A control method for drone swarms autonomously traversing two-dimensional curved pipelines under field of view constraints

Abstract

This invention discloses a method for controlling a drone swarm autonomously traversing a two-dimensional curved pipe under field-of-view constraints: Step 1: Establish a model for the problem of autonomous traversal of a two-dimensional curved pipe by a drone swarm under field-of-view constraints, including establishing a motion model, a field-of-view model, two region models, and a model of the two-dimensional curved pipe; Step 2: Assuming that the initial position of each drone is located inside the two-dimensional curved pipe, design a distributed control method for the autonomous traversal of the two-dimensional curved pipe by the drone swarm under field-of-view constraints. This invention solves the problem of autonomous traversal of a two-dimensional curved pipe by a drone swarm under field-of-view constraints, while simultaneously satisfying real-time performance, safety, and reliability, enabling the drone swarm to complete tasks efficiently and safely. It can be applied to fields such as rescue, photography, and agriculture.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) swarms, specifically relating to a distributed control method for UAV swarms autonomously traversing two-dimensional curved pipes under field-of-view constraints. Background Art

[0002] In recent years, research and achievements related to drone swarms have been widely applied in various fields. One common application scenario is traversing two-dimensional curved pipes. For this task, the drone swarm needs to reach the endpoint of the pipe while ensuring collision avoidance between drones throughout the process. The two-dimensional curved pipe can be a physical entity, such as a corridor, door, window, or tunnel, or a virtual entity, such as a virtual flight path designed for the drone swarm. However, the field of view of sensors mounted on drones is often limited, such as cameras and lidar with limited fields of view. Traditional drone swarm control methods often ignore the field of view constraints of sensors, assuming that drones have omnidirectional vision. Such methods require equipping each drone with multiple sensors to achieve omnidirectional vision, significantly increasing the cost of the drone swarm. Therefore, researching a distributed control method for drone swarms autonomously traversing two-dimensional curved pipes under field of view constraints is crucial and meaningful for fields such as rescue, photography, and agriculture. Summary of the Invention

[0003] This invention presents a distributed control method for autonomous traversal of a two-dimensional curved pipe swarm under field-of-view constraints. The method includes establishing a model for the autonomous traversal of a two-dimensional curved pipe swarm under field-of-view constraints and designing a distributed control method for this purpose. It solves the problem of autonomous traversal of a two-dimensional curved pipe swarm under field-of-view constraints, while ensuring that all drones meet collision avoidance conditions, enabling the drone swarm to complete the task efficiently and safely.

[0004] To achieve the above objectives, the implementation steps of the present invention are as follows:

[0005] Step 1: Establish a model for the problem of autonomous traversal of a two-dimensional curved pipe by a swarm of drones under field-of-view constraints; this includes establishing the drone's motion model, field-of-view model, two types of region models, and the model of the two-dimensional curved pipe, as detailed below:

[0006] Step 1.1: Establish the motion model of the UAVs. Assuming the number of UAVs in the swarm is M, the motion model of the i-th UAV is defined as:

[0007]

[0008] in, Let i be the position of the i-th drone. This is the speed control input for the i-th UAV. Unless otherwise specified, all two-dimensional vectors are assumed to be column vectors. A smooth function σ1(x,d1,d2) is defined as...

[0009]

[0010] in Let be the independent variable of the smooth function σ1(x,d1,d2), where d1 and d2 are the two parameters of the function, and d1 < d2. Furthermore, A1, B1, C1, D1, E1, and F1 are six intermediate variables related to d1 and d2, denoted as [equation missing in original text].

[0011]

[0012] The maximum speed of the i-th drone is v m,i Then the speed control input v of the i-th UAV c,i The following constraints exist:

[0013]

[0014] Where 0 < ∈ 1 < 1 is an adjustable control parameter. The initial speed control input is the one that has not undergone a saturation process. After the saturation process, it will have...

[0015] ||v c,i ||≤v m,i (5)

[0016] Furthermore, when ||v′ c,i || = 0, therefore v c,i =0.

[0017] Step 1.2: Establish two area models for the UAV. First, based on the physical size of the UAV, define the safe area for the i-th UAV. It is a circle:

[0018]

[0019] in Let be any point inside the circle. The radius of the circle is r. s A radius greater than 0 is called the safe radius of a drone. When the safe zones of drones do not overlap, it is considered that no collision has occurred.

[0020]

[0021] in This represents the safe zone of the i-th drone. Let represent the safe zone for the j-th drone. Eliminating collisions between drones is one of the design goals of the final distributed controller for the drone swarm. The next step is to define the obstacle avoidance zone for the i-th drone. For another circle:

[0022]

[0023] The radius r of the circle a A value greater than 0 is called the obstacle avoidance radius of the drone. The obstacle avoidance radius is defined as follows: when the obstacle avoidance area of ​​the i-th drone does not intersect with the safe area of ​​the j-th drone, i.e.:

[0024]

[0025] It is then assumed that neither of the two drones adopts an obstacle avoidance strategy. This represents the obstacle avoidance zone for the i-th drone. Let represent the safe zone of the j-th drone. Clearly, the relationship between the obstacle avoidance radius and the safe radius should satisfy:

[0026] r a >r s (10)

[0027] Step 1.3: Establish the UAV's field of view model. Assume that each UAV in the swarm is equipped with a sensor with a limited field of view, and this sensor can rotate by an angle η. i ∈(-π,π). Define the unit detection vector g of the i-th UAV. i for:

[0028] g i =[cosη i sinη i ] T (11)

[0029] like Figure 1 As shown, the field of view of the i-th drone is defined. For a sector:

[0030]

[0031] Where, r d >0 is called the detection radius of the UAV, and π < α < 2π is called the field of view of the UAV. <g i XP i >Represents vector g i sum vector xp i The angle between them. Define a set. For all within the field of vision A collection of IDs for other drones within the system:

[0032]

[0033] Where p j This indicates the position of the j-th drone.

[0034] Step 1.4: Establish a model of the two-dimensional curved pipeline. For example... Figure 2 As shown, in two-dimensional space, a generating line γ lies inside the curved pipe. The generating line γ is represented as:

[0035] γ(s)=[x(s) y(s)] T (14)

[0036] Where s∈[0,s f ] is the arc length parameter and s f >0. For any point on the generating line γ, its unit tangent vector t(s) is expressed as:

[0037]

[0038] Rotating the unit tangent vector t(s) counterclockwise by 90 degrees yields the unit normal vector n(s), which is expressed as:

[0039]

[0040] Two-dimensional curved pipeline based on the generator line γ Represented as:

[0041]

[0042] Where ρ∈[0,1], θ=0 or π, and λ(s,θ>0, it is called a curved pipe. The radius of the two-dimensional curved pipe. boundary Represented as:

[0043]

[0044] For any point γ(s1) on the generating line, s1∈[0, s f ], the transverse line passing through that point Represented as:

[0045]

[0046] Where ρ∈[0,1], θ=0 or π. (Transverse line) The width is equal to 2r t (s1), where r t (s1) is represented as:

[0047]

[0048] transverse line The center point is m(s1), which is represented as:

[0049]

[0050] When the i-th drone is located in the two-dimensional curved pipe Inside, that is It corresponds to a unique set of parameters, a set of s. i ,θ i ,ρ i ,Right now

[0051]

[0052] Parameter s i It can be uniquely determined by the following formula:

[0053]

[0054] Next, the parameter θ i It can be represented as

[0055]

[0056] Parameter ρ i It can be represented as

[0057]

[0058] Step 2: Based on the artificial potential field method and Lyapunov stability analysis, assuming that the initial position of each UAV is located inside the two-dimensional curved pipe, a distributed control method for the autonomous traversal of the UAV swarm through the two-dimensional curved pipe under the constraint of field of view is designed as follows:

[0059] Step 2.1: Design the velocity control components for the UAV moving along the two-dimensional curved pipe. When the i-th UAV is located in the two-dimensional curved pipe... Inside, the speed control component as it travels along the two-dimensional curved pipe. Designed for

[0060] u 1,i =v m,i t(s i (26)

[0061] Step 2.2: Design the anti-collision potential field function between UAVs. First, define two smooth functions. The first smooth function σ2(x,d1,d2) is expressed as...

[0062]

[0063] in Let be the independent variable of the smooth function σ²(x,d₁,d₂), where d₁ and d₂ are the two parameters of the function, and d₁ < d₂. Furthermore, A₂, B₂, C₂, D₂, E₂, F₂, G₂, and H₂ are eight intermediate variables related to d₁ and d₂, denoted as [equation missing in original text].

[0064]

[0065] The second smooth function s(x,∈ s ) represents

[0066]

[0067] in For a smooth function s(x,∈ s The independent variable of ) ∈ s These are the parameters of the function. Furthermore, A3, B3, C3, D3, E3, F3, and G3 are seven numbers that are related to ∈ s The relevant intermediate variables are represented as

[0068]

[0069] The positional error between the i-th drone and the j-th drone is defined as That is:

[0070]

[0071] Further design of the anti-collision potential field function between UAVs:

[0072]

[0073] Where ∈ m >0, ∈ s >0 s >0, k2>0 are design parameters. Function V m,ij It has the following properties:

[0074] i)V m,ij Always non-negative, i.e., V m,ij ≥0 always holds true if and only if When the equality sign is true, and This means that no obstacle avoidance strategy is adopted between the i-th drone and the j-th drone;

[0075] ii) It is always true, that is, when When V is used as the independent variable m,ij Decreasing;

[0076] iii) When Sometimes,

[0077]

[0078] At this point, if the design parameters ∈ m If the value is small enough, then V m,ij It can take arbitrarily large values. Based on function V m,ij Given the above characteristics, one of the design goals of the controller is to make V m,ij =0.

[0079] Step 2.3: Design the potential field function to confine the UAV within the two-dimensional curved pipe. Define the i-th UAV and its corresponding transverse section. The distance error between the boundaries is

[0080] d t,i =r t (s i )-||p i -m(s i (34)

[0081] Further design of the potential field function to confine the drone within a two-dimensional curved pipe.

[0082]

[0083] Where ∈ t >0, ∈ s >0, k3>0 are design parameters, r s ′ is the pipeline safety radius, defined as

[0084]

[0085] and Here we require that the following relation be satisfied: r a >r s ′>r s Function V t,i With V m,ij They share similar properties, which will not be elaborated upon here. One of the design goals of the controller is to make V... t,i =0.

[0086] Step 2.4: Design the speed control input for the UAV within the two-dimensional curved pipe. When the i-th UAV is located within the two-dimensional curved pipe... Internally, we require its unit probe vector g i It is always equal to the direction in which the drone moves along the two-dimensional curved pipe, that is...

[0087] g i =t(s i (37)

[0088] Based on the velocity control components of the UAV designed in step 2.1 as it moves along the two-dimensional curved pipe, and the two potential field functions designed in steps 2.2 and 2.3, the design of the i-th UAV's movement along the two-dimensional curved pipe is as follows. The internal speed control input is

[0089]

[0090] Where 0 < ∈ 2 < 1 is an adjustable control parameter, and has

[0091]

[0092] in Let i be the center point of the i-th UAV within the two-dimensional curved pipe. For the velocity control component of the i-th UAV moving along the two-dimensional curved pipe, Let i be the collision avoidance control component between the i-th drone and other drones. Let i be the control component that restricts the i-th UAV within the two-dimensional curved pipe. Let cosμ be the fusion control variable for the i-th UAV after the saturation process. i Indicate u c,i with u 1,i The cosine of the angle between them.

[0093] Based on Lyapunov stability analysis, it can be proven that the controller satisfies the following conditions: i) all UAVs reach the endpoint of the two-dimensional curved pipe; ii) all UAVs do not collide within the two-dimensional curved pipe; iii) all UAVs do not cross the pipe boundary within the two-dimensional curved pipe. Thus, the design of the distributed control method for UAV swarms traversing a two-dimensional curved pipe under field-of-view constraints is complete.

[0094] The advantages and beneficial effects of this invention are as follows: This invention innovatively designs a method for controlling a swarm of drones to autonomously traverse a two-dimensional curved pipeline under field-of-view constraints. In practical applications, this method eliminates the need for drones to be equipped with numerous sensors to acquire omnidirectional information about their surroundings, and also eliminates the need for communication between drones, thus reducing the requirements for the drones' perception and communication capabilities and lowering their hardware costs. This method also expands the application scope of drone swarms, enabling them to safely traverse complex environments such as corridors, doors, windows, and tunnels. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the drone's field of view.

[0096] Figure 2 This is a schematic diagram of a two-dimensional curved pipe model.

[0097] Figures 3a-3d The figure shows the simulation results of an unmanned aerial vehicle (UAV) autonomously traversing a two-dimensional curved pipeline under the constraint of the UAV swarm's field of view.

[0098] Figure 4a The image shows the simulation results of the minimum distance between drones.

[0099] Figure 4b The image shows the simulation results of the minimum distance between the drone and the pipeline boundary.

[0100] Figure 5 This is a flowchart of the present invention. Detailed Implementation

[0101] This invention provides a distributed control method for a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipe under field-of-view constraints. Taking a scenario where 20 UAVs are initially positioned inside the two-dimensional curved pipe as an example, the specific implementation method is further explained. Simulation and calculation were performed on a computer with a 3.70 GHz CPU and 32.0 GB of memory, using MATLAB R2022b under the Win10 operating system.

[0102] The specific steps for implementing this invention are as follows:

[0103] We consider a scenario where a swarm of drones autonomously traverses a two-dimensional curved pipe, where the number of drones is M = 20 and the safe radius of the drones is r. s =0.2m, obstacle avoidance radius is r a =0.4m, detection radius is r d =2m, field of view angle is α = 1.2π. The two-dimensional curved pipeline generation line is represented as:

[0104] γ(s)=[s 2sin(0.1πs)] T (40)

[0105] Where 0 ≤ s ≤ 30 are the parameters for generating the line. The radius of the two-dimensional curved pipe is expressed as...

[0106]

[0107] Where 0 ≤ s ≤ 30. The maximum speed of each drone is...

[0108]

[0109] The maximum speed is input as a parameter to the speed control component u of the i-th UAV moving along the two-dimensional curved pipe. 1,i In the middle. The collision avoidance control component u of the i-th UAV with other UAVs. 2,i The parameter is ∈ m =∈ s =10 -6k2 = 1. The control component u of the i-th UAV confined within the two-dimensional curved pipe. 3,i The parameter is ∈ t =∈ s =10 -6 k3 = 1. The fused control quantity u of the i-th UAV after the saturation process. c,i The parameter is ∈1=0.9. The velocity control input v of the i-th UAV in the two-dimensional curved pipe. c,i The parameter is ∈2=0.1.

[0110] like Figure 3a As shown, at the start of the simulation, all drones were uniformly distributed within a rectangle, and all drones had an initial velocity of zero. The simulation results are as follows. Figures 3a-3d As shown, the drone swarm moves forward along a two-dimensional curved pipe. During this process, the minimum distance between all drones is as follows: Figure 4a As shown, this value remains consistently at 2r. s = 0.4m or more (indicated by dashed lines). Similarly, the minimum distance between all drones and the pipeline boundary is as follows: Figure 4b As shown, this value always remains at r s =0.2m or more (indicated by dashed lines). This indicates that no conflicts occurred between the safe zones of each UAV during the entire process, and that no conflicts occurred between the safe zones of each UAV and the pipe wall. These results demonstrate the effectiveness of the proposed distributed control method for autonomous UAV swarm traversing a two-dimensional curved pipe under field-of-view constraints.

Claims

1. A method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints, characterized in that: The specific steps are as follows: Step 1: Establish a model for the problem of UAV swarm autonomously traversing a two-dimensional curved pipe under field-of-view constraints, including establishing the UAV's motion model, field-of-view model, two types of region models, and establishing the two-dimensional curved pipe model; Step 2: Assuming that the initial position of each UAV is inside the two-dimensional curved pipe, design a distributed control method for the UAV swarm to autonomously traverse the two-dimensional curved pipe under the constraint of field of view; The specific process for establishing the two-dimensional curved pipeline model is as follows: In two-dimensional space, a generating line γ lies inside the curved pipe; the generating line γ is represented as: γ(s)=[x(s) y(s)] T (1) Where s∈[0,s f ] is the arc length parameter and s f >0; For any point on the generating line γ, the unit tangent vector t(s) is expressed as: Rotating the unit tangent vector t(s) counterclockwise by 90 degrees yields the unit normal vector n(s), expressed as: Two-dimensional curved pipeline based on the generator line γ Represented as: Where ρ∈[0,1], θ=0 orπ, and λ(s,θ)>0 are called curved pipes. radius; two-dimensional curved pipe boundary Represented as: For any point γ(s1) on the generating line, s1∈[0, s f ], the transverse line passing through that point Represented as: Where ρ∈[0,1], θ=0 orπ; transverse line The width is equal to λ(s1,0)+λ(s1,π), and the transverse line... The half-width is r t (s1), then r t (s1) is represented as: transverse line The center point is m(s1), which is represented as:

2. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints as described in claim 1, characterized in that: The specific process for establishing the motion model of the UAV is as follows: Let M be the number of drones in the drone swarm. The motion model of the i-th drone is defined as follows: in, Let i be the position of the i-th drone. Let be the speed control input for the i-th UAV. Unless otherwise specified, all two-dimensional vectors are assumed to be column vectors. Define a smooth function σ1(x,d1,d2) as follows: in, Let be the independent variable of the smooth function σ1(x,d1,d2), where d1 and d2 are the two parameters of the function, and d1 < d2; and A1, B1, C1, D1, E1, and F1 are six intermediate variables related to d1 and d2, which are expressed as: The maximum speed of the i-th drone is v m,i Then the speed control input v of the i-th UAV c,i The following constraints exist: Where 0 < ∈ 1 < 1 is an adjustable control parameter. The initial speed control input before saturation will become: ||in c,i ||≤v m,i (13) Furthermore, when ||v′ c,i || = 0, therefore v c,i =0.

3. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints as described in claim 1, characterized in that: When the i-th drone is located in the two-dimensional curved pipe Inside, that is It corresponds to a unique set of parameters, a set of s. i ,θ i ,ρ i ,Right now: Parameter s i It is uniquely determined by the following formula: Next, the parameter θ i Represented as: Parameter ρ i Represented as:

4. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints as described in claim 1, characterized in that: The specific process of step two is as follows: Step 2.1: Design the velocity control components for the UAV as it moves along the two-dimensional curved pipe; Step 2.2: Design the anti-collision potential field function between UAVs; Step 2.3: Design the potential field function to confine the UAV within the two-dimensional curved pipe; Step 2.4: Design the speed control input for the UAV within the two-dimensional curved pipe.

5. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints according to claim 4, characterized in that: The specific process of step 2.1 is as follows: When the i-th UAV is inside the two-dimensional curved pipe, its velocity control component as it moves along the two-dimensional curved pipe Designed as follows: u 1,i =v m,i t(s i ) (18) The maximum speed of the i-th drone is v m,i .

6. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints according to claim 4, characterized in that: The specific process of step 2.2 is as follows: First, define two smooth functions. The first smooth function σ2(x,d1,d2) is expressed as: in, Let be the independent variable of the smooth function σ2(x,d1,d2), where d1 and d2 are the two parameters of the function, and d1 < d2; and A2, B2, C2, D2, E2, F2, G2, H2 are eight intermediate variables related to d1 and d2, which are expressed as: The second smooth function s(x,∈ s ) is represented as: in For a smooth function s(x,∈ s The independent variable of ) ∈ s These are the parameters of the function; furthermore, A3, B3, C3, D3, E3, F3, and G3 are seven integers that are related to ∈ s The relevant intermediate variables are represented as follows: The positional error between the i-th drone and the j-th drone is defined as That is: Further design of the anti-collision potential field function between UAVs: Where ∈ m >0, ∈ s >0, k2>0 are design parameters.

7. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints according to claim 6, characterized in that: function V m,ij It has the following properties: i)V m,ij Always non-negative, i.e., V m,ij ≥0 always holds true if and only if When the equality sign is true, and This means that no obstacle avoidance strategy is adopted between the i-th drone and the j-th drone; ii) It is always true, that is, when When V is used as the independent variable m,ij Decreasing; iii) When Sometimes, there are At this point, if the design parameters ∈ m If the value is small enough, then V m,ij To obtain arbitrarily large values; based on function V m,ij Given the above characteristics, one of the design goals of the controller is to make V m,ij =0.

8. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints according to claim 4, characterized in that: The specific process of step 2.3 is as follows: Define the i-th drone and its corresponding transverse line. The distance error between the boundaries is: Further design of the potential field function to confine the drone within a two-dimensional curved pipe: Where ∈ t >0, ∈ s >0, k3>0 are design parameters, r s ′ is the pipeline safety radius, defined as: and The following relationship must be satisfied: r a >r s ′>r s One of the design goals of the controller is to make V t,i =0.

9. The method for controlling a swarm of unmanned aerial vehicles (UAVs) autonomously traversing a two-dimensional curved pipeline under field-of-view constraints according to claim 4, characterized in that: The specific process of step 2.4 is as follows: When the i-th drone is located in the two-dimensional curved pipe Internally, it is required that its unit probe vector g i It is always equal to the direction in which the drone moves along the two-dimensional curved pipe, that is... g i =t(s i ) (29) Based on the velocity control components of the UAV designed in step 2.1 as it moves along the two-dimensional curved pipe, and the two potential field functions designed in steps 2.2 and 2.3, the design of the i-th UAV's movement along the two-dimensional curved pipe is as follows. The internal speed control input is: Where 0 < ∈ 2 < 1 is an adjustable control parameter, and has Among them, V m,ij Let v be the anti-collision potential field function between unmanned aerial vehicles. m,i Let be the maximum speed of the i-th drone. Let i be the center point of the i-th UAV within the two-dimensional curved pipe. For the velocity control component of the i-th UAV moving along the two-dimensional curved pipe, Let i be the collision avoidance control component between the i-th drone and other drones. Let i be the control component that restricts the i-th UAV within the two-dimensional curved pipe. Let cosμ be the fusion control variable for the i-th UAV after the saturation process. i Indicate u c,i with u 1,i The cosine of the angle between them.

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