Multi-unmanned ship formation inclusion control method and device

Abstract

The invention relates to the technical field of automatic control, and provides a multi-unmanned ship formation inclusion control method and device. The method comprises the following steps: respectively constructing a formation layer guidance law and an inclusion layer guidance law according to a kinematics model and a dynamics model of an unmanned ship so as to determine the position and the speed of each unmanned ship; constructing a distributed fixed time observer to estimate the state information and lumped disturbance of the unmanned ship; constructing a fixed time differentiator, and estimating acceleration information of the unmanned ship through the fixed time differentiator; constructing a formation containing double-layer control law based on the information, and controlling unmanned ships of a formation layer and a containing layer according to the formation containing double-layer control law; according to the method, the problems that the observation error of the unmanned ship in the unmanned ship system in the prior art cannot be converged to a balance point at the same time, so that the practicability of the unmanned ship system is poor, and the performance and effect of task execution are seriously influenced are solved.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and in particular to a multi-unmanned boat formation control method and device. Background Art

[0002] In recent years, the importance of unmanned boats in the fields of marine resource exploration and underwater environment monitoring has become increasingly prominent. Limited by the types and number of sensors carried by unmanned boats, a single unmanned boat cannot meet the current growing mission requirements. Through the collaborative operation of multiple unmanned boats, the system performance of unmanned boat systems, such as fault tolerance, robustness and rapidity during mission execution, can be significantly improved.

[0003] However, in the prior art, the unmanned boat system with multiple unmanned boats working together can only meet the basic stability requirements when performing tasks. But in actual working conditions, the unmanned boat system needs to achieve the desired control target within a fixed time, that is, to make the position and velocity distribution of the unmanned boats in the unmanned boat system reach the required state; it is also necessary to ensure the convergence speed and steady-state accuracy of the unmanned boat system, that is, to ensure that the time to reach the required state is within the expected range, and to ensure the stability of the required state.

[0004] The unmanned boat system in the prior art has problems such as being unable to simultaneously handle actuator failures, unmeasurable speed information, and unable to achieve global fixed time convergence. Specifically: when the unmanned boat is sailing, if an actuator failure occurs, the performance of actuators such as the servo and engine will be attenuated. When the unmanned boat with the actuator failure is not handled simultaneously, the unmanned boat system cannot achieve the expected mission objectives and may even stop working; if the unmanned boat's sensor cannot measure speed information, it will affect the control algorithm's calculation of the output control quantity, thereby failing to achieve automatic control of the unmanned boat system; if the convergence time of the observation error of the unmanned boat in the unmanned boat system cannot be guaranteed in complex sea areas, that is, if the expected speed, heading and formation are not achieved within a certain period of time, unstable factors such as collision and loss of control of the unmanned boat formation will occur; the above series of problems will cause the unmanned boat system to have problems such as formation disorder and low mission execution efficiency. The unmanned boat system has poor practicality, seriously affecting the performance and effect of mission execution, and cannot meet actual application needs.

[0005] In view of this, overcoming the defects of the prior art is an urgent problem to be solved in the field of this technology. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a control method and device for a multi-unmanned boat formation, the purpose of which is to enable the multi-unmanned boat system to achieve the desired control target within a fixed time, to ensure that the multi-unmanned boat cluster can make the formation including the double-layer control architecture reach a stable state within a fixed time, and to have strong practicality; it solves the problem that the observation errors of the unmanned boats in the unmanned boat system of the prior art often cannot converge to the equilibrium point at the same time, resulting in poor practicality of the unmanned boat system and seriously affecting the performance and effect of task execution.

[0007] The present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for controlling a multi-unmanned boat formation, comprising:

[0009] According to the kinematic model and dynamic model of the unmanned boat, the formation layer guidance law and the inclusion layer guidance law are constructed respectively;

[0010] Build a distributed fixed-time observer;

[0011] Constructing a fixed time differentiator, and estimating the acceleration information of the unmanned boat through the fixed time differentiator;

[0012] According to the formation layer guidance law, the inclusion layer guidance law, the distributed fixed-time observer and the fixed-time differentiator, a formation inclusion double-layer control law is constructed; the formation layer and the inclusion layer unmanned boats are controlled by the formation inclusion double-layer control law.

[0013] Furthermore, the formation layer guidance law and the inclusion layer guidance law are constructed respectively according to the kinematic model and the dynamic model of the unmanned boat, including:

[0014] Construct the kinematic and dynamic models of the unmanned boat;

[0015] Based on the kinematic model and the dynamic model, constructing a formation layer tracking error dynamic equation and an inclusion layer tracking error dynamic equation;

[0016] A formation layer guidance law and a contained layer guidance law are constructed to stabilize the formation layer tracking error dynamic equation and the contained layer tracking error dynamic equation.

[0017] Further, constructing the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation based on the kinematic model and the dynamic model includes:

[0018] Determine the formation layer position error and the inclusion layer position error; the dynamic equations of the formation layer position error and the inclusion layer position error are:

[0019] Among them, z i1The dynamic equation representing the position error of the formation layer, z i2 represents the dynamic equation including the layer position error, R(·) T Represents the rotation matrix of the attached coordinate system to the inertial coordinate system, a ij represents the communication relationship between unmanned boat i and unmanned boat j, a ij The value is 0 or 1. ik represents the communication relationship between unmanned boat i and unmanned boat k, a ik The value is 0 or 1. Represents the collection of leadership unmanned boats, represents the set of unmanned boats in the following layer, represents the set of super leader unmanned boats, p i =[x i ,y i ] T represents the x-axis and y-axis coordinates of the unmanned boat i, p j represents the x-axis and y-axis coordinates of the unmanned boat j, p k =[x k ,y k ] T represents the x-axis and y-axis coordinates of the unmanned boat k, Δp ij =[L ij cos(ψ ij ), L ij sin(ψ ij )] T , L ij represents the relative distance between unmanned boat i and unmanned boat j, ψ ij represents the relative angle between unmanned boat i and unmanned boat j, Δp ik =[L ik cos(ψ ik ), L ik sin(ψ ik )] T , L ik represents the relative distance between unmanned boat i and unmanned boat k, ψ ik represents the relative angle between unmanned boat i and unmanned boat k;

[0020] Construct an artificial potential energy function; the artificial potential energy function is expressed as:

[0021] Among them, d ij represents the distance between the i-th unmanned boat and the j-th unmanned boat, ζ ia is a constant, d ia Represents the obstacle avoidance detection distance, d ia ∈R + , d ia <Ra , R a represents the collision avoidance detection interval, α ia is a constant, 0<α ia <1;

[0022] Based on the artificial potential function, the formation layer position error and the inclusion layer position error are redefined to obtain the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation; the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation are:

[0023] Among them, the formation layer tracking error dynamic equation The inclusion layer tracking error dynamic equation represents the tracking error of the unmanned boat i in the following layer on the x-axis, represents the tracking error of the unmanned boat i in the following layer on the y-axis, represents the tracking error of the leading unmanned boat i on the x-axis, represents the tracking error of the leader unmanned boat i on the y-axis, represents the potential energy function value between unmanned boat i and unmanned boat j, represents the potential energy function value between unmanned boat i and completely failed boat k, N i represents the set of unmanned boats, N o Indicates a collection of disabled boats.

[0024] Furthermore, the formation layer guidance law is expressed as:

[0025]

[0026] The formula for the inclusion layer guidance law is:

[0027]

[0028] in, represents the expected heading of the unmanned boat i in the following layer, represents the expected speed of the unmanned boat i in the following layer, The combined speed of the unmanned boat i in the following layer is expressed as: represents the tracking error of the unmanned boat i in the following layer on the y-axis, v i represents the lateral velocity of the unmanned boat i, Δ, pg , qg , mg and ng are all preset positive odd numbers, ψ d represents the heading of the super leader unmanned boat, β i =atan2(v i ,u i ), Indicates the leadership's desired direction for the unmanned boat, represents the expected speed of the leadership unmanned boat l, The combined speed of the leadership unmanned boat l indicated that, Represents the tracking error of the leadership unmanned boat l on the y-axis.

[0029] Furthermore, the construction of a distributed fixed-time observer includes:

[0030] The distributed fixed-time observer is expressed as:

[0031]

[0032] in, i represents the i-th unmanned boat, represents the estimated x-axis position information of the i-th unmanned boat, represents the estimated value of the y-axis position information of the i-th unmanned boat, represents the estimated value of the heading information of the i-th unmanned boat, represents the estimated forward velocity of the i-th unmanned boat, represents the estimated lateral velocity of the i-th unmanned boat, represents the estimated angular velocity of the i-th unmanned boat, represents the forward disturbance estimate of the i-th unmanned boat, represents the estimated value of the lateral disturbance of the i-th unmanned boat, represents the estimated value of the angular direction disturbance of the i-th unmanned boat, X i is the first gain coefficient, α l1 ,α l2 ,α l3 ∈(0,1),β li >1(i=1,2,3),β li =iβ0-(i-1),α li =iα0-(i-1), α0∈(1-Δ,1), β0∈(1+Δ,∞), Δ is a constant, k l1 , k l2 , k l3 , l1 , l2 and λ l3 are all preset parameters greater than 0, ρ i represents the observer observation error, M -1 represents the inverse matrix of the inertia matrix of the unmanned boat, τ ci Represents the control quantity output by the unmanned boat, express express sgn(·) represents the sign function.

[0033] Furthermore, the step of constructing a fixed time differentiator and estimating the acceleration information of the unmanned boat by using the fixed time differentiator includes:

[0034] The fixed time differentiator is:

[0035]

[0036] Among them, z ψ,n (t) represents the nth derivative of the desired angular velocity, ψ p represents the desired heading angle, express express k ψ,1 , k ψ,2 , k ψ,3 and k ψ,4 Both represent the second gain coefficient, α ψ,i ∈(0,1),β ψ,i >1(i=1,2,3,4),α ψ,i =iα ψ -(i-1), β ψ,i =iβ ψ -(i-1), 0<α ψ <1, β ψ >1.

[0037] Further, constructing a formation inclusion double-layer control law according to the formation layer guidance law, the inclusion layer guidance law, the distributed fixed-time observer and the fixed-time differentiator includes:

[0038] defining a sliding surface; determining a formation-inclusion dual-layer control law based on the sliding surface, the formation-layer guidance law, the inclusion-layer guidance law, the distributed fixed-time observer, and the fixed-time differentiator;

[0039] The formation contains a two-layer control law expressed as:

[0040]

[0041] Among them, τ ri represents the double-layer control law of the formation-level unmanned boat, τ ui represents the double-layer control law of the unmanned boat, m 11 Represents the total mass of the unmanned boat in the longitudinal direction, m 33 represents the total vertical mass of the unmanned boat, represents the forward disturbance estimate of unmanned boat i, represents the estimated value of the lateral disturbance of the unmanned boat i, represents the estimated value of the angular direction disturbance of the unmanned boat i, represents the second-order derivative of the desired heading of the unmanned boat i, sat(·) represents the saturation function, k s , α s and β s are gain coefficients, represents the derivative of the heading error of unmanned boat i and α of the heading error of unmanned boat i s -1 power, h represents the saturation upper limit, h is a constant greater than zero, represents the derivative of the heading error of unmanned boat i and the heading error of unmanned boat i βs -1 power, s ψi represents the error between the expected heading and the actual heading of the unmanned boat i, s ui represents the error between the expected speed and the actual speed of unmanned boat i, k c , κ s and κ c are all constants greater than zero, p c ,q c 、m c and n c are all positive odd numbers and satisfy sgn(·) is the sign function.

[0042] Furthermore, the defining of the sliding surface includes:

[0043] The sliding surface is expressed as:

[0044]

[0045] Among them, s ψi The sliding surface expression of the heading of unmanned boat i is s ui The sliding surface expression of the speed of unmanned boat i is: represents the estimated value of the speed of unmanned boat i, u pi represents the expected value of the speed of unmanned boat i, represents the estimated value of the heading of the unmanned boat i, ψ pi represents the estimated value of the heading of the unmanned boat i, t represents the running time of the unmanned boat i, τ represents the independent variable of the definite integral, κ s represents the fifth gain coefficient, k s and κ s are all positive numbers, α s Represents the power index, 0<α s <1, β s represents the power exponent, β s >1.

[0046] In a second aspect, the present invention further provides a control device for a multi-unmanned boat formation, comprising:

[0047] At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the processor to execute the control method for the multi-unmanned boat formation described in the first aspect.

[0048] In a third aspect, the present invention further provides a non-volatile computer storage medium, which stores computer executable instructions, and the computer executable instructions are executed by one or more processors to complete the multi-unmanned boat formation control method described in the first aspect.

[0049] In a fourth aspect, a chip is provided, comprising: a processor and an interface, for calling and running a computer program stored in a memory, and executing the control method for a multi-unmanned boat formation as in the first aspect.

[0050] In a fifth aspect, a computer program product comprising instructions is provided. When the instructions are executed on a computer or a processor, the computer or the processor executes a control method for a multi-unmanned boat formation as described in the first to fourth aspects and any one of them.

[0051] In the sixth aspect, the present invention also provides a multi-unmanned boat formation inclusion control system, including the multi-unmanned boat formation inclusion control device as in the second aspect, and uses the multi-unmanned boat formation inclusion control method as described in the first aspect to complete the interaction of the multi-unmanned boat formation inclusion control device of the second aspect.

[0052] Different from the prior art, the present invention has at least the following beneficial effects:

[0053] The present invention designs a formation-containing double-layer control architecture, so that the formation-layer unmanned boats mainly carry sensing equipment and can form a safe convex hull domain for the inclusion-layer unmanned boats to perform tasks; the inclusion-layer unmanned boats mainly carry task equipment and can perform tasks with a larger task load in a safe area, further increasing the number of platforms in the unmanned boat cluster, not only improving the fault tolerance of the multi-unmanned boat system during task execution, but also enabling the position and velocity distribution of the unmanned boats in the multi-unmanned boat system to reach the required state more quickly, and ensuring that the position and velocity distribution of the unmanned boats are relatively stable. The present invention also provides a distributed fixed-time observer, which enables each unmanned boat to estimate its own state information and lumped disturbance well, while ensuring that the observation error can converge to the equilibrium position at the same time, so that the multi-unmanned boat system can achieve global fixed-time convergence and improve the convergence speed, avoiding the problems of formation system disorder and low task execution efficiency, and has strong practicality.

[0054] The present invention introduces an artificial potential energy function to construct a formation including a double-layer control law, realizing the unmanned boats' internal collision avoidance and external obstacle avoidance functions, so as to further ensure that the position error and tracking error of each unmanned boat can converge to the equilibrium position at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0056] Figure 1 It is a flowchart of a control method for a multi-unmanned boat formation provided by an embodiment of the present invention;

[0057] Figure 2 is a schematic diagram of a multi-unmanned boat formation system provided by an embodiment of the present invention;

[0058] Figure 3 is a flow chart of step 10 provided in an embodiment of the present invention;

[0059] Figure 4 is a schematic diagram of an unmanned boat coordinate system provided by an embodiment of the present invention;

[0060] Figure 5 is a flowchart of step 102 provided by an embodiment of the present invention;

[0061] Figure 6 is a schematic diagram of a simulation experiment result of a formation sailing motion trajectory provided by an embodiment of the present invention;

[0062] Figure 7 is a schematic diagram of an observation error obtained by a distributed fixed-time observer provided in an embodiment of the present invention;

[0063] Figure 8 It is a schematic diagram of the architecture of a multi-unmanned boat formation including a control device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0065] Unless the context requires otherwise, throughout the specification and claims, the term "including" is to be interpreted as open inclusion, that is, "including, but not limited to". In the description of the specification, the terms "one embodiment", "some embodiments", "exemplary embodiments", "examples", "specific examples" or "some examples" and the like are intended to indicate that specific features, structures, materials or characteristics associated with the embodiment or example are included in at least one embodiment or example of the present disclosure. The schematic representation of the above terms does not necessarily refer to the same embodiment or example. In addition, the specific features, structures, materials or characteristics may be included in any one or more embodiments or examples in any appropriate manner, that is, although they may be carried in the embodiments or examples of the above terms due to reasons such as the order and position of appearance, it is not limited to that they can be carried in combination by one embodiment or example.

[0066] In the description of the present invention, it is necessary to understand that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present disclosure and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present disclosure.

[0067] In the description of the present invention, the terms "first" and "second" are used only for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the embodiments of the present disclosure, unless otherwise specified, the meaning of "multiple" is two or more. In addition, for example, the same type of nouns may be described as two independent individuals by adding "A" and "B" at the end. In this case, the corresponding features defined as "A" and "B" are only used to distinguish the same type of individuals for description purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features.

[0068] When describing some embodiments, the expressions "coupling", "coupling" and "connection" and their derivatives may be used. For example, when describing some embodiments, the term "connection" may be used to indicate that two or more components are in direct physical or electrical contact with each other. For another example, when describing some embodiments, the term "coupling" may be used to indicate that two or more components are in direct physical or electrical contact. However, the terms "connection" or "coupling" may also refer to two or more components that are not in direct contact with each other, but still cooperate or interact with each other, such as "optical path coupling", "wireless connection", etc. The embodiments disclosed herein are not necessarily limited to the contents of the present invention.

[0069] In the description of the present invention, the expression "A and / or B" (where A and B are used to formally represent specific characteristic contents) will be involved, and the corresponding expressions include the following three combinations: only A, only B, and a combination of A and B.

[0070] As used herein, "about," "substantially," or "approximately" includes the stated value and an average value that is within an acceptable range of deviation from the particular value as determined by one of ordinary skill in the art taking into account the measurements in question and the errors associated with the measurement of the particular quantity (i.e., the limitations of the measurement system).

[0071] Embodiment 1:

[0072] In order to solve the above problems, an embodiment of the present invention provides a formation containing a double-layer control architecture; the formation-layer unmanned boats are mainly composed of sensing equipment, which can form a safe convex hull domain for the inclusion-layer unmanned boats to perform tasks; the inclusion-layer unmanned boats are mainly composed of mission equipment, which can perform tasks with a larger mission payload in a safe area, so as to further increase the number of platforms in the unmanned boat cluster and enhance the fault tolerance, rapidity and stability of the double-layer collaborative control system of the multi-unmanned boat formation during the task execution process; for the sake of ease of description, the following will use "multi-unmanned boat system" to refer to "multi-unmanned boat formation containing a double-layer collaborative control system"; specifically, if Figure 1 As shown, an embodiment of the present invention provides a multi-unmanned boat formation control method, comprising:

[0073] Step 10: Based on the kinematic model and dynamic model of the unmanned boat, construct the formation layer guidance law and the inclusion layer guidance law respectively.

[0074] Among them, the kinematic model of the unmanned boat is used to describe the change of the position, speed and direction of the unmanned boat over time, but does not involve the dynamic analysis of forces and torques, which are usually expressed using longitude and latitude or plane coordinate systems; the dynamic model of the unmanned boat takes into account the forces and torques acting on the unmanned boat, including propulsion, hydrodynamics, gravity, buoyancy, etc. The embodiment of the present invention models the running trajectory of the unmanned boat, and the model obtained by modeling can be used to obtain the state quantity and position coordinates of the unmanned boat at the next moment.

[0075] The guidance law is an algorithm that guides the unmanned boat to navigate according to the current state and target state. It can calculate the expected speed and angular velocity of the unmanned boat at the next moment according to the target position; the formation layer guidance law can maintain the formation structure of the unmanned boat, avoid collision, and follow the pilot boat and maintain relative position. The inclusion layer guidance law is used to guide the unmanned boat into the safe convex hull formed by the unmanned boats in the formation, which can be used to deal with external threats such as obstacles.

[0076] The multi-unmanned boat system of the embodiment of the present invention adopts an efficient collaborative strategy. It can flexibly allocate various equipment carried by the unmanned boats and equip more sensors on the formation-level unmanned boats, thereby constructing an action area for safe operations, ensuring that the included-layer unmanned boats can carry more mission payloads and navigate and operate in a safe action area; this not only improves the efficiency of mission execution, but also greatly enhances the safety of the multi-unmanned boat system.

[0077] Step 20: Build a distributed fixed-time observer.

[0078] The distributed fixed-time observer is a state observer used to estimate the current state of the unmanned boat, such as position, speed, and direction. Each unmanned boat uses the distributed fixed-time observer of the embodiment of the present invention to estimate its own state information and lumped disturbance, so that the observation error can converge to the equilibrium position at the same time.

[0079] Step 30: construct a fixed time differentiator, and estimate the acceleration information of the unmanned boat through the fixed time differentiator.

[0080] Step 40: construct a formation-inclusion double-layer control law according to the formation-layer guidance law, the inclusion-layer guidance law, the distributed fixed-time observer and the fixed-time differentiator; and control the unmanned boats of the formation layer and the inclusion layer by the formation-inclusion double-layer control law.

[0081] The embodiment of the present invention constructs a formation-inclusion double-layer control law based on the formation-layer guidance law, inclusion-layer guidance law, distributed fixed-time observer and fixed-time differentiator constructed above. Through the formation-inclusion double-layer control law, the multi-unmanned boat system can achieve the control target within a fixed time, ensuring the convergence speed and steady-state accuracy of the multi-unmanned boat system. Figure 2 The figure shows the control schematic diagram of the multi-unmanned boat system. First, each unmanned boat relies on the formation layer guidance law and the inclusion layer guidance law to solve the target angular velocity and forward velocity of the formation layer and inclusion layer unmanned boats respectively; then, relying on the distributed fixed-time observer, the lumped disturbance, state information and other unmanned boat state information of the unmanned boat system in which it is located are estimated; finally, the estimated value and target speed are sent to the controller, and the controller combines the current state information and relies on the formation inclusion double-layer control law to solve the value of the output control quantity to realize the control of the formation layer and inclusion layer unmanned boats.

[0082] The present invention designs a formation-containing double-layer control architecture, so that the formation-layer unmanned boats mainly carry sensing equipment and can form a safe convex hull domain for the inclusion-layer unmanned boats to perform tasks; the inclusion-layer unmanned boats mainly carry task equipment and can perform tasks with a larger task load in a safe area, further increasing the number of platforms in the unmanned boat cluster, not only improving the fault tolerance of the multi-unmanned boat system during task execution, but also enabling the position and velocity distribution of the unmanned boats in the multi-unmanned boat system to reach the required state more quickly, and ensuring that the position and velocity distribution of the unmanned boats are relatively stable. The present invention also provides a distributed fixed-time observer, which enables each unmanned boat to estimate its own state information and lumped disturbance well, while ensuring that the observation error can converge to the equilibrium position at the same time, so that the multi-unmanned boat system can achieve global fixed-time convergence and improve the convergence speed, avoiding the problems of formation system disorder and low task execution efficiency, and has strong practicality.

[0083] First, the embodiments of the present invention respectively design a formation layer guidance law and a containment layer guidance law to ensure that the unmanned boat can maintain a safe distance from other unmanned boats and improve the safety of the multi-unmanned boat system. Figure 3 As shown, the step 10 includes:

[0084] Step 101: Construct a kinematic model and a dynamic model of the unmanned boat.

[0085] Since the actuators equipped on the unmanned boat cannot cover all degrees of freedom, the embodiment of the present invention reasonably simplifies the kinematic model and the dynamic model, and designs it into a three-degree-of-freedom model of the multi-unmanned boat system that only designs feedback based on the bow motion, longitudinal motion and lateral motion, and establishes the kinematic model and dynamic model of the unmanned boat.

[0086] like Figure 4 The figure shows a schematic diagram of the coordinate system of the unmanned boat according to an embodiment of the present invention, and the kinematic model is expressed as follows:

[0087]

[0088] The initial kinetic model is expressed as:

[0089]

[0090] Among them, m ii (i=1,2,3) represents the inertia matrix parameters of the unmanned boat, v i represents the lateral speed of the unmanned boat i, r i represents the angular velocity of unmanned boat i, u i represents the forward speed of unmanned boat i, u ii (i=1,2,3), d ui represents the damping matrix parameter in the forward velocity direction of the unmanned boat, d vi represents the damping matrix parameter in the lateral velocity direction of the unmanned boat, d ri represents the damping matrix parameters in the angular velocity direction of the unmanned boat, τ d,ui represents the disturbance in the forward velocity direction, τ d,vi represents the disturbance in the lateral velocity direction, τ d,ri represents the disturbance in the direction of angular velocity.

[0091] Considering the impact of possible actuator failure and unmeasurable speed information on the multi-unmanned boat system, the dynamic model of the unmanned boat reconstructed in the embodiment of the present invention is:

[0092]

[0093] Among them, Γ in represents the aggregate disturbance in all directions, where each direction refers to the forward velocity direction, the lateral velocity direction, and the angular velocity direction, n = 1, 2, 3, ψ i Indicates the heading of the unmanned boat i.

[0094] Step 102: Based on the kinematic model and the dynamic model, construct a formation layer tracking error dynamic equation and an inclusion layer tracking error dynamic equation.

[0095] Step 103: Constructing a formation layer guidance law and a contained layer guidance law to stabilize the formation layer tracking error dynamic equation and the contained layer tracking error dynamic equation.

[0096] The embodiments of the present invention define the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation respectively, and design the distributed fixed-time formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation to solve the expected heading angle and speed of each unmanned boat.

[0097] Specifically, if Figure 5 As shown, step 102 includes:

[0098] Step 1021: Determine the formation layer position error and the inclusion layer position error.

[0099] The communication topology structure in the multi-unmanned boat system of the embodiment of the present invention is as follows: the multi-unmanned boat system includes M+N unmanned boats, that is, N follower unmanned boats and M leader unmanned boats. The communication relationship between the unmanned boats can be converted into a topological graph composed of edges and nodes, represented as G={V,E}, where V={V F ,V L ,V S}, V represents a point set, which is used to represent the unmanned boat node, V F represents the follower node, V L represents the leader node, V S represents the super leader node; E = {(i, j) ∈ V × V} represents the edge set, which is used to indicate whether there is communication between unmanned boats. Node (i, j) means that node i receives information from node j, and node j is also called the neighbor node of node i. N i ={j∈V|(i,j)∈E},N i represents the neighbor set of unmanned boat i; the communication relationship of each node can be obtained through the adjacency matrix A = [a ij ] shows that if (i,j)∈E, then a ij =1, otherwise a ij = 0. In order to describe the number of messages that each unmanned boat can receive, the in-degree diagonal matrix D is defined, whose diagonal elements are The non-diagonal elements are 0. The dynamic equations of the formation layer position error and the inclusion layer position error are:

[0100] Among them, z i1 The dynamic equation representing the position error of the formation layer, z i2 represents the dynamic equation including the layer position error, R(·) T Represents the rotation matrix of the attached coordinate system to the inertial coordinate system, a ij represents the communication relationship between unmanned boat i and unmanned boat j, a ij The value is 0 or 1. ik represents the communication relationship between unmanned boat i and unmanned boat k, a ik The value is 0 or 1. Represents the collection of leadership unmanned boats, represents the set of unmanned boats in the following layer, represents the set of super leader unmanned boats, p i =[x i ,y i ] T represents the x-axis and y-axis coordinates of the unmanned boat i, p jrepresents the x-axis and y-axis coordinates of the unmanned boat j, p k =[x k ,y k ] T represents the x-axis and y-axis coordinates of the unmanned boat k, Δp ij =[L ij cos(ψ ij ), L ij sin(ψ ij )] T , L ij represents the relative distance between unmanned boat i and unmanned boat j, ψ ij represents the relative angle between unmanned boat i and unmanned boat j, Δp ik =[L ik cos(ψ ik ), L ik sin(ψ ik )] T , L ik represents the relative distance between unmanned boat i and unmanned boat k, ψ ik represents the relative angle between unmanned boat i and unmanned boat k; where z i1 represents the sum of the errors between the i-th unmanned boat and its neighbor unmanned boats in the leadership layer and the errors between the i-th unmanned boat and the super leader boat, z i2 It represents the sum of the errors between the i-th unmanned boat and its neighbor unmanned boats and the errors between the i-th unmanned boat and the leader boat in the inclusion layer.

[0101] Step 1022: Construct an artificial potential energy function.

[0102] In order to ensure the safety of multiple unmanned boats in the process of driving, the position error is redefined in combination with the artificial potential energy function to keep a safe distance between the unmanned boats and between the unmanned boats and obstacles, and realize the unmanned boats' internal collision avoidance and external obstacle avoidance functions. The artificial potential energy function is expressed as:

[0103] Among them, d ij represents the distance between the i-th unmanned boat and the j-th unmanned boat, ζ ia is a constant, ζ ia ∈R + , d ia Represents the obstacle avoidance detection distance, d ia ∈R + , d ia <R a , d ia ∈R + , satisfying d ia <R a (That is, when d ij <R aWhen the collision avoidance mechanism takes effect), R a represents the collision avoidance detection interval, α ia represents a constant, satisfying 0<α ia <1, wherein the constant in the artificial potential energy function is determined by those skilled in the art based on specific usage scenarios and experience, and is not limited here.

[0104] Step 1023: Based on the artificial potential function, redefine the formation layer position error and the inclusion layer position error to obtain the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation.

[0105] The formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation are:

[0106] Among them, the formation layer tracking error dynamic equation The inclusion layer tracking error dynamic equation represents the tracking error of the unmanned boat i in the following layer on the x-axis, represents the tracking error of the unmanned boat i in the following layer on the y-axis, represents the tracking error of the leading unmanned boat i on the x-axis, represents the tracking error of the leader unmanned boat i on the y-axis, represents the potential energy function value between unmanned boat i and unmanned boat j, represents the potential energy function value between unmanned boat i and completely failed boat k, N i represents the set of unmanned boats, N o Indicates a collection of disabled boats.

[0107] The formation layer guidance law and the inclusion layer guidance law of the embodiment of the present invention are both a fixed-time distributed collision avoidance guidance law, and the formation layer guidance law is expressed as:

[0108]

[0109] The formula for the inclusion layer guidance law is:

[0110]

[0111] in, represents the expected heading of the unmanned boat i in the following layer, represents the expected speed of the unmanned boat i in the following layer, The combined speed of the unmanned boat i in the following layer is expressed as: represents the tracking error of the unmanned boat i in the following layer on the y-axis, v i represents the lateral velocity of the unmanned boat i, Δ, pg , qg ,mg and ng are all preset positive odd numbers, ψ d represents the heading of the super leader unmanned boat, β i =atan2(v i ,u i ), Indicates the leadership's desired direction for the unmanned boat, represents the expected speed of the leadership unmanned boat l, The leadership of the unmanned boat l said that Represents the tracking error of the leadership unmanned boat l on the y-axis.

[0112] in, That is, the expected total speed, k represents the gain coefficient, x e represents the x-axis tracking error, y e represents the y-axis tracking error, U d Indicates the desired direction of the resultant velocity, Δ>0, k, Δ, p g ,q g 、m g and n g are all positive odd numbers and satisfy p g / q g <1m g / n g >1, and the specific value of the positive odd number in the layer guidance law is determined by those skilled in the art based on specific usage scenarios and experience, and is not limited here.

[0113] In order to deal with the impact of actuator failure and unmeasurable speed information on the multi-unmanned boat system, ensure that the observation errors of the unmanned boats in the system converge to the equilibrium point at the same time, and further improve the estimation speed and accuracy of the observer, the embodiment of the present invention constructs a distributed fixed-time observer, which is expressed as:

[0114]

[0115] in, i represents the i-th unmanned boat, represents the estimated x-axis position information of the i-th unmanned boat, represents the estimated value of the y-axis position information of the i-th unmanned boat, represents the estimated value of the heading information of the i-th unmanned boat, represents the estimated forward velocity of the i-th unmanned boat, represents the estimated lateral velocity of the i-th unmanned boat, represents the estimated angular velocity of the i-th unmanned boat, represents the forward disturbance estimate of the i-th unmanned boat, represents the estimated value of the lateral disturbance of the i-th unmanned boat, represents the estimated value of the angular direction disturbance of the i-th unmanned boat, X i is the first gain coefficient, α l1 ,α l2 ,α l3 ∈(0,1),β li >1(i=1,2,3),β li =iβ0-(i-1),α li =iα0-(i-1), α0∈(1-Δ,1), β0∈(1+Δ,∞), Δ is a constant, k l1 , k l2 , k l3 , l1 , l2 and λ l3 are all preset parameters greater than 0, ρ i represents the observer observation error, M -1 represents the inverse matrix of the inertia matrix of the unmanned boat, τ ci Represents the control quantity output by the unmanned boat, express express sgn(·) represents the sign function. a ij Represents the communication relationship between the unmanned boat i and the unmanned boat j. Among them, the constants and preset parameters in the distributed fixed time observer are determined by those skilled in the art according to specific usage scenarios and experience, and are not limited here.

[0116] Through the expression of the distributed fixed-time observer, the observation error dynamics can be expressed as:

[0117]

[0118] Since it is difficult to measure the acceleration of an unmanned boat in actual engineering, an embodiment of the present invention provides a fixed time differentiator for estimating the acceleration of the unmanned boat to avoid the differential explosion phenomenon. The fixed time differentiator is:

[0119]

[0120] Among them, z ψ,n (t) represents the nth derivative of the desired angular velocity, ψ p represents the desired heading angle, express express k ψ,1 , kψ,2 , k ψ,3 and k ψ,4 Both represent the second gain coefficient, α ψ,i ∈(0,1),β ψ,i >1(i=1,2,3,4),α ψ,i =iα ψ -(i-1), β ψ,i =iβ ψ -(i-1), 0<α ψ <1, β ψ >1.

[0121] The fixed-time differentiator used in the embodiment of the present invention is a third-order differentiator, which can estimate the first-order derivative information of the velocity and angular velocity within a fixed time.

[0122] In order to illustrate the formation inclusion double-layer control law, the step 40 includes: defining a sliding surface; determining the formation inclusion double-layer control law based on the sliding surface, the formation layer guidance law, the inclusion layer guidance law, the distributed fixed-time observer and the fixed-time differentiator.

[0123] First, in order to complete the formation control task of the multi-unmanned boat system, the sliding surface is defined as follows:

[0124] The sliding surface is expressed as:

[0125]

[0126] Among them, s ψi The sliding surface expression of the heading of unmanned boat i is s ui The sliding surface expression of the speed of unmanned boat i is: represents the estimated value of the speed of unmanned boat i, u pi represents the expected value of the speed of unmanned boat i, represents the estimated value of the heading of the unmanned boat i, ψ pi represents the estimated value of the heading of the unmanned boat i, t represents the running time of the unmanned boat i, τ represents the independent variable of the definite integral, κ s represents the fifth gain coefficient, k s and κ s are all positive numbers, α s Represents the power index, 0<α s <1, β s represents the power exponent, β s >1. The positive numbers and power exponents in the sliding surface are determined by those skilled in the art according to specific usage scenarios and experience, and are not limited here.

[0127] The formation contains a two-layer control law expressed as:

[0128]

[0129] Among them, τ ri represents the double-layer control law of the formation-level unmanned boat, τ ui represents the double-layer control law of the unmanned boat, m 11 Represents the total mass of the unmanned boat in the longitudinal direction, m 33 represents the total vertical mass of the unmanned boat, represents the forward disturbance estimate of unmanned boat i, represents the estimated value of the lateral disturbance of the unmanned boat i, represents the estimated value of the angular direction disturbance of the unmanned boat i, represents the second-order derivative of the desired heading of the unmanned boat i, sat(·) represents the saturation function, k s , α s and β s are gain coefficients, represents the derivative of the heading error of unmanned boat i and α of the heading error of unmanned boat i s -1 The power, h represents the saturation upper limit, h is a constant greater than zero, represents the derivative of the heading error of unmanned boat i and the heading error of unmanned boat i βs -1 power, s ψi represents the error between the expected heading and the actual heading of the unmanned boat i, s ui represents the error between the expected speed and the actual speed of unmanned boat i, k c , κ s and κ c are all constants greater than zero, p c ,q c 、m c and n c are all positive odd numbers and satisfy sgn(·) is a sign function. Among them, the constant, positive odd number and saturation upper limit value in the formation containing the double-layer control rate are determined by those skilled in the art according to specific usage scenarios and experience.

[0130] In the related art, there is a solution to adjust the running path by solving the angular velocity. On the one hand, since the change of the angular velocity of the unmanned boat needs a certain amount of time to accumulate, the angular velocity control usually has a certain hysteresis, which leads to a decrease in the control accuracy and stability of the unmanned boat's running path. It is likely that the convergence time of the observation error of the unmanned boat cannot be guaranteed, and the observation error of the unmanned boat in the unmanned boat system cannot converge to the equilibrium point at the same time, which seriously affects the performance and effect of task execution, and has poor practicality. In order to solve the above problems, the embodiment of the present invention provides a solution for guiding the unmanned boat to adjust the path by a formation containing a double-layer control law. Specifically, the formation of the embodiment of the present invention contains a double-layer control law for: guiding the unmanned boat to adjust the running path according to the target and its own state during operation, so as to facilitate its completion of the task; the formation of the embodiment of the present invention contains a double-layer control law. The result of solving the solution is the speed and heading of the unmanned boat. Compared with the angular velocity, the heading is easier to control and achieve. Moreover, when the formation of the embodiment of the present invention contains a double-layer control law, the heading control can be achieved directly by adjusting the propulsion force and steering torque of the unmanned boat, and the unmanned boat can directly receive and execute the heading control instruction.

[0131] On the other hand, angular velocity control algorithms often require more complex mathematical models and algorithm support. The implementation difficulty and computational complexity of these algorithms are relatively high, which is not conducive to the implementation of unmanned boat systems. The heading control algorithm is usually based on a simple proportional-integral-derivative (PID) controller, etc., and more complex models can be used to achieve heading control according to specific needs. It has a wide range of applicable scenarios and strong practicality.

[0132] The formation of the embodiment of the present invention includes a double-layer control law, which is a complex fixed-time sliding mode controller. Compared with the backstepping controller in the prior art, the control effect is improved. Among them, the control parameters of the backstepping controller are often more and the mathematical expression is complex, which makes the parameter tuning more complicated and the workload more during actual use. In addition, since the backstepping controller involves the coordination of multiple subsystems and multiple control links in the unmanned boat system, it can often only guarantee asymptotic stability. In actual use, multiple unmanned boats in the unmanned boat system may not be able to reach the expected speed, heading and formation within the expected time, and it is difficult to guarantee the performance and effect of task execution. When the formation of the embodiment of the present invention includes a double-layer control law, the upper bound of the convergence time is a constant, so it can ensure that the state of the unmanned boat system converges to the equilibrium point quickly, avoiding the oscillation of the state of the unmanned boat system near the equilibrium point, and the system has high stability and high control accuracy.

[0133] The multi-unmanned boat formation of the present invention includes a control method that, in order to achieve the goal of global fixed-time stability, focuses on ensuring that the unmanned boats in the unmanned boat system are stable within a fixed time in each link of the design and control of the unmanned boat system; in particular, through distributed fixed-time observers and fixed-time differentiators, it is ensured that the unmanned boat system can converge to a fixed time value, avoiding the risks of unmanned boat collision, loss of control, etc. caused by slow convergence.

[0134] Embodiment 2:

[0135] In order to illustrate the effectiveness of the control method for the multi-unmanned boat formation described in Example 1, the embodiment of the present invention provides a specific example of simulation verification, which is as follows:

[0136] Taking a specific unmanned boat as the research object, a multi-unmanned boat system is set up, which includes three leader unmanned boats and five follower unmanned boats. The communication topology relationship is as follows: Figure 6 The kinematic model and dynamic model parameters of the unmanned boat are: m 11 =2652.52kg, m 22 =2825.57kg, m 33 =4201.68kg, d 11 =848.13,d 22 =10162.44,d 33 =22721.63. Some parameters of the controller are set as: k s =3,κ s =3, k c =2,κ c =2,β s =1.2,β o =1.2,β ψ =1.2,α o =0.9,α s =0.8,α ψ =0.9.

[0137] The trajectory of the virtual leader is:

[0138]

[0139] The external disturbance is set as:

[0140]

[0141] like Figure 6The figure shows the simulation experiment results of the navigation trajectory of the formation when a specific kinematic model and a dynamic model are used as the controlled objects and the multi-unmanned boat formation inclusion control method of the embodiment of the present invention is used; the multi-unmanned boat formation is a formation inclusion double-layer control architecture, including 8 unmanned boats, 7 formation-layer unmanned boats and 1 inclusion-layer unmanned boat, and the driving trajectory of each unmanned boat is shown by lines of different colors. The 8 unmanned boats are arranged in irregular positions, such as Figure 6 The three formation-layer unmanned boats constructed a safe triangular convex hull domain, and the included unmanned boats successfully entered the convex hull domain for navigation and operation. During this period, the purple route unmanned boat had a complete actuator failure, and the other unmanned boats could avoid it to ensure the safety of the unmanned boat system. The 7 formation-layer unmanned boats changed their positions within a fixed time and arrived at the following position: Figure 6 The position shown in the upper left corner, and the observation errors of the 7 formation-layer unmanned boats converge to the equilibrium point at the same time to form a preset formation, so that the formation containing a double-layer control architecture reaches a stable state. The control method of the embodiment of the present invention can ensure that the unmanned boats of the formation layer form a preset formation within a fixed time, and ensure that the unmanned boats of the containing layer enter a safe convex hull domain for navigation, and has strong practicality.

[0142] like Figure 7 Graph 1 shows the observation error obtained by using the distributed fixed-time observer according to an embodiment of the present invention; Figure 7 Taking the position information of the unmanned boat on the blue route as an example, it shows that the designed extended state observer can realize the position information ρ x , y and ρ ψ An accurate estimate of x is the sum of the estimated errors of the x-axis coordinate values ​​of each unmanned boat, ρ y is the sum of the estimated errors of the y-axis coordinate values ​​of each unmanned boat, ρ ψ It is the sum of the heading estimation errors of each unmanned boat. The blue line is the estimated effect of the multi-unmanned boat formation control method using the embodiment of the present invention. The orange line is the estimated effect of the traditional extended state observer. It can be seen that compared with the yellow curve, the blue curve converges to zero significantly faster. Compared with the asymptotically stable control algorithm in the prior art, the distributed fixed-time observer in the embodiment of the present invention can ensure that the errors of each link converge to zero at a faster speed, thereby improving the rapidity and fault tolerance of the multi-unmanned boat system.

[0143] Embodiment 3:

[0144] like Figure 8, which is a schematic diagram of the architecture of a multi-unmanned boat formation including a control device according to an embodiment of the present invention. The multi-unmanned boat formation in this embodiment includes a control device including one or more processors 21 and a memory 22. Figure 8 A processor 21 is taken as an example.

[0145] The processor 21 and the memory 22 may be connected via a bus or other means. Figure 8 The example of connecting through bus is taken in the following.

[0146] The memory 22 is a non-volatile computer-readable storage medium that can be used to store non-volatile software programs and non-volatile computer executable programs, such as the multi-unmanned boat formation inclusion control method in this embodiment. The processor 21 executes the multi-unmanned boat formation inclusion control method by running the non-volatile software programs and instructions stored in the memory 22.

[0147] The memory 22 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the memory 22 may optionally include a memory remotely arranged relative to the processor 21, and these remote memories may be connected to the processor 21 via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0148] The program instructions / modules are stored in the memory 22, and when executed by the one or more processors 21, the multi-unmanned boat formation control method in the above-mentioned embodiment is executed, for example, the various steps of the multi-unmanned boat formation control method in the embodiment of the present invention described above are executed.

[0149] An embodiment of the present invention further provides a non-volatile computer storage medium, wherein the computer storage medium stores computer executable instructions, and the computer executable instructions are executed by one or more processors, such as Figure 8 A processor 21 can enable the above one or more processors to execute the multi-unmanned boat formation control method in the specific embodiment of the present invention, for example, to execute the various steps of the multi-unmanned boat formation control method in the embodiment of the present invention described above; it can also realize Figure 8 The modules and units described above; or executing the multi-unmanned boat formation control method in the specific implementation of the present invention, for example, executing the multi-unmanned boat formation control method in the embodiment of the present invention described above; it can also be realized Figure 8 The various modules and units described.

[0150] It is worth noting that the information interaction, execution process, etc. between the modules and units within the above-mentioned devices and systems are based on the same concept as the processing method embodiment of the present invention. The specific contents can be found in the description of the method embodiment of the present invention and will not be repeated here.

[0151] A person skilled in the art may understand that all or part of the steps in the various methods of the embodiments may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the storage medium may include: a read-only memory (ROM), a random access memory (RAM), a disk or an optical disk, etc.

[0152] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-unmanned boat formation control method, characterized in that: include: According to the kinematic model and dynamic model of the unmanned boat, the formation layer guidance law and the inclusion layer guidance law are constructed respectively; Build a distributed fixed-time observer; Constructing a fixed time differentiator, and estimating the acceleration information of the unmanned boat through the fixed time differentiator; According to the formation layer guidance law, the inclusion layer guidance law, the distributed fixed-time observer and the fixed-time differentiator, a formation inclusion double-layer control law is constructed; the formation layer and the inclusion layer unmanned boats are controlled by the formation inclusion double-layer control law.

2. The multi-unmanned boat formation control method according to claim 1, characterized in that: According to the kinematic model and dynamic model of the unmanned boat, the formation layer guidance law and the inclusion layer guidance law are respectively constructed, including: Construct the kinematic and dynamic models of the unmanned boat; Based on the kinematic model and the dynamic model, constructing a formation layer tracking error dynamic equation and an inclusion layer tracking error dynamic equation; A formation layer guidance law and a contained layer guidance law are constructed to stabilize the formation layer tracking error dynamic equation and the contained layer tracking error dynamic equation.

3. The multi-unmanned boat formation control method according to claim 2 is characterized in that: The constructing of the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation based on the kinematic model and the dynamic model comprises: Determine the formation layer position error and the inclusion layer position error; the dynamic equations of the formation layer position error and the inclusion layer position error are: Among them, z i1 The dynamic equation representing the position error of the formation layer, z i2 represents the dynamic equation including the layer position error, R(·) T Represents the rotation matrix of the attached coordinate system to the inertial coordinate system, a ij represents the communication relationship between unmanned boat i and unmanned boat j, a ij The value is 0 or 1. ik represents the communication relationship between unmanned boat i and unmanned boat k, a ik The value is 0 or 1. Represents the collection of leadership unmanned boats, represents the set of unmanned boats in the following layer, represents the set of super leader unmanned boats, p i =[x i ,y i ] T represents the x-axis and y-axis coordinates of the unmanned boat i, p j represents the x-axis and y-axis coordinates of the unmanned boat j, p k =[x k ,y k ] T represents the x-axis and y-axis coordinates of the unmanned boat k, Δp ij =[L ij cos(ψ ij ), L ij sin(ψ ij )] T , L ij represents the relative distance between unmanned boat i and unmanned boat j, ψ ij represents the relative angle between unmanned boat i and unmanned boat j, Δp ik =[L ik cos(ψ ik ), L ik sin(ψ ik )] T , L ik represents the relative distance between unmanned boat i and unmanned boat k, ψ ik represents the relative angle between unmanned boat i and unmanned boat k; Construct an artificial potential energy function; the artificial potential energy function is expressed as: Among them, d ij represents the distance between the i-th unmanned boat and the j-th unmanned boat, ζ ia is a constant, d ia Represents the obstacle avoidance detection distance, d ia ∈R + , d ia <R a , R a represents the collision avoidance detection interval, α ia is a constant, 0<α ia <1; Based on the artificial potential function, the formation layer position error and the inclusion layer position error are redefined to obtain the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation; the formation layer tracking error dynamic equation and the inclusion layer tracking error dynamic equation are: Among them, the formation layer tracking error dynamic equation The inclusion layer tracking error dynamic equation represents the tracking error of the unmanned boat i in the following layer on the x-axis, represents the tracking error of the unmanned boat i in the following layer on the y-axis, represents the tracking error of the leading unmanned boat i on the x-axis, represents the tracking error of the leader unmanned boat i on the y-axis, represents the potential energy function value between unmanned boat i and unmanned boat j, represents the potential energy function value between unmanned boat i and completely failed boat k, N i represents the set of unmanned boats, N o Indicates a collection of disabled boats.

4. The multi-unmanned boat formation control method according to claim 3 is characterized in that: The formation-level guidance law is expressed as: The formula for the inclusion layer guidance law is: in, represents the expected heading of the unmanned boat i in the following layer, represents the expected speed of the unmanned boat i in the following layer, The combined speed of the unmanned boat i in the following layer is expressed as: represents the tracking error of the unmanned boat i in the following layer on the y-axis, v i represents the lateral velocity of the unmanned boat i, Δ, pg , qg , mg and ng are all preset positive odd numbers, ψ d represents the heading of the super leader unmanned boat, β i =atan2(v i ,u i ), Indicates the leadership's desired direction for the unmanned boat, represents the expected speed of the leadership unmanned boat l, The leadership of the unmanned boat l said that Represents the tracking error of the leadership unmanned boat l on the y-axis.

5. The multi-unmanned boat formation control method according to claim 1, characterized in that: The construction of a distributed fixed-time observer comprises: The distributed fixed-time observer is expressed as: in, i represents the i-th unmanned boat, represents the estimated x-axis position information of the i-th unmanned boat, represents the estimated value of the y-axis position information of the i-th unmanned boat, represents the estimated value of the heading information of the i-th unmanned boat, represents the estimated forward velocity of the i-th unmanned boat, represents the estimated lateral velocity of the i-th unmanned boat, represents the estimated angular velocity of the i-th unmanned boat, represents the forward disturbance estimate of the i-th unmanned boat, represents the estimated value of the lateral disturbance of the i-th unmanned boat, represents the estimated value of the angular direction disturbance of the i-th unmanned boat, X i is the first gain coefficient, α l1 ,α l2 ,α l3 ∈(0,1),β li >1(i=1,2,3),β li =iβ0-(i-1),α li =iα0-(i-1), α0∈(1-Δ,1), β0∈(1+Δ,∞), Δ is a constant, k l1 , k l2 , k l3 , l1 , l2 and λ l3 are all preset parameters greater than 0, ρi represents the observer observation error, M -1 represents the inverse matrix of the inertia matrix of the unmanned boat, τ ci Represents the control quantity output by the unmanned boat, express express n=1,2,3, sgn(·) represents the sign function.

6. The multi-unmanned boat formation control method according to claim 1, characterized in that: The method of constructing a fixed time differentiator and estimating the acceleration information of the unmanned boat by using the fixed time differentiator includes: The fixed time differentiator is: Among them, z ψ,n (t) represents the nth derivative of the desired angular velocity, ψ p represents the desired heading angle, express express n=1,2,3 ,4 , k ψ,1 , k ψ,2 , k ψ,3 and k ψ,4 Both represent the second gain coefficient, α ψ,i ∈(0,1),β ψ,i >1(i=1,2,3,4),α ψ,i =iα ψ -(i-1), β ψ,i =iβ ψ -(i-1), 0<α ψ <1, β ψ >1.

7. The multi-unmanned boat formation control method according to claim 1, characterized in that: The constructing of a formation inclusion double-layer control law according to the formation layer guidance law, the inclusion layer guidance law, the distributed fixed-time observer and the fixed-time differentiator comprises: defining a sliding surface; determining a formation-inclusion dual-layer control law based on the sliding surface, the formation-layer guidance law, the inclusion-layer guidance law, the distributed fixed-time observer, and the fixed-time differentiator; The formation contains a two-layer control law expressed as: Among them, τ ri represents the double-layer control law of the formation-level unmanned boat, τ ui represents the double-layer control law of the unmanned boat, m 11 Represents the total mass of the unmanned boat in the longitudinal direction, m 33 represents the total vertical mass of the unmanned boat, represents the forward disturbance estimate of unmanned boat i, represents the estimated value of the lateral disturbance of the unmanned boat i, represents the estimated value of the angular direction disturbance of the unmanned boat i, represents the second-order derivative of the desired heading of the unmanned boat i, sat(·) represents the saturation function, k s , α s and β s are gain coefficients, represents the derivative of the heading error of unmanned boat i and α of the heading error of unmanned boat i s -1 power, h represents the saturation upper limit, h is a constant greater than zero, represents the derivative of the heading error of unmanned boat i and the β of the heading error of unmanned boat i s -1 power, s ψi represents the error between the expected heading and the actual heading of the unmanned boat i, s ui represents the error between the expected speed and the actual speed of unmanned boat i, k c , κ s and κ c are all constants greater than zero, p c ,q c 、m c and n c are all positive odd numbers and satisfy sgn(·) is the sign function.

8. The control method of a multi-unmanned boat formation according to claim 7, characterized in that: The definition of the sliding surface includes: The sliding surface is expressed as: Among them, s ψi The sliding surface expression of the heading of unmanned boat i is s ui The sliding surface expression of the speed of unmanned boat i is: represents the estimated value of the speed of unmanned boat i, u pi represents the expected value of the speed of unmanned boat i, represents the estimated value of the heading of the unmanned boat i, ψ pi represents the estimated value of the heading of the unmanned boat i, t represents the running time of the unmanned boat i, τ represents the independent variable of the definite integral, κ s represents the fifth gain coefficient, k s and κ s are all positive numbers, α s Represents the power index, 0<α s <1, β s represents the power exponent, β s >1.

9. A multi-unmanned boat formation includes a control device, characterized in that: The multi-unmanned boat formation includes a control device including at least one processor and a memory. The at least one processor and the memory are connected via a data bus. The memory stores instructions that can be executed by the at least one processor. After being executed by the processor, the instructions are used to implement the multi-unmanned boat formation control method described in any one of claims 1-8.

10. A non-volatile computer storage medium, characterized in that: The computer storage medium stores computer executable instructions, and the computer executable instructions are executed by one or more processors to complete the multi-unmanned boat formation control method described in any one of claims 1-8.

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