A multi-circle formation control method for a nonholonomic constraint vehicle based on a directional angle

Abstract

A multi-circle formation control method for nonholonomic vehicles based on directional angle is proposed, which belongs to the field of multi-vehicle cooperative control. The relative information of adjacent vehicles in the sensor network is collected by on-board sensors and visual markers. According to the collected relative information, i.e. the directional angle between vehicles, a virtual center vehicle and a virtual leader vehicle are designed, and a control law with distributed saturated input is designed according to these information. Without communication equipment, the linear velocity and angular velocity of the vehicle are calculated in real time by the control law, ensuring that all vehicles maintain the desired radius, speed and spacing. The asymptotic stability of the system is proved by Lyapunov stability theory and linear matrix inequality method, and the effectiveness of the method is verified by numerical simulation. This method is suitable for complex traffic environments such as autonomous driving and regional monitoring, and has wide application prospects.

Description

Technical Field

[0001] The present invention belongs to the field of multi-vehicle cooperative control, and in particular to a multi-vehicle multi-circle formation control method based on a non-holonomic constraint vehicle multi-circle formation. Background Art

[0002] With the continuous development of intelligent vehicle technology, the limitations of a single intelligent vehicle in complex traffic environments are becoming increasingly apparent. Consequently, research on multi-vehicle cooperative control has garnered increasing attention. Compared to single intelligent vehicle control, multi-vehicle cooperative systems, through the collaborative cooperation of multiple intelligent vehicles, can achieve higher efficiency, greater robustness, and flexible spatial distribution in complex traffic scenarios.

[0003] Circular formation control, as a key research direction in this field, has been widely used in scenarios such as autonomous driving and drone formations. Circular formations can maintain a stable geometric shape and are suitable for tasks such as target tracking and area monitoring. Multi-circular formation control is further studied on this basis. Reference 1 (J Zhang, X Shao, W Zhang, Z Zuo, Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles: A path-following framework [J]. Defence Technology, 2024, 31: 278-287.) proposes a multi-circular path following formation control method with reinforced transient profiles to solve the collaborative path tracking problem of non-holonomic constrained vehicles connected by a directed graph on an implicit multi-circular path. Reference 2 (X Shao, J Zhang, W Zhang and Z Zuo, Robust path-following control for multiple autonomous vehicles along an implicit elliptical curve[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(11): 6778-6791.) proposes a robust path tracking control method based on projection arc length, which effectively solves the collaborative path tracking problem of multiple autonomous vehicles along an implicit elliptical curve. Summary of the Invention

[0004] The application aims at the problem of multi-circle formation control of nonholonomic vehicles, and provides a multi-circle formation control method for nonholonomic vehicles based on direction angle.

[0005] To achieve the above-mentioned application purposes, the application provides the following technical solutions.

[0006] A multi-circle formation control method for nonholonomic vehicles based on direction angle comprises the following steps.

[0007] 1) Establishing a single vehicle kinematics model and giving nonholonomic constraints.

[0008] 2) Assuming that communication equipment is not available, each vehicle is equipped with a sensor to collect relevant information in real time.

[0009] 3) Describing the information interaction form between vehicle sensors based on graph theory, each vehicle can only measure the relative information of adjacent vehicles in the sensor network, and establishing a formation control objective function.

[0010] 4) Designing a multi-circle formation control law for nonholonomic vehicles with distributed saturated input, and calculating the linear velocity and angular velocity required for formation control in real time.

[0011] 5) Substituting the control law into the kinematics model established in step 1), calculating the linear velocity and angular velocity of the vehicle in real time, and realizing the multi-circle formation control of the vehicle.

[0012] In step 1), the establishment of a single vehicle kinematics model and the giving of nonholonomic constraints specifically comprises the following steps.

[0013] (1) The vehicle queue is composed of N+1 vehicles numbered 0, 1, …, N, wherein the No. 0 vehicle is the target, i.e. the center of the multi-circle formation, and the No. 1, …, N vehicles are formation vehicles.

[0014] (2) Establishing a single vehicle kinematics model and constraining the linear velocity and angular velocity thereof.

[0015] In step 2), the real-time collection of relevant information by the vehicle-mounted sensor refers to the real-time collection by a camera or a laser radar, and specifically comprises the following steps.

[0016] The vehicle periodically observes target or neighbor vehicle information through vehicle-mounted sensors and visual markers, assuming that only part of the vehicles can directly observe the target through vehicle-mounted sensors, and the rest of the vehicles can only obtain the azimuth angle and relative heading angle between them and the vehicle provided with visual markers through vehicle-mounted sensors.

[0017] In step 3), the specific steps of describing the information interaction form between vehicle sensors based on graph theory and establishing the formation control objective function can be:

[0018] (1) Defining the vehicle sensor network topology based on graph theory, i.e. the vehicles that each vehicle can observe, and giving the definitions of adjacency matrix and Laplacian matrix;

[0019] (2) Setting the difference between the vehicle-target distance and the expected distance, the difference between the current azimuth angle and the expected azimuth angle, and the difference between the separation angle with other adjacent vehicles and the expected separation angle as independent variables, and establishing a formation control objective function to achieve the expected formation shape.

[0020] In step 4), the specific steps of designing a non-holonomic constraint vehicle multi-circle formation control law with distributed saturated input and real-time solving the linear velocity and angular velocity required for formation control can be:

[0021] (1) Designing a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicle converge to the expected radius and the expected spacing;

[0022] (2) Designing a distributed saturated input control law to calculate the linear velocity and angular velocity of the vehicle;

[0023] (3) Based on Lyapunov stability theory and linear matrix inequality method, it is proved that the vehicle can converge to the expected radius and the expected spacing, and the sufficient condition for guaranteeing the asymptotic stability of the vehicle queue control system is obtained.

[0024] The present application collects and measures the relative information of adjacent vehicles in the sensor network through vehicle-mounted sensors and visual markers, according to the collected relative information, i.e. the azimuth angle between vehicles, and by designing a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicle converge to the expected radius and the expected spacing, and according to the design of a control law with distributed saturated input, the control objective of multi-circle formation control is achieved.

[0025] Compared with the prior art, the present application has the following outstanding technical effects and advantages:

[0026] 1. No need to rely on communication equipment: The present application realizes the information interaction between vehicles through vehicle-mounted sensors (such as cameras, laser radars) and visual markers, avoiding the limitation of relying on communication equipment in traditional methods. Not only reduces the system cost, but also improves the adaptability and robustness in complex electromagnetic environment.

[0027] 2. Adaptation to non-holonomic vehicles: The invention designs a control law with distributed saturated inputs, taking into account the characteristics of non-holonomic vehicles (such as intelligent cars, which can only move forward and turn). This control law fully considers the kinematic constraints of the vehicle, ensuring the effectiveness and practicality of the control strategy.

[0028] 3. Distributed control strategy: The invention uses a distributed control strategy, where each vehicle only needs to make decisions based on the information of adjacent vehicles. This strategy not only improves the flexibility and scalability of the system, but also reduces the computational burden and communication requirements of the central controller.

[0029] 4. Design of virtual center vehicle and virtual leader vehicle: By introducing the concepts of virtual center vehicle and virtual leader vehicle, the invention provides a clear convergence target and direction for the vehicles. This allows the vehicles to more easily converge to the desired radius and spacing, thereby maintaining a stable formation.

[0030] 5. Information interaction description based on graph theory: The invention uses graph theory to describe the form of information interaction between vehicle sensors, providing a powerful mathematical tool for system modeling and analysis. By defining the adjacency matrix and Laplacian matrix, the connection relationship and communication topology between vehicles can be clearly described.

[0031] 6. The invention not only solves the communication dependency problem in traditional methods, but also adapts to the characteristics of non-holonomic vehicles, achieving efficient and stable multi-vehicle cooperative control. It is suitable for complex traffic environments such as autonomous driving and regional monitoring, and has wide application prospects. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is the flowchart of the formation control method of the embodiment of the invention.

[0033] Figure 2 is the schematic diagram of a certain vehicle and its virtual center vehicle and virtual leader vehicle of the embodiment of the invention.

[0034] Figure 3 is the sensor network topology of the embodiment of the invention.

[0035] Figure 4 is the 50-second vehicle trajectory numerical simulation diagram of the embodiment of the invention.

[0036] Figure 5 is the vehicle separation angle numerical simulation diagram of the embodiment of the invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical scheme and advantages of the present application more clear, the following embodiments will be further described in combination with the drawings. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application. On the contrary, the present application covers any substitution, modification, equivalent method and scheme defined by the claims within the essence and scope of the present application.

[0038] The flowchart of the platoon control method of the embodiment of the present application is shown in Figure 1 The present application aims to solve the multi-circle platoon control problem of nonholonomic vehicles, and proposes a control method based on direction angle. The relative information of adjacent vehicles is collected through vehicle-mounted sensors and visual markers, a virtual center vehicle and a virtual leader vehicle are designed, and a control law with distributed saturated input is designed accordingly to achieve multi-circle platoon control. The platoon control system of the present application assumes that only part of the vehicles can directly observe the target through vehicle-mounted sensors, and the remaining vehicles can only obtain the azimuth angle and relative heading angle between them and the vehicles provided with visual markers. Assuming that the kth vehicle is the neighbor vehicle of the ith vehicle, the ith vehicle can obtain the direction angle between it and the virtual follower of the designed kth vehicle Assuming that the ith vehicle can observe the target, the azimuth angle b i0 between it and the target is obtained; assuming that the ith vehicle cannot observe the target, the direction angle b between it and the virtual center vehicle of the designed kth vehicle is obtained. According to the obtained information, a control law with distributed saturated input is designed, and the ideal angular velocity ω i and ideal linear velocity v i of the ith vehicle are calculated, so as to complete the multi-circle platoon control.

[0039] The embodiment of the present application specifically comprises the following steps:

[0040] Step 1: Establishing single vehicle kinematics model and nonholonomic constraint: the vehicle platoon is composed of N+1 vehicles numbered 0, 1, …, N, wherein the 0th vehicle is the target, i.e. the center of the multi-circle platoon, and the 1st, …, Nth vehicles are platoon vehicles. The single vehicle kinematics model is established, the position, heading angle, linear velocity and angular velocity of the vehicle are considered, and the linear velocity and angular velocity are subjected to nonholonomic constraint.

[0041] The schematic diagram of a vehicle and its virtual center vehicle and virtual leader vehicle of the embodiment of the present application is shown in Figure 2 , wherein θ i represents the heading angle of the ith vehicle relative to the inertial system, b i0 represents the azimuth angle between the ith vehicle and the target, b ik represents the azimuth angle between the ith vehicle and the kth vehicle, and d i0denotes the distance between the ith vehicle and the target, the virtual leader vehicle k f is set at the position of the vehicle k in the vehicle coordinate system (0, r kd -r id ) of the vehicle k c is set at the position of the vehicle k in the vehicle coordinate system (0, r kd ) of the vehicle k.

[0042] Step 1.1: Considering the position, heading angle, linear velocity and angular velocity of the vehicle, a kinematic model of the ith vehicle in the vehicle platoon is established:

[0043]

[0044] where p i = [x i y i ] T denotes the absolute position of the ith vehicle, θ i denotes the heading angle of the ith vehicle relative to the inertial system, u i = [v i ω i ] T denotes the linear velocity and angular velocity of the ith vehicle.

[0045] Step 1.2: The non-holonomic constraint of each vehicle is given, i.e. the following physical velocity limits are given:

[0046] v i ∈ [v min v max ], ω i ∈ [-ω max ω max ]#(2)

[0047] where v min denotes the minimum value of the linear velocity, v max denotes the maximum value of the linear velocity, and ω max denotes the maximum value of the angular velocity.

[0048] Step 1.3: According to the geometric relationship of Figure 2 , it can be known that:

[0049] b ik = atan2(-(x k -x i )sinθ i +(y k -y i )cosθ i ,(x k -x i )cosθ i +(y k -yi )sinθ i )#(3)

[0050] When -(x k -x i )sinθ i +(y k -y i )cosθ i = 0 and (x k -x i )cosθ i +(y k -y i )sinθ i = 0, b ik = 0.

[0051] where b ik denotes the direction angle between the i-th vehicle and the k-th vehicle, (x i , y i ) denotes the absolute position of the i-th vehicle, (x k , y k ) denotes the absolute position of the k-th vehicle, and θ i denotes the heading angle of the i-th vehicle relative to the inertial system.

[0052] Step 2: Information collection: assuming that communication devices are not available, each vehicle is equipped with on-board sensors (such as cameras, lidar) to collect information in real time, and relevant information is collected in real time through on-board sensors.

[0053] Step 2.1: Vehicles periodically observe target or neighbor vehicle information through on-board sensors and visual markers, mainly including azimuth angle and relative heading angle between vehicles.

[0054] Step 2.2: Assuming that only part of the vehicles can directly observe the target through on-board sensors, the rest of the vehicles can only obtain the azimuth angle and relative heading angle between them and the vehicles provided with visual markers through on-board sensors.

[0055] Step 3: Information interaction and formation control objective function based on graph theory: graph theory is used to describe the form of information interaction between vehicle sensors, and the vehicle sensor network topology is defined, including adjacency matrix and Laplacian matrix. Each vehicle can only measure the relative information of adjacent vehicles in the sensor network, and the distance difference between the vehicle and the target vehicle, the azimuth angle difference, and the separation angle difference with adjacent vehicles are set as independent variables, and a formation control objective function is established to achieve the desired formation shape. Figure 3 Sensor network topology for the invention embodiment, where 0 denotes the target center, and 1-6 denote the formation vehicles.

[0056] Step 3.1: Based on graph theory, define the vehicle sensor network topology as a directed graph A finite set of nodes Represents N vehicles in a platoon, and the edge set It contains a directed edge from j to i, that is, the i-th car can observe the j-th car, describing the connectivity relationship of the sensor network.

[0057] Step 3.2: Add the target, i.e. the center of the multi-circle formation, as node 0 to the directed graph. Defined as Finite set of nodes and edge sets Define the set of vehicle nodes observable by the i-th vehicle and And make the following assumptions:

[0058] Assumption 1: Directed Graph Contains a directed spanning tree with node 0 as its root.

[0059] Assumption 2: Graph Contains a directed spanning tree with a root node and no directed edges from other nodes pointing to the root node.

[0060] Assumption 3: Directed Graph The subgraph of does not contain directed cycles.

[0061] Step 3.3: Define the adjacency matrix of the directed graph When vehicle i can observe vehicle j, m ij =1; otherwise m ij = 0. Define the Laplace matrix as follows:

[0062]

[0063] Step 3.4: Define vector a=col(a1,…,a N ), where a i <a i+1 <2π, i=1,…,N-1, then the separation angle between the two vehicles can be defined as a ji =a j -a i , i≠j. Set the difference between the distance between the vehicle and the target and the expected distance, the difference between the current azimuth and the expected azimuth, and the separation angle from other adjacent vehicles and the expected separation angle as independent variables, and establish the formation control objective function, which satisfies:

[0064]

[0065] Among them, d i0denotes the distance between the ith vehicle and the target, r id denotes the desired distance between the ith vehicle and the target; b i0 denotes the azimuth angle between the ith vehicle and the target, is the desired azimuth angle between the ith vehicle and the target; denotes the current separation angle between the ith vehicle and the jth vehicle, which is adjacent to the ith vehicle in the sensor network, a ij denotes the desired separation angle between the ith vehicle and the jth vehicle, wrapTo2π(·) denotes a function that can limit the angle to [0, 2π], denotes the set of platoon vehicle nodes, denotes the set of nodes that the ith vehicle can observe in the sensor network.

[0066] Step 4: Design a distributed saturated input control law: design a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicles converge to the desired radius and desired spacing. Design a multi-circle platoon control law for non-holonomic constrained vehicles with distributed saturated input, and according to the collected relative information and the position of the virtual vehicle, real-time calculate the linear velocity and angular velocity required for platoon control. Using Lyapunov stability theory and linear matrix inequality method, it is proved that the vehicle can converge to the desired radius and spacing, and the asymptotic stability of the vehicle queue control system is ensured.

[0067] Step 4.1: Design a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicles converge to the desired radius and desired spacing; for any vehicle i, each neighbor vehicle k is assigned a virtual leader vehicle k f , the position of vehicle k f is at the vehicle coordinate system (0, r kd -r id ) of vehicle k. Further assume that vehicle i cannot directly observe the target, then each neighbor vehicle k of vehicle i is assigned a virtual center vehicle k c , the position of vehicle k c is at the vehicle coordinate system (0, r kd )

[0068] .

[0069] Step 4.2: The designed control law with distributed saturated input is as follows:

[0070] where v i denotes the ideal linear velocity of the ith vehicle calculated according to the control law, ω i denotes the ideal angular velocity of the ith vehicle calculated according to the control law, ω id denotes the desired angular velocity of the ith vehicle, rid represents the expected distance of the i-th vehicle, Indicates that the kth vehicle is the neighbor vehicle of the ith vehicle, represents the direction angle between the i-th vehicle and the virtual following vehicle of the designed k-th vehicle, a ki represents the expected separation angle between the i-th vehicle and the k-th vehicle, represents the direction angle between the i-th vehicle and the virtual center vehicle of the designed k-th vehicle, b i0 represents the azimuth angle between the i-th vehicle and the target, k1, k2 and μ represent the parameters to be designed.

[0071] When the i-th vehicle can directly observe the target, α i =0,β i =1; otherwise, β i =0. Among them, It represents the number of cars that the i-th car can observe.

[0072] In order to satisfy the nonholonomic constraints, the values ​​of k1 and k2 should satisfy: k2∈(0,ω max -ω id -k1); where v min Indicates the minimum value of linear velocity, v max Indicates the maximum value of linear velocity, ω max Indicates the maximum value of angular velocity; r id represents the expected distance, ω id represents the expected angular velocity of the i-th vehicle.

[0073] Step 4.3: According to the given control law, prove that the vehicle with direct observation of the target can converge to the desired circle.

[0074] The closed-loop system is defined as follows:

[0075]

[0076] When the i-th vehicle can directly observe the target, the vehicle angular velocity control law is as follows:

[0077]

[0078] Substituting equation (10) into equation (9), the system can be rewritten as:

[0079]

[0080] The Lyapunov function is defined as follows:

[0081]

[0082] where x i =[d i0 b i0 ] T .

[0083] V i (x i ) in d i0 = 0 is continuous but not differentiable. But even if there is a moment t0 such that d i0 = 0, but the controller is still effective at this moment and the speed remains greater than the lower speed limit v in the nonholonomic constraint min , which means d i0 It will not always stay at 0, so V i (x i ) is piecewise continuously differentiable along the direction of the solution of systems (8) and (11). For this case, i (x i ) Take the upper right time derivative along the direction of the solution of systems (8) and (11).

[0084] D + V i (x i )=-k2r id d i0 cos 2 b i0 ≤0#(13)

[0085] Therefore, S i ={x i |D + V i (x i )=0} relative to d i0 ∈[0,+∞) and b i0 ∈[-π,π) is globally asymptotically stable, i.e., d i0 cos 2 b i0 = 0. Since d i0 It will not always stay at 0, then there is cos 2 b i0 =0, that is, b i0 will converge to or According to the system's dynamic equations (8) and (11), we can obtain:

[0086]

[0087] After analysis, we know that d i0 will converge to a constant and will converge to 0. Therefore, Relative to d i0 ∈ [0, +∞) and b i0 ∈ [-π, +π) globally asymptotically stable.

[0088] Step 4.4: According to the given control law and mathematical induction, it is proved that the vehicle which cannot directly observe the target can converge to the desired circle.

[0089] Define the closed-loop system as follows:

[0090]

[0091] where,

[0092] Assume that the neighbor vehicle k of the ith vehicle can converge to its desired circle, i.e., satisfies

[0093] When the ith vehicle cannot directly observe the target, the vehicle angular velocity control law is as follows:

[0094]

[0095] Substitute equation (18) into (17), the system can be rewritten as:

[0096]

[0097] Divide the system (16) and (19) into two parts, the nominal system and the disturbance system:

[0098]

[0099] According to Step 4.3, the nominal system is asymptotically stable. By introducing the relevant lemma, it is only necessary to prove that the disturbance system converges to 0 as time tends to infinity, i.e., to prove converges to 0. That is, it is proved that:

[0100]

[0101] According to the geometric relationship of Figure 2 , we have:

[0102]

[0103] According to the previous assumption, we have then It is proved that the disturbance system converges to 0 as time tends to infinity. According to the given control law and mathematical induction, it is proved that the vehicle which cannot directly observe the target can converge to the desired circle.

[0104] Step 4.5: According to the given control law, it is proved that the vehicles can converge to the desired distance.

[0105] Assumption 4: All vehicles are assumed to have the same angular velocity to maintain the desired spacing.

[0106] Assumption 5: Assume that the virtual leader vehicle is consistent with its own node in the graph, and k and k f In the figure The CCP uses the same node.

[0107] according to Figure 2 The geometric relationship shows that:

[0108]

[0109] When all vehicles are traveling on their desired circles, the introduction of a virtual leader vehicle reveals that:

[0110]

[0111] definition And λ=col(λ1,…,λ N ), then:

[0112]

[0113] Among them, the matrix is a directed graph The Laplace matrix of .

[0114] According to Assumption 2, suppose node 1 is a graph Root node, definition For the picture The Laplace matrix after removing node 1. According to this assumption, we can know and X=col(X2,…,X N ), i≥2. If the i-th car can observe the 1st car, then a i1 =1, otherwise a i1 =0. Then we have:

[0115]

[0116] The Lyapunov function is defined as follows:

[0117]

[0118] in, Taking its derivative we get:

[0119]

[0120] According to the relevant lemma, it can be proved that V(X) is positive definite. Negative definite, we can prove Then there is This proves that the distance between vehicles can converge to the desired distance.

[0121] Step 5: Implement multi-circle formation control: Substitute the designed control law into the vehicle kinematic model to calculate and adjust the vehicle's linear and angular velocity in real time. Onboard sensors continuously collect information and update the control law to achieve multi-circle formation control.

[0122] Figure 4 FIG1 is a numerical simulation diagram of a 50-second vehicle trajectory according to an embodiment of the present invention, where Vehicle 1 represents number 1 in the sensor network topology, and so on; Figure 4 As shown in Table 1, after 50 seconds, all vehicles converge to the circle of the desired distance, where r 1d Indicates the expected distance between vehicle 1 and the target, which is r in Table 1. id The first element of , and so on. Figure 5 is a numerical simulation diagram of vehicle separation angles according to an embodiment of the present invention, wherein a21 represents the separation angle between Vehicle 1 and Vehicle 2, and so on; Figure 5 As shown, the distances between all vehicles can also converge to the desired distance a set in Table 1, that is, a21=a2-a1, where a1 is the first element of a in Table 1, a2 is the second element of a in Table 1, and so on.

[0123] The relevant parameter settings of the embodiment of the present invention are shown in Table 1.

[0124] Table 1

[0125]

[0126] according to Figure 4 and Figure 5 , through numerical simulation, it can be verified that all vehicles can converge to the expected distance r set in Table 1 id , where r 1d Indicates the expected distance between vehicle 1 and the target, which is r in Table 1. id The first element of , and so on; the distance between all vehicles can also converge to the desired distance a set in Table 1, that is, a21 = a2-a1, where α1 is the first element of α in Table 1, α2 is the second element of α in Table 1, and so on. Figure 4 and Figure 5 Simulation results show that the proposed multi-circle formation control method can effectively converge all vehicles to the desired radius and spacing. The relative positions and azimuths between vehicles meet the expected requirements, demonstrating the effectiveness and practicality of the proposed method.

[0127] In summary, this invention utilizes information collected by on-board sensors and visual markers to design virtual vehicles and a distributed saturation input control law to achieve multi-circle formation control for vehicles with nonholonomic constraints. This method, which requires no communication equipment, offers advantages such as strong adaptability, high robustness, and flexible scalability. It is suitable for complex traffic environments such as autonomous driving and regional monitoring, and has broad application prospects.

[0128] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A nonholonomically constrained vehicle multi-circle formation control method based on direction angle, characterized in that: The following steps are involved: 1) Establish a kinematic model for a single vehicle and assign nonholonomic constraints. The vehicle platoon consists of N+1 vehicles, numbered 0, 1, ..., N, where vehicle 0 is the target, i.e., the center of the multi-circle formation, and vehicles 1, ..., N are the platoon vehicles. The kinematic model includes the vehicle's position, heading angle, linear velocity, and angular velocity, with nonholonomic constraints on the linear velocity and angular velocity. 2) Under the assumption that communication equipment is unavailable, the relative information between vehicles, including azimuth and relative heading angles, is collected in real time through on-board sensors; 3) Based on graph theory, the information exchange between vehicle sensors is described. The vehicle sensor network topology is defined as a directed graph, consisting of a set of nodes and a set of edges. Each vehicle can only measure the relative information of adjacent vehicles in the sensor network. A formation control objective function is established, which includes the difference between the distance between the vehicle and the target and the desired distance, the difference between the current azimuth and the desired azimuth, and the difference between the separation angle with other adjacent vehicles and the desired separation angle. 4) Design a control law for a nonholonomically constrained multi-circle platooning system with distributed saturation inputs. This involves designing a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angles that allow the vehicles to converge to the desired radius and spacing. The distributed saturation input control law is designed to calculate the linear and angular velocities of the vehicles in real time. Lyapunov stability theory and linear matrix inequality methods are used to prove that the vehicles can converge to the desired radius and spacing, while ensuring the asymptotic stability of the platoon control system. 5) Substitute the control law into the kinematic model established in step 1) to calculate the linear velocity and angular velocity of the vehicle in real time to achieve multi-circle formation control of the vehicle.

2. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles according to claim 1, characterized in that: The kinematic model established in step 1) is: b ik =atan2(-(x k -x i )sinθ i +(y k -y i )cosθ i ,(x k -x i )cosθ i +(y k -y i )sinθ i ) When -(x k -x i )sinθ i +(y k -y i )cosθ i = 0 and (x k -x i )cosθ i +(y k -y i )sinθ i = 0, then b ik = 0; Among them, b ik represents the direction angle between the i-th vehicle and the k-th vehicle, (x i ,y i ) represents the absolute position of the i-th vehicle, (x k ,y k ) represents the absolute position of the kth vehicle, θ i represents the heading angle of the i-th vehicle relative to the inertial system.

3. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles according to claim 1, characterized in that: The real-time collection of relative information between vehicles through on-board sensors in step 2) refers to real-time collection through cameras or lidar, which specifically includes the following steps: vehicles periodically observe target or neighboring vehicle information through on-board sensors and visual markers. It is assumed that only some vehicles can directly observe the target through on-board sensors, and the remaining vehicles can only obtain the azimuth and relative heading angle between themselves and the vehicle with the visual marker through on-board sensors.

4. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles according to claim 1, characterized in that: The formation control objective function defined in step 3) is: Among them, d i0 represents the distance between the i-th vehicle and the target, r id represents the expected distance between the i-th vehicle and the target; b i0 represents the azimuth angle between the i-th vehicle and the target, is the expected bearing angle between the i-th vehicle and the target; represents the current separation angle between the i-th vehicle and the j-th vehicle. The j-th vehicle is adjacent to the i-th vehicle in the sensor network. ij represents the desired separation angle between the i-th vehicle and the j-th vehicle, wrapTo2π(·) represents a function that can limit the angle to [0,2π], ν represents the set of vehicle nodes in the formation, represents the set of nodes that the i-th vehicle can observe in the sensor network.

5. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles according to claim 1, characterized in that: The distributed saturation input control law designed in step 4) is: Among them, v i represents the ideal linear velocity of the i-th vehicle calculated according to the control law, ω i represents the ideal angular velocity of the i-th vehicle calculated according to the control law, ω id represents the expected angular velocity of the i-th vehicle, r id represents the expected distance of the i-th vehicle, Indicates that the kth vehicle is the neighbor vehicle of the ith vehicle, represents the direction angle between the i-th vehicle and the virtual following vehicle of the designed k-th vehicle, a ki represents the expected separation angle between the i-th vehicle and the k-th vehicle, represents the direction angle between the i-th vehicle and the virtual center vehicle of the designed k-th vehicle, b i0 represents the azimuth angle between the i-th vehicle and the target, k1, k2 and μ represent the parameters to be designed; When the i-th vehicle can directly observe the target, α i =0,β i =1; otherwise, β i =0; where represents the number of vehicles that the i-th vehicle can observe; in order to satisfy the nonholonomic constraints, the values ​​of k1 and k2 should satisfy: k2∈(0,ω max -oh id -k1) Among them, v min Indicates the minimum value of linear velocity, v max Indicates the maximum value of linear velocity, ω max Indicates the maximum value of angular velocity; r id represents the expected distance, ω id represents the expected angular velocity of the i-th vehicle.

6. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles according to claim 1, characterized in that: In step 4), based on Lyapunov stability theory and linear matrix inequality method, it is proved that the vehicles can converge to the desired radius and desired spacing, and sufficient conditions are obtained to ensure the asymptotic stability of the vehicle platoon control system.

7. The method for controlling a multi-circle formation of vehicles with non-holonomic constraints based on direction angles as claimed in claim 1, characterized in that: In step 5), the control law is substituted into the kinematic model to calculate the linear velocity and angular velocity of the vehicle in real time, and the multi-circle formation control of the vehicle is realized by using the on-board actuator.

8. A nonholonomically constrained vehicle multi-circle formation control system, characterized in that: The method according to any one of claims 1 to 7 is adopted to realize multi-circle formation control of vehicles.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

10. A computer device comprising a processor and a memory, characterized in that: A computer program is stored in the memory, and when the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

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