Incomplete constraint vehicle multi-circle formation control method based on direction angle

Abstract

The invention discloses an incomplete constraint vehicle multi-circle formation control method based on a direction angle, and belongs to the field of multi-vehicle cooperative control. Relative information of adjacent vehicles in a sensor network is collected and measured through a vehicle-mounted sensor and a visual mark, a virtual center vehicle and a virtual leader vehicle are designed according to the collected relative information, namely the azimuth angle between the vehicles, and a control law with distributed saturation input is designed according to the information. Communication equipment is not needed, the linear speed and the angular speed of the vehicle are calculated in real time through the control law, and it is ensured that all vehicles keep the expected radius, speed and distance. The asymptotic stability of the system is proved through a Lyapunov stability theory and a linear matrix inequality method, and the effectiveness of the method is verified through numerical simulation. The method is suitable for complex traffic environments such as automatic driving and area monitoring, and has a wide application prospect.

Description

Technical Field

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

[0002] With the continuous development of intelligent vehicle technology, the limitations of a single intelligent vehicle in a complex traffic environment have become increasingly apparent. Therefore, the research on multi-vehicle cooperative control has received more and more attention. Compared with the control of a single intelligent vehicle, the multi-vehicle cooperative system can achieve higher efficiency, better robustness and flexible spatial distribution in complex traffic scenarios through the collaborative cooperation of multiple intelligent vehicles.

[0003] As a key research direction in this field, circular formation control has been widely used in scenarios such as autonomous driving and drone formation. 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 problem of collaborative path tracking 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 purpose of the present invention is to provide a non-holonomic constrained vehicle multi-circle formation control method based on direction angle for the problems of non-holonomic constrained vehicle multi-circle formation control. The method collects relative information of adjacent vehicles in the sensor network through on-board sensors and visual markers, designs a virtual center vehicle and a virtual leader vehicle, and designs a control law with distributed saturation input based on this information to realize multi-circle formation control. Ensure that all vehicles in the system maintain the desired radius, speed and spacing.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions.

[0006] A nonholonomic constrained vehicle multi-circle formation control method based on direction angles comprises the following steps:

[0007] 1) Establish a single vehicle kinematic model and give non-holonomic constraints;

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

[0009] 3) Based on graph theory, the information interaction between vehicle sensors is described. Each vehicle can only measure the relative information of adjacent vehicles in the sensor network, and establish the formation control objective function;

[0010] 4) Design a nonholonomic constrained vehicle multi-circle formation control law with distributed saturation input, and calculate the linear velocity and angular velocity required for formation control in real time;

[0011] 5) Substitute the control law into the kinematic model established in step 1), calculate the linear velocity and angular velocity of the vehicle in real time, and realize the multi-circle formation control of the vehicle.

[0012] In step 1), the establishment of a single vehicle kinematic model and the provision of nonholonomic constraints specifically include the following steps:

[0013] (1) 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;

[0014] (2) Establish a kinematic model of a single vehicle and constrain its linear velocity and angular velocity.

[0015] In step 2), the real-time collection of relevant information by vehicle-mounted sensors refers to real-time collection by cameras or laser radars, which specifically includes the following steps:

[0016] Vehicles periodically observe target or neighbor 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 visual markers through on-board 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 may be:

[0018] (1) Based on graph theory, the topology of the vehicle sensor network is defined, that is, the vehicles that each vehicle can observe, and the definitions of the adjacency matrix and the Laplacian matrix are given;

[0019] (2) 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 difference between the separation angle with other adjacent vehicles and the expected separation angle are set as independent variables, and the formation control objective function is established to achieve the desired formation.

[0020] In step 4), the design of the nonholonomic constrained vehicle multi-circle formation control law with distributed saturation input and the real-time calculation of the linear velocity and angular velocity required for formation control may be carried out in the following specific steps:

[0021] (1) Designing a virtual center vehicle and a virtual leader vehicle to obtain an azimuth angle that enables the vehicles to converge to a desired radius and a desired spacing;

[0022] (2) Design a distributed saturation input control law to calculate the linear and angular velocities of the vehicle;

[0023] (3) Based on Lyapunov stability theory and linear matrix inequality method, it is proved that 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.

[0024] The present invention collects and measures relative information of adjacent vehicles in a sensor network through on-board sensors and visual markers, and based on the collected relative information, that is, the azimuth angles between vehicles, and by designing a virtual center vehicle and a virtual leader vehicle, obtains the azimuth angles that can make the vehicles converge to a desired radius and a desired spacing, and designs a control law with distributed saturation input based on it, thereby achieving the control goal of multi-circle formation control.

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

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

[0027] 2. Adaptation to non-holonomically constrained vehicles: Aiming at the characteristics of non-holonomically constrained vehicles (such as smart cars that can only move forward and turn), the present invention designs a control law with distributed saturation input. This control law fully considers the kinematic constraints of the vehicle to ensure the effectiveness and practicality of the control strategy.

[0028] 3. Distributed control strategy: The present invention adopts 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 computing burden and communication requirements of the central controller.

[0029] 4. Design of virtual center vehicle and virtual leader vehicle: By introducing the concept of virtual center vehicle and virtual leader vehicle, the present invention provides vehicles with clear convergence targets and directions, making it easier for vehicles to converge to the desired radius and spacing, thereby maintaining a stable formation.

[0030] 5. Description of information interaction based on graph theory: The present 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 Laplace matrix, the connection relationship and communication topology between vehicles can be clearly described.

[0031] 6. The present invention can not only solve the communication dependence and other problems in the traditional method, but also adapt to the characteristics of non-completely constrained vehicles to achieve efficient and stable multi-vehicle collaborative control; it is suitable for complex traffic environments such as automatic driving and regional monitoring, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of a formation control method according to an embodiment of the present invention.

[0033] Figure 2 It is a schematic diagram of a certain vehicle and its virtual central vehicle and virtual leading vehicle according to an embodiment of the present invention.

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

[0035] Figure 4 It is a numerical simulation diagram of a 50-second vehicle trajectory according to an embodiment of the present invention.

[0036] Figure 5 4 is a numerical simulation diagram of the vehicle separation angle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the following embodiments will further illustrate the present invention in conjunction with the accompanying drawings. 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. On the contrary, the present invention covers any substitution, modification, equivalent method and scheme made on the essence and scope of the present invention as defined by the claims.

[0038] The flow chart of the formation control method according to the embodiment of the present invention is as follows: Figure 1 As shown, the present invention aims to solve the multi-circle formation control problem of non-holonomically constrained vehicles and proposes a control method based on azimuth angles. Relative information of adjacent vehicles is collected through on-board sensors and visual markers, a virtual center vehicle and a virtual leader vehicle are designed, and a control law with distributed saturation input is designed accordingly to achieve multi-circle formation control. The formation control system of the present invention assumes that only some vehicles can directly observe the target through on-board sensors, and the remaining vehicles can only obtain the azimuth angle and relative heading angle between themselves and the vehicle with the visual marker through on-board sensors. Assuming that the kth vehicle is a neighbor vehicle of the i-th vehicle, the i-th vehicle can obtain the azimuth angle between itself and the virtual follower vehicle designed for the kth vehicle. Assuming that the i-th vehicle can observe the target, the azimuth angle b between it and the target is obtained i0 ; Assuming that the i-th vehicle cannot observe the target, obtain the direction angle between it and the virtual center vehicle of the designed k-th vehicle According to the information obtained, a control law with distributed saturation input is designed to calculate the ideal angular velocity ω of the i-th vehicle. i With the ideal linear velocity v i Thus, multi-circle formation control is completed.

[0039] The implementation of the present invention specifically comprises the following steps:

[0040] Step 1: Establish a single vehicle kinematic model and 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 platoon vehicles. Establish a single vehicle kinematic model, considering the vehicle's position, heading angle, linear velocity, and angular velocity, and impose nonholonomic constraints on its linear velocity and angular velocity.

[0041] A schematic diagram of a vehicle and its virtual center vehicle and virtual leader vehicle according to an embodiment of the present invention is shown in FIG. Figure 2 As shown in the figure, θ i represents the heading angle of the i-th vehicle relative to the inertial system, b i0 represents the azimuth angle between the i-th vehicle and the target, b ik represents the azimuth angle between the i-th vehicle and the k-th vehicle, d i0represents the distance between the i-th vehicle and the target, and the virtual leader vehicle k is set f The position of vehicle k is in the vehicle coordinate system (0, r kd -r id ), the virtual center vehicle k is set c The position of vehicle k is in the vehicle coordinate system (0, r kd ) place.

[0042] Step 1.1: Considering the position, heading angle, linear velocity and angular velocity of the vehicle, establish the kinematic model of the i-th vehicle in the vehicle queue:

[0043]

[0044] Among them, p i =[x i y i ] T represents the absolute position of the i-th vehicle, θ i represents the heading angle of the i-th vehicle relative to the inertial system, u i =[v i ω i ] T represents the linear velocity and angular velocity of the i-th vehicle.

[0045] Step 1.2: Give the nonholonomic constraints for each vehicle, that is, give the following physical speed limits:

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

[0047] 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 the angular velocity.

[0048] Step 1.3: According to Figure 2 The geometric relationship shows 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] 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.

[0052] Step 2: Information collection: Assuming that communication equipment is unavailable, each vehicle is equipped with on-board sensors (such as cameras, lidar) to collect information in real time. Relevant information is collected in real time through on-board sensors.

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

[0054] Step 2.2: Assume that only some vehicles can directly observe the target through the on-board sensors, and the remaining vehicles can only obtain the azimuth and relative heading angle between themselves and the vehicle with the visual mark through the on-board sensors.

[0055] Step 3: Information interaction and formation control objective function based on graph theory: Use graph theory to describe the information interaction between vehicle sensors and define the vehicle sensor network topology, including the adjacency matrix and the Laplace matrix. Each vehicle can only measure the relative information of adjacent vehicles in the sensor network. Set the distance difference between the vehicle and the target vehicle, the azimuth difference, and the separation angle difference with the adjacent vehicle as independent variables, and establish the formation control objective function to achieve the desired formation. Figure 3 : This is the sensor network topology of an embodiment of the invention, where number 0 represents the target center and numbers 1-6 represent platoon 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 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 Limited set of nodes and edge set 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, in which there is a root node and no directed edges from other nodes point 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 Laplacian matrix as follows:

[0062]

[0063] Step 3.4: Define the 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. 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 are set as independent variables to establish the formation control objective function, which satisfies:

[0064]

[0065] Among them, d i0represents 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 azimuth 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], 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.

[0066] Step 4: Design a distributed saturation input control law: Design a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicle converge to the desired radius and desired spacing. Design a non-holonomic constrained vehicle multi-circle formation control law with distributed saturation input. According to the collected relative information and the position of the virtual vehicle, the linear velocity and angular velocity required for formation control are calculated in real time. 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 platoon control system is ensured.

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

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

[0070] Among them, v i represents the ideal linear speed 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.

[0071] When the i-th vehicle can directly observe the target, α i =0,β i =1; otherwise, β i =0. Among them, It indicates 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: Based on the given control law, prove that the vehicle that can directly observe 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 =[di0 b i0 ] T .

[0083] V i (x i ) in d i0 = 0 but is not differentiable. However, even if there is a time 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 that d i0 will not always remain 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, V i (x i )Evaluate 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, that is, 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) is globally asymptotically stable.

[0088] Step 4.4: Based on the given control law and mathematical induction, prove that the vehicle that cannot directly observe the target can converge to the desired circle.

[0089] The closed-loop system is defined as follows:

[0090]

[0091] in,

[0092] Assume that the neighbor vehicle k of the i-th vehicle can converge to its desired circle, that is, satisfy

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

[0094]

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

[0096]

[0097] The systems (16) and (19) are divided into two parts: the nominal system and the perturbation system:

[0098]

[0099] According to step 4.3, the nominal system is asymptotically stable. By introducing the relevant lemma, we can prove that we only need to prove that the perturbation system converges to 0 as time tends to infinity. converges to 0. That is, prove:

[0100]

[0101] according to Figure 2 The geometric relationship shows that:

[0102]

[0103] According to the previous assumptions, there is Then there is 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 can be proved that the vehicle that cannot directly observe the target can converge to the desired circle.

[0104] Step 4.5: Based on the given control law, prove 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 same node is used in the middle.

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

[0108]

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

[0110]

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

[0112]

[0113] Among them, the matrix For 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. Based on this assumption, we know and X=col(X2,…,X N ), i ≥ 2. If the i-th car can observe car 1, 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 definiteness 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, calculate and adjust the vehicle's linear velocity and angular velocity in real time. Continuously collect information through on-board sensors and update the control law to achieve multi-circle formation control of the vehicle.

[0122] Figure 4 50s vehicle trajectory numerical simulation diagram of an embodiment of the present invention, Vehicle 1 represents No. 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 expected distance, where r 1d represents 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 of 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 represents the expected distance between vehicle 1 and the target, which is r in Table 1. id The first element of , and so on; the distances 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. According to Figure 4 and Figure 5 The simulation results show that the multi-circle formation control method proposed in the present invention can effectively make all vehicles converge to the desired radius and spacing. The relative positions and azimuths between vehicles can meet the expected requirements, proving the effectiveness and practicality of the method of the present invention.

[0127] In summary, the present invention collects information through on-board sensors and visual markers, designs virtual vehicles and distributed saturation input control laws, and realizes multi-circle formation control of non-holonomically constrained vehicles. This method does not need to rely on communication equipment, has the advantages of strong adaptability, high robustness, flexibility and scalability, and 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 cannot 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 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 of a single vehicle and give 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 vehicles in the formation. The kinematic model includes the position, heading angle, linear velocity, and angular velocity of the vehicle, and nonholonomic constraints are imposed 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 angle, is collected in real time through on-board sensors; 3) Based on graph theory, the information interaction between vehicle sensors is described, and the vehicle sensor network topology is defined as a directed graph, including a set of nodes and a set of edges. Each vehicle can only measure the relative information of adjacent vehicles in the sensor network, and establish a formation control objective function, which includes 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 difference between the separation angle with other adjacent vehicles and the expected separation angle; 4) Design a non-holonomic constrained vehicle multi-circle formation control law with distributed saturated input, including designing a virtual center vehicle and a virtual leader vehicle to obtain the azimuth angle that makes the vehicle converge to the desired radius and the desired spacing, design a distributed saturated input control law to calculate the linear velocity and angular velocity of the vehicle in real time, and prove that the vehicle can converge to the desired radius and the desired spacing based on Lyapunov stability theory and linear matrix inequality method, while ensuring the asymptotic stability of the vehicle platoon control system; 5) Substitute the control law into the kinematic model established in step 1), calculate the linear velocity and angular velocity of the vehicle in real time, and realize the multi-circle formation control of the vehicle.

2. A non-holonomic constrained vehicle multi-circle formation control method based on direction angle as claimed in 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. A non-holonomic constrained vehicle multi-circle formation control method based on direction angle as claimed in 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 lidars, and specifically includes the following steps: vehicles periodically observe target or neighbor 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 provided with visual markers through on-board sensors.

4. A 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: 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 azimuth 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 as claimed in claim 1, characterized in that: The distributed saturation input control law designed in step 4) is: Among them, v i represents the ideal linear speed 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 non-holonomic 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. A 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 4), based on Lyapunov stability theory and linear matrix inequality method, it is proved that the vehicle can converge to the expected radius and expected spacing, and sufficient conditions are obtained to ensure the asymptotic stability of the vehicle platoon control system.

7. A 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 non-holonomic constrained vehicle multi-circle formation control system, characterized in that: The multi-circle formation control of vehicles is realized by adopting the method described in any one of claims 1 to 7.

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.

Images