A trajectory tracking control method for an underactuated underwater robot

Abstract

The application discloses a trajectory tracking control method of an underactuated underwater robot, and is a preset time bidirectional fuzzy brain emotion learning trajectory tracking control method of the underactuated underwater robot with a tunnel type error constraint. The application is based on a practical preset time theory, converts the error by using a tunnel type performance function, and adopts a bidirectional fuzzy brain emotion learning control strategy, so that the underactuated underwater robot still has high stability and robustness under the condition of having ocean external disturbance and model uncertainty, and meets the compact preset performance constraint of the system during transient and steady states and the stability of the system at a preset time point.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of three-dimensional trajectory tracking control, and particularly relates to a trajectory tracking control method for an underactuated underwater robot. BACKGROUND

[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) are increasingly valued for their key role in tasks such as ocean exploration, target detection, and deep-sea exploration. Among these underwater robots, underactuated underwater robots are of great interest due to their reduced number of actuators, which effectively reduces energy consumption and system mass, while improving 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 tasks and is a research hotspot in the field of motion control. However, the underactuated underwater robot system has high nonlinearity and strong coupling, coupled with uncertain ocean current disturbances in the marine environment, making the control problem more complex. Therefore, it is of great research value and practical significance to study how to design an effective controller to ensure that the underactuated underwater robot can smoothly and reliably perform trajectory tracking tasks in complex marine environments. This not only improves the performance of underwater robots but also provides technical support for the exploration and utilization of marine resources.

[0004] In the field of trajectory tracking control for underactuated underwater robots, traditional control methods include PID control, sliding mode control, and adaptive backstepping control. PID control is widely popular due to its simplicity and low dependence on system models, but its performance is insufficient in the presence of strong disturbances and rapid environmental changes. Sliding mode control is favored for its fast response and robustness to parameter changes, and it can maintain stability after the system state reaches the predetermined sliding surface, but it may produce chattering phenomena near the sliding surface, affecting control accuracy and accelerating actuator wear. Adaptive backstepping control adjusts parameters in real time to adapt to external disturbances, but it has a large amount of calculation and numerous parameters, increasing the complexity of design. Moreover, the above control methods are developed based on system model information and the integration of various complex advanced technologies, and the controller design process is complex, with 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, and neural network control.

[0005] The brain emotional learning control algorithm is inspired by the biological mechanism and operates independently of the system model, bypassing the traditional constraints of model information-dependent control strategies. This control algorithm employs a dual-network architecture, reflecting the human brain's process of processing sensory information and emotional response. The first network represents the amygdala, responsible for generating optimal emotional responses to various stimuli and influencing memory; the second network mimics the orbitofrontal cortex, focusing on perceptual and emotional regulation learning. Therefore, the brain emotional learning control algorithm has good estimation ability and fast learning speed. This network not only effectively reduces tracking errors but also reduces the dependence on accurate system models, reducing the complexity of controller design. It has important research value for promoting the development of underactuated underwater robot technology.

[0006] Secondly, in the field of underactuated underwater robot control, error convergence is usually based on asymptotic convergence or finite-time convergence theory. The convergence speed of systems guided by these theories is affected by the initial state, leading to difficulties in accurately predicting convergence time during different task executions due to the uncertainty of the initial state, which limits the practicality of control methods. To solve this problem, fixed-time control theory is proposed, aiming to make the convergence time independent of the initial condition. However, the fixed-time control theory is limited in design parameter selection, and its convergence time expression provides an upper bound rather than an exact value, resulting in a conservative control strategy. Therefore, the preset time convergence theory emerges as the times require. This theory can accurately preset the system convergence time and is not limited by the initial condition, providing strong support for underactuated underwater robots to perform diverse trajectory tracking tasks and significantly improving the practicality and flexibility of control strategies.

[0007] In addition, when performing trajectory tracking control, to meet performance requirements, physical limitations, and safety issues, tracking accuracy of the trajectory becomes particularly critical. Prescribed performance control methods are of interest due to their ability to constrain system errors, thereby improving tracking accuracy in transient and steady states. However, the existing prescribed performance control methods mostly use symmetric performance boundaries, resulting in funnel-shaped error boundary constraints. Therefore, the performance boundary is relatively loose during the transient phase, and the system error may produce a large overshoot during the transient phase, affecting the accuracy of trajectory tracking. To solve this problem, the curve shape of the prescribed performance boundary must be improved to narrow the transient error feasibility interval, significantly improving the control accuracy of the prescribed performance control method.

[0008] Therefore, through the above analysis, although there are many researches on trajectory tracking control of underactuated underwater robots at present, and many effective methods are also proposed, most of the controllers rely on detailed model information, and the system error is not limited in a preset interval, in addition, these controllers are usually based on asymptotic convergence or finite time convergence, which makes the control reliability and practicability lower. SUMMARY

[0009] In view of the above problems in the prior art, the trajectory tracking control method of the underactuated underwater robot provided by the present application solves the problems of the influence of external disturbance and model uncertainty on system stability during trajectory tracking of the underactuated underwater robot, the problem of over-complex design caused by the dependence of the controller on detailed model information, the problem of difficult direct control of the convergence time of the system error, and the problem of redundancy of the transient error boundary interval in the existing preset performance control.

[0010] In order to achieve the above-mentioned purposes, the technical scheme adopted by the present application is as follows: a trajectory tracking control method of an underactuated underwater robot, comprising the following steps:

[0011] S1, citing the practical preset time control theory and its proof lemma, constructing a five-degree-of-freedom kinematics and dynamics model of the underactuated underwater robot;

[0012] S2, determining the tracking error of the underactuated underwater robot by the line-of-sight method based on the constructed five-degree-of-freedom kinematics and dynamics model;

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

[0014] S4, designing a preset time virtual control law according to the determined preset performance constraint;

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

[0016] S6, adaptively compensating the output control law of the bidirectional fuzzy brain emotion learning control network to obtain an actual control law, and using the actual control law to perform trajectory tracking control on the underactuated underwater robot.

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

[0018]

[0019] wherein:

[0020]

[0021] wherein, denotes the rotation matrix between the earth coordinate system and the underwater robot body coordinate system, denotes the mass inertia matrix, denotes the hydrodynamic damping coefficient matrix, denotes the Coriolis and centripetal force matrix of the underwater robot, denotes the buoyancy and gravity vectors, , denotes the true displacement of the underactuated autonomous underwater robot, denotes the yaw angle, denotes the pitch angle, denotes the first derivative of , , denote the true velocities in the x, y, z directions, respectively, denotes the first derivative of denotes the control input, denotes the time-varying position ocean disturbance, denote the ocean disturbances in the x, y, z directions, respectively, denotes the water density, denotes the gravity acceleration, denotes the displacement, denotes the longitudinal metacentric height, , , , , , , and 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. , , , and denote 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.

[0022] Further, in the underactuated underwater robot five-degree-of-freedom kinematics and dynamics model, there are:

[0023] , and ;

[0024] and the position, velocity, and acceleration in the x, y, z directions, and their first and second derivatives are bounded.

[0025] Further, the tracking error of the underactuated underwater robot in step S2 includes position error, pitch angle error and yaw angle error, and the corresponding derivative form is expressed as:

[0026]

[0027] Wherein:

[0028]

[0029] In the formula, respectively represent the position error determined by the sight distance method , pitch angle error and yaw angle error corresponding derivative, represents the expected time-varying three-dimensional trajectory, represents corresponding first derivative.

[0030] Further, in step S3, the tunnel type performance constraint is expressed as:

[0031]

[0032]

[0033] In the formula, represents the upper boundary of the error constraint, represents the lower boundary of the error constraint, represents the decision parameter of the initial error constraint boundary value, , and all represent positive adjustment parameters for adjusting the final upper and lower boundaries of the system error in the steady state stage, represents the initial value of the error, represents the parameter for determining convergence speed, represents preselected convergence time; wherein subscript ;

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

[0035]

[0036] In the formula, , , 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] wherein, denote the position error, the pitch angle error and the yaw angle error after the error conversion formula, denote the original position error, the pitch angle error and the yaw angle error.

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

[0041]

[0042]

[0043]

[0044]

[0045] wherein, , and denote the preset time virtual control law in surge, pitch and yaw directions respectively, denote the time-varying scaling transformation function, denote the first derivative of , denote the position error, the pitch angle error and the yaw angle error after the error conversion formula respectively, , , , all denote normal numbers, denote the pitch angle, , and denote the position error, the pitch angle error and the yaw angle error in the tracking error respectively.

[0046] Further, the bidirectional fuzzy brain emotional learning control network constructed in the step S5 includes a sensory input layer, a wavelet sensory cortex, an amygdala space, an orbitofrontal cortex space and an output space;

[0047] The sensory input of the sensory input layer is represented as wherein, , denote the nth input node of the underwater robot, and the derived virtual control rate is subtracted from the actual velocity to obtain the error , inputs of the two-way fuzzy brain emotional learning control network in surge, pitch and yaw directions acting on the underactuated underwater robot, whose fuzzy inference rules are expressed as:

[0048] When , , , , , , ,

[0049] When , , , , , , ,

[0050] In the formula, , is defined as the fuzzy rule of the first layer input of the underwater robot, and respectively represent the outputs of the amygdala network space and the orbitofrontal cortex network space, represents the characteristic signal output value in the sensory cortex, represents the network weight of the amygdala space, represents the network weight of the orbitofrontal cortex space; In the wavelet sensory cortex, the sensory input of each layer is fuzzy quantized by a wavelet function, which is expressed as:

[0051]

[0052]

[0053] In the formula, represents the wavelet function corresponding to the first input in the first layer, and respectively represent the center vector and the width vector that determine the activation degree of the wavelet function;

[0054] In the wavelet sensory cortex, when the input signal in the sensory cortex is analyzed by the wavelet function, the maximum value of the characteristic signal is identified and transmitted to the amygdala space as the key feature;

[0055] The amygdala space is expressed as:

[0056] ​

[0057] wherein, represents the network weights of the amygdala space, represents the connection weights of the sensory cortical feature signals to the amygdala;

[0058] The output of the orbitofrontal cortex space is represented as:

[0059]

[0060] wherein, represents the network weights of the orbitofrontal cortex space;

[0061] The output of the output space is represented as:

[0062] .

[0063] Further, the bidirectional fuzzy emotional learning control network adjusts the weights of the amygdala space and the orbitofrontal cortex space, and the feature signals in the sensory cortex, through a bidirectional adjustment mechanism based on the reward, and the update formula is:

[0064]

[0065]

[0066]

[0067] wherein, represents the network weights of the updated amygdala space, represents the network weights of the current amygdala space, represents the change amount of the network weights of the amygdala space during the update interval, represents the connection weights of the updated sensory cortical feature signals to the amygdala, represents the connection weights of the current sensory cortical feature signals to the amygdala, represents the change amount of the connection weights of the sensory cortical feature signals to the amygdala during the update interval, represents the network weights of the updated orbitofrontal cortex space, represents the network weights of the current orbitofrontal cortex space, represents the change amount of the network weights of the orbitofrontal cortex space during the update interval, and respectively represent the learning rates of the update algorithm in the amygdala space and the orbitofrontal cortex space; represents the reward signal, , and represent the positive gain parameters.

[0068] ​Further, in the step S6, the output control law of the bidirectional fuzzy brain emotional learning control network is adaptively compensated by constructing an adaptive compensator.

[0069] The adaptive compensator is expressed as:

[0070]

[0071]

[0072] wherein, and are normal numbers, is an estimated value of , and satisfies , represents the residual error between the output values of the bidirectional fuzzy brain emotional 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 output value of the ideal controller, 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 estimated value of the adaptive rate of the compensator, represents a time-varying scaling transformation function, represents the estimated value of the adaptive law in the compensator.

[0073] The actual control law is:

[0074] .

[0075] The present application has the following beneficial effects:

[0076] 1. The trajectory tracking controller design of most traditional underactuated underwater robots depends on complex system models, resulting in a cumbersome design and calculation process. The present application simplifies the controller design process, proposes a new adaptive intelligent control method based on a bidirectional fuzzy brain emotional learning algorithm, and designs an adaptive compensator to optimize control performance. This method does not require accurate system models and still has good control effect in an environment with uncertain external disturbances, improving the feasibility of the controller in practical applications.

[0077] 2. In the existing preset performance control, a symmetrical performance boundary is mostly used, the system error has a larger feasible interval in the transient stage, and the possibility of error overshoot is generated, so the error accuracy of the system in the transient stage cannot be effectively ensured. The error is converted by combining a tunnel type performance function in the application, the feasible interval of the tracking error in the transient stage is effectively reduced to reduce the overshoot amount, and the tracking performance of the system in the transient and steady states is ensured.

[0078] 3. In the existing trajectory tracking technology of the underactuated underwater robot, the tracking error is mostly in the form of asymptotic convergence or finite time convergence, the error convergence time of this form cannot be accurately predicted and set in advance. Based on the practical preset time stability theory, the error convergence time can be preset in advance, and is not affected by the initial state of the system, and the application range and reliability of the controller are further improved. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 The trajectory tracking control method flow chart of the underactuated underwater robot provided by the application is shown.

[0080] Figure 2 The bidirectional fuzzy brain emotion learning network structure provided by the application is shown.

[0081] Figure 3 The control flow provided by the application is shown.

[0082] Figure 4 The three-dimensional trajectory tracking diagram of the underactuated underwater robot provided by the application is shown.

[0083] Figure 5 The planar trajectory tracking diagram of the underactuated underwater robot provided by the application is shown.

[0084] Figure 6 The tracking error diagram of the underactuated underwater robot provided by the application is shown.

[0085] Figure 7 The control input diagram provided by the application is shown. DETAILED DESCRIPTION

[0086] The specific embodiments of the application are described below to facilitate those skilled in the art to understand the application, but it should be clear that the application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the application defined and determined by the appended claims, and all applications utilizing the concept of the application are within the scope of protection.

[0087] The application embodiment provides a trajectory tracking control method of an underactuated underwater robot, as shown in Figure 1 the following steps are included.

[0088] S1, reference utility preset time control theory and its proof lemma, construct the five degree of freedom kinematics and dynamics model of the underactuated underwater robot;

[0089] S2, based on the constructed five degree of freedom kinematics and dynamics model, the tracking error of the underactuated underwater robot is determined by the sight distance method;

[0090] S3, a tunnel type performance function is constructed, and the tracking error of the underactuated underwater robot is converted, and then the preset performance constraint is determined;

[0091] S4, according to the determined preset performance constraint, a preset time virtual control law is designed;

[0092] S5, a bidirectional fuzzy brain emotion learning control network for outputting an approximate ideal control law of the underactuated underwater robot is constructed, and the surge, pitch and yaw directions of the underactuated underwater robot based on the preset time virtual control law are taken as inputs of the bidirectional fuzzy brain emotion learning control network;

[0093] S6, the output control law of the bidirectional fuzzy brain emotion learning control network is adaptively compensated to obtain an actual control law, and the actual control law is used for trajectory tracking control of the underactuated underwater robot.

[0094] In step S1 of the embodiment of the application, in the utility preset time control theory:

[0095] Consider the following nonlinear system:

[0096] (1)

[0097] In the formula, , is a continuous nonlinear function, and , is the solution of the system . If there exists , so that , then is true, and the solution of is preset time stable; if there exists , , so that , then is true, and the solution of is utility preset time stable.

[0098] In the related proof lemma:

[0099] Lemma 1. Assuming that a radial unconstrained positive definite Lyapunov function , if , can be made:

[0100] (2)

[0101] , and when , ; and when , , the system is practically preset time stable. is a new type of time-varying scaling transformation function:

[0102] (3)

[0103] where, , and , and . has the following two properties

[0104] Property 1: on , is a continuous and increasing function, and , .

[0105] Property 2: on , , which represents is n-order derivable.

[0106] Lemma 2. For any , the following inequality holds:

[0107] (4)

[0108] where, satisfies .

[0109] Lemma 3. According to the style inequality, for any and , the inequality holds.

[0110] 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 represented as:

[0111] (5)

[0112] where:

[0113] In the formula, denotes the rotation matrix between the earth coordinate system and the body coordinate system of the underwater robot, denotes the mass inertia matrix, denotes the hydrodynamic damping coefficient matrix, denotes the Coriolis and centripetal force matrix of the underwater robot, denotes the vector of buoyancy and gravity, , denotes the real displacement of the underactuated autonomous underwater robot, denotes the yaw angle, denotes the pitch angle, denotes the first derivative of , , denote the real velocity in the direction, respectively, denotes the first derivative of , denotes the control input, denotes the time-varying position ocean disturbance, denote the ocean disturbance in the direction, respectively, denotes the water density, denotes the gravity acceleration, denotes the displacement, denotes the longitudinal metacentric height, , , , and 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, , , , and denote 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.

[0114] In the above underactuated underwater robot five-degree-of-freedom kinematics and dynamics model, there are:

[0115] , and ;

[0116] and the position , velocity and acceleration in the direction, and their first and second derivatives are bounded.

[0117] Specifically, since the underactuated underwater robot has a stable center restoring force, it is not likely that the pitch angle of the underactuated underwater robot will exceed the range, so it is reasonable to assume that the pitch angle of the underactuated underwater robot must satisfy .

[0118] In step S2 of the embodiment of the present application, the tracking position error of the underactuated underwater robot in the body coordinate system can be expressed as:

[0119] (6)

[0120] wherein, represents the desired time-varying three-dimensional trajectory.

[0121] Then according to the sight distance method, the position error , the pitch angle error and the yaw angle error are expressed as:

[0122] (7)

[0123] Further, from the formula (5), the formula (6) and the formula (7), the following two relationships can be derived:

[0124] (8)

[0125] (9)

[0126] Finally, according to the above analysis, the tracking error of the underactuated underwater robot includes the position error, the pitch angle error and the yaw angle error, and the corresponding derivative form is expressed as:

[0127] (10)

[0128] wherein,

[0129] (11)

[0130] In the formula, respectively represent the position error , the pitch angle error and the yaw angle error determined by the sight distance method, the corresponding derivative, represents the desired time-varying three-dimensional trajectory, represents the corresponding first derivative.

[0131] In step S3 of the embodiment of the present application, the error conversion is performed through the position error, the pitch angle error, the yaw angle error and the tunnel type preset performance to realize the preset performance constraint.

[0132] In this embodiment, the tunnel type performance constraint is expressed as:

[0133] (12)

[0134] (13)

[0135] wherein, represents the upper boundary of the error constraint, represents the lower boundary of the error constraint, represents a decision parameter of the initial error constraint boundary value, , and all represent positive adjustment parameters for adjusting the final upper boundary and lower boundary of the system error in the steady state stage, represents an initial value of the error, represents a parameter for deciding the convergence speed, represents a preselected convergence time of ; wherein, subscript ;

[0136] When the tunnel type performance function is error converted with the tracking error of the underactuated underwater robot, the tracking error satisfies:

[0137] (14)

[0138] wherein, , , and respectively represent a position error, a pitch angle error and a yaw angle error in the tracking error;

[0139] The formula for error conversion is:

[0140] (15)

[0141] wherein, represents the position error, the pitch angle error and the yaw angle error after the error conversion formula, represents the original position error, the pitch angle error and the yaw angle error.

[0142] In step S4 of the embodiment of the application, in the process of designing the virtual control law of the preset time, the Lyapunov function is constructed as follows:

[0143] (16)

[0144] Reviewing the result of formula (10), in order to facilitate subsequent derivation, the following symbol definition is given:

[0145] (17)

[0146] (18)

[0147] (19)

[0148] Then, the derivative of formula (16) is obtained as follows:

[0149] (20)

[0150] Further, the preset time virtual control law of the design is expressed as:

[0151] (21)

[0152] In the formula, , and respectively represent the preset time virtual control law in the surge, pitch and yaw directions, represents a time-varying scaling transformation function, represents the first derivative of , respectively represent the position error, pitch angle error and yaw angle error after the error conversion formula, , , , all represent normal numbers, represents the pitch angle, , and respectively represent the position error, pitch angle error and yaw angle error in the tracking error.

[0153] In step S5 of the embodiment of the application, the constructed bidirectional fuzzy brain emotional learning control network includes a sensory input layer, a wavelet sensory cortex, an amygdala space, an orbitofrontal cortex space and an output space;

[0154] The sensory input of the sensory input layer is expressed as wherein, , represents the nth input node of the underwater robot, and the derived virtual control rate is subtracted from the actual speed to obtain the error , is expressed as the input of the bidirectional fuzzy brain emotional learning control network in the surge, pitch and yaw directions acting on the underactuated underwater robot, and the fuzzy reasoning rule is expressed as:

[0155] When is , is , is When ;

[0156] When is , is , …, is , then ;

[0157] In the formula, , is defined as the fuzzy rule of the first layer input of the underwater robot, 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 weight of the amygdala space, represents the network weight of the orbitofrontal cortex space. 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 represented as:

[0158]

[0159] (22)

[0160] In the formula, represents the wavelet function corresponding to the th input in the th layer, and represent the center vector and the width vector that determine the activation degree of the wavelet function, and represent the translation and expansion adjustment when the wavelet membership function is associated with the th input in the th layer.

[0161] In the wavelet sensory cortex, when the input signal in the sensory cortex is analyzed by the wavelet function, the maximum value of the characteristic signal is identified and transmitted to the amygdala space as the key feature, and the maximum value is defined as the characteristic signal of the sensory cortex.

[0162] (23)

[0163] The amygdala space is represented as:

[0164] (24) ​

[0165] wherein, represents the network weight of the amygdala space, represents the connection weight of the sensory cortex feature signal transmitted to the amygdala;

[0166] The signal converted by the wavelet sensory cortex is delivered to the orbitofrontal cortex space, and the output of the orbitofrontal cortex space is defined as:

[0167] (25)

[0168] wherein, represents the network weight of the orbitofrontal cortex space;

[0169] In the output space, the output of the bidirectional fuzzy emotional learning control network is the output value of the amygdala space minus the output value of the orbitofrontal cortex space, and the output is represented as:

[0170] (26)

[0171] In the embodiment of the present application, the bidirectional fuzzy emotional learning control network adjusts and updates the weights of the amygdala space and the orbitofrontal cortex space and the feature signal in the wavelet sensory cortex through a bidirectional adjustment mechanism based on rewards, and the reward mechanism includes positive reward signals and negative reward signals, and the update formula is:

[0172] (27)

[0173] (28)

[0174] (29)

[0175] wherein, represents the network weight of the updated amygdala space, represents the network weight of the current amygdala space, represents the change amount of the network weight of the amygdala space during the update interval, represents the connection weight of the sensory cortex feature signal of the updated amygdala, represents the connection weight of the sensory cortex feature signal of the current amygdala, represents the change amount of the connection weight of the sensory cortex feature signal of the amygdala during the update interval, represents the network weight of the updated orbitofrontal cortex space, represents the network weight of the current orbitofrontal cortex space, represents the change amount of the network weight of the orbitofrontal cortex space during the update interval, and ​respectively represent the learning rate of the update algorithm in the amygdala space and the orbitofrontal cortex space respectively; represents a reward signal:

[0176] (30)

[0177] wherein, and represent positive gain parameters.

[0178] In step S6 of the embodiment of the present application, the output control law of the bidirectional fuzzy brain emotional learning control network is adaptively compensated by constructing an adaptive compensator;

[0179] The adaptive compensator is represented as:

[0180] (31)

[0181] (32)

[0182] wherein, and are both normal numbers, is an estimated value of , and satisfies , represents the residual error between the output value of the bidirectional fuzzy brain emotional 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 output value of the ideal controller, 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 estimated value of the adaptive rate of the compensator, represents a time-varying scaling transformation function, represents the estimated value of the adaptive law in the compensator;

[0183] Finally, the actual control law is the sum of the output of the bidirectional fuzzy brain emotional learning control network and the output of the adaptive compensator, and is represented as:

[0184] (33)

[0185] In the embodiment of the present application, according to the method described above, it is proved that the preset time bidirectional fuzzy brain emotional learning strategy is effective in the trajectory design method of the underactuated underwater robot.

[0186] Considering the kinematic model and dynamic model of underactuated underwater vehicle and based on the assumption 1 and assumption 2, the preset time virtual control rate proposed above , the output of the bidirectional fuzzy brain emotional learning controller , the updating mechanism of network weights and the adaptive compensator to ensure the stability of the system . Therefore, even under the influence of external disturbance and model uncertainty, the underactuated underwater vehicle can complete accurate tracking of the desired trajectory within the preset time.

[0187] The proof is as follows:

[0188] Definition respectively as the almond kernel space and the orbitofrontal cortex space network weight error, since and where is the gain value, , This means converges to the neighborhood of zero under the adjustment of the adaptive compensator , so is bounded. Then, the derivatives of and are taken respectively, and the following can be obtained:

[0189] (34)

[0190] (35)

[0191] (36)

[0192] where is a positive constant, satisfying ; .

[0193] The Lyapunov function is selected as follows:

[0194] (37)

[0195] The derivative of is taken, and is substituted to obtain:

[0196] (38)

[0197] Substitute into The following can be obtained:

[0198] (39)

[0199] Definition and satisfies and According to Lemma 2 and Lemma 3, the following inequality holds:

[0200] (40)

[0201] where

[0202]

[0203] According to , it can be concluded that Therefore, according to the practical preset time theory and Lemma 1, the following conclusions can be further obtained:

[0204] (41)

[0205] Therefore, according to Lemma 1 and , all the variables in can converge and reach a stable state within the preset time In addition, according to and the inherent characteristics of the preset performance control, it can be concluded that for all , hold, and the proof is complete.

[0206] In the embodiments of the present application, in order to verify the effectiveness of the method of the present application, simulation experiments are carried out, which are as follows:

[0207] The desired trajectory of the underwater robot is: , , The initial position of the underwater robot is set to: , and the time-varying external disturbance is set to:

[0208]

[0209] ; the performance function related parameters are , .

[0210] The model parameters are shown in Table 1, and the control system parameters are shown in Table 2:

[0211] Table 1: Model parameters

[0212]

[0213] Table 2: Control system parameters

[0214]

[0215] Figure 2 The structure of the bidirectional fuzzy brain emotional learning control network is shown, Figure 3 The control flow of the entire system is shown. The simulation results are Figures 4-7 . The three-dimensional trajectory tracking effect diagram of the underactuated underwater robot, and Further, the trajectory tracking effect is shown in detail from the X-Y and X-Z planes, and the results show that the underactuated underwater robot can accurately move along the desired trajectory, and the trajectory is smooth, showing good tracking performance; The convergence effect of the position error , the pitch angle error and the yaw angle error of the underactuated underwater robot under the constraint of the tunnel type performance function can be clearly seen. The errors can all converge to an area close to zero within the preset time , and are all constrained within the error boundary of the tunnel type, showing high precision and no obvious jitter; The control input diagram of the underactuated underwater robot system is shown, which shows that the outputs of the controller are smooth and continuous, and have fast response boundedness. The simulation results verify the robustness, fast convergence speed and convergence time of the proposed controller, which is not affected by the initial value of the system, thereby confirming the effectiveness and practicality of the controller.

[0216] The principles and implementation modes of the present application are described by specific embodiments in the present application. The above embodiment is only used to help understand the method and core idea of the present application; at the same time, for those skilled in the art, according to the idea of the present application, the specific implementation mode and application range will be changed; in summary, the content of the specification should not be understood as a limitation of the present application.

[0217] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

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-degree-of-freedom kinematic and dynamic models, the tracking error of the underactuated underwater vehicle is determined by the line-of-sight method; S3. Construct a tunnel-type performance function and perform error conversion with the tracking error of the underactuated underwater vehicle to determine the preset performance constraints; S4. Designing a preset time virtual control law based on the determined preset performance constraints; S5. Constructing a bidirectional fuzzy brain emotion learning control network for outputting an approximate ideal control law for the underactuated underwater robot, and using the surge, pitch, and yaw directions of the underactuated underwater robot obtained based on the preset time virtual control law as inputs to 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 an actual control law, and use the actual control law to perform trajectory tracking control on the underactuated underwater robot; In step S3, the constructed tunnel performance constraint is expressed as: ； ； Where, 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, Denotes the decision error constraint function The convergence rate 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: ； Where, , 、 and Respectively represent the position error, pitch angle error and yaw angle error in the tracking error; The formula for error conversion is: ； Where, 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.

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, Represents the rotation matrix between the earth coordinate system and the underwater robot body coordinate system, represents the mass inertia matrix, represents the hydrodynamic damping coefficient matrix, represents the Coriolis force and centripetal force matrix of the underwater robot, are vectors representing buoyancy and gravity, , represents the true displacement of the underactuated autonomous underwater vehicle, represents the yaw angle, represents the pitch angle, express The first derivative of , Respectively True speed in direction, express The first derivative of represents the control input, represents the time-varying position ocean disturbance, Respectively Directional ocean disturbances, represents the water density, represents the acceleration due to gravity, Indicates the amount of water discharged. represents the longitudinal metacentric height, 、 、 、 and They represent 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. 、 、 、 and They represent the linear damping coefficients along the x-axis, the y-axis, and the z-axis, and the rotational damping coefficients around the y-axis and 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 vehicle, there are: ,and ; as well as, Position, velocity, and acceleration in a direction, as well as their first and second 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: ； Where, 、 and Represents the position error determined by the line-of-sight method , pitch angle error and yaw error The corresponding derivative, represents the desired time-varying 3D trajectory, express The corresponding first-order derivative.

5. 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: ； ； ； ； Where, 、 and Represents the preset time virtual control law for surge, pitch and yaw directions respectively, represents the time-varying scaling transformation function, express The first derivative of Respectively represent the position error, pitch angle error and yaw angle error after the error conversion formula, , , , are positive numbers, represents the pitch angle, 、 and They represent the position error, pitch angle error and yaw angle error in the tracking error respectively.

6. 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 Respectively with actual speed Subtract 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 vehicle, and its fuzzy inference rules are expressed as: when for 、 for 、…、 for When ; when for 、 for 、…、 for When ; Where, , Defined as underwater robot , The fuzzy rules of the layer input, and Represent the outputs 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, Network weights representing orbitofrontal cortical space; In the wavelet sensory cortex, the sensory input of each layer is fuzzy quantized by the wavelet function, which is expressed as: ； Where, Indicates Layer 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 to the amygdala space as a key feature; The amygdala space is represented as: ； Where, 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: ； Where, Network weights representing orbitofrontal cortical space; The output of the output space is expressed as: 。 7. The trajectory tracking control method of an underactuated underwater robot according to claim 6, characterized in that: The bidirectional fuzzy emotional 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 regulation mechanism. The update formula is: ； ； ； Where, represents the updated network weights in the amygdala space, Represents the network weight of the current amygdala space, represents the change in the network weights in the amygdala space during the update interval, represents the connection weight of the updated amygdala sensory cortex feature signal, represents the connection weight of the current amygdala sensory cortex feature signal, represents the change in the connection weights of the sensory cortex feature signal 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 an update interval, and Represent the learning rates of the update algorithm in the amygdala space and orbitofrontal cortex space respectively; represents the reward signal, , and Represents the positive gain parameter.

8. The trajectory tracking control method of an underactuated underwater robot according to claim 6, 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: ； ； Where, 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, Indicates 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: 。

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