A speed-constrained formation collision avoidance control method for multiple unmanned vessels considering quantization and dead zone

Abstract

The present invention provides a method for speed-constrained formation collision avoidance control of multiple unmanned vessels that considers quantization and dead zones. The method includes: constructing kinematic and dynamic models of unmanned surface vessels with dead zones and quantization, combining ship collision avoidance, obstacle avoidance, and connection protection conditions with consideration of speed constraints; designing virtual and actual control rates by introducing error variables and combining them with Lyapunov functions; and performing stability analysis on the control scheme based on the designed virtual and actual control rates and the Lyapunov functions. This method addresses the problem of speed-constrained formation collision avoidance control for multiple unmanned vessels under unified design and analysis conditions. This method ensures the safety of high-speed unmanned vessels during collision and obstacle avoidance, even when subject to the nonlinear characteristics of actuators and sensors.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned ship collision avoidance, and in particular to a multi-unmanned ship speed-constrained formation collision avoidance control method considering quantization and dead zones. Background Art

[0002] During the motion of unmanned ships, actuators, sensors and other components often have some non-smooth nonlinear characteristics. Therefore, for the sake of formation stability and accuracy, for unmanned surface ships, if non-smooth nonlinear characteristics such as sensor dead zones are ignored in the control design module stage, the tracking accuracy will be reduced. For actuators, when considering the limited communication bandwidth, it is necessary to consider reducing the data transmission rate. In the motion control process of unmanned ships, in addition to some non-smooth nonlinear characteristics, the constraints of some state signals of the unmanned ships need to be considered. However, the existing control methods cannot achieve the two different requirements of speed constraints and no speed constraints at the same time through a single constraint method;

[0003] When sensors have dead zones, control accuracy is severely impacted. Control methods for unmanned vessels with dead zones have focused on the actuators, making existing control methods for sensor dead zones inapplicable. Quantization is essential in the data transmission channels of unmanned vessels. It enables a low communication rate while ensuring sufficient accuracy. For the actuators, in the quantization mechanism, the raw signal output by the control module is first converted into a discrete sequence by a quantizer before being transmitted to the actuator. This change in the control signal effectively reduces the communication burden. While addressing issues with the internal components of unmanned vessels, collision avoidance between vessels and with obstacles is unavoidable in obstructed marine environments. For safety reasons, the speed of unmanned vessels also needs to be limited. However, for formation control of unmanned vessels, a unified analysis and design approach that considers both constrained and unconstrained control without changing the control structure is highly desirable. This can effectively reduce the complexity of control module design. Summary of the Invention

[0004] To address the aforementioned technical issues, a method for speed-constrained formation collision avoidance control of multiple unmanned vessels (UAVs) is provided, taking into account quantization and dead zones. This invention addresses the problem of speed-constrained formation collision avoidance control for UAVs with speed constraints, addressing the issue under unified design and analysis conditions. This method ensures the safety of high-speed UAVs during collision and obstacle avoidance, even when subject to the nonlinear characteristics of actuators and sensors.

[0005] The technical means adopted in the present invention are as follows:

[0006] A multi-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone, comprising:

[0007] S1. Combined with the ship collision avoidance, obstacle avoidance and connection protection conditions and considering the speed constraint problem, the kinematic and dynamic models of the unmanned surface ship with dead zone and quantization are constructed;

[0008] S2. Introduce error variables and combine them with Lyapunov function to design virtual control rate and actual control rate;

[0009] S3. Combine the designed virtual control rate, actual control rate and Lyapunov function to perform stability analysis on the control scheme.

[0010] Furthermore, the specific implementation process of step S1 is as follows:

[0011] S11. Construct the kinematic and dynamic model of the unmanned ship's existence quantification and dead zone, and give the i-th model as follows:

[0012]

[0013] in, represents the center of mass position of the i-th unmanned ship in the Earth-fixed reference frame, and η i Output for the unmanned ship; represents the inertia matrix; The vectors representing the surge velocity, roll velocity, and yaw velocity within the fixed frame of the airframe; represents the nonlinear term of the unmanned ship; Q(τ i )=[Q(τ iu ), 0, Q(τ ir )] T represents the control signal to be quantized, Q(τ iu ) and Q(τ ir ) is the input of the system, taking the quantized value; τ iw (t) = [τ iwu (t), τ iwv (t), τ iwr (t)] T It is a bounded environmental disturbance caused by waves and currents; The rotation matrix is ​​defined as:

[0014]

[0015] S12. Construct a dead zone model for unmanned ships. In the unmanned ship existence quantification and dead zone kinematic and dynamic models, η i =[D z (x i ),D z (y i ),ψ i ] T is the dead zone output, then the symmetrical dead zone nonlinearity is described by the following dead zone model:

[0016]

[0017] Among them, k xi >0 and b xi >0 indicates the slope and width of the dead zone; D z (y i ) is equal to D z (x i ), rewrite the above formula as:

[0018]

[0019] where ε i is a positive constant, and x i For η i Taking the derivative of (1,1) we get:

[0020]

[0021] mean and and

[0022] S13, build a quantitative model of the unmanned ship, and the system input Q(τ ik ) is defined as:

[0023]

[0024] Among them, k represents u or r, and χ ik =[(1-λ ik ) / (1+λ ik )], parameter τ minik >0,0<χ ik <1;Q(τ ik ) belongs to the set Parameter τ minik >0 means Q(τ ik ) dead zone range;

[0025] S14. Introducing potential function, so that collision avoidance and connection protection between unmanned ships are included in the control design during the formation control process;

[0026] S15. Construct an unmanned boat with surge speed limited by the following function:

[0027] will u i With constraint boundary g i1 ,g i2 The distance between them is specifically described as:

[0028]

[0029] Among them, c i1 ,c i2 is a strictly positive time-varying smooth function, is a positive integer, g i1 (u i ,c i1 ),g i2 (u i ,c i2 ) is assumed to be a bounded function;

[0030] In order to implement variable constraints, construct the following function:

[0031]

[0032] in, There are three properties:

[0033] When u i (t) If there is no constraint requirement, then i1 (t) = c i2 (t)=+∞,g i1 (u i ,c i1 )=g i2 (u i ,c i2 )=1, that is

[0034]

[0035] If and only if u i =0.

[0036] Furthermore, the specific implementation process of step S14 is as follows:

[0037] S141. Collision avoidance. In order to avoid collisions between unmanned ships during formation control, the following potential function is introduced:

[0038]

[0039] Among them, p ij =p i -p j =[x i -x j ,y i -y j ] T , Indicates the minimum safety radius and detection range for collision avoidance. When p ij ≤ l c Perform collision avoidance maneuvers, Pij Partial derivatives give:

[0040]

[0041] Where 02 = [0,0] T ;

[0042] S142, obstacle avoidance. In order to avoid collision between the unmanned ship and static obstacles during formation control, the following potential function is introduced:

[0043]

[0044] Among them, p ik =p i -p k ; l o > l o >0 indicates the radius of the detection and avoidance area, and the distance between obstacles is assumed to be greater than right Taking the derivative we get:

[0045]

[0046] S143, connection protection, in order to ensure the connectivity of the communication link between unmanned ships, the potential functions of maintaining connectivity are:

[0047]

[0048] in, Indicates the maximum and minimum values ​​of the connection range. Taking the derivative we get:

[0049]

[0050] Furthermore, the specific implementation process of step S2 is as follows:

[0051] S21. Design the corresponding error variables for each step of the i-th unmanned ship, and introduce the error variables as follows:

[0052]

[0053] Among them, v ir is the kinematic control law,

[0054] S22. Design virtual controller:

[0055] S221, based on the unmanned ship existence quantification and dead zone kinematic and dynamic model formula and error variable z constructed in step S11 i2 , calculate the error variable z i1The time derivative of , we can get:

[0056]

[0057] in, S=[0,-1,0],let and Therefore, we can get:

[0058]

[0059] S222. Select a Lyapunov function. The function is:

[0060]

[0061] S223, calculate v i1 Differentiating with respect to time t, we get:

[0062]

[0063] Where G = diag{d i ,δ i0};

[0064] S224. In order to obtain the required virtual control rate, it is defined as follows:

[0065]

[0066] in, Represents the auxiliary virtual controller, defined as:

[0067]

[0068] S225, can be rewritten as:

[0069]

[0070] S226. Design the virtual control rate as follows:

[0071]

[0072] in, And k i1 >0 represents a constant, where Δ i1 >0 is a constant, and

[0073] S227. Combine steps S224, S225, and S226 to obtain the result of combining the virtual control rate with the Lyapunov function, as follows:

[0074]

[0075] S228. Introduce a filtering method to update w k ,as follows:

[0076]

[0077] Among them, λ and λ′ are both positive parameters;

[0078] S229, To obtain the smooth motion trajectory of the unmanned ship, let a i1 By a second-order linear tracking differentiator:

[0079]

[0080] Among them, v ir and Represents α i1 and The estimated value of i is designed to be a positive parameter;

[0081] S230, define two constant sets, there exists a positive constant and So that:

[0082]

[0083] S23, design actual control rate:

[0084] S231, based on the unmanned ship existence quantification and dead zone kinematics and dynamics model formulas constructed in step S11 and the formulas in step S229, obtain z i2 The equation is:

[0085]

[0086] S232. Define the Lyapunov function as follows:

[0087]

[0088] in and Γ Wi2 is a positive design parameter;

[0089] S233, combining the formula in step S227 and the formula in step S231, calculate v i2 The derivative of is as follows:

[0090]

[0091] S234. Use a neural network to approximate some variables of the formula in step S233. Define the neural network as follows:

[0092]

[0093] Where Z∈Ω Z is the input vector, represents the weight vector; Usually a Gaussian function is chosen such as:

[0094]

[0095] Among them, ε i is the receiving center, r i is the width of the Gaussian function

[0096] S235. According to the universal approximation theorem, any compact set Ω z Any continuous function f(z) in can be expressed as:

[0097]

[0098] Among them, W * is the ideal constant weight, set as the ideal weight W * The estimate is The weight estimation error is defined as Estimate F(z):

[0099]

[0100] S236: Calculate the variables that need to be approximated in the neural network and the formula in step S233 to obtain:

[0101]

[0102] Among them, Z i =[u i ,v i, x i, y i ,x j ,y j ,u j ,r i ,ψ i ,ψ j ,ζ i (u i )] T ;

[0103] S237. Change the formula in step S233 into the following form:

[0104]

[0105] S238. Design the dynamic control law and neural network adaptive law at the dynamic level as follows:

[0106]

[0107] S239: Substitute the formula in step S238 into the formula in step S237 to obtain the result of combining the actual control rate with the Lyapunov function:

[0108]

[0109] Furthermore, the specific implementation process of step S3 is as follows:

[0110] The theoretical basis for the following definition:

[0111] Considering a closed-loop system composed of multiple unmanned ships subject to input quantization, output dead zone and speed constraints, combined with the designed virtual control rate and actual control rate and Lyapunov function, based on assumptions 1 and 2, all signals in the closed-loop system composed of multiple unmanned ships are bounded. At the same time, when no one is outside the collision avoidance and connectivity maintenance areas, path manipulation can be achieved within a limited time.

[0112] Furthermore, the theoretical basis of the definition is proved as follows:

[0113] Based on the two Lyapunov functions, a new Lyapunov function V for all unmanned ships i=1,…,M is constructed as follows:

[0114]

[0115] Calculate the derivative of V as:

[0116]

[0117] in, Then we get:

[0118]

[0119] make:

[0120]

[0121] Further we get:

[0122]

[0123] In summary, we can see that all signals are bounded, so:

[0124]

[0125] Introduce an even-smooth Nussbaum-type function N(ξ) that satisfies:

[0126]

[0127] List functions that satisfy the definition, such as ξ 2 cos(ξ),ξ 2 sin(ξ),exp(ξ 2 )cos(ξ);

[0128] Lemma 1: Let V(t) and ξ(t) be defined in [0,t f ), where V(t)≥0, If there exist constants C>0, E>0, and the following inequality holds for If established, then there is

[0129]

[0130] Among them, γ i is a suitable positive constant, V(t),ξ(t), In [0,t f ) is bounded;

[0131] Therefore, calling Lemma 1, V(t), ξ i (t) and With [0,t f ) as the boundary, then:

[0132]

[0133] in addition, With [0,t f ) as the boundary;

[0134] make:

[0135]

[0136] You can get:

[0137]

[0138] Among them, z i1 =[z 11 ,...,z N1 ];definition And s i =P i -p id -P0, and get:

[0139]

[0140] Established, proof completed.

[0141] Compared with the prior art, the present invention has the following advantages:

[0142] 1. The speed-constrained formation collision avoidance control method for multiple unmanned ships considering quantization and dead zones provided by the present invention uses Nussbaum-type functions and hysteresis quantizers in the design of the internal control module of the unmanned ships, which can reduce the impact of the decline in sensor control accuracy while reducing the data transmission burden of the unmanned ships.

[0143] 2. The multi-unmanned vessel speed constraint formation collision avoidance control method provided by the present invention, which takes into account quantization and dead zone, realizes unified processing of speed constraints in both constrained and unconstrained situations by using a universal constraint function to limit the maximum speed, effectively reducing the complexity of the control module design while ensuring safety when avoiding obstacles.

[0144] Based on the above reasons, the present invention can be widely promoted in fields such as unmanned ships. BRIEF DESCRIPTION OF THE DRAWINGS

[0145] 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.

[0146] Figure 1 Flow chart of the method of the present invention.

[0147] Figure 2 This is a time-varying formation collision avoidance trajectory formed by multiple unmanned ships provided in an embodiment of the present invention.

[0148] Figure 3 This is the roll control input of the unmanned ship provided by the embodiment of the present invention and the transmission signal curve after roll quantization.

[0149] Figure 4 This is the bow control input of the unmanned vessel provided by the embodiment of the present invention and the input signal curve after the bow is quantified.

[0150] Figure 5 This is the constrained speed curve and bow pitch rate curve of the unmanned ship provided by the embodiment of the present invention.

[0151] Figure 6 The tracking error curves for the lateral position and longitudinal position of the parameter path provided by the embodiment of the present invention.

[0152] Figure 7The Nussbaum function related to the dead zone of the horizontal and vertical error output position provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0153] 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.

[0154] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes 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 inherent to these processes, methods, products or devices.

[0155] like Figure 1 As shown, the present invention provides a multi-unmanned ship speed-constrained formation collision avoidance control method considering quantization and dead zone, including:

[0156] S1. Combining the ship collision avoidance, obstacle avoidance and connection protection conditions and considering the speed constraint problem, a kinematic and dynamic model of the unmanned surface ship with dead zone and quantization is constructed;

[0157] S2. Introduce error variables and combine them with Lyapunov function to design virtual control rate and actual control rate;

[0158] S3. Combine the designed virtual control rate, actual control rate and Lyapunov function to perform stability analysis on the control scheme.

[0159] In specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S1 is as follows:

[0160] S11. Construct the kinematic and dynamic model of the unmanned ship's existence quantification and dead zone, and give the i-th model as follows:

[0161]

[0162] in, represents the center of mass position of the i-th unmanned ship in the Earth-fixed reference frame, and η i Output for the unmanned ship; represents the inertia matrix; The vectors representing the surge velocity, roll velocity, and yaw velocity within the fixed frame of the airframe; represents the nonlinear term of the unmanned ship; Q(τ i )=[Q(τ iu ), 0, Q(τ ir )] T represents the control signal to be quantized, Q(τ iu ) and Q(τ ir ) is the input of the system, taking the quantized value; τ iw (t) = [τ iwu (t), τ iwv (t), τ iwr (t)] T It is a bounded environmental disturbance caused by waves and currents; The rotation matrix is ​​defined as:

[0163]

[0164] S12. Construct a dead zone model for unmanned ships. In the unmanned ship existence quantification and dead zone kinematic and dynamic models, η i =[D z (x i ),D z (y i ),ψ i ] T is the dead zone output, then the symmetrical dead zone nonlinearity is described by the following dead zone model:

[0165]

[0166] Among them, k xi >0 and b xi >0 indicates the slope and width of the dead zone; D z (y i ) is equal to D z (x i ), rewrite the above formula as:

[0167]

[0168] where ε i is a positive constant, and x i For η i Taking the derivative of (1,1) we get:

[0169]

[0170] mean and and

[0171] S13, build a quantitative model of the unmanned ship, and the system input Q(τ ik ) is defined as:

[0172]

[0173] Among them, k represents u or r, and χ ik =[(1-λ ik ) / (1+λ ik )], parameter τ minik >0,0<χ ik <1;Q(τ ik ) belongs to the set Parameter τ minik >0 means Q(τ ik ) dead zone range;

[0174] S14, introducing a potential function so that collision avoidance and connection protection between unmanned ships are included in the control design during the formation control process; the specific implementation process of step S14 is as follows:

[0175] S141. Collision avoidance. In order to avoid collisions between unmanned ships during formation control, the following potential function is introduced:

[0176]

[0177] Among them, p ij =p i -p j =[x i -x j ,y i -y j ] T , Indicates the minimum safety radius and detection range for collision avoidance. When p ij ≤ l c Perform collision avoidance maneuvers, P ij Partial derivatives give:

[0178]

[0179] Where 02 = [0,0] T ;

[0180] S142, obstacle avoidance. In order to avoid collision between the unmanned ship and static obstacles during formation control, the following potential function is introduced:

[0181]

[0182] Among them, p ik =p i -p k ; l o > l o >0 indicates the radius of the detection and avoidance area, and the distance between obstacles is assumed to be greater than right Taking the derivative we get:

[0183]

[0184] S143, connection protection, in order to ensure the connectivity of the communication link between unmanned ships, the potential functions of maintaining connectivity are:

[0185]

[0186] in, Indicates the maximum and minimum values ​​of the connection range. Taking the derivative we get:

[0187]

[0188] S15. Construct an unmanned boat with surge speed limited by the following function:

[0189] will u i With constraint boundary g i1 ,g i2 The distance between them is specifically described as:

[0190]

[0191]

[0192] Among them, c i1 ,c i2 is a strictly positive time-varying smooth function, is a positive integer, g i1 (u i ,c i1 ),g i2 (u i ,c i2 ) is assumed to be a bounded function;

[0193] In order to implement variable constraints, construct the following function:

[0194]

[0195] in, There are three properties:

[0196] When ui (t) If there is no constraint requirement, then i1 (t) = c i2 (t)=+∞,g i1 (u i ,c i1 )=g i2 (u i ,c i2 )=1, that is

[0197] If and only if u i =0.

[0198] In specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S2 is as follows:

[0199] S21. Design the corresponding error variables for each step of the i-th unmanned ship, and introduce the error variables as follows:

[0200]

[0201] Among them, v ir is the kinematic control law,

[0202] S22. Design virtual controller:

[0203] S221, based on the unmanned ship existence quantification and dead zone kinematic and dynamic model formula and error variable z constructed in step S11 i2 , calculate the error variable z i1 The time derivative of , we can get:

[0204]

[0205] in, S=[0,-1,0],let and Therefore, we can get:

[0206]

[0207] S222. Select a Lyapunov function. The function is:

[0208]

[0209] S223, calculate v i1 Differentiating with respect to time t, we get:

[0210]

[0211] Where G = diag{d i ,δ i0};

[0212] S224. In order to obtain the required virtual control rate, it is defined as follows:

[0213]

[0214] in, Represents the auxiliary virtual controller, defined as:

[0215]

[0216] S225, can be rewritten as:

[0217]

[0218] S226. Design the virtual control rate as follows:

[0219]

[0220] in, And k i1 >0 represents a constant, where Δ i1 >0 is a constant, and

[0221] S227. Combine steps S224, S225, and S226 to obtain the result of combining the virtual control rate with the Lyapunov function, as follows:

[0222]

[0223] S228. Introduce a filtering method to update w k ,as follows:

[0224]

[0225] Among them, λ and λ′ are both positive parameters;

[0226] S229, To obtain the smooth motion trajectory of the unmanned ship, let a i1 By a second-order linear tracking differentiator:

[0227]

[0228] Among them, v ir and Represents α i1 and The estimated value of iis designed to be a positive parameter;

[0229] S230, define two constant sets, there exists a positive constant and So that:

[0230]

[0231] S23, design actual control rate:

[0232] S231, based on the unmanned ship existence quantification and dead zone kinematics and dynamics model formulas constructed in step S11 and the formulas in step S229, obtain z i2 The equation is:

[0233]

[0234] S232. Define the Lyapunov function as follows:

[0235]

[0236] in and Γ Wi2 is a positive design parameter;

[0237] S233, combining the formula in step S227 and the formula in step S231, calculate v i2 The derivative of is as follows:

[0238]

[0239] S234. Use a neural network to approximate some variables of the formula in step S233. Define the neural network as follows:

[0240]

[0241] Where Z∈Ω Z is the input vector, represents the weight vector; Usually a Gaussian function is chosen such as:

[0242]

[0243] Among them, ε i is the receiving center, r i is the width of the Gaussian function

[0244] S235. According to the universal approximation theorem, any compact set Ω z Any continuous function f(z) in can be expressed as:

[0245]

[0246] Among them, W * is the ideal constant weight, set as the ideal weight W * The estimate is The weight estimation error is defined as Estimate F(z):

[0247]

[0248] S236: Calculate the variables that need to be approximated in the neural network and the formula in step S233 to obtain:

[0249]

[0250] Among them, Z i =[u i ,v i, x i, y i ,x j ,y j ,u j ,r i ,ψ i ,ψ j ,ζ i (u i )] T ;

[0251] S237. Change the formula in step S233 into the following form:

[0252]

[0253] S238. Design the dynamic control law and neural network adaptive law at the dynamic level as follows:

[0254]

[0255] S239: Substitute the formula in step S238 into the formula in step S237 to obtain the result of combining the actual control rate with the Lyapunov function:

[0256]

[0257] In specific implementation, as a preferred embodiment of the present invention, the specific implementation process of step S3 is as follows:

[0258] The theoretical basis for the following definition:

[0259] Considering a closed-loop system composed of multiple unmanned ships subject to input quantization, output dead zone and speed constraints, combined with the designed virtual control rate and actual control rate and Lyapunov function, based on assumptions 1 and 2, all signals in the closed-loop system composed of multiple unmanned ships are bounded. At the same time, when no one is outside the collision avoidance and connectivity maintenance areas, path manipulation can be achieved within a limited time.

[0260] In specific implementation, as a preferred embodiment of the present invention, the theoretical basis of the definition is proved, and the proof process is as follows:

[0261] Based on the two Lyapunov functions, a new Lyapunov function V for all unmanned ships i=1,...,M is constructed as follows:

[0262]

[0263] Calculate the derivative of V as:

[0264]

[0265] in, Then we get:

[0266]

[0267] make:

[0268]

[0269] Further we get:

[0270]

[0271] In summary, we can see that all signals are bounded, so:

[0272]

[0273] Introduce an even-smooth Nussbaum-type function N(ξ) that satisfies:

[0274]

[0275] List functions that satisfy the definition, such as ξ 2 cos(ξ),ξ 2 sin(ξ),exp(ξ 2 )cos(ξ);

[0276] Lemma 1: Let V(t) and ξ(t) be defined in [0,t f ), where V(t)≥0, If there exist constants C>0, E>0, and the following inequality holds for If established, then there is

[0277]

[0278] Among them, γ i is a suitable positive constant, V(t),ξ(t), In [0,t f ) is bounded;

[0279] Therefore, calling Lemma 1, V(t), ξ i (t) and With [0,t f ) as the boundary, then:

[0280]

[0281] in addition, With [0,t f ) as the boundary;

[0282] make:

[0283]

[0284] You can get:

[0285]

[0286] Among them, z i1 =[z 11 ,...,z N1 ];definition And s i =P i -p id -P0, and get:

[0287]

[0288] Established, proof completed.

[0289] Example

[0290] In this embodiment, five Norwegian University of Science and Technology Smart Ship II ships are used as a basis to verify the effectiveness of the designed multi-unmanned ship speed constraint formation collision avoidance control method considering quantization and dead zone.

[0291] The reference trajectory is generated by a parameterized trajectory described as:

[0292] η 0d (θ(t))=[0.15θ+2,0.15θ+2,arctan1]

[0293] The desired formation settings are:

[0294] η 1d =[0,0,0] T ,

[0295] in t<400 and t≥400

[0296] The initial positions and yaw angles of the five unmanned ships are set as:

[0297] η3=[4,0,0] T ,

[0298] The relevant control parameters of the control method are as follows:

[0299] K i1 =diag{0.02,0.02},K i2 =diag{8,6},Δ i1 =Δ i2 =2,δ i0 =0.2,λ=10,λ'=10,

[0300] τ miniu =τ minir =0.2, χ i =10,k xi =k yi =1,b xi =b yi =0.3

[0301] The predefined velocity constraint boundaries are set as:

[0302] -0.5e -0.1t -0.3<u i <0.5e -0.1t +0.3

[0303] The positions of the two obstacles with a radius of 6 are [35, 55] and [55, 35] respectively.

[0304] The simulation results are as follows Figure 2-7As shown in the relevant graph, it can be observed that the designed control method realizes the time-varying formation of five unmanned ships, and the parameterized path is provided when the virtual leader guides. At the same time, it can be observed that the proposed control method can effectively avoid collisions between vehicles and obstacles. The actual control input and the quantized transmission signal are shown in the relevant graph. Obviously, the designed control scheme ensures the smoothness and boundedness of the actuator input. The speed and bow angular rate of the unmanned ship are shown in the figure. It can be observed that the speed is within the predefined constraint range. A bounded formation error is generated during the unmanned ship formation process. During the period from 300 seconds to 400 seconds, a large error is generated because the unmanned ship needs to avoid collisions with obstacles. As shown Figure 7 The following is Nussbaum's related parameter curve.

[0305] 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-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone, characterized by: include: S1. Combined with the ship collision avoidance, obstacle avoidance and connection protection conditions and considering the speed constraint problem, the kinematic and dynamic models of the unmanned surface ship with dead zone and quantization are constructed; S2. Introduce error variables and combine them with the Lyapunov function to design the virtual control rate and actual control rate. The specific implementation process is as follows: S21. Design the corresponding error variables for each step of the i-th unmanned ship, and introduce the error variables as follows: Among them, v ir is the kinematic control law, S22. Design virtual controller: S221, based on the unmanned ship existence quantification and dead zone kinematic and dynamic model formula and error variable z constructed in step S11 i2 , calculate the error variable z i1 The time derivative of , we can get: in, S=[0,-1,0],let and Therefore, we can get: S222. Select a Lyapunov function. The function is: S223, calculate v i1 Differentiating with respect to time t, we obtain: Where G = diag{d i ,δ i0 }; S224. In order to obtain the required virtual control rate, it is defined as follows: in, Represents the auxiliary virtual controller, defined as: S225, can be rewritten as: S226. Design the virtual control rate as follows: in, And k i1 >0 represents a constant, where Δ i1 >0 is a constant, and S227. Combine steps S224, S225, and S226 to obtain the result of combining the virtual control rate with the Lyapunov function, as follows: S228. Introduce a filtering method to update w k ,as follows: Among them, λ and λ′ are both positive parameters; S229, To obtain the smooth motion trajectory of the unmanned ship, let a i1 By a second-order linear tracking differentiator: Among them, v ir and Represents α i1 and The estimated value of i is designed to be a positive parameter; S230, define two constant sets, there exists a positive constant and So that: S23, design actual control rate: S231, based on the unmanned ship existence quantification and dead zone kinematics and dynamics model formulas constructed in step S11 and the formulas in step S229, obtain z i,2 The equation is: S232. Define the Lyapunov function as follows: in and Γ Wi2 is a positive design parameter; S233, combining the formula in step S227 and the formula in step S231, calculate v i2 The derivative of is as follows: S234. Use a neural network to approximate some variables of the formula in step S233. Define the neural network as follows: Where Z∈Ω Z is the input vector, represents the weight vector; Usually a Gaussian function is chosen such as: Among them, ε i is the receiving center, r i is the width of the Gaussian function; S235. According to the universal approximation theorem, any compact set Ω z Any continuous function f(z) in can be expressed as: Among them, W * is the ideal constant weight, set as the ideal weight W * The estimate is The weight estimation error is defined as Estimate F(z): S236: Calculate the variables that need to be approximated in the neural network and the formula in step S233 to obtain: Among them, Z i =[u i ,v i, x i, y i ,x j ,y j ,u j ,r i ,ψ i ,ψ j ,g i (u i )] T ; S237. Change the formula in step S233 into the following form: S238. Design the dynamic control law and neural network adaptive law at the dynamic level as follows: S239: Substitute the formula in step S238 into the formula in step S237 to obtain the result of combining the actual control rate with the Lyapunov function: S3. Combine the designed virtual control rate, actual control rate and Lyapunov function to perform stability analysis on the control scheme.

2. The multi-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone according to claim 1 is characterized in that: The specific implementation process of step S1 is as follows: S11. Construct the kinematic and dynamic model of the unmanned ship's existence quantification and dead zone, and give the i-th model as follows: in, represents the center of mass position of the i-th unmanned ship in the Earth-fixed reference frame, and η i Output for the unmanned ship; represents the inertia matrix; The vectors representing the surge velocity, roll velocity, and yaw velocity within the fixed frame of the airframe; represents the nonlinear term of the unmanned ship; Q(τ i )=[Q(τ iu ), 0Q(τ ir )] T represents the control signal to be quantized, Q(τ iu ) and Q(τ ir ) is the input of the system, taking the quantized value; τ iw (t) = [τ iwu (t), τ iwv (t), τ iwr (t)] T It is a bounded environmental disturbance caused by waves and currents; The rotation matrix is ​​defined as: S12. Construct a dead zone model for unmanned ships. In the unmanned ship existence quantification and dead zone kinematic and dynamic models, η i =[D z (x i ),D z (y i ),ψ i ] T is the dead zone output, then the symmetrical dead zone nonlinearity is described by the following dead zone model: Among them, k xi >0 and b xi >0 indicates the slope and width of the dead zone; D z (y i ) is equal to D z (x i ), rewrite the above formula as: where ε i is a positive constant, and x i For η i Taking the derivative of (1,1) we get: mean and and S13, build a quantitative model of the unmanned ship, and the system input Q(τ ik ) is defined as: Among them, k represents u or r, and χ ik =[(1-λ ik ) / (1+λ ik )], parameter τ minik >0,0<χ ik <1;Q(τ ik ) belongs to the set Parameter τ minik >0 means Q(τ ik ) dead zone range; S14. Introducing potential function, so that collision avoidance and connection protection between unmanned ships are included in the control design during the formation control process; S15. Construct an unmanned boat with surge speed limited by the following function: will u i With constraint boundary g i1 ,g i2 The distance between them is specifically described as: Among them, c i1 ,c i2 is a strictly positive time-varying smooth function, is a positive integer, g i1 (u i ,c i1 ),g i2 (u i ,c i2 ) is assumed to be a bounded function; In order to implement variable constraints, construct the following function: in, There are three properties: i (t) If there is no constraint requirement, then i1 (t) = c i2 (t)=+∞,g i1 (u i ,c i1 )=g i2 (u i ,c i2 )=1, that is If and only if u i =0.

3. The multi-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone according to claim 2 is characterized in that: The specific implementation process of step S14 is as follows: S141. Collision avoidance. In order to avoid collisions between unmanned ships during formation control, the following potential function is introduced: in, Indicates the minimum safety radius and detection range for collision avoidance. When p ij ≤ l c Perform collision avoidance maneuvers, P ij Partial derivatives give: Where 02 = [0,0] T ; S142, obstacle avoidance. In order to avoid collision between the unmanned ship and static obstacles during formation control, the following potential function is introduced: Among them, p ik =p i -p k ; l o > l o >0 indicates the radius of the detection and avoidance area, and the distance between obstacles is assumed to be greater than right Taking the derivative we get: S143, connection protection, in order to ensure the connectivity of the communication link between unmanned ships, the potential functions of maintaining connectivity are: in, Indicates the maximum and minimum values ​​of the connection range. Taking the derivative we get:

4. The multi-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone according to claim 1 is characterized in that: The specific implementation process of step S3 is as follows: The theoretical basis for the following definition: Considering a closed-loop system composed of multiple unmanned ships subject to input quantization, output dead zone and speed constraints, combined with the designed virtual control rate and actual control rate and Lyapunov function, based on assumptions 1 and 2, all signals in the closed-loop system composed of multiple unmanned ships are bounded. At the same time, when no one is outside the collision avoidance and connectivity maintenance areas, path manipulation can be achieved within a limited time.

5. The multi-unmanned vessel speed-constrained formation collision avoidance control method considering quantization and dead zone according to claim 4 is characterized in that: The theoretical basis of the definition is proved as follows: Based on the two Lyapunov functions, a new Lyapunov function V for all unmanned ships i=1,...,M is constructed as follows: Calculate the derivative of V as: in, Then we get: make: Further we get: In summary, we can see that all signals are bounded, so: Introduce an even-smooth Nussbaum-type function N(ξ) that satisfies: List functions that satisfy the definition, such as ξ 2 cos(ξ),ξ 2 sin(ξ),exp(ξ 2 )cos(ξ); Lemma 1: Let V(t) and ξ(t) be defined in [0,t f ), where If there exist constants C>0, E>0, and the following inequality holds for If established, then there is Among them, γ i is a suitable positive constant, In [0,t f ) is bounded; Therefore, calling Lemma 1, V(t), ξ i (t) and With [0,t f ) as the boundary, then: in addition, With [0,t f ) as the boundary; make: You can get: Among them, z i1 =[z 11 ,...,z N1 ];definition And s i =P i -p id -P0, and get: Established, proof completed.

Images