator, which can be expressed as:

[0182]

[0183] In the embodiment of the present invention, according to the aforementioned method, the effectiveness of the preset time-based bidirectional fuzzy mood learning strategy in the under-actuated underwater robot trajectory design method is demonstrated.

[0184] Considering the kinematic model and dynamic model (5) of the underactuated underwater machine, and on the basis of following assumptions 1 and 2, the above-mentioned preset time virtual control rate (21), the output of the bidirectional fuzzy brain emotion learning controller (26), the network weight update mechanism (27)(28)(29) and the adaptive compensator (31) are used to ensure the stability of the system (40). Therefore, even under the influence of external interference and model uncertainty, the underactuated underwater robot can accurately track the desired trajectory within the preset time.

[0185] The proof is as follows:

[0186] definition and are the network weight errors in the amygdala space and orbitofrontal cortex space, respectively. and Where L2 is the gain value, This means and

[0187] In the adaptive compensator Under the regulation of , it converges to the neighborhood of zero, so and is bounded. Then, we can calculate u e ,q e and r e Taking the derivative, we can get:

[0188]

[0189]

[0190]

[0191] in is a normal number, satisfying m u =1 / m 11 ,m q =1 / m 55 ,m r =1 / m 66 .

[0192] The Lyapunov function is selected as follows:

[0193]

[0194] Taking the derivative of (27) and substituting (21) into it, we can obtain:

[0195]

[0196] Substituting (31)(32) into (38), we can obtain:

[0197]

[0198] definition and And satisfy 0≤|ε u |≤d u ,0≤|ε q |≤d q and 0≤|ε r |≤d r ,According to Lemma 2 and Lemma 3, the following inequality (40) holds:

[0199]

[0200] in

[0201] According to (40), we can conclude Therefore, according to the practical preset time theory and Lemma 1, we can further draw the following conclusions:

[0202]

[0203] Therefore, according to Lemma 1 and (41), all variables in V2 can be c converges and reaches a stable state. In addition, according to and the inherent characteristics of preset performance control, it can be concluded that for all All are established, the proof is complete.

[0204] In the embodiment of the present invention, in order to verify the effectiveness of the method of the present invention, a simulation experiment was carried out, as follows:

[0205] The expected trajectory of the underwater robot is: y d =10coa(0.02t)+1,z d =sin(0.02t)+10cos(0.02t)-15l. The initial position of the underwater robot is set as: The time-varying external disturbance is set as: ωu (t)=0.2sign(u)+0.5sin(t / 10),ω v (t)=0.1sign(v)+0.2sin(t / 10),

[0206] ω w (t)=0.3sign(w)+0.2sin(t / 10),ω q (t)=0.4sign(q)+0.3sin(t / 10),

[0207] ω r (t) = 0.5sign(r) + 0.1sin(t / 10); the performance function related parameters are T c =25s.

[0208] The model parameters are shown in Table 1, and the control system parameters are shown in Table 2:

[0209] Table 1: Model parameters

[0210]

[0211] Table 2: Control system parameters

[0212]

[0213] Figure 2 The structure of the bidirectional fuzzy brain emotion learning control network is shown. Figure 3 The control flow of the entire system is shown. The simulation results are Figure 4 to Figure 7 . Figure 4 This is the three-dimensional trajectory tracking effect diagram of the underactuated underwater robot. Figure 5 The trajectory tracking effect is further demonstrated in detail from the XY and XZ planes. The results show that the underactuated underwater robot can move accurately along the desired trajectory with a smooth trajectory, showing good tracking performance; Figure 6 The position error ρ of the underactuated underwater robot is shown e , pitch angle error θ e and yaw error The convergence effect under the tunnel performance function constraint clearly shows that the error can be reduced within the preset time T c = It converges to a region close to zero within 25s and is constrained within the tunnel-type error boundary, showing high accuracy and no obvious jitter; Figure 7The control input diagram of the underactuated underwater robot system shows that the controller output is smooth and continuous, and has fast response boundedness. The simulation results verify the robustness of the proposed controller, the fast convergence speed, and the convergence time that is not affected by the initial value of the system, thus confirming the effectiveness and practicality of the controller.

[0214] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0215] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A trajectory tracking control method for an underactuated underwater robot, characterized in that: The following steps are involved: S1. Use practical preset time control theory and its proof lemma to construct a five-degree-of-freedom kinematic and dynamic model of an underactuated underwater robot; S2. Based on the constructed five-DOF kinematic and dynamic models, the tracking error of the underactuated underwater robot is determined by the line-of-sight method; S3, constructing a tunnel-type performance function, and performing error conversion with the tracking error of the underactuated underwater robot, thereby determining the preset performance constraints; S4. Designing a preset time virtual control law according to the determined preset performance constraints; S5, constructing a bidirectional fuzzy brain emotion learning control network for outputting an approximate ideal control law of an underactuated underwater robot, and using the surge, pitch and yaw directions of the underactuated underwater robot obtained based on a preset time virtual control law as inputs of the bidirectional fuzzy brain emotion learning control network; S6. Adaptively compensate the output control law of the bidirectional fuzzy brain emotion learning control network to obtain the actual control law, and use the actual control law to perform trajectory tracking control on the under-actuated underwater robot.

2. The trajectory tracking control method of an underactuated underwater robot according to claim 1, characterized in that: In step S1, the constructed five-degree-of-freedom kinematic and dynamic model of the underactuated underwater robot is expressed as: in: Where J(η) represents the rotation matrix between the earth coordinate system and the underwater robot body coordinate system, M represents the mass inertia matrix, represents the hydrodynamic damping coefficient matrix, represents the Coriolis force and centripetal force matrix of the underwater robot, g(η) represents the vector of buoyancy and gravity, x, y, z represent the real displacement of the underactuated autonomous underwater robot, represents the yaw angle, θ represents the pitch angle, represents the first-order derivative of η, u,ν,w,q,r represent x,y,z,θ, The true speed in the direction, express The first-order derivative of , τ represents the control input, F = [ω u ,ω v ,ω w ,ω q ,ω r ] T represents the time-varying position ocean disturbance, ω u ,ω v ,ω w ,ω q ,ω r Represent x, y, z, θ, The ocean disturbance in the direction, ρ represents the water density, g represents the gravitational acceleration, Indicates displacement, M L Indicates the longitudinal metacentric height, m 11 、m 22 、m 33 、m 55 and m 66 Denote the equivalent mass along the x-axis, along the y-axis, along the z-axis, around the y-axis, and around the z-axis, respectively. 11 d 22 d 33 d 55 and d 66 They represent the linear damping coefficients along the x-axis, along the y-axis, along the z-axis, and the rotational damping coefficients around the y-axis and around the z-axis, respectively.

3. The trajectory tracking control method of an underactuated underwater robot according to claim 2, characterized in that: In the five-degree-of-freedom kinematics and dynamics model of the underactuated underwater robot, there are: and Also, the position, velocity, and acceleration in the x, y, and z directions, as well as their first- and second-order derivatives, are bounded.

4. The trajectory tracking control method of an underactuated underwater robot according to claim 2, characterized in that: In step S2, the tracking error of the underactuated underwater robot includes position error, pitch angle error and yaw angle error, and the corresponding derivative forms are expressed as: in: In the formula, and They represent the position error ρ determined by the line-of-sight method respectively. e , pitch angle error θ e and yaw error The corresponding derivative, (x d ,y d ,z d ) represents the desired time-varying 3D trajectory, It means (x d ,y d ,z d ) corresponds to the first-order derivative.

5. The trajectory tracking control method of an underactuated underwater robot according to claim 2, characterized in that: In step S3, the constructed tunnel-type performance constraint is expressed as: In the formula, represents the upper bound of the error constraint, represents the lower bound of the error constraint, represents the decision parameter of the initial error constraint boundary value, and Both represent positive adjustment parameters, which are used to adjust the final upper and lower bounds of the system error in the steady-state stage. represents the initial value of the error, Express decision The convergence speed parameter, express The preselected convergence time of When the tunnel-type performance function is converted into the tracking error of the underactuated underwater robot, the tracking error satisfies: In the formula, z u =ρ e ,z q =θ e , ρ e ,θ e and Respectively represent the position error, pitch angle error and yaw angle error in the tracking error; The formula for error conversion is: In the formula, It represents the position error, pitch angle error and yaw angle error after the error conversion formula. Represents the original position error, pitch angle error, and yaw angle error.

6. The trajectory tracking control method of an underactuated underwater robot according to claim 1, characterized in that: In step S4, the designed preset time virtual control law is expressed as: In the formula, u c ,q c and r represent the preset time virtual control laws for surge, pitch and yaw directions, respectively, κ(t) represents the time-varying scaling function, represents the first-order derivative of κ(t), l u , l q and l r They represent the position error, pitch angle error and yaw angle error after the error conversion formula, respectively, 2u ,k 2q ,k 2r ,k 1u ≥2,k 1q ≥2,k 1r ≥2 indicates a positive constant, θ indicates the pitch angle, ρ e ,θ e and They represent the position error, pitch angle error and yaw angle error in the tracking error respectively.

7. The trajectory tracking control method of an underactuated underwater robot according to claim 2, characterized in that: In step S5, the constructed bidirectional fuzzy brain emotion learning control network includes a sensory input layer, a wavelet sensory cortex, an amygdala space, an orbitofrontal cortex space, and an output space; The sensory input of the sensory input layer is represented as in, represents the nth input node of the underwater robot, and the derived virtual control rate u c ,q c ,r c Subtract the actual speed u, q, r to get the error It is represented as the input of the bidirectional fuzzy brain emotion learning control network acting on the surge, pitch and yaw directions of the underactuated underwater robot, and its fuzzy inference rules are expressed as: when for for for When when for for for When In the formula, Defined as the nth underwater robot j , mth k The fuzzy rules of the layer input, and Represent the output of the amygdala network space and the orbitofrontal cortex network space, respectively. represents the characteristic signal output value in the sensory cortex, represents the network weights in the amygdala space, The network weights representing the orbitofrontal cortical space; In the wavelet sensory cortex, the sensory input of each layer is fuzzy quantized by a wavelet function, which is expressed as: In the formula, Indicates that the mth k The nth layer j The wavelet function corresponding to the input is and They represent the center vector and width vector that determine the activation degree of the wavelet function respectively; In the wavelet sensory cortex, when the input signal in the sensory cortex is subjected to time-frequency analysis by the wavelet function, the maximum value of the characteristic signal is identified. and pass it on to the amygdala space as a key feature; The amygdala space is represented as: In the formula, represents the network weights in the amygdala space, Represents characteristic signals from the sensory cortex to the amygdala The connection weight of The output of the orbitofrontal cortex space is represented as: In the formula, The network weights representing the orbitofrontal cortical space; The output of the output space is expressed as:

8. The trajectory tracking control method of an underactuated underwater robot according to claim 7, characterized in that: The bidirectional fuzzy mood learning control network adjusts and updates the weights of the amygdala space and the orbitofrontal cortex space, as well as the characteristic signals in the wavelet sensory cortex through a reward-based bidirectional adjustment mechanism. The update formula is: In the formula, represents the updated network weights in the amygdala space, represents the network weights of the current amygdala space, represents the change in the network weights in the amygdala space during the update interval, represents the connection weights of the updated sensory cortex feature signals of the amygdala, represents the connection weight of the current amygdala sensory cortex feature signal, represents the change in the connection weights of the characteristic signal of the sensory cortex of the amygdala during the update interval, represents the updated network weights in the orbitofrontal cortex space, represents the network weights in the current orbitofrontal cortex space, represents the change in the network weights in orbitofrontal cortical space during the update interval, and Respectively represent the learning rates of the update algorithm in the amygdala space and orbitofrontal cortex space; represents the reward signal, and Represents the positive gain parameter.

9. The trajectory tracking control method of an underactuated underwater robot according to claim 7, characterized in that: In the step S6, an adaptive compensator is constructed to adaptively compensate the output control law of the bidirectional fuzzy brain emotion learning control network; The adaptive compensator is expressed as: In the formula, and are all normal numbers, for The estimated value of and meet represents the residual between the output value of the bidirectional fuzzy brain emotion learning controller and the ideal controller, represents the actual adaptive law in the compensator, represents the error between the actual adaptive law in the compensator and the estimated value, represents the ideal controller output value, Represents the output value of the control network output space, represents the output value of the adaptive compensator, Represents the error between the virtual control rate and the actual speed, represents the derivative of the compensator adaptation rate estimate, represents the time-varying scaling transformation function, represents the estimated value of the adaptive law in the compensator; The actual control law for:

Images