Autonomous underwater vehicle MPC controller parameter optimization method

Abstract

The invention is suitable for the technical field of autonomous underwater vehicle control, and provides an autonomous underwater vehicle MPC controller parameter optimization method comprising the following steps: constructing an AUV motion mathematical model including a horizontal plane motion continuous time linear state space equation and a vertical plane motion linear state space equation; designing an MPC controller, and defining a target function minimization weight matrix and parameters of a prediction time domain; and parameter optimization is carried out by adopting an IBKA algorithm, and the optimized parameters are applied to an MPC controller, so that AUV course or depth control is realized. According to the method, the lens imaging reverse learning strategy is introduced into the BKA, and the IBKA algorithm and the MPC controller are combined through the fitness function, so that parameter optimization of the controller is realized, the control performance of the controller is improved, and a new thought is provided for parameter selection of the MPC controller.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of autonomous underwater vehicle control, and particularly relates to an MPC controller parameter optimization method for autonomous underwater vehicles. BACKGROUND

[0002] As an important tool in the fields of ocean resource exploration, environmental monitoring, military reconnaissance, etc., the motion control performance of an autonomous underwater vehicle (AUV) directly determines the efficiency and reliability of task execution. Heading control and depth control are both core links of AUV motion control, and the AUV can be made to travel stably according to a predetermined target by adjusting the outputs of the propeller and the rudder. At present, the academic circle invests a lot of effort in researching and developing optimized AUV motion controllers. These researches cover a wide range of fields from classical control theory to modern control theory, and are committed to improving the control accuracy and response speed of the system.

[0003] In common research, the method for selecting MPC controller parameters is often not introduced, and the performance of the MPC controller depends largely on the selection of the weight matrix. Traditional controller parameter selection methods usually rely on experience or trial-and-error methods, which are difficult to achieve optimal control performance in complex environments. Such methods require a lot of time and the support of experienced experts. At the same time, when the objective function is updated, the weight parameters need to be adjusted manually. Therefore, it is necessary to propose an MPC controller parameter optimization algorithm based on a heuristic algorithm, and to construct a coefficient-adjustable fitness function for quickly solving the MPC weight parameters under different control requirements. In summary, the research on PID and LQR parameter optimization in the academic circle is relatively mature, but there is less research on the optimization of more complex MPC controller parameters. At the same time, the existing research has the problem of unclear optimization mechanism, which leads to the problems of unclear MPC controller optimization parameters and incomplete fitness function construction. SUMMARY

[0004] The purpose of the embodiment of the application is to provide an MPC controller parameter optimization method for autonomous underwater vehicles, which aims to solve the problems proposed in the background.

[0005] The embodiment of the application is implemented in the following way: an MPC controller parameter optimization method for autonomous underwater vehicles, comprising the following steps: Step 1: AUV motion mathematical model construction; Treating the AUV as a rigid body with uniformly distributed mass, the six-degree-of-freedom motion equations of the AUV in the coordinate system are derived using hydrodynamic principles. An NPS AUV II is selected, and its nonlinear motion equations are linearized before designing the MPC controller. The linear motion state equations of the AUV in the horizontal and vertical planes are obtained by linearizing the six-degree-of-freedom nonlinear motion equations, consisting of the sway, roll, pitch, and yaw motion equations, in the neighborhood of the equilibrium position. The linearization derivation process assumes no external disturbances. In the linearization process of the AUV's horizontal plane motion equations, only the sway and yaw motions need to be considered. After simplification, the continuous-time linear state-space equations are obtained: (1); in, Indicates sway speed, Indicates the bow roll angular velocity. Indicates the heading angle. Indicates the vertical rudder angle. The derivative representing the sway velocity, The derivative of the bow roll angular velocity, The derivative of the heading angle, The equations of transverse motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. The coefficient.

[0006] In the linearization of the equations of motion in the vertical plane, only heave and pitch motion need to be considered. After simplification, the continuous-time linear state-space equation (2) is obtained, which is then introduced... Then, the linear state-space equation (3) containing the navigation depth as a state variable can be obtained: (2); (3); in, Indicates the heave velocity. Indicates pitch angular velocity, Indicates pitch angle, Indicates depth, Indicates the horizontal rudder angle. The derivative representing the heave velocity, The derivative of pitch angular velocity, The derivative of the pitch angle, The derivative representing depth, The equations of heave motion are obtained after linearization. coefficient, The equations of heave motion are obtained after linearization. coefficient, The equations of heave motion are obtained after linearization. coefficient, The pitch motion equations are obtained after linearization. coefficient, The pitch motion equations are obtained after linearization. coefficient, The pitch motion equations are obtained after linearization. coefficient, The equations of heave motion are obtained after linearization. coefficient, The pitch motion equations are obtained after linearization. coefficient, Indicates the oscillation speed.

[0007] Step 2: Design of the MPC controller; First, an MPC controller needs to be designed based on the motion mathematical equations of the AUV. For the AUV motion mathematical model constructed in step 1, the MPC algorithm is used to implement the heading control and depth control of the AUV respectively. When using MPC to implement the motion control of the AUV, the continuous system of equations (1) and (3) is first discretized into the form of equation (4): (4); in, Represents the state vector. Represents the input vector. Indicates the output vector. and These represent the corresponding coefficient matrices. Indicates the current moment; Based on the state equations of the AUV motion mathematical model, assume the state variables of the AUV motion. At any moment It can be measured, and the predicted state variables can be obtained by deriving the state equation. The calculation formula (5) is generalized to formula (6): (5); (6); The constraint condition is: (7); (8); (9); (10); In the formula, denotes the prediction time domain, the value range of is , denotes the state variable at the time of prediction at the current time , denotes the control variable at the time of prediction at the current time , denotes the state variable at the time of prediction at the current time , denotes the state variable of the AUV at each prediction time, is the corresponding input control variable, and are the augmented coefficient matrices, and is predicted by formula (6) , and is obtained in the prediction range; After constructing the discrete state space equation of the system, the objective function to be minimized is set, that is, the optimization problem considering formula (11) is: (11); The constraint condition is: (12); (13); (14); In the above formula, the value range of is ; formula (12) is the system state equation for predicting the future state, (13) and (14) are the constraint conditions of the system state variable and the input control respectively, and denote the maximum and minimum values of the state variable respectively, and denote the maximum and minimum values of the control variable respectively; and are the corresponding weighting matrices for shaping the response, denotes a semi-positive definite matrix, denotes a positive definite matrix.

[0008] Step 3: parameter optimization is performed by using the IBKA algorithm; The IBKA algorithm introduces the LOBL strategy after the migration behavior of the Black Kite Algorithm (BKA), and determines the final leader of the current iteration by comparing the fitness of With .

[0009] The autonomous underwater vehicle MPC controller parameter optimization method provided by the embodiment of the application has the following beneficial effects: (1) Efficient parameter optimization: the IBKA algorithm enhances the global search capability through the LOBL strategy, solves the problem that the traditional method is prone to local optimization, and improves the optimization efficiency; (2) Control performance improvement: in the AUV heading control, the MPC controller optimized by the IBKA algorithm makes the heading angle And respectively decrease by 16.15% and 42.09%; in the depth tracking, And respectively decrease by 21.01% and 45.16%; (3) Flexible fitness function: the weighting factor is adjustable, and is suitable for different control scenarios; (4) Multi-dimensional parameter collaborative optimization: the weight matrix , and the prediction horizon are optimized at the same time, and the dynamic control performance is improved. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 is the basic principle of model predictive control; Figure 2 is the MPC heading control result under parameter optimization; Figure 3 is the convergence curve comparison of different algorithms in the heading control experiment; Figure 4 is the MPC depth tracking result under parameter optimization; Figure 5 is the MPC depth tracking error under parameter optimization; Figure 6 is the parameter optimization MPC depth tracking result of different optimization algorithms; Figure 7 is the parameter optimization MPC depth tracking error of different optimization algorithms; Figure 8 is the convergence curve comparison of the IBKA algorithm and the classical optimization algorithm. DETAILED DESCRIPTION

[0011] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0012] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0013] like Figure 1 As shown, an embodiment of the present invention provides a method for optimizing the parameters of an autonomous underwater vehicle (AUV) MPC controller, comprising the following steps: Step 1: Construction of the mathematical model for AUV motion; The nonlinear AUV motion equations can be expressed in both the ship's hull coordinate system and the ground coordinate system. In this study, the AUV is treated as a rigid body with uniformly distributed mass, and the six-degree-of-freedom motion equations of the AUV in the coordinate system are derived using hydrodynamic principles. An NPSAUV II is selected, and its nonlinear motion equations need to be linearized before designing the MPC controller. The linear motion state equations of the AUV in the horizontal and vertical planes are obtained by linearizing the six-degree-of-freedom nonlinear motion equations, consisting of the sway, roll, pitch, and bow motion equations, in the neighborhood of the equilibrium position, assuming no external interference during the linearization derivation process. In the linearization process of the AUV's horizontal plane motion equations, only the sway and bow motions need to be considered. After a series of simplifications, the continuous-time linear state-space equations are obtained: (1); in, Indicates sway speed, Indicates the bow roll angular velocity. Indicates the heading angle. Indicates the vertical rudder angle. The derivative representing the sway velocity, The derivative of the bow roll angular velocity, The derivative of the heading angle, The equations of transverse motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. the coefficients of In the linearization process of the vertical plane motion equation, only heave motion and pitch motion are considered. After a series of simplifications, the continuous-time linear state space equation (2) is obtained, introducing , the linear state space equation (3) containing the state variable of navigation depth is obtained: (2); (3); wherein, denotes the heave velocity, denotes the pitch angular velocity, denotes the pitch angle, denotes the depth, denotes the rudder angle, denotes the derivative of the heave velocity, denotes the derivative of the pitch angular velocity, denotes the derivative of the pitch angle, denotes the derivative of the depth, denotes the coefficients of obtained by linearizing the heave motion equation, denotes the coefficients of obtained by linearizing the heave motion equation, denotes the coefficients of obtained by linearizing the heave motion equation, denotes the coefficients of obtained by linearizing the pitch motion equation, denotes the coefficients of obtained by linearizing the pitch motion equation, denotes the coefficients of obtained by linearizing the pitch motion equation, denotes the coefficients of obtained by linearizing the heave motion equation, denotes the coefficients of obtained by linearizing the pitch motion equation, denotes the surge velocity.

[0014] Step 2: Design of MPC controller; Model predictive control (MPC) is an advanced control method that predicts the future behavior of the controlled system by using the process model. Based on this prediction ability, MPC determines the optimal control amount by solving a constrained optimization problem. As one of the few control methods that directly consider system constraints, MPC usually adopts a specific form of cost function construction, which calculates the prediction time domain time steps, so that the system output can meet the requirements in the control time domain Continuously track the expected value of a given state variable within a time step. To achieve weight optimization of the MPC controller based on the Improved Black-winged Kite Algorithm (IBKA), the MPC controller must first be designed according to the motion mathematical equations of the AUV. For the AUV motion mathematical model constructed in step 1, the MPC algorithm is used to implement the heading control and depth control of the AUV respectively, so as to verify the effect of the IBKA algorithm on the weight optimization of the MPC controller with specific examples. When using MPC to implement the motion control of the AUV, the continuous system of equations (1) and (3) is first discretized into the form of equation (4).

[0015] (4); in, Represents the state vector. Represents the input vector. Indicates the output vector. and These represent the corresponding coefficient matrices. Indicates the current moment.

[0016] Based on the state equations of the AUV motion mathematical model, assume the state variables of the AUV motion. At any moment Time can be measured, and the predicted state variables can be obtained by deriving the state equation. Its calculation formula (5) can be generalized to formula (6).

[0017] (5); (6); The constraints are: (7); (8); (9); (10); In the above formula, Indicates the prediction time domain, The range of values ​​is , Indicates the current moment Predicted The state variable at time t, Indicates the current moment Predicted The amount of control at any given moment This represents the state variables of the AUV at each prediction time. is the corresponding input control variable, and is the augmented coefficient matrix, which is predicted by formula (6) and obtains the predicted range ; After constructing the discrete state space equation of the system, in order to realize the solution of the optimal control variable of the MPC controller, the objective function to be minimized is set, that is, the optimization problem of formula (11) is considered: (11); The constraint condition is: (12); (13); (14); In the above formula, The value range of ; formula (12) is the system state equation for predicting future states, and (13) and (14) are the constraint conditions of the system state variable and the input control respectively, and represent the maximum and minimum values of the state variable respectively, and represent the maximum and minimum values of the control variable respectively; and are the corresponding weighting matrices for shaping the response, represents a positive semi-definite matrix, represents a positive definite matrix.

[0018] Step 3: Design of IBKA algorithm; BKA algorithm is a new type of intelligent optimization algorithm, which is inspired by the flight behavior of black-winged kite in the process of predation. By simulating the behaviors of circling, diving and predation of black-winged kite, the algorithm can quickly find the optimal solution in the search space. In view of the problem that the attack behavior and migration behavior in BKA algorithm may be limited by the initial population distribution and fall into local optimum, LOBL strategy is introduced in these two processes. LOBL strategy generates the reverse solution of the current solution, so that the algorithm not only searches around the current solution, but also explores the reverse area, avoiding the premature limitation of search range. The reverse solution and the original solution are symmetric in space, which can enrich the distribution of population solutions, reduce the similarity of individuals, and prevent the algorithm from converging prematurely due to high similarity of population. By comparing the fitness of the original solution and the reverse solution, the better solution is retained and the poor solution is quickly eliminated, guiding the population to move to a better area and shortening the optimization time. IBKA algorithm introduces lens imaging reverse learning strategy after migration behavior, which compares and The fitness of the MPC controller is used to determine the final leader for this iteration. The IBKA algorithm optimizes the parameters of the MPC controller, that is, the weight matrix in equation (11). , and prediction time domain The optimization process is based on a fitness function that aligns with the goals of the actual application. Therefore, optimizing controller parameters requires designing a fitness function with practical optimization value. Currently, it is necessary to design a fitness function that meets the performance optimization requirements of the MPC controller and complete parameter optimization in conjunction with the design principles of the MPC controller.

[0019] Step 3.1: Fitness function design; This method aims to determine the optimal parameters of the MPC controller in an AUV system using the IBKA algorithm. The key to obtaining the optimal controller parameters lies in exploring the cooperative matching relationship between the optimization algorithm, fitness function, MPC controller type, and controlled object. Currently, commonly used indicators for evaluating controller performance include integral absolute error (IAE), time-weighted absolute error (ITAE), and integral of the absolute value for the variation of the control signal (IAVU). To determine the optimal controller parameters using the algorithm proposed in this method, a new objective function is constructed, which is a linear combination of overshoot (OV), IAE, ITAE, and IAVU. Its expression is shown in equation (15): (15); The constraints are: (16); (17); (18); (19); in, This represents the value of the fitness function. The weighting factor for the fitness function. This represents the maximum value of the system output response. This represents the steady-state value of the system output. Indicates time, Represents the expected value of a state variable. This represents the actual value of the state variable. This indicates a control input.

[0020] Step 3.2: Population initialization; In the IBKA algorithm, the first step is population initialization, which involves creating a set of random solutions. When creating random solutions, the constraints of the actual problem must be considered, specifically, a lower bound on the position of the black-winged kite must be provided. and upper limit The required number of random solutions is obtained using equation (20). Since the position of each black-winged kite corresponds to a feasible solution in the search space, the position of each black-winged kite (BK) can be represented by the following matrix (21): (20); (twenty one); in, Indicates the first The solution for the black-winged kite is randomly generated by equation (20) in the initial population; Indicates the range of values ​​within random numbers, This indicates the number of potential solutions. This indicates the dimensionality of the solution to a given problem. It is the first The first black-winged kite Dimensional solution, The range of values ​​is , The range of values ​​is ; During population initialization, the IBKA algorithm selects the black-winged kite individual with the optimal fitness function. As the leader in the initial population, if the optimal solution is to minimize the fitness function, then the expression shown in equation (22) can be given to find the fitness function value in the initial population. The individual corresponding to the minimum and will As the leader, it also considers the leader's position to be the best habitat for the black-winged kite. This indicates the position of the leader at a certain iteration of the BKA algorithm. Here, the leader in the initial population is given. The mathematical expression (23): (twenty two); (twenty three); in, The optimal fitness is represented by the value of the individual, which is calculated by substituting the individual into the fitness function.

[0021] Step 3.3: Attack behavior; To better understand the biomimetic principle of the IBKA algorithm, the attack behavior of the black-winged kite will be described from a biomimetic perspective, with its core being hovering flight and precise capture. The black-winged kite has a variety of attack behaviors for global exploration and searching. The mathematical expression of the attack behavior is shown in (24), and equation (25) is the calculation process of the coefficients. When fighting, it adjusts the angle of its wings and tail feathers according to the wind speed, silently hovers to observe its prey, and once it locks onto its target prey, it will quickly dive down to launch an attack.

[0022] (twenty four); (25); in, and They represent the first The first black-winged kite The solution of dimension is in the th dimension and The value taken in the next iteration; It is a constant; Indicates the current iteration number. Indicates the maximum number of iterations. This represents a coefficient that varies with the number of iterations in the attack behavior. Step 3.4: Migration Behavior; The migration behavior of black-winged kites is usually dominated by the population leader. Therefore, based on the natural behavior of black-winged kites, the algorithm needs to provide a mathematical strategy to optimize the population. That is, after achieving the local optimum of the population leader in the attack behavior, the global optimum is found through the migration behavior. Therefore, according to biomimicry, if the fitness of a randomly generated individual is better than that of the current population leader, the leader will abandon the current leadership and join the migration team, and the newly generated individual will become the population leader. Here, the mathematical expression of the migration behavior is given (26), and equation (27) is the calculation process of the coefficients. Conversely, the current population leader will continue to lead. This strategy can dynamically select excellent population leaders to ensure successful migration.

[0023] (26); (27); in, Indicates the first In the current iteration number, the black-winged kite in the dimension The leading scorer in the group; Indicates the first The fitness value of any individual Blackwing Kite in the next iteration; Indicates the first The fitness value of a randomly selected individual black-winged kite in the next iteration; represents the coefficient in the migration behavior.

[0024] Step 3.5: Lens imaging reverse learning strategy; In order to solve the problem of falling into local optimum caused by the limitation of initial population distribution in attack behavior and migration behavior, LOBL strategy is introduced after migration behavior. LOBL strategy generates the reverse solution of the current solution, so that the algorithm not only searches around the current solution, but also explores the reverse area, avoiding the premature limitation of search range in local area. The reverse solution and the original solution are in a symmetrical relationship in space, which can enrich the distribution of population solutions, reduce the similarity of individuals, and prevent the algorithm from converging prematurely due to high similarity of population. By comparing the fitness of the original solution and the reverse solution, the better solution is retained and the poor solution is quickly eliminated, guiding the population to move to a better area and shortening the optimization time. IBKA algorithm introduces lens imaging reverse learning strategy with mathematical expressions of formula (28)-(29) after migration behavior, and determines the final leader of this iteration by comparing the fitness of and .

[0025] (28); (29); wherein, represents the position of the leader of a certain round of BKA algorithm, represents the new position generated by the lens imaging reverse learning strategy, is a coefficient related to the current iteration number and the maximum iteration number.

[0026] After introducing LOBL strategy after migration behavior, IBKA algorithm is obtained. Subsequently, taking the heading control of AUV horizontal plane motion and the depth control of AUV vertical plane motion as application scenarios, the weight matrix , and prediction horizon of MPC algorithm are innovatively used as population, and the best individual is solved by using fitness function. Therefore, the adjustment of the proposed controller can be set as a constrained optimization problem, and its mathematical expression is shown in formula (30).

[0027] (30); wherein, and represent the lower bound and upper bound of the variable in the constrained optimization problem.

[0028] In order to understand the implementation process of IBKA algorithm, please refer to the pseudo code in Table 1 below, which details the key steps and logic.

[0029] Table 1

[0030]

[0031]

[0032]

[0033] As a preferred embodiment of the present application, the experimental research of IBKA parameter optimized MPC controller in AUV motion control system is carried out here. The simulation experiment is carried out based on the AUV motion mathematical model derived in step 1, and the performance advantages of IBKA parameter optimized MPC controller are verified by analyzing the step response of the system course control and the depth trajectory tracking performance. In order to compare the performance of IBKA-MPC controller, four MPC controllers optimized by classical optimization algorithms are selected in the experiment, and the simulation results of IBKA-MPC are compared with them to quantitatively evaluate their performance. All numerical simulation experiments are completed on MATLAB 2023a platform, and the simulation environment is deployed on a computing device with Intel i7-12700F processor and 32GB memory. The IBKA algorithm parameters are configured as follows: the number of iterations is set to 30, and the population size is set to 10.

[0034] (1) Course control experiment This subsection is based on the AUV motion mathematical model constructed in step 1 to verify the controller performance of IBKA-MPC in course control. Specifically, first set the surge velocity of AUV , and determine the sampling time as , and then discretize the continuous-time mathematical model to obtain the discrete-time system. In this experiment, based on the fitness function formula (15), according to different control objectives, the fitness function coefficients are set to and for experiment. Through the comparison experiment of IBKA-MPC, BKA-MPC and traditional MPC, the effectiveness of black-winged kite algorithm in MPC controller parameter optimization and the improvement of LOBL strategy on BKA optimization performance are verified. Table 2 lists all the parameters optimized for MPC controller tuning, including weight matrix , and prediction horizon and their search range. To determine the optimal parameters of the controller, the program of IBKA-MPC and BKA-MPC is run repeatedly for 20 times, and the parameter scheme with the optimal fitness is finally selected.

[0035] Table 2 Search range of parameter optimization in course control experiment

[0036] In the heading control experiment of the AUV, its initial heading angle was set to... The desired heading angle is For the fitness function, the coefficients are set to... and The parameters of the MPC controller were optimized using the IBKA and BKA algorithms, and the following results were obtained. Figure 2 The heading angle variation process of the IBKA-MPC controller, BKA-MPC controller, and traditional MPC controller in an AUV heading control experiment is demonstrated. It can be seen that when the fitness function coefficient is... and Under these conditions, the simulation results of the IBKA-MPC controller outperform both the BKA-MPC controller and the traditional MPC controller in terms of overshoot and steady-state error. Here, 20 repeated experiments were conducted on the optimization processes of different IBKA-MPC and BKA-MPC controllers, and the results were processed to calculate the 95% confidence interval of the experimental data in each iteration to reflect the statistical fluctuation range of the data. Figure 3 This shows how the fitness value changes with the number of iterations. The left axis represents the coefficients. The graph shows how the IBKA fitness value and BKA fitness value change with the number of iterations. The right-hand axis represents the coefficients. The graph shows how the IBKA fitness value and BKA fitness value change with the number of iterations. Different colors represent the confidence intervals of the corresponding optimization algorithms, and the broken line represents the average fitness value for the corresponding iteration round. From... Figure 3 It can be observed that, under different fitness function coefficient conditions, there is always... The results are valid, indicating that IBKA outperforms BKA in optimizing MPC parameters, thus verifying the effectiveness of the LOBL strategy in improving the BKA algorithm.

[0037] After processing the experimental results, Tables 3 and 4 present the fitness function coefficients, respectively. and The optimal individual and its corresponding fitness value at that time can be obtained. From this, the optimized MPC controller weight matrix can be derived. , and prediction time domain .

[0038] Table 3 coefficients are Parameter optimization results of different controllers during heading control

[0039] Table 4 coefficients are Parameter optimization results of different controllers during heading control

[0040] As shown in the table, under the MPC controller parameter optimization scenarios corresponding to different fitness function coefficients, the following conditions are met: .

[0041] Tables 5 and 6 present the performance metrics for different controllers. (Coefficients) It gives overshoot Greater weight, which also means The magnitude of the value affects the fitness function The impact is more significant.

[0042] Table 5 coefficients are Performance indicators of different controllers during heading control

[0043] Table 6 coefficients are Performance indicators of different controllers during heading control

[0044] Therefore, as can be seen from Table 5, the overshoot of the IBKA-MPC controller and the BKA-MPC controller... All parameters are much smaller than the initial parameters of the MPC controller. Where, at that time, the fitness function coefficients were... At that time, the absolute integral error of the MPC controller optimized by IBKA Compared to the initial parameters of the MPC controller Decreased by 15.97%, time-weighted absolute integral error Compared A decrease of 41.91%, Compared It decreased by 37.18%. At that time, the fitness function coefficient was... hour, Compared A decrease of 16.15%, Compared A decrease of 42.09%, Compared A decrease of 36.60%. Meanwhile, comparing the optimization results of the IBKA-MPC controller and the BKA-MPC controller, the optimization results obtained by IBKA... , and These results are also lower than those of the BKA-MPC controller. These results indicate that IBKA outperforms BKA in optimization performance, and the optimized parameters significantly improve the performance of the MPC controller.

[0045] (2) Depth tracking experiment; This subsection is based on the AUV motion mathematical model constructed in Step 1, and the depth tracking experiment of IBKA-MPC controller is carried out. Specifically, first, the surge velocity of AUV is set to , the sampling time is determined as , and the continuous-time mathematical model is discretized to obtain the discrete-time system. Here, based on the fitness function formula (15), the fitness function coefficient is set to , and the comparative experiments of IBKA-MPC, BKA-MPC and traditional MPC are carried out to verify the superiority of IBKA-MPC. The remaining parameter settings are consistent with the heading control experiment, and the programs of IBKA-MPC and BKA-MPC are also run 20 times, and finally the optimal parameter scheme is selected according to the optimal fitness.

[0046] In the depth tracking experiment of AUV, the initial value of its depth is set to , and the depth tracking trajectory is set to . Figure 4 The depth variation curves of IBKA-MPC controller, BKA-MPC controller and traditional MPC controller in AUV trajectory tracking are shown. It can be seen from Figure 5 that the depth tracking error of IBKA-MPC controller is smaller than that of BKA-MPC controller and traditional MPC controller, that is, the depth tracking performance of IBKA-MPC controller is better than that of BKA-MPC controller.

[0047] After data processing of the experimental results, Table 7 gives the optimal individual and corresponding fitness value when the fitness function coefficient is , and thus the optimized MPC controller weight matrix , and prediction horizon can be obtained. It can be seen from the data in the table that when the fitness function coefficient is , the fitness value obtained by IBKA optimization is smaller than the fitness value obtained by BKA optimization, that is, the fitness of IBKA is better after parameter optimization. Table 8 shows the performance indicators of different controllers, from which it can be found that the , and of IBKA-MPC controller in depth tracking are smaller than those of the MPC controller with initial parameters. When the fitness function coefficient is is reduced by 21.01% compared with , is reduced by 21.01% compared with ​A decrease of 45.16%. Meanwhile, in the IBKA-MPC controller and BKA-MPC controller... In close proximity, there exists , Therefore, it can be concluded that the IBKA-MPC controller outperforms the BKA-MPC controller.

[0048] Table 7 coefficients are Parameter optimization results of different controllers during depth tracking

[0049] Table 8 coefficients are Performance metrics of different controllers during time-depth tracking

[0050] (3) Comparative experiments with classical optimization algorithms; To investigate the convergence characteristics of the algorithm, four classic optimization algorithms—whale optimization, particle swarm optimization, genetic optimization, and gray wolf optimization—were compared with the IBKA algorithm in a comparative experiment, each running independently 20 times under the same simulation conditions. Based on the coefficient settings in the previous section, an AUV depth tracking experiment was conducted. Figure 6 The paper presents the depth variation curves of the MPC controller's optimal parameters corresponding to different optimization algorithms in AUV depth tracking experiments. Combined with... Figure 7 It can be seen that the IBKA-MPC depth tracking error The tracking error is smaller than that of other classic optimization algorithms, thus verifying the superior optimization performance of the IBKA algorithm. Here, the results of 20 repeated experiments with different algorithms are processed to calculate the 95% confidence interval of the experimental data in each iteration to reflect the statistical fluctuation range of the data, resulting in... Figure 8 The fitness value changes with the number of iterations. Different colors represent the confidence intervals of the corresponding optimization algorithms, and the broken line represents the average fitness value for the corresponding iteration rounds. It can be observed that after 30 iterations, the optimal parameters obtained by the IBKA algorithm minimize the fitness value in the IBKA-MPC simulation results, indicating that its optimization capability is superior to classical optimization algorithms.

[0051] After processing the experimental results of different classical optimization algorithms, Table 9 presents the optimal individual and fitness value for each algorithm, from which the optimized MPC controller weight matrix can be obtained. , and prediction time domain Analysis of the data in the table shows that, in the deep tracking experiment with the MPC controller using the optimal parameters, The fitness value is lower than that of other classic algorithms. Table 10 shows the performance metrics of the controller under different algorithm optimizations. When IBKA-MPC controller in depth tracking when approaching and significantly less than the MPC controller optimized by the classical algorithm. The above experimental results show that the IBKA algorithm with the introduction of the LOBL strategy has better control effect than the optimal parameters of the whale optimization algorithm, particle swarm optimization algorithm, genetic optimization algorithm and grey wolf optimization algorithm, further proving that IBKA has superior optimization performance.

[0052] Table 9 Parameter optimization results of MPC controllers under different optimization algorithms

[0053] Table 10 Comparison of control performance of MPC controllers under different optimization algorithms

[0054] The method first introduces the black-winged kite algorithm into the field of MPC controller parameter optimization, innovatively improves the BKA algorithm by introducing the LOBL strategy, designs a coefficient-adjustable fitness function, and is applied to the autonomous underwater vehicle motion control field for different control targets and scenes. After 20 repeated experiments, the results show that the MPC controller optimized by IBKA has significantly improved performance indicators in the heading control and depth tracking scenes compared with the simulation results of the unoptimized MPC, effectively solving the problem of the MPC weight matrix 、 and the prediction horizon traditionally selected by experience. At the same time, through comparison experiments with the whale optimization algorithm, particle swarm optimization algorithm, genetic optimization algorithm and grey wolf optimization algorithm, it is verified that the IBKA algorithm with the introduction of the LOBL strategy has better convergence performance.

[0055] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of autonomous underwater vehicle MPC controller parameter optimization, characterized in that, The method comprises the following steps: Step 1: constructing a mathematical model of AUV motion, including a continuous time linear state space equation of horizontal plane motion and a linear state space equation of vertical plane motion; Step 2: Design of MPC controller, defining parameters of the prediction horizon and the weight matrix implementing the minimization of the target function , and the prediction horizon . Step 3: performing parameter optimization by using an IBKA algorithm, and applying the optimized parameters to an MPC controller to realize AUV heading or depth control; The IBKA algorithm introduces the LOBL strategy after the attack behavior and the migration behavior of the BKA algorithm, and determines the final leader of the current iteration by comparing the fitness of and , wherein, represents the position of the leader of a certain iteration of the BKA algorithm, represents a new position generated by the LOBL strategy.

2. The autonomous underwater vehicle MPC controller parameter optimization method of claim 1, wherein, The step 1 comprises the following specific steps: An AUV is regarded as a rigid body with uniformly distributed mass, and six-degree-of-freedom motion equations of the AUV in a coordinate system are derived by using hydrodynamic principles, and are linearized and solved in a neighborhood of an equilibrium position; in the linearization process of the AUV horizontal plane motion equation, only sway motion and yaw motion are considered, and after simplification, a continuous time linear state space equation is obtained: （1）； in, Indicates sway speed, Indicates the bow roll angular velocity. Indicates the heading angle. Indicates the vertical rudder angle. The derivative of the sway velocity, The derivative of the bow roll angular velocity, The derivative of the heading angle, The equations of transverse motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. coefficient, The equations of transverse motion are obtained after linearization. coefficient, The equations representing the bow roll motion are obtained after linearization. The coefficient; In the linearization process of the vertical plane motion equation, only the heave motion and the pitch motion are considered; the continuous time linear state space equation (2) is obtained by simplification, and the Then, the linear state space equation (3) containing the state variable of the sailing depth is obtained. （2）； （3）； wherein, denotes the heave velocity, denotes the pitch angular velocity, denotes the pitch angle, denotes the depth, denotes the rudder angle, denotes the derivative of the heave velocity, denotes the derivative of the pitch angular velocity, denotes the derivative of the pitch angle, denotes the derivative of the depth, denotes the coefficient of obtained by linearizing the heave motion equation, denotes the coefficient of obtained by linearizing the heave motion equation, denotes the coefficient of obtained by linearizing the heave motion equation, denotes the coefficient of obtained by linearizing the pitch motion equation, denotes the coefficient of obtained by linearizing the pitch motion equation, denotes the coefficient of obtained by linearizing the pitch motion equation, denotes the coefficient of obtained by linearizing the heave motion equation, denotes the coefficient of obtained by linearizing the pitch motion equation, denotes the surge velocity.

3. The autonomous underwater vehicle MPC controller parameter optimization method of claim 2, wherein, The step 2 comprises the following specific steps: First, an MPC controller is designed according to a mathematical equation of AUV motion, and for the mathematical model of AUV motion constructed in step 1, MPC algorithm is used to realize AUV heading control and depth control; when MPC is used to realize AUV motion control, first, continuous systems of formula (1) and (3) are discretized into formula (4): （4）； wherein, denotes a state vector, denotes an input vector, denotes an output vector, and denote corresponding coefficient matrices, denotes the current time instant; According to the state equation of the AUV motion mathematical model, the state variables of the AUV motion are assumed to be At time The predicted state variables can be measured by deriving the state equation The calculation formula (5) is extended to formula (6): （5）； （6）； The constraint condition is: （7）； （8）； （9）； （10）； In the above formula, Indicates the prediction time domain, The range of values ​​is , Indicates the current moment Predicted The state variable at time t, Indicates the current moment Predicted The amount of control at any given moment This represents the state variables of the AUV at each prediction time. It is the corresponding input control quantity. and The augmented coefficient matrix is ​​used to predict the coefficients using formula (6). and obtain the prediction range ; After the discrete state space equation of the system is constructed, a minimum target function is set, that is, an optimization problem of formula (11) is considered: （11）； The constraint condition is: （12）； （13）； （14）； In the above formula, the value range of ; formula (12) is a system state equation for predicting future states, (13) and (14) are constraint conditions of system state variables and input controls respectively, and respectively represent the maximum and minimum values of the state variables, and respectively represent the maximum and minimum values of the control variables; and are corresponding weight matrices for shaping the response, represents a positive semi-definite matrix, represents a positive definite matrix.

4. The autonomous underwater vehicle MPC controller parameter optimization method of claim 3, wherein, The step 3 comprises the following specific steps: Step 3.1: fitness function design; Constructing a new objective function from With A linear combination of the two objective functions, whose expression is shown in equation (15): （15）； The constraint condition is: （16）； （17）； （18）； （19）； wherein represents a value of the fitness function of the IBKA algorithm, is a weighting factor for the fitness function, represents a maximum value of the system output response, represents a steady state value of the system output, represents time, represents a desired value of the state variable, represents an actual value of the state variable, represents a control input; Step 3.2: population initialization; In the operation of IBKA algorithm, firstly, the population initialization is carried out to create a set of random solutions, and in the creation of random solutions, the constraint conditions of the actual problem are considered, that is, the lower limit of the position of black-winged kite is given and the upper limit The random solution of the required group is obtained by using formula (20); the position of each black-winged kite is represented by the following matrix (21): （20）； （21）； wherein, represents the i th solution of the i th black kite, which is randomly generated by equation (20) in the initialization population; represents a random number with a value range of represents the number of potential solutions, represents the dimension size of the solution of a given problem, is the i th solution of the i th black kite in the i th dimension, the value range of is ; In the initialization process of population, the IBKA algorithm selects the individual of black kite with the optimal fitness function As the leader in the initialization population, the optimal solution is the minimum fitness function, and its expression is shown in equation (22). The individual with the minimum fitness function value is found in the initialization population The individual corresponding to the minimum And the position of the leader is considered as the best habitat of the black kite As the leader, the position of the leader is considered as the best habitat of the black kite The position of the leader of the BKA algorithm at a certain iteration number is represented by the position of the leader of the BKA algorithm at a certain iteration number, which is given in the initialization population The mathematical expression (23) of the leader （22）； （23）； wherein, represents the best fitness, calculated by substituting the individual into the fitness function; Step 3.3: attack behavior; A mathematical expression of the attack behavior is shown in formula (24), and formula (25) is a calculation process of a coefficient; （24）； （25）； wherein, and respectively represent the first the first dimensional solution of the and value in the kth iteration; is a constant; represents the current iteration number, represents the maximum iteration number, represents the coefficient varying with iteration number in the attacking behavior; Step 3.4: migration behavior; If the fitness of a randomly generated individual is better than that of a current population leader, the leader gives up the leadership of the current population and joins a migration team, and the newly generated individual is taken as a leader of the population; a mathematical expression of the migration behavior is shown in formula (26), and formula (27) is a calculation process of a coefficient; otherwise, the leader of the current population continues to lead; （26）； （27）； wherein, denotes the leading score of a black kite in the current iteration number of dimensions; denotes the value of the fitness of an arbitrary black kite individual in the denotes the value of the fitness of a randomly selected black kite individual in the denotes a coefficient in the migration behavior; Step 3.5: lens imaging reverse learning strategy; The IBKA algorithm introduces the lens imaging reverse learning strategy of mathematical expressions for formulas (28)-(29) after the migration behavior, and determines the final leader of this iteration by comparing the fitness of and ; （28）； （29）； wherein, represents the position of the leader of a certain iteration number of the BKA algorithm, represents a new position generated by the lens imaging reverse learning strategy, is a coefficient related to the current iteration number and the maximum iteration number; Subsequently, the heading control of the AUV horizontal plane movement and the depth control of the vertical plane movement are taken as the application scenarios, the weight matrix , and the prediction time domain of the MPC algorithm are taken as the population, and the optimal individual is solved by means of the fitness function ; therefore, the adjustment of the proposed controller is set as a constraint optimization problem, and the mathematical expression is shown in equation (30); （30）； wherein, and denote lower and upper bounds on the variables in the constrained optimization problem.

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