Cooperative collision and obstacle avoidance strategy of under-actuated unmanned ship considering input and state quantification

Abstract

The invention provides a collaborative collision and obstacle avoidance strategy of an underactuated unmanned ship considering input and state quantification. The collaborative collision and obstacle avoidance strategy comprises the following steps: establishing a mathematical model of the underactuated unmanned ship; a distributed guidance rule is constructed in the USV kinematics subsystem by using an auxiliary variable method, and a repulsive force function of an improved artificial potential field method is introduced to reconstruct the guidance rule, so that collaborative collision avoidance and obstacle avoidance at the kinematics level and expected trajectory tracking of the underactuated USV are realized; designing an extended state observer to solve the influence of unknown items in the system and quantitative state variables in the communication process on the formation control system; a linear time-varying model is adopted to describe a quantizer, so that a bottom-layer quantization controller does not need to predict specific information of quantization parameters; and proving the stability of the constructed USV formation tracking control system according to an input-state stability theory. According to the invention, starting from two aspects of input quantization and state quantization, the problem of USV formation tracking control in the marine environment with limited communication bandwidth and complex quantization environment is solved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and in particular to a collaborative collision and obstacle avoidance strategy for an underactuated unmanned vessel that considers input and state quantization. Background Art

[0002] With the continuous development of ship automation and intelligence, the field of intelligent navigation has received widespread attention. Unmanned surface vehicles (USVs), as small, multi-purpose, and intelligent unmanned marine vehicles, have significant potential for performing specialized tasks in complex marine environments. They not only improve ship energy efficiency and reduce maintenance costs, but also have significant advantages in the industry. In contrast, multi-USV systems can provide superior solutions for complex marine engineering tasks. By collaborating with each other to complete tasks that cannot be completed by a single traditional USV, they can improve overall efficiency and robustness.

[0003] In maritime practice, information between sensor components must be quantized and encoded before it can be transmitted across the channel. Quantization techniques not only reduce communication rates but also ensure the system operates within a given bandwidth. Therefore, considering input quantization is crucial for multi-USV formation control. Furthermore, while existing research on collision and obstacle avoidance for single unmanned vessels is relatively extensive, research on collaborative collision and obstacle avoidance for multiple unmanned vessels remains relatively limited. Summary of the Invention

[0004] According to the tracking control problem of USV formation based on signal quantization and collision and obstacle avoidance conditions proposed above, a cooperative collision and obstacle avoidance strategy for under-actuated unmanned vessels considering input and state quantization is provided.

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

[0006] A cooperative collision and obstacle avoidance strategy for underactuated unmanned vessels considering input and state quantization is proposed, including:

[0007] S1. Establish a mathematical model of the underactuated unmanned vessel;

[0008] S2. Using the auxiliary variable method, a distributed guidance law is constructed in the USV kinematic subsystem. The repulsive function of the improved artificial potential field method is introduced to reconstruct the guidance law, achieving collaborative collision avoidance at the kinematic level and desired trajectory tracking of the underactuated USV.

[0009] S3. Design an extended state observer to account for unknowns in the system and the impact of quantified state variables on the formation control system during communication.

[0010] S4. Use a linear time-varying model to describe the quantizer, so that the underlying quantization controller does not need to predict the specific information of the quantization parameters;

[0011] S5. Based on the input-state stability theory, the stability of the constructed USV formation tracking control system is proved.

[0012] Furthermore, step S1 specifically includes:

[0013] S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the USV formation system as follows:

[0014]

[0015] Among them, x i 、y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively;

[0016] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned vessel as follows:

[0017]

[0018] 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 .

[0019] Furthermore, step S2 specifically includes:

[0020] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is expressed as:

[0021]

[0022] Among them,iu and o ir They represent the quantizer coefficients respectively;

[0023] S22. Assuming that the following unmanned ships in the formation have the same potential energy, the potential function of the collision avoidance repulsion field between the following unmanned ships in the formation and the obstacle avoidance potential function between each unmanned ship and the obstacle are expressed as:

[0024]

[0025] Where i,j=1...n,i≠j means there are n agents, b=1,...,m means there are m obstacles, and the Euclidean distance between any two agents in the formation is given by The Euclidean distance between the agent and the obstacle is represented by Indicates that, [x i ,y i ] T and [x j ,y j ] T Indicates the position coordinates of the i-th agent and the j-th agent, [x k ,y k ] T represents the position coordinates of the kth obstacle, R>0, Represents the upper and lower bounds of the collision avoidance area; the repulsive field potential function is 0 outside the upper bound of the detection area, and the repulsive field potential function is infinite at the lower bound of the detection area; if the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input; the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input;

[0026] By finding the negative gradient of the repulsive potential function, we can obtain the corresponding repulsive function, which is expressed as:

[0027]

[0028] S23. Represent all USV individuals in the formation as a non-empty node set ν={ν1,ν2,ν3,...,ν n}, each individual i corresponds to a node ν i , each edge ε ij =(ν i ,ν j )∈ε represents the influence of node i on node j, and the relationship between each USV in the formation corresponds to the edge set in the graph Whether there is information exchange between formation USVs is determined by the adjacency matrix To describe; element a ij Represents the corresponding edge ε ij The edge weights of ij =0, non-diagonal element a ij >0 means there is information flow communication from node i to j, otherwise a ij =0;

[0029] S24. Set the control goal to complete the USV formation trajectory tracking task under the premise of meeting the collision and obstacle avoidance requirements, which includes the trajectory tracking task and the collision and obstacle avoidance task, wherein:

[0030] The trajectory tracking task is: Consider a continuously differentiable parameterized path Make the formation USV follow the parameterized path, so that lim|x le |→0,lim|y le |→0, each follower USV follows the leader USV to form the required formation to ensure

[0031] The collision and obstacle avoidance tasks are to avoid collisions between unmanned vessels and between USV and obstacles, so as to ensure that ||p i (t)-p j (t)||≥ R ,||p i (t)-p b (t)||≥ R o .

[0032] Furthermore, step S3 specifically includes:

[0033] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0034]

[0035] in, ν i =[u i ,v i ,r i ] T , J i is a rotation matrix that satisfies:

[0036]

[0037] S32. Design an extended state observer (ESO) as follows:

[0038]

[0039] Among them, ε i Represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed values ​​of Represents the system uncertainty term The observed value, J i Represents a rotation matrix based on state quantization, and satisfies:

[0040]

[0041] S33. Definition And satisfy:

[0042]

[0043] Then we get:

[0044]

[0045] S34. Due to That is, there is a constant greater than 0 and Make

[0046] S35. Define the dynamic error of the extended state observer ESO as follows:

[0047]

[0048] in,

[0049] S36. For the designed extended state observer ESO, there exists a positive definite matrix Satisfy the given conditions so that the error subsystem of the extended state observer ESO is input-to-state stable;

[0050] S37, Order in, And The derivative is:

[0051]

[0052] in,

[0053] S38, according to There is a constant greater than 0 satisfy

[0054] S39. In order to analyze the stability of the error system of the extended state observer ESO, two inequalities are given as follows:

[0055]

[0056] Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of and satisfies

[0057] S310. Design the Lyapunov function as follows:

[0058]

[0059] in, Represents a positive definite matrix, and the derivative of the above formula is:

[0060]

[0061] S311, when satisfied Then we get:

[0062]

[0063] Among them, 0<o i <1, and satisfies in and The matrices The maximum and minimum eigenvalues ​​of

[0064] S312, due to Then we get:

[0065]

[0066] Therefore, the error subsystem of the extended state observer ESO is stable from input to state.

[0067] Furthermore, step S4 specifically includes:

[0068] S41. In the kinematic subsystem, a distributed guidance law is designed based on the auxiliary variable method, and a repulsive force function of the improved artificial potential field method is introduced. By reconstructing the guidance law, the coordinated collision and obstacle avoidance of the underactuated unmanned ship formation and the tracking of the desired trajectory are achieved;

[0069] S42. In the dynamic subsystem, a linear analytical model is used to describe the quantization process, and the system control law and adaptive law are designed based on the sliding mode control strategy.

[0070] Furthermore, step S41 specifically includes:

[0071] S411. Define the distributed formation tracking error as follows:

[0072]

[0073] in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix that satisfies:

[0074]

[0075] S412. Derivative the defined distributed formation tracking error to obtain:

[0076]

[0077] in,

[0078] S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows:

[0079]

[0080] Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we can obtain:

[0081]

[0082] Among them, h i =diag{d i ,δ0},

[0083] S414, Definition in,

[0084] S415. From step S3, it is known that the designed extended state observer ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the extended state observer ESO is designed as follows:

[0085]

[0086] in, is a positive constant, ξ i is a positive constant;

[0087] S416. According to step S415, the kinematic error is expressed as

[0088] Furthermore, step S42 specifically includes:

[0089] S421: Based on the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established in step S32, the following is obtained:

[0090]

[0091] make And both are bounded, then:

[0092]

[0093] 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:

[0094]

[0095] Among them, q 11iu (t) and q 11ir (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 11iu (t)>0,q 11ir (t)>0; In addition, if |τ iu (t)|<b and|τ ir (t)|<b, considering Q(τ iu (t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies

[0096] S423. Set the control target of the dynamics subsystem as follows:

[0097]

[0098] Wherein, a1 and a2 are both small positive integers;

[0099] S424. Define the integral synovial surface as follows:

[0100]

[0101] Among them, b iu >0 and b ir >0, take the derivative of the above formula and we get:

[0102]

[0103] S425. According to step S424, the following is obtained:

[0104]

[0105]

[0106] Among them, l iu ,η iu ,l ir ,η ir Both represent constants greater than 0, η iu ≥ψ+η ud ,η ir ≥ψ+η rd And η ud >0,η rd >0;

[0107] S426, 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:

[0108]

[0109] Among them, γ1,γ2,ρ iu ,ρ ir , All represent constants greater than 0;

[0110] S427, based on s iu , sir , The kinematic and dynamic error systems are expressed as:

[0111]

[0112] Furthermore, step S5 specifically includes:

[0113] S51. Considering the USV formation collision avoidance and obstacle avoidance system with signal quantization, combined with the designed extended state observer ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in terms of input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded;

[0114] S52. Define the Lyapunov function as follows:

[0115]

[0116] S53, deriving the defined Lyapunov function, and combining step S426 and step S52 to obtain:

[0117]

[0118] in,

[0119] S54. Combining the designed control law and adaptive law, we get:

[0120]

[0121] Among them, K i '=K i / Π i ;

[0122] S55. Due to Then we get:

[0123]

[0124] S56, taking into account q 1iu >0,q 1ir >0,-η iu |s iu |+ε iu s iu ≤0,-η ir |s ir |+εir s ir ≤0, then we get:

[0125]

[0126] S57. Based on S56, we obtain:

[0127]

[0128] S58, due to Then we get:

[0129]

[0130] in,

[0131] S59, Definitions u =[s 1u ,s 2u ,...,s Nu ] T , s r =[s 1r ,s 2r ,...,s Nr ] T ,

[0132] q=[q1,q2,...,q N ] T , The following conclusions are obtained:

[0133] In the collision avoidance zone In addition, therefore, And the Lyapunov function is rewritten as Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics:

[0134]

[0135] Among them, P c =diag{1,1 / 2γ2μ 1u ,...,1 / 2γ2μ Nu ,1 / 2γ4μ 1r ,...,1 / 2γ4μ Nr ,1 / 2γ1,1 / 2γ3}, and

[0136] In the collision avoidance area, the Lyapunov function is expressed as:

[0137]

[0138] Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics:

[0139]

[0140] Compared with the prior art, the present invention has the following advantages:

[0141] 1. The present invention provides a collaborative collision and obstacle avoidance strategy for under-actuated unmanned vehicles that considers input and state quantization. Starting from input quantization and state quantization, it solves the problem of USV formation tracking control in a marine environment with limited communication bandwidth and a relatively complex quantization environment. In order to eliminate the need for quantizer parameter information, a linear model is used to describe the quantization process.

[0142] 2. The present invention provides a collaborative collision and obstacle avoidance strategy for under-actuated unmanned ships that takes into account input and state quantization. A linear analysis model is used to describe the input quantization process, and a collaborative collision and obstacle avoidance strategy with input and state quantization is designed. This strategy can save the communication of control input signals while realizing the collision and obstacle avoidance tasks of a multi-unmanned ship formation system.

[0143] 3. The present invention provides a collaborative collision and obstacle avoidance strategy for under-actuated unmanned ships that considers input and state quantization. A comparative experiment of the unmanned ship formation control system before and after quantization was conducted based on the Matlab platform. At the same time, an adaptive quantized tracking controller was designed to track the trajectory of the unmanned ship formation and avoid collisions and obstacles. The system control input curve is more in line with navigation engineering practice.

[0144] Based on the above reasons, the present invention can be widely promoted in fields such as artificial intelligence. 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 2This is a diagram of the distributed formation tracking control results of unmanned ships provided by an embodiment of the present invention.

[0148] Figure 3 A comparison curve chart of the lateral tracking error of the unmanned ship formation provided by an embodiment of the present invention.

[0149] Figure 4 A comparison curve diagram of the longitudinal tracking error of the unmanned ship formation provided by an embodiment of the present invention.

[0150] Figure 5 A comparison curve diagram of the propulsion force input for the unmanned ship formation control provided by an embodiment of the present invention.

[0151] Figure 6 A comparison curve of the input bow torque for the unmanned ship formation control provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0152] 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.

[0153] 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.

[0154] like Figure 1 As shown, the present invention provides a collaborative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization, including:

[0155] S1. Establish a mathematical model of the underactuated unmanned vessel;

[0156] S2. Using the auxiliary variable method, a distributed guidance law is constructed in the USV kinematic subsystem. The repulsive function of the improved artificial potential field method is introduced to reconstruct the guidance law, achieving collaborative collision avoidance at the kinematic level and desired trajectory tracking of the underactuated USV.

[0157] S3. Design an extended state observer to account for unknowns in the system and the impact of quantified state variables on the formation control system during communication.

[0158] S4. Use a linear time-varying model to describe the quantizer, so that the underlying quantization controller does not need to predict the specific information of the quantization parameters;

[0159] S5. Based on the input-state stability theory, the stability of the constructed USV formation tracking control system is proved.

[0160] In specific implementation, as a preferred embodiment of the present invention, step S1 specifically includes:

[0161] S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the USV formation system as follows:

[0162]

[0163] Among them, x i 、y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading angle; u i 、v i and r i They represent the surge speed, sway speed and rotation speed of the ship respectively;

[0164] S12. Establish a nonlinear dynamic mathematical model of the underactuated unmanned vessel as follows:

[0165]

[0166] 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 .

[0167] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0168] S21. Use a uniform quantizer to quantize the state variables and control inputs in the system. The specific quantization process is expressed as:

[0169]

[0170] Among them, iu and o ir They represent the quantizer coefficients respectively;

[0171] S22. Assuming that the following unmanned ships in the formation have the same potential energy, the potential function of the collision avoidance repulsion field between the following unmanned ships in the formation and the obstacle avoidance potential function between each unmanned ship and the obstacle are expressed as:

[0172]

[0173] Where i,j=1...n,i≠j means there are n agents, b=1,...,m means there are m obstacles, and the Euclidean distance between any two agents in the formation is given by The Euclidean distance between the agent and the obstacle is represented by Indicates that, [x i ,y i ] T and [x j ,y j ] T Indicates the position coordinates of the i-th agent and the j-th agent, [x k ,y k ] T represents the position coordinates of the kth obstacle, R>0, Represents the upper and lower bounds of the collision avoidance area; the repulsive field potential function is 0 outside the upper bound of the detection area, and the repulsive field potential function is infinite at the lower bound of the detection area; if the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input; the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input;

[0174] By finding the negative gradient of the repulsive potential function, we can obtain the corresponding repulsive function, which is expressed as:

[0175]

[0176] S23. In a multi-USV formation system, each USV needs to consider the connection with other neighboring individuals. In order to describe the connection process between each USV, graph theory is used to express it. All USV individuals in the formation are represented as a non-empty node set ν={ν1,ν2,ν3,...,ν n}, each individual i corresponds to a node ν i , each edge ε ij =(ν i ,νj )∈ε represents the influence of node i on node j, and the relationship between each USV in the formation corresponds to the edge set in the graph Whether there is information exchange between formation USVs is determined by the adjacency matrix To describe; element a ij Represents the corresponding edge ε ij The edge weights of ij =0, non-diagonal element a ij >0 means there is information flow communication from node i to j, otherwise a ij =0;

[0177] S24. Set the control goal to complete the USV formation trajectory tracking task under the premise of meeting the collision and obstacle avoidance requirements, which includes the trajectory tracking task and the collision and obstacle avoidance task, wherein:

[0178] The trajectory tracking task is: Consider a continuously differentiable parameterized path Make the formation USV follow the parameterized path, so that lim|x le |→0,lim|y le |→0, each follower USV follows the leader USV to form the required formation to ensure

[0179] The collision and obstacle avoidance tasks are to avoid collisions between unmanned vessels and between USV and obstacles, so as to ensure that ||p i (t)-p j (t)||≥ R ,||p i (t)-p b (t)||≥ R o .

[0180] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0181] S31. According to step S11 and step S12, the mathematical model of the i-th USV is rewritten as follows:

[0182]

[0183] in, ν i =[u i ,v i ,r i ] T , J i is a rotation matrix that satisfies:

[0184]

[0185] S32. Design an extended state observer (ESO) as follows:

[0186]

[0187] Among them, ε i Represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed values ​​of Represents the system uncertainty term The observed value, J i Represents a rotation matrix based on state quantization, and satisfies:

[0188]

[0189] S33. Definition And satisfy:

[0190]

[0191] Then we get:

[0192]

[0193] S34. Due to That is, there is a constant greater than 0 and Make

[0194] S35. Define the dynamic error of the extended state observer ESO as follows:

[0195]

[0196] in,

[0197] S36. For the designed extended state observer ESO, there exists a positive definite matrix Satisfy the given conditions so that the error subsystem of the extended state observer ESO is input-to-state stable;

[0198] S37, Order in, And The derivative is:

[0199]

[0200] in,

[0201] S38, according to There is a constant greater than 0 satisfy

[0202] S39. In order to analyze the stability of the error system of the extended state observer ESO, two inequalities are given as follows:

[0203]

[0204] Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of and satisfies

[0205] S310. Design the Lyapunov function as follows:

[0206]

[0207] in, Represents a positive definite matrix, and the derivative of the above formula is:

[0208]

[0209] S311, when satisfied Then we get:

[0210]

[0211] Among them, 0<o i <1, and satisfies in and The matrices The maximum and minimum eigenvalues ​​of

[0212] S312, due to Then we get:

[0213]

[0214] Therefore, the error subsystem of the extended state observer ESO is stable from input to state.

[0215] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0216] S41. In the kinematic subsystem, a distributed guidance law is designed based on the auxiliary variable method, and a repulsive force function of the improved artificial potential field method is introduced. By reconstructing the guidance law, the coordinated collision and obstacle avoidance of the underactuated unmanned ship formation and the tracking of the desired trajectory are achieved;

[0217] S42. In the dynamic subsystem, a linear analytical model is used to describe the quantization process, and the system control law and adaptive law are designed based on the sliding mode control strategy.

[0218] In specific implementation, as a preferred embodiment of the present invention, step S41 specifically includes:

[0219] S411. Define the distributed formation tracking error as follows:

[0220]

[0221] in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix that satisfies:

[0222]

[0223] S412. Derivative the defined distributed formation tracking error to obtain:

[0224]

[0225] in,

[0226] S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows:

[0227]

[0228] Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we can obtain:

[0229]

[0230] Among them, h i =diag{d i ,δ0},

[0231] S414, Definition in,

[0232] S415. From step S3, it is known that the designed extended state observer ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the extended state observer ESO is designed as follows:

[0233]

[0234] in, is a positive constant, ξ i is a positive constant;

[0235] S416. According to step S415, the kinematic error is expressed as

[0236] In specific implementation, as a preferred embodiment of the present invention, step S42 specifically includes:

[0237] S421: Based on the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established in step S32, the following is obtained:

[0238]

[0239] make And both are bounded, then:

[0240]

[0241] 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:

[0242]

[0243] Among them, q 11iu (t) and q 11ir (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 11iu (t)>0,q 11ir (t)>0; In addition, if |τ iu (t)|<b and|τ ir (t)|<b, considering Q(τ iu (t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies

[0244] S423. Set the control target of the dynamics subsystem as follows:

[0245]

[0246] Wherein, a1 and a2 are both small positive integers;

[0247] S424. Define the integral synovial surface as follows:

[0248]

[0249] Among them, b iu >0 and b ir >0, take the derivative of the above formula and we get:

[0250]

[0251] S425. According to step S424, the following is obtained:

[0252]

[0253] Among them, l iu ,η iu ,l ir ,η ir Both represent constants greater than 0, η iu ≥ψ+η ud ,η ir ≥ψ+η rd And η ud >0,η rd >0;

[0254] S426, 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:

[0255]

[0256] Among them, γ1,γ2,ρ iu ,ρir , All represent constants greater than 0;

[0257] S427, based on s iu , s ir , The kinematic and dynamic error systems are expressed as:

[0258]

[0259] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0260] S51. Considering the USV formation collision avoidance and obstacle avoidance system with signal quantization, combined with the designed extended state observer ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in terms of input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded;

[0261] S52. Define the Lyapunov function as follows:

[0262]

[0263] S53, deriving the defined Lyapunov function, and combining step S426 and step S52 to obtain:

[0264]

[0265] in,

[0266] S54. Combining the designed control law and adaptive law, we get:

[0267]

[0268] Among them, K i '=K i / Π i ;

[0269] S55. Due to Then we get:

[0270]

[0271] S56, taking into account q 1iu >0,q1ir >0,-η iu |s iu |+ε iu s iu ≤0,-η ir |s ir |+ε ir s ir ≤0, then we get:

[0272]

[0273] S57. Based on S56, we obtain:

[0274]

[0275] S58, due to Then we get:

[0276]

[0277] in,

[0278] S59, Definitions u =[s 1u ,s 2u ,...,s Nu ] T , s r =[s 1r ,s 2r ,...,s Nr ] T ,

[0279] q=[q1,q2,...,q N ] T , The following conclusions are obtained:

[0280] In the collision avoidance zone In addition, therefore, And the Lyapunov function is rewritten as Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics:

[0281]

[0282] Among them, P c =diag{1,1 / 2γ2μ 1u,...,1 / 2γ2μ Nu ,1 / 2γ4μ 1r ,…,1 / 2γ4μ Nr ,1 / 2γ1,1 / 2γ3}, and

[0283] In the collision avoidance area, the Lyapunov function is expressed as:

[0284]

[0285] Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics:

[0286]

[0287] Example

[0288] To verify the effectiveness of the fault-tolerant control method and system for multiple unmanned ship formations with input / state quantization proposed in this invention, this embodiment uses MATLAB / Simulink for computer simulation research. The parameters are set as follows:

[0289] Consider an underactuated formation system consisting of 1 leader USV and 4 USVs, where the leader follows the desired trajectory p d (t)=[t,1.12t-2.61], the parameters of the five unmanned ships are selected as follows:

[0290] m iu ={12.9kg,25.8kg,38.7kg,51.6kg,64.5kg}

[0291] m ir ={1.38kg·m 2 ,2.76kg·m 2 ,4.14kg·m 2 ,5.52kg·m 2 ,6.90kg·m 2}

[0292] f iu (·)=-5.87u 3 -1.33|u|u-0.72u+m iv vr+1.0948r 2

[0293] f ir (·)=-0.75|r|r-1.90r+0.08|v|r+(m iu -miv )uv-1.0948ur

[0294] The initial position state of USVs is set as:

[0295] p1=[2,3] T

[0296] p2=[-1,3] T

[0297] p3=[2,0] T

[0298] p4=[-4,3] T

[0299] p5=[4,-3] T

[0300] The desired formation settings are:

[0301] p 1d =[0,0] T

[0302] p 2d =[-3.5+cos((t+30) / 32),0] T

[0303] p 3d =[0,-3.5+cos((t+30) / 32)] T

[0304] p 4d =[-7+cos((t+30) / 16,0] T

[0305] p 5d =[0,-7+cos((t+30) / 16] T ;

[0306] The controller parameters are set as: K i =diag{0.1,0.1}, δ0=0.1, ε i =0.01,η iu =η ir =2,γ3=γ4=3.

[0307] The parameters of the potential function are: R=5, R o =2, R ts =5,η s =100000.

[0308] The simulation results are as follows Figures 2 to 6 As shown. Figure 2 It can be seen that the four following USVs can maintain a certain formation to track the leader, the red leader USV sails along a specific parameterized trajectory, and there is no collision risk between the USVs in the formation and obstacles; Figure 3 、 Figure 4 This is a comparison curve of the tracking errors of each unmanned vessel in the formation. When there is a collision risk, collision and obstacle avoidance take priority over maintaining the formation. In the collision-free zone, the formation error converges to a small neighborhood near the equilibrium point. Figure 5 、 Figure 6 The plot shows a comparison of the control input torque and the bow torque. Analysis of the simulation results indicates that the kinematic guidance law with reverse repulsive velocity designed in this paper enables the USV formation control system to achieve collision and obstacle avoidance while maintaining formation. The constructed dynamic control law can quickly track the guidance law provided by the kinematic subsystem, enabling tracking control of the underactuated unmanned vessel formation.

[0309] 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 collaborative collision and obstacle avoidance strategy for underactuated unmanned vessels considering input and state quantization, characterized by: include: S1. Establish a mathematical model of the underactuated unmanned vessel; S2. Using the auxiliary variable method, a distributed guidance law is constructed in the USV kinematic subsystem. The repulsive function of the improved artificial potential field method is introduced to reconstruct the guidance law, realizing cooperative collision avoidance at the kinematic level and desired trajectory tracking of the underactuated USV. S3. Design an extended state observer to account for unknowns in the system and the impact of quantified state variables on the formation control system during communication. S4. Use a linear time-varying model to describe the quantizer, so that the underlying quantization controller does not need to predict the specific information of the quantization parameters; S5. Based on the input-state stability theory, the stability of the constructed USV formation tracking control system is proved.

2. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 1 is characterized in that: Step S1 specifically includes: S11. Given an underactuated USV formation, establish the kinematic model of the motion of the i-th unmanned vessel in the USV formation system as follows: Among them, x i 、y i Indicates the coordinates of the ship's center of mass described in the geodetic coordinate system; Indicates the ship's heading 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 cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state 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: Among them, iu and o ir They represent the quantizer coefficients respectively; S22. Assuming that the following unmanned ships in the formation have the same potential energy, the potential function of the collision avoidance repulsion field between the following unmanned ships in the formation and the obstacle avoidance potential function between each unmanned ship and the obstacle are expressed as: Where i,j=1...n,i≠j means there are n agents, b=1,...,m means there are m obstacles, and the Euclidean distance between any two agents in the formation is given by The Euclidean distance between the agent and the obstacle is represented by Indicates that, [x i ,y i ] T and [x j ,y j ] T Indicates the position coordinates of the i-th agent and the j-th agent, [x k ,y k ] T represents the position coordinates of the kth obstacle, Represents the upper and lower bounds of the collision avoidance area; the repulsive field potential function is 0 outside the upper bound of the detection area, and the repulsive field potential function is infinite at the lower bound of the detection area; if the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input; the distance between the two agents satisfies Collision avoidance potential function is greater than zero and the potential function is valid in the additional control input; By finding the negative gradient of the repulsive potential function, we can obtain the corresponding repulsive function, which is expressed as: S23. Represent all USV individuals in the formation as a non-empty node set ν={ν1,ν2,ν3,...,ν n }, each individual i corresponds to a node ν i , each edge ε ij =(ν i ,ν j )∈ε represents the influence of node i on node j, and the relationship between each USV in the formation corresponds to the edge set in the graph Whether there is information exchange between formation USVs is determined by the adjacency matrix To describe; element a ij Represents the corresponding edge ε ij The edge weights of ij =0, non-diagonal element a ij >0 means there is information flow communication from node i to j, otherwise a ij =0; S24. Set the control goal to complete the USV formation trajectory tracking task under the premise of meeting the collision and obstacle avoidance requirements, which includes the trajectory tracking task and the collision and obstacle avoidance task, wherein: The trajectory tracking task is: Consider a continuously differentiable parameterized path Make the formation USV follow the parameterized path, so that lim|x le |→0,lim|y le |→0, each follower USV follows the leader USV to form the required formation to ensure The collision and obstacle avoidance tasks are to avoid collisions between unmanned vessels and between USV and obstacles, so as to ensure that ||p i (t)-p j (t)||≥ R ,||p i (t)-p b (t)||≥ R o .

4. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 1, 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: in, J i is a rotation matrix that satisfies: S32. Design an extended state observer (ESO) as follows: Among them, ε i Represents a constant greater than 0, and is the observer state, and Represent the quantized state variables and Q(ν i )=[Q(u i ),Q(v i ),Q(r i )] T Observed values ​​of Represents the system uncertainty term The observed value, J i Represents a rotation matrix based on state quantization, and satisfies: S33. Definition And satisfy: Then we get: S34. Due to That is, there is a constant greater than 0 and Make S35. Define the dynamic error of the extended state observer ESO as follows: in, S36. For the designed extended state observer ESO, there exists a positive definite matrix Satisfy the given conditions so that the error subsystem of the extended state observer ESO is input-to-state stable; S37, Order in, And The derivative is: in, S38, according to There is a constant greater than 0 satisfy S39. In order to analyze the stability of the error system of the extended state observer ESO, two inequalities are given as follows: Among them, ∈ i >0, represents the yaw angular velocity r i The upper bound of and satisfies S310. Design the Lyapunov function as follows: in, Represents a positive definite matrix, and the derivative of the above formula is: S311, when satisfied Then we get: Among them, 0<o i <1, and satisfies in and The matrices The maximum and minimum eigenvalues ​​of S312, due to Then we get: Therefore, the error subsystem of the extended state observer ESO is stable from input to state.

5. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 1, characterized in that: Step S4 specifically includes: S41. In the kinematic subsystem, a distributed guidance law is designed based on the auxiliary variable method, and a repulsive force function of the improved artificial potential field method is introduced. By reconstructing the guidance law, the coordinated collision and obstacle avoidance of the underactuated unmanned ship formation and the tracking of the desired trajectory are achieved; S42. In the dynamic subsystem, a linear analytical model is used to describe the quantization process, and the system control law and adaptive law are designed based on the sliding mode control strategy.

6. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 5, characterized in that: Step S41 specifically includes: S411. Define the distributed formation tracking error as follows: in, represents the estimated value of the actual position of USVs in the formation, P0 represents the actual position of the virtual leader, represents a rotation matrix that satisfies: S412. Derivative the defined distributed formation tracking error to obtain: in, S413. In order to eliminate the influence of under-actuation on the USV formation control system, the error transformation is set as follows: Wherein, δ0∈R is a constant greater than 0, and combined with step S412, we can obtain: Among them, h i =diag{d i ,δ0}, S414, Definition in, S415. From step S3, it is known that the designed extended state observer ESO is stable and the observation error can converge to a smaller residual set. Therefore, the kinematic guidance law based on the extended state observer ESO is designed as follows: in, is a positive constant, ξ i is a positive constant; S416. According to step S415, the kinematic error is expressed as 7. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 5, characterized in that: Step S42 specifically includes: S421: Based on the nonlinear dynamic mathematical model of the under-actuated unmanned vessel established in step S32, the following is obtained: make And both are bounded, then: 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 11iu (t) and q 11ir (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 11iu (t)>0,q 11ir (t)>0; In addition, if |τ iu (t)|<b and|τ ir (t)|<b, considering Q(τ iu (t)) and Q(τ ir (t)) is bounded, then q 12iu (t) and q 12ir (t) is also bounded and satisfies S423. Set the control target of the dynamics subsystem as follows: Wherein, a1 and a2 are both small 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, η iu ≥ψ+η ud ,η ir ≥ψ+η rd And η ud >0,η rd >0; S426, 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,ρ iu ,ρ ir , All represent constants greater than 0; S427, based on s iu , s ir , The kinematic and dynamic error systems are expressed as:

8. The cooperative collision and obstacle avoidance strategy for an underactuated unmanned vessel considering input and state quantization according to claim 1, characterized in that: Step S5 specifically includes: S51. Considering the USV formation collision avoidance and obstacle avoidance system with signal quantization, combined with the designed extended state observer ESO, kinematic guidance rate, dynamic control rate and adaptive law, with state s iu ,s ir , and input Ω iu ,Ω ir The formation tracking control system is stable in terms of input state, the tracking error can converge to a small residual set, and all signals in the designed control system are uniformly and ultimately bounded; S52. Define the Lyapunov function as follows: S53, deriving the defined Lyapunov function, and combining step S426 and step S52 to obtain: in, S54. Combining the designed control law and adaptive law, we get: Among them, K i '=K i / Π i ; S55. Due to Then we get: S56, taking into account q 1iu >0,q 1ir >0,-η iu |s iu |+ε iu s iu ≤0,-η ir |s ir |+ε ir s ir ≤0, then we get: S57. Based on S56, we obtain: S58, due to Then we get: in, S59, Definitions u =[s 1u ,s 2u ,...,s Nu ] T , s r =[s 1r ,s 2r ,...,s Nr ] T , q=[q1,q2,...,q N ] T , The following conclusions are obtained: In the collision avoidance zone In addition, therefore, And the Lyapunov function is rewritten as Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics: Among them, P c =diag{1.1 / 2γ2μ 1u ,…,1 / 2g2m Nu ,1 / 2c4m 1r ,...,1 / 2c4m Nr ,1 / 2γ1,1 / 2γ3}, and In the collision avoidance area, the Lyapunov function is expressed as: Notice Make in The error of the distributed formation control closed-loop system is uniformly and ultimately bounded, and has the following characteristics:

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