Unmanned system swarm formation control method based on angle measurement

Abstract

The unmanned system cluster formation control method under angle measurement solves the problem of the existing unmanned system formation control that when the distance or relative position cannot be measured, each intelligent agent can only measure the relative angle with its adjacent intelligent agent in its local coordinate system, and belongs to the field of autonomous unmanned system technology. The present invention includes: working scenario one, the intelligent agents in the unmanned system cluster formation cannot use the sensors carried by themselves to perceive other intelligent agents, which is divided into two situations: with GPS signal reception and without GPS signal reception. When GPS signal reception is available, a strategy of simultaneous positioning and formation control is adopted. When there is no GPS signal reception, communication is carried out between intelligent agents to achieve global stability of the formation. Working scenario two, the intelligent agents in the unmanned system cluster formation cannot use the sensors carried by themselves to perceive other intelligent agents, and a method of global rigid construction and a corresponding control gain selection scheme are given.

Description

Technical Field

[0001] The present invention relates to an unmanned system cluster formation control method under angle measurement, belonging to the technical field of autonomous unmanned systems. Background Art

[0002] The application areas of unmanned systems technology have experienced rapid growth over the past decade. This development has significantly transformed human life, with mature applications in search and rescue. Drones and mobile robots can enter dangerous or inaccessible areas to provide assistance to trapped personnel or equipment. Furthermore, drones and unmanned vehicles are being used in the transportation industry for rapid and safe cargo transport. In agriculture, they are being used for tasks such as crop planting, fertilization, and pesticide spraying. In construction, unmanned systems can perform dangerous or repetitive tasks. These systems are bringing about significant changes in numerous fields and are currently developing towards a clustered approach.

[0003] Compared to a single unmanned system, unmanned system swarms offer numerous advantages. First, through collaboration and division of labor, they integrate the performance and resources of multiple unmanned systems, improving the ability and efficiency to complete complex or large-scale missions. Second, through their distributed structure and complementary capabilities, unmanned system swarms enhance overall reliability and robustness. Even if one system fails, the entire system can continue to execute its mission, reducing the risk of mission interruption. Finally, the diverse capabilities and characteristics of different subsystems within an unmanned system swarm enable the system to adapt to diverse mission requirements and environmental changes, resulting in greater mission scalability. Based on these advantages, the enormous application value of unmanned system swarms is being recognized by various countries.

[0004] Based on the different measurement information in the formation controller, the current research and application of unmanned system swarm formations can be divided into: formations based on global position measurement, formations based on relative position measurement, formations based on azimuth measurement, and formations based on angle measurement. The global position measurement-based formation method requires the working scene to provide the swarm system with status information in the global coordinate system. However, in environments such as GPS denial, global position information is difficult for the swarm system to obtain. The relative position measurement-based formation method requires the agents in the swarm to be equipped with relatively expensive ranging sensors such as lidar. Relatively cheap sensors that can only measure relative orientation, such as monocular cameras, cannot support the operation of this type of swarm formation. Formation control based on azimuth measurement uses azimuth angle information between agents, which is easier to measure than the previous two methods. However, the disadvantage of this method is that the coordinate systems of different agents need to be synchronized. Angle-rigid formation can avoid these shortcomings. The information exchange between agents is an angle scalar, which can complete the formation control of swarm systems under angular configurations and has great application value. When existing angle-rigidity-based unmanned system formation control encounters an inability to measure distance or relative position, each agent can only measure the relative angle with its neighboring agents in its local coordinate system. Summary of the Invention

[0005] In view of the problem that in existing unmanned system formation control, when distance or relative position cannot be measured, each intelligent agent can only measure the relative angle with its adjacent intelligent agents in its local coordinate system, the present invention provides an unmanned system cluster formation control method under angle measurement.

[0006] The present invention provides a method for controlling an unmanned system swarm formation using angle measurement. The unmanned system includes N intelligent agents. The method includes: a leading intelligent agent sensing other intelligent agents in the swarm; when an intelligent agent in the swarm formation cannot sense other intelligent agents using its own sensors and the leading intelligent agent detects a GPS signal, the leading intelligent agent obtains its current position in a global coordinate system in real time; and intelligent agents exchange their own positions, desired positions, and measured angles in real time.

[0007] The following agent obtains its own expected position estimate based on the expected position and angle of the leading agent using the expected position estimation law.

[0008] The following agent uses its expected position estimate, the measured angle, and the current position of the leader agent to obtain its current position estimate using the current position estimation law.

[0009] Follow the agent as it moves from its estimated current position to its estimated desired position;

[0010] When the agents in the cluster formation cannot use their own sensors to perceive other agents, and the pilot agent does not detect the GPS signal, the pilot agent divides the agents in the formation into two groups, with the first three agents in one group, to establish the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on the above, a general angular rigid formation of N agents is established, in which there is no position configuration in which three agents are collinear or four agents are cocircular; a control law using relative position measurement is used, in which two of the first three agents are required to have the ability to measure relative distances, and the error between the desired angle formed between the agents in the formation and the measured angle is used as the control target. The formation control of the first three agents is determined using relative position measurement, and based on the formation control of the first three agents, the formation control of the 4th to Nth agents using only angle measurement is determined;

[0011] When the agents in the cluster formation can sense other agents using their own sensors, the leading agent groups the first three agents in the formation into a group and establishes the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on this, a global angle rigid formation of N agents is established, in which each of the global angle rigid formations is 123 The equivalent triangle formation is also related to Δ 123 Congruent; using the control law of relative position measurement, among the first three intelligent agents, two of them are required to have the ability to measure relative distances. The error between the desired angle and the measured angle formed between the intelligent agents in the formation is used as the control target. The relative position measurement is used to determine the formation control of the first three intelligent agents. Based on the formation control of the first three intelligent agents, the formation control of the 4th to Nth intelligent agents with only angle measurement is determined.

[0012] Preferably, the expected position estimation law is:

[0013]

[0014]

[0015] in, is the estimated expected position of the following agent, is the desired position of the pilot agent;

[0016] is the estimated expected velocity of the following agent, is the expected speed of the pilot agent;

[0017]

[0018]

[0019] n f is the number of following agents, n l is the number of pilot agents;

[0020] Angle measurement matrix

[0021] is the angle measurement matrix of the following agent, is the angle measurement matrix of the pilot agent;

[0022] α * is the desired angle of the formation;

[0023]

[0024]

[0025] Following the agent's desired velocity

[0026] v max is the maximum pilot speed, a max It is the maximum value of pilot acceleration.

[0027] As an optimal method, the current position estimation law is:

[0028]

[0029] in:

[0030] is the estimated current position of the following agent, p l (t) is the current position of the pilot agent; s1 is the setting parameter;

[0031]

[0032]

[0033] n f +n l =n, They represent the error parameters of the following agent,

[0034] They represent the disturbance terms corresponding to the following agent respectively;

[0035] For the parameters of the angle measured by the leader agent and the follower agent, construct Same thing.

[0036] Preferably, the control law for following the agent to move from the estimated current position to the estimated desired position is:

[0037]

[0038]

[0039] in: represents the set of following agents;

[0040]

[0041]

[0042]

[0043] α jki , α ijk , α kij They represent the measured angles in triangle Δijk respectively;

[0044] Indicates the angle α kij The rotation matrix of is the set of measurable interior angles, Represents the current position estimate of nodes i, j, and k, I2 represents the identity matrix, j = j1, j2, j3, k = k1, k2, k3.

[0045] As a preferred option, the formation control law for the first three agents in a general angle rigid formation is:

[0046] u1=0

[0047] u2=-s2e2(t)

[0048] u3=-s3e3(t)

[0049] u1, u2, and u3 represent the control quantities of the first three agents, respectively. The first three agents use the relative distance formation error e i (t), i = 1, 2, 3, s2 represents the setting parameter, s3 represents the setting parameter.

[0050] Preferably, the formation control law of the 4th to Nth agents in the general angle rigid formation is:

[0051]

[0052] in, are the angle errors calculated by the j1th agent and the j2th agent based on the measurement information, represents the orientation vector of the j2th agent to the i-th agent;

[0053] Represents the orientation vector of the j1th agent relative to the ith agent.

[0054] As a preferred option, the formation control law for the first three agents in the global angle rigid formation is:

[0055] u1=-s1e1

[0056]

[0057]

[0058] u1, u2, and u3 represent the control quantities of the first three agents, respectively. The first three agents use the relative distance formation error e i (t), i=1,2,3, s1, s2, s3 are all set parameters, b 21 represents the orientation vector of the first agent to the second agent; b 32 Represents the orientation vector of the second agent relative to the third agent.

[0059] Preferably, the formation control law of the 4th to Nth agents in the global angular rigid formation is:

[0060]

[0061] Among them, k i1 ,k i2 ,k i3 ,k i4 is a constant control gain, the orientation measurement of the i-th agent itself

[0062]

[0063]

[0064] φ i represents an intermediate variable, It means that the i-th agent measures the angle of the orientation vector of the j1-th agent and the j2-th agent, It represents the angle of the orientation vector of the j2nd and j3rd agents measured by the i-th agent; represents the desired angle formed between the agents in the formation;

[0065] They represent the distance norms of the j1th, j3th, and j2th agents to the i-th agent respectively.

[0066] The beneficial effects of the present invention are as follows: ① It takes into account the two working conditions of cluster formations: one in which the sensor can perceive other intelligent agents and the other in which the sensor cannot perceive other intelligent agents due to the limitation of the perception range. It is more comprehensive and has application value; ② When other intelligent agents cannot be perceived, such as when the cluster cannot receive GPS signals, 1 to 3 intelligent agents in the cluster act as navigators and implement a control method for relative position measurement. A formation control method based on angle measurement only is designed for 4 to N intelligent agents in the cluster, which improves the robustness of the intelligent agents to coordinate system transformation and measurement noise. If the cluster receives GPS signals, it simultaneously locates and implements formation control, constructs angle constraints, and realizes angle-rigid formation; when other intelligent agents can be perceived, a global rigidity construction method and a control gain selection method are given to realize formation control based on angle measurement only; ③ Compared with distance-rigid formation, angle-rigid formation reduces the demand for intelligent agents to carry sensors, requires fewer sensor measurements, and can reduce the implementation cost of formation control; ④ The designed controller has a simple structure and small computational complexity, and can be actually deployed on intelligent agents to run with low energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is the description method for ∠ijk;

[0068] Figure 2 The geometric relationship for the angle bisector;

[0069] Figure 3 For positioning and control framework, which uses

[0070] Figure 4 It is a method for constructing rigid formations at general angles;

[0071] Figure 5 Add operation diagram for vertex. DETAILED DESCRIPTION

[0072] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments 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 any creative efforts shall fall within the scope of protection of the present invention.

[0073] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0074] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0075] In this embodiment, the intelligent agents of the unmanned system cluster move in a two-dimensional plane and are all regarded as a first-order single integrator dynamic model:

[0076]

[0077] in, Represents the position of the i-th agent, N ≥ 4, the position of the agent is in a fixed global coordinate system ∑ g The following describes, is the control input of the i-th agent.

[0078] Definition of angle-constrained configuration: A new combined structural configuration that describes the positional relationship under angle measurement formation. First, the agents in the formation are regarded as vertices, and the set of vertices is represented as The set of vertices in the formation is greater than or equal to 3.

[0079] The positions of all vertices are represented as It is assumed that the positions of all agents in this embodiment will not overlap.

[0080] Use the ordered triples (i, j, k) to describe the signed angle ∠ijk, and define the angle to be measured counterclockwise, such as Figure 1 As shown, the range is [0,2π).

[0081] The angle is calculated as follows:

[0082]

[0083] in By b ji Vector rotates counterclockwise The resulting vector.

[0084] Denote the angle set as The number of angle sets is M.

[0085] The vertex collection Angle Collection The position vectors p of all agents are combined and named as the angle-constrained configuration, which is expressed as

[0086] Angle-dependent linear equations: Angle-induced linear equations are an efficient way to transform nonlinear positioning problems into linear least squares problems, which describe the geometric relationships of the agents using linear algebraic equations.

[0087] from Figure 2In the Δijk in the equation, the angle-dependent linear equation can be derived.

[0088]

[0089] In Δijk, equation (3) can be expressed as

[0090]

[0091] Among them, the coefficient matrix is ​​only related to the measured internal angle α jki ,α ijk ,α kij related.

[0092]

[0093] Note that when p i ,p j ,p k When three points are collinear, the linear equation fails.

[0094] By writing all the angle-induced linear equations in the formation into a compact set, we can get is defined as the angle measurement matrix as follows.

[0095]

[0096] The row modules of the angle measurement matrix are composed of The triangle index in the column module is The vertex index in . The angle measurement matrix has the following properties, and its rank is at most 2n-4, which is due to The kernel space always contains the translation, rotation and scaling of the position vector p.

[0097] Angular rigidity: Angular rigidity is a key concept in implementing angular measurement formations. Here, we first introduce two prerequisite concepts that help define angular rigidity and global angular rigidity: equivalence and congruence.

[0098] Define two angle constraint configurations and Have the same and For all There is ∠ijk(p i ,p j ,p k )=∠ijk(p' i ,p' j ,p' k ) holds, then the two angle-constrained configurations are said to be equivalent. There is ∠ijk(p i,p j ,p k )=∠ijk(p' i ,p' j ,p' k ) holds, then the two angle-constrained configurations are said to be congruent.

[0099] Global angular rigidity: constraining the configuration to an angle If every equivalent angularly constrained configuration is also congruent to it, then the angularly constrained configuration is said to be globally angularly rigid. When this rigidity property holds only locally, the concept of angular rigidity is given.

[0100] Angle constraint configuration There exists ε>0, and every angle-constrained configuration equivalent to it If the condition ||p'-p||<ε is satisfied and the angle-constrained configuration is congruent with it, then the angle-constrained configuration is said to be angle-rigid.

[0101] General Angular Rigidity: Angular Constraint Configuration The position vector of is general, that is, there is no position configuration where three agents are collinear or four agents are cocircular. The angle-constrained configuration is called general angle-rigid.

[0102] This embodiment provides a method for controlling an unmanned system cluster formation under angle measurement. The unmanned system includes N intelligent agents. The method of this embodiment includes:

[0103] For scenarios where agents in a swarm formation are constrained by their perception range and cannot use their onboard sensors to perceive other agents, or where they are manually determined to be unable to perceive distant agents, agents communicate with each other, exchanging state information, and a formation control law is designed to achieve global stability of formation control under angle measurement. For scenarios where agents in a swarm formation can use their onboard sensors to perceive other agents, or where they are manually determined to be able to perceive close distances, agents do not communicate with each other, and a formation control law is designed to achieve local stability of formation control under angle measurement.

[0104] The relative distances between agents in a cluster are detected. When agents in a cluster formation cannot sense other agents using their own sensors, a formation control law based solely on angle measurement is designed to achieve global stability in the unmanned system's formation control. The agent formations operate under environmental constraints, such as electromagnetic interference, and are divided into operating environments with and without GPS signals. For environments with GPS signals, a strategy of simultaneous positioning and position control is adopted, with agents exchanging information to achieve stable formation control under angle measurement. For environments with GPS signals denied, agents also exchange information, and a control law based on angle measurement is designed to achieve global stability in formation control under angle measurement.

[0105] When the pilot agent detects the GPS signal, it obtains its current position in the global coordinate system in real time. The agents exchange their own positions, expected positions, and measured angles in real time. The follower agent uses the expected position estimation law to obtain its own expected position estimate based on the expected position and angle of the pilot agent.

[0106] The following agent uses its own expected position estimate, the measured angle, and the current position of the leader agent to obtain its own current position estimate using the current position estimation law. The following agent moves from the estimated current position to the estimated expected position as follows:

[0107] The control law is designed by using the “pilot-follower” control structure. The two-dimensional multi-agent system in this invention consists of n l ≥2 pilots and n f >0 follower agents. The leader node is defined as The position of the pilot is The speed of the navigator is Define the node that follows the agent as The position of the following agent is The speed of the following agent is The position of the leader is known to itself, while the position of the followers is unknown. The number of leaders and followers satisfies n f +n l =n.

[0108] use Figure 3 The positioning and control framework shown in the figure is as follows: for the leader, it is equipped with a GPS receiver and can obtain its own position in the global coordinate system in real time. For the followers, an estimation law is first designed to determine their desired positions. Then, a simultaneous positioning and formation control algorithm is designed to drive the following agents from their initial positions to the desired positions while determining their positions.

[0109] According to the state of the navigator, it is divided into three types: a stationary navigator, a navigator moving at a fixed speed, and a navigator moving at a variable speed, and the position of the navigator is represented as p l , the expected position of the navigator is expressed as

[0110] Denote the positions of all following agents as p f , and the expected position of the following agent is recorded as It is determined by the formation desired angle α * and the navigator's desired position The only certainty.

[0111] The desired angle α of the formation * Depend on Definition, desired angle constraint configuration Satisfies the localizability. For a stationary multi-agent system, the localization problem can be modeled as a least squares optimization problem, and the indicator function is

[0112]

[0113] in, To follow the position of the agent In addition, the angle measurement matrix can be Split into pilot part and follower agent Partially satisfied The relationship between. Define the matrix According to the above The splitting logic is expressed as a block matrix:

[0114]

[0115] The expression of each submatrix is ​​as follows:

[0116]

[0117] Will Defined as a multi-agent system The angular positioning matrix of the stationary multi-agent system is When is a non-singular matrix, the multi-agent system is localizable, that is, can be uniquely identified.

[0118] In the present invention, the two states of a stationary leader and a leader moving at a fixed speed are regarded as a special case of a leader moving at a varying speed. The leader moving at a varying speed is taken as an example to design the formation control law and estimation law.

[0119] The navigator moving at a time-varying speed satisfies the following relationship:

[0120]

[0121] And the neighbor agent speed Not necessarily equal.

[0122] Design of formation estimation and control methods for a leader moving at varying speeds, and design of expected position estimation and expected velocity estimation laws for follower agents:

[0123] The desired position of the leader can be expressed as:

[0124]

[0125] where κ(t) is a non-zero scaling factor, is the rotation matrix of the angle θ(t), is the translation vector, and by appropriately selecting θ(t) and κ(t) can perform the desired translation, rotation, and scaling formation maneuvers.

[0126] For example, choose θ(t) = θ(0) + ω1t, and let If the value is constant, the formation system will perform circular formation movement. Let |a1|≠|b1| be a non-zero constant, ω2,κ,θ be constant values, and the formation system will perform elliptical formation motion.

[0127] The leader moves at a time-varying speed and needs to keep track of the desired position of the following agent. and expected movement speed Make an estimate.

[0128] Design the expected position estimation law and expected velocity estimation law of the following agent:

[0129]

[0130]

[0131] is the estimated expected position of the following agent, is the desired position of the pilot agent;

[0132] is the estimated expected velocity of the following agent, is the expected speed of the pilot agent;

[0133]

[0134]

[0135] n f is the number of following agents, n l is the number of pilot agents;

[0136] Angle measurement matrix

[0137] is the angle measurement matrix of the following agent, is the angle measurement matrix of the pilot agent;

[0138] α * is the desired angle of the formation;

[0139] The expected position estimation law designed by formula (12) Requires expected angle information and the expected position estimate sent by the neighboring agents to the i-th agent The parameters in formula (12) and (13) satisfy:

[0140]

[0141]

[0142] represents the expected speed of the following agent. The designed estimation law can make the expected position estimation of the following agent and expected speed estimation Converges to in finite time and v max is the maximum pilot speed, a max It is the maximum value of pilot acceleration.

[0143] Simultaneous positioning and formation control algorithm design:

[0144] The position estimation law is designed to estimate the position of the following agent in the global coordinate system as shown in the formula, and the formation control law is designed to make the following agents converge to their desired positions as shown in the formula.

[0145]

[0146]

[0147] in:

[0148]

[0149]

[0150] is the estimated current position of the following agent, p l (t) is the current position of the pilot agent; s1 is the setting parameter;

[0151] n f +n l =n, They represent the error parameters of the following agent, Respectively

[0152] Follow the disturbance term corresponding to the agent;

[0153] For the parameters of the angle measured by the leader agent and the follower agent, construct and Same thing.

[0154] Considering that the estimation law designed by formula (12) and formula (13) converges in a finite time, it can be used after the finite convergence time. to replace

[0155] The simultaneous positioning formation control algorithm of the i-th following agent is shown in Equations (20) and (21):

[0156]

[0157]

[0158]

[0159] in: represents the set of following agents;

[0160]

[0161]

[0162]

[0163] α jki , α ijk , α kij They represent the measured angles in triangle Δijk respectively;

[0164] Indicates the angle α kij The rotation matrix of is the set of measurable interior angles, Represents the current position estimate of nodes i, j, and k, I2 represents the identity matrix, j = j1, j2, j3, k = k1, k2, k3.

[0165] The estimators (12)-(13) and controllers (16)-(17) designed above may cause the system to converge slowly due to the use of the tanh function. Therefore, we can try to replace it with the following function:

[0166]

[0167] When the agents in the cluster formation cannot use their own sensors to perceive other agents, and the leading agent does not detect the GPS signal, the agents in the formation are divided into two groups, with the first three agents in one group, to establish the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on the above, a general angular rigid formation of N agents is established, in which there is no position configuration in which three agents are collinear or four agents are cocircular. A control law using relative position measurement is used. Among the first three agents, two of them need to have the ability to measure relative distances. The error between the desired angle formed between the agents in the formation and the measured angle is used as the control target. The formation control of the first three agents is determined using relative position measurement. Based on the formation control of the first three agents, the formation control of the 4th to Nth agents using only angle measurement is determined, specifically including:

[0168] In an environment without GPS signals, the agents in the formation are divided into two groups, the first three agents in one group and 4-N agents in another group. The general angle rigid formation of N agents is established according to the following two steps: Figure 4 shown.

[0169] Step 1: Use three angle constraints Create the first triangle formation Δ 123 .

[0170] Step 2: Construct angle constraints based on the original triangle formation (when the agent has 1 and 2 neighbors) or angle constraints (When agent 4 has three neighbors 1, 2, and 3), add the fourth agent by constructing the angle constraint as above. Further, for the kth agent, use the same construction method to construct the angle constraint or Among them, j1,j2,j3∈{1,...,k-1}.

[0171] In order to ensure the uniqueness of the position of each agent in the formation, for the newly added i-th agent in the formation (i>3), the angle constraint is constructed It is required that the positions of {i, j1, j2, j3} satisfy generality, that is, the formation satisfies general angular rigidity.

[0172] The control law design is carried out in two steps.

[0173] Step 1: Design of control laws for the first three agents’ formation

[0174] We first design a formation control law for the first three agents using only angle measurements, achieving the following local stability control objectives:

[0175]

[0176] in, represents the desired angle between the agents in the formation,

[0177] Indicates the error in the angle definition.

[0178] Considering the control objective of Equation (22), the control law for the formation of the first three agents that only measure the angle is designed:

[0179]

[0180] In a closed-loop system, the formation error defined by angle is used It converges to 0 at an exponential rate.

[0181] The control law designed by equation (23) that only measures angles cannot form a formation with a specified size and direction. In order to fix the size and direction of the formation formed by the agents in the formation, a control law using relative position measurement is designed. Among the first three agents, two of them need to have the ability to measure relative distances, so as to achieve the following global stability of the control objective:

[0182]

[0183] Among them, ξ 21 ξ 32 ξ 13 are the expected position vectors between agents 2 and 1, between agents 3 and 2, and between agents 1 and 3, respectively. They are used to determine the formation composition between agents 1, 2, and 3. Considering the control objective of equation (24), the formation control law for the first three agents using relative position measurement is designed:

[0184]

[0185] In the closed-loop system, the formation error e defined by relative distance is usedi (t),i=1,2,3 will converge to 0 at an exponential rate.

[0186] Step 2: Design of control law for 4-N agents with only angle measurement

[0187] Based on the formation of the first three agents, the control law for the fourth agent is designed:

[0188]

[0189] in, are the angular errors measured by the first and second agents in the system, α 412 It is measured by the azimuth sensor of the first agent and sent to the fourth agent via wireless communication.

[0190]

[0191] Similarly, α 421 It is measured by the azimuth sensor of the second agent and sent to the fourth agent via wireless communication.

[0192]

[0193] Extend Equation (26) to the control law of the i-th agent:

[0194]

[0195] in, are the angle errors calculated by the j1th agent and the j2th agent in the system based on the measurement information, The angle measured by the azimuth sensor of the j1th agent and sent to the i-th agent via wireless communication, The angle measured by the azimuth sensor of the j2th agent and sent to the i-th agent via wireless communication.

[0196] For the i-th agent, the control law of formula (29) is adopted, and the initial position p of the agent in the formation is i (0), If the generality is satisfied, the angle error The global convergence is 0. Note that in the controller (26), since agents 1 and 2 are required to communicate with agent 4, this inevitably introduces communication delay. Assuming that the communication delay between agents is a constant value τ, the controller (26) needs to be rewritten as

[0197]

[0198] Simulations show that when the delay τ is small enough, the system can still converge, especially when the expected formation is static or moving at a constant speed, the stability of the formation system is not affected by the small delay τ.

[0199] When the agents in the cluster formation can sense other agents using their own sensors, the first three agents form a group and establish the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on the above, a global angular rigid formation of N agents is established. Using the control law of relative position measurement, two of the first three agents are required to have the ability to measure relative distances. The error between the desired angle and the measured angle formed between the agents in the formation is used as the control target. The formation control of the first three agents is determined using relative position measurement. Based on the formation control of the first three agents, the formation control of the 4th to Nth agents using only angle measurement is determined:

[0200] When the distance is close, a formation control law based on angle measurement alone is designed to achieve local stability of the unmanned system formation control. In this case, the intelligent agent formation is subject to environmental constraints such as communication interference and restrictions during operation, and there is no information exchange between intelligent agents.

[0201] The formation control in this case is divided into two stages: the first stage constructs the global rigidity, and the second stage calculates the control gain to perform formation control.

[0202] Global rigid construction method:

[0203] In order to ensure that the configuration of the entire formation is uniquely determined after the unmanned system achieves stable control at certain angles, we need to study how to construct a rigid angle-constrained configuration. Add vertex i to it to get the set And define the added vertex set as

[0204] Therefore, this embodiment starts from Δ123 and takes the addition of unmanned system 4 as an example to construct the angle constraint in and Shared vertices 2 and 4, under angle constraints Ensure that the unmanned system 4 is in the arc On sports, Ensure that the unmanned system 4 is in the arc Upward movement, arc With arc There is only one intersection vertex 4, so under the angle constraint and This ensures that the position of the unmanned system 4 is uniquely determined. The same steps can be used to extend this addition method to the i-th agent. The vertex addition method for the fourth agent and the vertex addition method for the i-th agent are shown in the figure:

[0205] Control gain calculation and formation control method:

[0206] After giving the method of global rigid construction, the control gain calculation method for realizing the above-mentioned global angular rigid formation is given, and finally the local stability of the angular rigid formation control is achieved under close distance conditions.

[0207] Formation control is divided into two steps: formation control of the first three agents and formation control of the remaining agents (4-N agents).

[0208] Step 1: Formation control of the first three agents

[0209] We first design a formation control law for the first three agents using only angle measurements, achieving the following local stability control objectives:

[0210]

[0211] in, represents the desired angle between the agents in the formation, Indicates the error in the angle definition.

[0212] Considering the control objective of formula (30), the control law for the formation of the first three agents that only measure the angle is designed:

[0213]

[0214] In a closed-loop system, the formation error defined by angle is used It converges to 0 at an exponential rate.

[0215] The control law designed by equation (31) that only measures angles cannot form a formation with a specified size and direction. In order to fix the size and direction of the formation formed by the agents in the formation, a control law using relative position measurement is designed. Among the first three agents, two of them need to have the ability to measure relative distances, so as to achieve the following global stability of the control objective:

[0216] Given the control objectives of the first three agents:

[0217]

[0218] Among them, ξ 21 ξ 32 ξ 13These are the expected position vectors between agents 2 and 1, between agents 3 and 2, and between agents 1 and 3. They are used to determine the formation composition between agents 1, 2, and 3, and to design the control laws for the first three agents:

[0219]

[0220] The local gradual stability of the formation system can be achieved.

[0221] Step 2: 4-N Agent Formation Control

[0222] Add 4-N agents to the formation according to the Type I or Type II vertex addition scheme, and design the control law to achieve local stability of formation control:

[0223] For the i-th agent, the control law is designed as follows:

[0224]

[0225] where k i1 ,k i2 ,k i3 ,k i4 is a constant control gain, the selection of which needs to satisfy the rule. The i-th agent only needs to measure its own position. There is no need to exchange information with neighboring agents.

[0226] When i=4, the control law is as follows:

[0227]

[0228] Taking the fourth agent as an example, we introduce the control gain k 41 ,k 42 ,k 43 ,k 44 The selection method is as shown in formula (36):

[0229]

[0230]

[0231] Among them, l jk =||p j -p k ||.

[0232] Extended to the i-th agent, the control gain selection method is as follows (38):

[0233]

[0234]

[0235] This embodiment designs control laws based on two working scenarios: the inability of agents in an unmanned system cluster formation to perceive other agents using their own sensors, and the ability of agents in a cluster formation to perceive other agents using their own sensors. These control laws include: Working Scenario 1: The inability of agents in an unmanned system cluster formation to perceive other agents using their own sensors. This is divided into two situations: with and without GPS signal reception. When GPS signals are received, a strategy of simultaneous positioning and formation control is adopted. When GPS signals are not received, communication is performed between agents to achieve global stability of the formation. Working Scenario 2: The agents in an unmanned system cluster formation can perceive other agents using their own sensors. A global rigidity construction method and a corresponding control gain selection scheme are proposed.

[0236] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments.

Claims

1. An unmanned system cluster formation control method based on angle measurement, characterized in that: The unmanned system includes N intelligent agents, and the method includes: a leading intelligent agent sensing other intelligent agents in the cluster; when an intelligent agent in the cluster formation cannot sense other intelligent agents using its own sensors and the leading intelligent agent detects a GPS signal, the leading intelligent agent obtains its current position in the global coordinate system in real time; and the intelligent agents exchange their own positions, desired positions, and measured angles in real time; The following agent obtains its own expected position estimate based on the expected position and angle of the leading agent using the expected position estimation law. The following agent uses its expected position estimate, the measured angle, and the current position of the leader agent to obtain its current position estimate using the current position estimation law. Follow the agent as it moves from its estimated current position to its estimated desired position; When the agents in the cluster formation cannot use their own sensors to perceive other agents, and the pilot agent does not detect the GPS signal, the pilot agent divides the agents in the formation into two groups, with the first three agents in one group, to establish the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on the above, a general angular rigid formation of N agents is established, in which there is no position configuration in which three agents are collinear or four agents are cocircular; a control law using relative position measurement is used, in which two of the first three agents are required to have the ability to measure relative distances, and the error between the desired angle formed between the agents in the formation and the measured angle is used as the control target. The formation control of the first three agents is determined using relative position measurement, and based on the formation control of the first three agents, the formation control of the 4th to Nth agents using only angle measurement is determined; When the agents in the cluster formation can sense other agents using their own sensors, the leading agent groups the first three agents in the formation into a group and establishes the first triangle formation Δ 123 ; The 4th to Nth agents form a group, and each agent is in a triangle formation Δ 123 Based on this, a global angle rigid formation of N agents is established, in which each of the global angle rigid formations is 123 The equivalent triangle formation is also related to Δ 123 Congruent; using the control law of relative position measurement, among the first three intelligent agents, two of them are required to have the ability to measure relative distances. The error between the desired angle and the measured angle formed between the intelligent agents in the formation is used as the control target. The relative position measurement is used to determine the formation control of the first three intelligent agents. Based on the formation control of the first three intelligent agents, the formation control of the 4th to Nth intelligent agents with only angle measurement is determined.

2. The unmanned system cluster formation control method based on angle measurement according to claim 1 is characterized in that: The expected position estimation law is: in, is the estimated expected position of the following agent, is the desired position of the pilot agent; is the estimated expected velocity of the following agent, is the expected speed of the pilot agent; n f is the number of following agents, n l is the number of pilot agents; Angle measurement matrix is the angle measurement matrix of the following agent, is the angle measurement matrix of the pilot agent; α * is the desired angle of the formation; Following the agent's desired velocity v max is the maximum pilot speed, a max is the maximum value of the pilot acceleration, n f +n l =n.

3. The unmanned system cluster formation control method under angle measurement according to claim 2, characterized in that: The current position estimation law is: in: is the estimated current position of the following agent, p l (t) is the current position of the pilot agent; s1 is the setting parameter; I2 represents the identity matrix; They represent the error parameters of the following agent, They represent the disturbance terms corresponding to the following agent respectively; For the parameters of the angle measured between the leader agent and the follower agent, construct and Same thing.

4. The unmanned system cluster formation control method based on angle measurement according to claim 3 is characterized in that: The control law for the following agent to move from the estimated current position to the estimated desired position is: in: represents the set of following agents; α jki , α ijk , α kij They represent the measured angles in triangle Δijk respectively; Indicates the angle α kij The rotation matrix of is the set of measurable interior angles, Represents the estimated current position of nodes i, j, and k, j = j1, j2, j3, and k = k1, k2, k3.

5. The unmanned system cluster formation control method based on angle measurement according to claim 1, characterized in that: The formation control laws for the first three agents of the general angle rigid formation are: u1＝0 u2=-s2e2(t) u3=-s3e3(t) u1, u2, and u3 represent the control quantities of the first three agents, respectively. The first three agents use the relative distance formation error e i (t), i = 1, 2, 3, s2 represents the setting parameter, s3 represents the setting parameter.

6. The unmanned system cluster formation control method based on angle measurement according to claim 5, characterized in that: The formation control law of the 4th to Nth agents in the general angle rigid formation is: in, are the angle errors calculated by the j1th agent and the j2th agent based on the measurement information, represents the orientation vector of the j2th agent to the i-th agent; Represents the orientation vector of the j1th agent relative to the ith agent.

7. The unmanned system cluster formation control method based on angle measurement according to claim 1, characterized in that: The formation control law for the first three agents of the global angle rigid formation is: u1=-s1e1 u1, u2, and u3 represent the control quantities of the first three agents, respectively. The first three agents use the relative distance formation error e i (t), i=1,2,3, s1, s2, s3 are all set parameters, b 21 represents the orientation vector of the first agent to the second agent; b 32 Represents the orientation vector of the second agent relative to the third agent.

8. The unmanned system cluster formation control method based on angle measurement according to claim 7, characterized in that: The formation control law of the 4th to Nth agents in the global angle rigid formation is: Among them, k i1 ,k i2 ,k i3 ,k i4 is a constant control gain, the orientation measurement of the i-th agent itself φ i represents the intermediate variable, It means that the i-th agent measures the angle of the orientation vector of the j1-th agent and the j2-th agent, It represents the angle of the orientation vector of the j2nd and j3rd agents measured by the i-th agent; represents the desired angle formed between the agents in the formation; They represent the distance norms of the j1th, j3th, and j2th agents to the i-th agent respectively.

9. A computer-readable storage device storing a computer program, characterized in that: When the computer program is executed, the unmanned system cluster formation control method under angle measurement as described in any one of claims 1 to 8 is implemented.

10. An unmanned system cluster formation control device under angle measurement, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that: The processor executes the computer program to implement the unmanned system cluster formation control method under angle measurement as described in any one of claims 1 to 8.

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