Multi-USV trajectory tracking control method with ESO and signal quantization

Abstract

The invention provides a multi-USV trajectory tracking control method with ESO and signal quantization, and the method comprises the steps: obtaining the sea condition information of a surrounding environment and other surrounding ships, and building a trajectory control mathematical model of an under-actuated unmanned ship formation; a uniform quantizer is adopted to quantize control input and state variables in the control system; estimating the required quantization state information and uncertain items existing in the model by using the ESO technology; according to the idea of inner and outer rings, a kinematic guidance law and a dynamic quantitative tracking control law are designed, and a linear model is introduced to describe a quantitative process, so that a designed controller does not need to quantize prior information of parameters any more, and an event-triggered formation control strategy is provided to further reduce communication burden; based on the Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed multi-USV formation trajectory tracking control system with signal quantization are proved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a multi-USV trajectory tracking control method with ESO and signal quantization. Background Art

[0002] With the rapid development of automation and unmanned driving technologies, unmanned systems have made significant progress. Unmanned surface vehicles (USVs) have received widespread attention in the maritime industry and are widely used in marine engineering due to their small size, lack of human piloting, affordability, simple control, and ability to effectively reduce the risk of personal injury. One of the main advantages of USVs is their ability to navigate accurately and easily in challenging marine environments. Since there are no crew members on board, the risk of casualties in dangerous situations is greatly reduced, significantly improving the safety of marine operations. As the demand for more efficient and effective marine solutions continues to increase, the use of USVs is expected to become more and more widespread.

[0003] Compared with a single USV, a multi-USV formation control system has stronger fault tolerance and adaptability. Cluster control through collaboration between multiple USVs can not only reduce the workload of operators, but also improve the sustainability, scalability and intelligence of marine operations. In order to improve the trajectory tracking performance of underactuated unmanned surface vessels, researchers have proposed a variety of control methods, such as PID control, sliding mode control, adaptive control and model predictive control. However, most of these methods rely on high-precision sensors and continuous communication signals, which may lead to excessive communication burden and high energy consumption in practical applications, and even fail to meet real-time requirements. Therefore, it is particularly important to achieve efficient and robust trajectory tracking control under limited communication resources and computing power.

[0004] In actual ocean control systems, communication resources and computing power are limited. In order to improve the efficiency and economy of the system, signal quantization technology has gradually become a research hotspot. Signal quantization refers to the discretization of continuous signal values ​​into a finite number of quantization levels, thereby reducing the amount of data transmission and computational complexity. Through signal quantization, unmanned surface vessels can achieve more efficient control signal transmission within a limited communication bandwidth. For unmanned marine vehicles with faults and disturbances, a robust sliding mode controller has been designed to ensure the stability of the system through adaptive quantization. Despite this, most current research still focuses on the function of input or state quantization in ocean formation control systems. Therefore, it is crucial to develop a distributed formation control strategy that combines input and state quantization.

[0005] In recent years, significant progress has been made in the research on trajectory tracking control of unmanned surface vessels. Researchers have proposed a variety of control strategies based on extended state observers (ESOs), which perform well in dealing with system uncertainties and external disturbances. However, despite the significant advantages of ESO in trajectory tracking control, its practical application still faces challenges. For example, the performance of ESO is highly dependent on the selection of observer parameters, and the parameter adjustment process is relatively complex. Therefore, it is necessary to further optimize the performance of ESO and combine it with signal quantization to make it better adapt to the trajectory tracking control needs of unmanned surface vessels. In summary, it is of great significance to study control systems that combine ESO and signal quantization. Summary of the Invention

[0006] According to the tracking control problem of USV formation under the unmanned ship formation control condition based on signal quantization proposed above, a multi-USV trajectory tracking control method with ESO and signal quantization is provided.

[0007] The technical means adopted in the present invention are as follows:

[0008] A multi-USV trajectory tracking control method with ESO and signal quantization, comprising:

[0009] S1. Obtain information about the surrounding environment and sea conditions of other ships, and establish a mathematical model for trajectory control of the under-actuated unmanned ship formation;

[0010] S2, using a uniform quantizer to quantize the control input and state variables in the control system;

[0011] S3. Use ESO technology to estimate the required quantitative state information and the uncertainties in the model;

[0012] S4. Based on the idea of ​​inner and outer loops, a kinematic guidance law and a dynamic quantized tracking control law are designed. A linear model is introduced to describe the quantization process, so that the designed controller no longer requires prior information on the quantization parameters. An event-triggered formation control strategy is proposed to further reduce the communication burden.

[0013] S5. Based on Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed multi-USV formation trajectory tracking control system with signal quantization are proved.

[0014] Furthermore, step S1 specifically includes:

[0015] S11. Given an underactuated multi-USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the multi-USV formation system as follows:

[0016]

[0017] Among them, H ix 、H iy Represents the coordinates of the ship's center of mass described in the geodetic coordinate system; θ i Indicates the ship's pitch angle; U i represents the cruising speed of the ship; β i is the drift angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively;

[0018] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned vessel as follows:

[0019]

[0020] in, Indicates the mass of the USV; Both represent hydrodynamic derivative terms; I z Represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir quantized value of .

[0021] Furthermore, step S2 specifically includes:

[0022] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is expressed as:

[0023]

[0024] in, H iy ,θ i ,u i ,v i ,r i ,U i and χ>0 indicates quantization step size, I1=χ and I i+1 =I i +χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as

[0025] S22, define the ideal trajectory as Where H0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory H0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that the ideal parameter trajectory is smooth and stable over time, that is, there is a constant H k satisfy

[0026] S23. Use a graph of Λ = {T, Φ} to represent the relationship between N USVs and the virtual leader; where Φ = (i, j)∈Γ×Γ represents the set of edges, T = n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0;

[0027] S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraint, that is:

[0028]

[0029] Among them, H i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, H id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

[0030] Furthermore, step S3 specifically includes:

[0031] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0032]

[0033] Among them, u i =U i cosβ i , v i =U i sinβ i ;

[0034] S32. According to S31, the dynamic model is reformulated as:

[0035]

[0036] in,

[0037] S33, in order to facilitate the design of extended state observer (ESO), define Δ iU =d iU +F iU , Δ ir =d ir +F ir , then:

[0038]

[0039] S34, the extended state observer ESO is used to estimate U i ,Δ i U ,r i ,Δ ir , Δ ir are the observed values ​​of the corresponding variables, and the ESO design is as follows:

[0040]

[0041] in, is the observer parameter;

[0042] S35. According to the designed ESO, its error system is:

[0043]

[0044] Among them, the definition And taking its derivative we can get:

[0045]

[0046] S36. Define the error state equation of the observer as follows:

[0047]

[0048] in,

[0049] S37. Define the Lyapunov function as follows:

[0050]

[0051] And take its derivative to get:

[0052]

[0053] S38. Further deduce the derived Lyapunov function and obtain:

[0054]

[0055] Among them, λ min (Q i ) is Q i The minimum eigenvalue of When , the convergence condition of ESO is obtained as

[0056] Furthermore, step S4 specifically includes:

[0057] S41. Design a guidance law based on actuators to track the ideal trajectory of the unmanned ship formation.

[0058] S42. Use a linear analytical model to describe the quantization process to save communication resources, and design the system control law and adaptive law based on the sliding mode control strategy.

[0059] Furthermore, step S41 specifically includes:

[0060] S411. According to the mathematical model of USV, the system is under-driven and only U i It is impossible to track both x and y directions, so the ideal angle θ id It is necessary to use it as a controlled object to solve the under-actuation problem of USV. Then we have:

[0061]

[0062] S412. Define the distributed formation tracking error as follows:

[0063]

[0064] in, is the relative error between USVs, and represents the estimated value of the actual positions of multiple USVs in the formation, H0 represents the actual position of the virtual leader;

[0065] S413. Derivative the defined distributed formation tracking error to obtain:

[0066]

[0067] in,

[0068] S414, Definition and but:

[0069]

[0070] S415. Design the guidance law as follows:

[0071]

[0072] in, and and are all constants greater than zero;

[0073] S416. The linear velocity guidance law of multiple USVs is obtained from S411 as follows:

[0074]

[0075] because If θ id The range of is (-π / 2,π / 2), then Among them, θ id Design the required angle for the outer ring position guidance law;

[0076] S417. Define θ ie =θ i -θ id , Taking the derivative of the above formula and considering ESOs yields:

[0077]

[0078] S418. Design the attitude guidance law as follows:

[0079]

[0080] Among them, k iθ >0;

[0081] S419, U ixc , U iyc Insert the error equation get:

[0082]

[0083] Furthermore, step S42 specifically includes:

[0084] S421, re-expressing the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established according to steps S33 and S34 as follows:

[0085]

[0086] in,

[0087] S422, let Q(τ iu )=q 11iu (t)τ iu +q 12iu (t), Q(τ ir )=q 11ir (t)τ ir +q 12ir (t), and:

[0088]

[0089] Among them, q 1iU (t) and q 1ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 1iU (t)>0,q 1ir (t)>0; In addition, if and Considering Q(τ iU (t)) and Q(τ ir (t)) is bounded, then q 2iU (t) and q 2ir (t) is also bounded and satisfies

[0090] S423. Set the control target of the dynamics subsystem as follows:

[0091]

[0092] in, Both represent smaller positive integers;

[0093] S424. Define the integral synovial surface as follows:

[0094]

[0095] Among them, b iU >0 and b ir >0, take the derivative of the above formula and we get:

[0096]

[0097] S425. According to step S424, the following is obtained:

[0098]

[0099] Among them, l iU ,η iU ,l ir ,η irBoth represent constants greater than 0, μ iU ≥μ Ud ,μ ir ≥μ rd And μ Ud >0,μ rd >0;

[0100] S426, Definition Then we get:

[0101]

[0102] S427, due to q 1iU (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu (t) and q 1ir (t) is estimated; the time-varying gain η is defined iU =1 / q 1iU (t) min and η ir =1 / q 1ir (t) min , where q 1iU (t) min and q 1ir (t) min q 1iU (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows:

[0103]

[0104] Among them, γ1,γ2,c U ,c r ,ω U ,ω r and All represent constants greater than 0;

[0105] S428. Design the dynamic error system as follows:

[0106]

[0107] Furthermore, step S5 specifically includes:

[0108] S51. Consider a quantized USV formation tracking and collision avoidance control system, combined with the designed ESO, guidance rate, control rate and adaptive law, with state θ ie , s iU , s ir , and input ΛiU , Λ ir The formation tracking control system is eventually uniformly bounded, and the tracking error can converge to a smaller residual set;

[0109] S52. Define the Lyapunov function as follows:

[0110]

[0111] And take the derivative of the defined Lyapunov function:

[0112]

[0113] S53, combining step S426 and step S52 to obtain:

[0114]

[0115] S54. Combining the designed control law and adaptive law, we get:

[0116]

[0117] S55. Due to but make So we get:

[0118]

[0119] S56, taking into account Then we get:

[0120]

[0121] S57, due to and Then we get:

[0122]

[0123] in, and They are all positive numbers and satisfy

[0124] S58, Order Then we get:

[0125]

[0126] Where C = min{2l iU +1,2l ir +1,γ1ω iU ,γ2ω ir ,2λ min (χi ),2k iθ}, D = Λ iU +Λ ir ;

[0127] S59, the closed-loop system consists of the ESOs, motion subsystem, and power subsystem designed in S35. It is ultimately uniformly bounded, and the following Lyapunov function is designed:

[0128] V3=V1+V2

[0129] Then there is It is proved that the trajectory tracking control system of multiple USVs is bounded and the system error converges to a very small residual set.

[0130] Compared with the prior art, the present invention has the following advantages:

[0131] 1. This invention provides a multi-USV trajectory tracking control method with ESO and signal quantization. This method considers both signal quantization and ESO inner and outer loop control strategies, addressing the challenges of multi-USV formation tracking control in marine environments with limited communication bandwidth and complex quantization. By combining signal quantization with inner and outer loop control strategies, this method improves the robustness and efficiency of the control system, surpassing traditional methods. While conserving communication resources, it also better meets the practical needs of navigation.

[0132] 2. The present invention provides a multi-USV trajectory tracking control method with ESO and signal quantization, which uses ESO to address the impact of quantized state variables on the control system during signal transmission. ESO can be used to estimate and compensate for the uncertainty caused by quantization, thereby improving the overall robustness and reliability of the control system.

[0133] 3. This invention provides a multi-USV trajectory tracking control method with ESO and signal quantization. This method uses a linear model to describe the quantization process, effectively eliminating the need for the controller to obtain prior information on the quantization parameters. This approach not only simplifies the design complexity of the control algorithm but also reduces the reliance on precise quantization parameters. This improvement allows for more flexible implementation and adjustment of the control system under varying operating conditions, ensuring the system remains efficient and stable in the face of various environmental changes. Furthermore, this solution enhances the system's adaptability, enabling it to operate more reliably in uncertain marine environments and meet complex mission requirements.

[0134] 4. This invention provides a multi-USV trajectory tracking control method with ESO and signal quantization. Comparative experiments were conducted on a Matlab platform using an unmanned vessel formation control system before and after quantization. Furthermore, an adaptive quantized tracking controller was designed to achieve trajectory tracking control for the unmanned vessel formation. By considering signal quantization, the actuator execution frequency and control amplitude were reduced, and the system control input curve was more compatible with maritime engineering practice.

[0135] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0136] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0137] Figure 1 Flow chart of the method of the present invention.

[0138] Figure 2 This is a diagram of the trajectory tracking control results of the distributed formation of unmanned ships provided by an embodiment of the present invention.

[0139] Figure 3 This is a speed change diagram of five unmanned ships provided in an embodiment of the present invention.

[0140] Figure 4 A diagram showing the changes in bow angular velocity of five unmanned ships provided in an embodiment of the present invention.

[0141] Figure 5 A diagram showing the speed changes of five unmanned ships in two directions provided by an embodiment of the present invention.

[0142] Figure 6 This is a diagram of the course and speed changes of five unmanned ships provided in an embodiment of the present invention.

[0143] Figure 7 A comparison chart of the control inputs before and after quantization of the five unmanned ships provided in an embodiment of the present invention.

[0144] Figure 8 A comparison chart of the control inputs before and after quantization of the five unmanned ships provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0145] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0146] It should be noted that the terms "including" and "having" and any variations thereof in the specification and claims of the present invention and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or are inherent to these processes, methods, products or apparatuses.

[0147] like Figure 1 As shown, the present invention provides a multi-USV trajectory tracking control method with ESO and signal quantization, comprising:

[0148] S1. Obtain information about the surrounding environment and sea conditions of other ships, and establish a mathematical model for trajectory control of the under-actuated unmanned ship formation;

[0149] S2, using a uniform quantizer to quantize the control input and state variables in the control system;

[0150] S3. Use ESO technology to estimate the required quantitative state information and the uncertainties in the model;

[0151] S4. Based on the idea of ​​inner and outer loops, a kinematic guidance law and a dynamic quantized tracking control law are designed. A linear model is introduced to describe the quantization process, so that the designed controller no longer requires prior information on the quantization parameters. An event-triggered formation control strategy is proposed to further reduce the communication burden.

[0152] S5. Based on Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed multi-USV formation trajectory tracking control system with signal quantization are proved.

[0153] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0154] S11. Given an underactuated multi-USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the multi-USV formation system as follows:

[0155]

[0156] Among them, H ix 、H iy Represents the coordinates of the ship's center of mass described in the geodetic coordinate system; θ i Indicates the ship's pitch angle; U i represents the cruising speed of the ship; β i is the drift angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively;

[0157] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned vessel as follows:

[0158]

[0159] in, Indicates the mass of the USV; Both represent hydrodynamic derivative terms; I z Represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir quantized value of .

[0160] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0161] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is expressed as:

[0162]

[0163] in, H iy ,θ i ,u i ,v i ,r i ,U i and χ>0 indicates quantization step size, I1=χ and I i+1 =I i +χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as

[0164] S22, define the ideal trajectory as Where H0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory H0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that the ideal parameter trajectory is smooth and stable over time, that is, there is a constant H k satisfy

[0165] S23. Use a graph of Λ = {T, Φ} to represent the relationship between N USVs and the virtual leader; where Φ = (i, j)∈Γ×Γ represents the set of edges, T = n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0;

[0166] S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraint, that is:

[0167]

[0168] Among them, H i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, H id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

[0169] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0170] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0171]

[0172] Among them, u i =U i cosβ i , v i =U i sinβ i ;

[0173] S32. According to S31, the dynamic model is reformulated as:

[0174]

[0175] in,

[0176] S33, in order to facilitate the design of extended state observer (ESO), define Δ iU =d iU +F iU , Δ ir =d ir +F ir , then:

[0177]

[0178] S34, the extended state observer ESO is used to estimate U i ,Δ i U ,r i ,Δ ir , Δ ir are the observed values ​​of the corresponding variables, and the ESO design is as follows:

[0179]

[0180] in, is the observer parameter;

[0181] S35. According to the designed ESO, its error system is:

[0182]

[0183] Among them, the definition And taking its derivative we can get:

[0184]

[0185] S36. Define the error state equation of the observer as follows:

[0186]

[0187] in,

[0188] S37. Define the Lyapunov function as follows:

[0189]

[0190] And take its derivative to get:

[0191]

[0192] S38. Further deduce the derived Lyapunov function and obtain:

[0193]

[0194] Among them, λ min (Q i ) is Q i The minimum eigenvalue of When , the convergence condition of ESO is obtained as

[0195] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0196] S41. Design a guidance law based on actuators to track the ideal trajectory of the unmanned ship formation.

[0197] S42. Use a linear analytical model to describe the quantization process to save communication resources, and design the system control law and adaptive law based on the sliding mode control strategy.

[0198] In specific implementation, as a preferred embodiment of the present invention, step S41 specifically includes:

[0199] S411. According to the mathematical model of USV, the system is under-driven and only U i It is impossible to track both x and y directions, so the ideal angle θ id It is necessary to use it as a controlled object to solve the under-actuation problem of USV. Then we have:

[0200]

[0201] S412. Define the distributed formation tracking error as follows:

[0202]

[0203] in, is the relative error between USVs, and represents the estimated value of the actual positions of multiple USVs in the formation, H0 represents the actual position of the virtual leader;

[0204] S413. Derivative the defined distributed formation tracking error to obtain:

[0205]

[0206] in,

[0207] S414, Definition and but:

[0208]

[0209] S415. Design the guidance law as follows:

[0210]

[0211] in, and and are all constants greater than zero;

[0212] S416. The linear velocity guidance law of multiple USVs is obtained from S411 as follows:

[0213]

[0214] because If θ id The range of is (-π / 2,π / 2), then Among them, θ id Design the required angle for the outer ring position guidance law;

[0215] S417. Define θ ie =θ i -θ id , Taking the derivative of the above formula and considering ESOs yields:

[0216]

[0217] S418. Design the attitude guidance law as follows:

[0218]

[0219] Among them, k iθ >0;

[0220] S419, U ixc , U iyc Insert the error equation get:

[0221]

[0222] In specific implementation, as a preferred embodiment of the present invention, step S42 specifically includes:

[0223] S421, re-expressing the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established according to steps S33 and S34 as follows:

[0224]

[0225] in,

[0226] S422, let Q(τ iu )=q 11iu (t)τ iu +q 12iu (t), Q(τ ir )=q 11ir (t)τ ir +q 12ir (t), and:

[0227]

[0228] Among them, q 1iU (t) and q 1ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 1iU (t)>0,q 1ir (t)>0; In addition, if and Considering Q(τ iU (t)) and Q(τ ir (t)) is bounded, then q 2iU (t) and q 2ir (t) is also bounded and satisfies

[0229] S423. Set the control target of the dynamics subsystem as follows:

[0230]

[0231] in, Both represent smaller positive integers;

[0232] S424. Define the integral synovial surface as follows:

[0233]

[0234] Among them, b iU >0 and b ir >0, take the derivative of the above formula and we get:

[0235]

[0236] S425. According to step S424, the following is obtained:

[0237]

[0238] Among them, l iU,η iU ,l ir ,η ir Both represent constants greater than 0, μ iU ≥μ Ud ,μ ir ≥μ rd And μ Ud >0,μ rd >0;

[0239] S426, Definition Then we get:

[0240]

[0241] S427, due to q 1iU (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu (t) and q 1ir (t) is estimated; the time-varying gain η is defined iU =1 / q 1iU (t) min and η ir =1 / q 1ir (t) min , where q 1iU (t) min and q 1ir (t) min q 1iU (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows:

[0242]

[0243] Among them, γ1,γ2,c U ,c r ,ω U ,ω r and All represent constants greater than 0;

[0244] S428. Design the dynamic error system as follows:

[0245]

[0246] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0247] S51. Consider a quantized USV formation tracking and collision avoidance control system, combined with the designed ESO, guidance rate, control rate and adaptive law, with state θie , s iU , s ir , and input Λ iU , Λ ir The formation tracking control system is eventually uniformly bounded, and the tracking error can converge to a smaller residual set;

[0248] S52. Define the Lyapunov function as follows:

[0249]

[0250] And take the derivative of the defined Lyapunov function:

[0251]

[0252] S53, combining step S426 and step S52 to obtain:

[0253]

[0254] S54. Combining the designed control law and adaptive law, we get:

[0255]

[0256] S55. Due to but make So we get:

[0257]

[0258] S56, taking into account Then we get:

[0259]

[0260] S57, due to and Then we get:

[0261]

[0262] in, and They are all positive numbers and satisfy

[0263] S58, Order Then we get:

[0264]

[0265] Where C = min{2l iU +1,2lir +1,γ1ω iU ,γ2ω ir ,2λ min (χ i ),2k iθ}, D = Λ iU +Λ ir ;

[0266] S59, the closed-loop system consists of the ESOs, motion subsystem, and power subsystem designed in S35. It is ultimately uniformly bounded, and the following Lyapunov function is designed:

[0267] V3=V1+V2

[0268] Then there is It is proved that the trajectory tracking control system of multiple USVs is bounded and the system error converges to a very small residual set.

[0269] Example

[0270] To verify the effectiveness of the multi-USV trajectory tracking control method and system with ESO and signal quantization proposed in this invention, this embodiment uses MATLAB / Simulink for computer simulation research. The model parameters are selected as follows:

[0271] m u =25.8kg

[0272] m v =33.8kg

[0273] m r =2.76kg·m 2

[0274]

[0275] f v (·)=-36.5|v|v-0.8896v-0.805v|r|-m u u i r

[0276] f r (·)=-0.75|r|r-1.90r+0.08|v|r+(m u -m v )u i v-1.0948u i r

[0277] The time-varying parameter trajectory of the virtual leader is designed as p0(t) = [8sin(0.02t), 1-cos(0.02t)] TThe initial state of the five USVs in the formation is designed to be P1 = [0,10] T , P2=[0,2] T and P3=[0,-6] T The ideal initial position of the formation is designed to be P 1d =[0,10] T ,P 2d =[0,2] T and P 3d =[0,-6] T Controller design parameters are μ iU =μ ir =2,b iU =b ir =10, c iU =c ir =0.02,ω iU =ω ir =0.20, γ1=3, γ2=2, χ=0.1.

[0278] Figure 2-Figure 8 The simulation results of the multi-USV trajectory tracking strategy are presented. Figure 2 The dynamic reference trajectories of multiple USVs are shown. It can be seen that through signal quantization, these USVs can efficiently track the desired trajectory from the initial position in a very short time, while always maintaining the prescribed vehicle distance and formation, and the tracking error can be minimized to a small residual set. Figure 3 and Figure 4 The speed and ROT of the USV after signal quantization are shown respectively. The data show that the USV after signal quantization can achieve speed synchronization in a shorter time, and the tracking errors of speed and ROT can converge effectively. Figure 5 The velocity components in both directions are compared, showing a smooth convergence behavior. Figure 6 The performance of the USV's heading control with quantized state feedback is demonstrated. The results show that the proposed control scheme can maintain the USV's heading with high precision, keeping the heading angle tracking error within a small residual range. This excellent heading-keeping capability complements the control system's robustness to signal discretization and ensures precise heading maintenance within the constraints of digital communication. Figure 7 and Figure 8Comparison of the control inputs in

[15] shows that while quantization leads to a decrease in the smoothness of the control signal, tracking performance remains robust. Importantly, the quantized control scheme effectively reduces the communication bandwidth requirement while maintaining satisfactory control performance. These results demonstrate that the proposed control strategy achieves both reliable trajectory tracking and efficient use of communication resources, making it suitable for multi-USV formation systems operating in bandwidth-constrained environments. The quantization approach achieves a good balance between tracking accuracy and communication efficiency.

[0279] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-USV trajectory tracking control method with ESO and signal quantization, characterized in that: include: S1. Obtain information about the surrounding environment and sea conditions of other ships, and establish a mathematical model for trajectory control of the under-actuated unmanned ship formation; S2, using a uniform quantizer to quantize the control input and state variables in the control system; S3. Use ESO technology to estimate the required quantitative state information and the uncertainties in the model; S4. Based on the idea of ​​inner and outer loops, a kinematic guidance law and a dynamic quantized tracking control law are designed. A linear model is introduced to describe the quantization process, so that the designed controller no longer requires prior information on the quantization parameters. An event-triggered formation control strategy is proposed to further reduce the communication burden. S5. Based on Lyapunov stability theory, the observation error of the extended state observer and the stability of the designed multi-USV formation trajectory tracking control system with signal quantization are proved.

2. A multi-USV trajectory tracking control method with ESO and signal quantization according to claim 1, characterized in that: Step S1 specifically includes: S11. Given an underactuated multi-USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the multi-USV formation system as follows: Among them, H ix 、H iy Represents the coordinates of the ship's center of mass described in the geodetic coordinate system; θ i Indicates the ship's pitch angle; U i represents the cruising speed of the ship; β i is the drift angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively; S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned vessel as follows: in, Indicates the mass of the USV; Both represent hydrodynamic derivative terms; I z Represents the moment of inertia around the z-axis; function f iu (·),f iv (·),f ir (·) represents nonlinear uncertainties such as fluid dynamic damping and centripetal force; τ iuw ,τ ivw ,τ irw The disturbance caused by unknown ocean factors is represented by Q(τ iu ) and Q(τ ir ) represent the system control input τ iu and τ ir quantized value of .

3. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 1 is characterized in that: Step S2 specifically includes: S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is expressed as: in, and χ>0 indicates quantization step size, I1=χ and I i+1 =I i +χ; therefore, the quantization error of the uniform quantizer is bounded and is expressed as S22, define the ideal trajectory as Where H0(t) represents a continuously differentiable parameter trajectory; the ideal parameter trajectory H0(t) is differentiable, and its first-order derivative and second-order derivative are bounded; this indicates that the ideal parameter trajectory is smooth and stable over time, that is, there is a constant H k satisfy S23. Use a graph of Λ = {T, Φ} to represent the relationship between N USVs and the virtual leader; where Φ = (i, j)∈Γ×Γ represents the set of edges, T = n0,n1,...,n N represents a set of points; in this case, n i ,n j represents the communication flow from node j to node i; the adjacency matrix is ​​expressed as If there is an edge (n j ,n i )∈Φ, then a ij =1; otherwise, a ij =0; S24. The main control objective is to enable each USV in the ship formation system to track the ideal trajectory of time variation under the condition of communication bandwidth constraint, that is: Among them, H i (t) = [x i ,y i ] T represents the actual position of each USV in the formation, H id (t) represents the position deviation of each USV relative to the parameter trajectory of the virtual leader, and ζ represents a constant greater than zero.

4. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 1 is characterized in that: Step S3 specifically includes: S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows: among them, u i =U i cosβ i ,v i =U i sinβ i ; S32. According to S31, the dynamic model is reformulated as: in, S33, in order to facilitate the design of the extended state observer, define Δ iU =d iU +F iU , Δ ir =d ir +F ir , then: S34, the extended state observer ESO is used to estimate U i ,Δ iU ,r i ,Δ ir , Δ ir are the observed values ​​of the corresponding variables, and the ESO design is as follows: in, is the observer parameter; S35. According to the designed ESO, its error system is: Among them, the definition And taking its derivative we can get: S36. Define the error state equation of the observer as follows: in, S37. Define the Lyapunov function as follows: And take its derivative to get: S38. Further deduce the derived Lyapunov function and obtain: Among them, λ min (Q i ) is Q i The minimum eigenvalue of When , the convergence condition of ESO is obtained as 5. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 1 is characterized in that: Step S4 specifically includes: S41. Design a guidance law based on actuators to track the ideal trajectory of the unmanned ship formation. S42. Use a linear analytical model to describe the quantization process to save communication resources, and design the system control law and adaptive law based on the sliding mode control strategy.

6. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 5 is characterized in that: Step S41 specifically includes: S411. According to the mathematical model of USV, the system is under-driven and only U i It is impossible to track both x and y directions, so the ideal angle θ id It is necessary to use it as a controlled object to solve the under-actuation problem of USV. Then we have: S412. Define the distributed formation tracking error as follows: in, is the relative error between USVs, and represents the estimated value of the actual positions of multiple USVs in the formation, H0 represents the actual position of the virtual leader; S413. Derivative the defined distributed formation tracking error to obtain: in, S414, Definition and but: S415. Design the guidance law as follows: in, and and are all constants greater than zero; S416. The linear velocity guidance law of multiple USVs is obtained from S411 as follows: because If θ id The range of is (-π / 2,π / 2), then Among them, θ id Design the required angle for the outer ring position guidance law; S417. Define θ ie =θ i -θ id , Taking the derivative of the above formula and considering ESOs yields: S418. Design the attitude guidance law as follows: Among them, k iθ >0; S419, U ixc , U iyc Insert the error equation get:

7. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 5 is characterized in that: Step S42 specifically includes: S421, re-expressing the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established according to steps S33 and S34 as follows: in, S422. Let Q(τ iu ) = q 11iu (t)τ iu + q 12iu (t), Q(τ ir ) = q 11ir (t)τ ir + q 12ir (t), and: Among them, q 1iU (t) and q 1ir (t) is an unknown parameter; since the sign remains unchanged during the entire quantization process, it can be seen from the above formula that q 1iU (t)>0,q 1ir (t)>0; In addition, if and Considering Q(τ iU (t)) and Q(τ ir (t)) is bounded, then q 2iU (t) and q 2ir (t) is also bounded and satisfies S423. Set the control target of the dynamics subsystem as follows: in, Both represent smaller positive integers; S424. Define the integral synovial surface as follows: Among them, b iU >0 and b ir >0, take the derivative of the above formula and we get: S425. According to step S424, the following is obtained: Among them, l iU ,η iU ,l ir ,η ir Both represent constants greater than 0, μ iU ≥μ Ud ,μ ir ≥μ rd And μ Ud >0,μ rd >0; S426, Definition Then we get: S427, due to q 1iU (t) and q 1ir (t) is unknown and time-varying, so an adaptive method is used to estimate its boundary. In order to prevent the singular problem when the estimated value tends to zero, q 1iu (t) and q 1ir (t) is estimated; the time-varying gain η is defined iU =1 / q 1iU (t) min and η ir =1 / q 1ir (t) min , where q 1iU (t) min and q 1ir (t) min q 1iU (t) and q 1ir (t), therefore, the USV formation tracking control law is designed as follows: Among them, γ1,γ2,c U ,c r ,ω U ,ω r and All represent constants greater than 0; S428. Design the dynamic error system as follows:

8. The multi-USV trajectory tracking control method with ESO and signal quantization according to claim 1 is characterized in that: Step S5 specifically includes: S51. Consider a quantized USV formation tracking and collision avoidance control system, combined with the designed ESO, guidance rate, control rate and adaptive law, with state θ ie , s iU ,s ir , and input Λ iU , Λ ir The formation tracking control system is eventually uniformly bounded, and the tracking error can converge to a smaller residual set; S52. Define the Lyapunov function as follows: And take the derivative of the defined Lyapunov function: S53, combining step S426 and step S52 to obtain: S54. Combining the designed control law and adaptive law, we get: S55. Due to but make So we get: S56, taking into account Then we get: S57, due to and Then we get: in, and They are all positive numbers and satisfy S58, Order Then we get: where, C = min{2l iU +1, 2l ir +1, γ1ω iU , γ2ω ir , 2λ min (χ i ), 2k iθ}, D = Λ iU + Λ ir ; S59, the closed-loop system consists of the ESOs, motion subsystem, and power subsystem designed in S35. It is ultimately uniformly bounded, and the following Lyapunov function is designed: V3=V1+V2 Then there is It is proved that the trajectory tracking control system of multiple USVs is bounded and the system error converges to a very small residual set.

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