Multi-unmanned aerial vehicle model prediction flight formation control method in narrow space

Abstract

The invention discloses a multi-unmanned aerial vehicle model prediction flight formation control method in a narrow space, which belongs to the field of multi-unmanned aerial vehicle formation control, and mainly comprises the following steps: when an unmanned aerial vehicle formation encounters a loose obstacle, each unmanned aerial vehicle can autonomously calculate an obstacle avoidance path by means of a local MPC target function to realize self-obstacle avoidance; after the unmanned aerial vehicle is separated from the obstacle by a safe distance and complete obstacle avoidance is determined, a normal formation state is automatically recovered; when the unmanned aerial vehicle formation faces a narrow space and needs to avoid an obstacle, the dynamic event trigger function sends a control signal to the MPC according to a preset trigger condition, adjusts a distance parameter and an angle parameter of formation consistency in the MPC, and drives the formation to be switched to a form adaptive to the narrow space to complete crossing; and after the formation passes through the obstacle and reaches a safe distance, the dynamic event trigger function further controls each unmanned aerial vehicle to recover to the initial or target formation in sequence, so that a mechanism of cooperative work of dynamic event trigger function obstacle avoidance and MPC obstacle avoidance is realized.

Description

Technical Field

[0001] This invention belongs to the field of multi-UAV formation control design and application, specifically involving a dynamic event-triggered control method based on consensus algorithm and distributed model prediction, which can realize rapid formation, stable maintenance and real-time obstacle avoidance of formation in narrow environments. Background Technology

[0002] Multi-drone swarm control, with its flexibility and cost-effectiveness in complex missions, is widely used in key areas such as flood control and disaster relief, search and rescue, agricultural and forestry operations, and the military. For example, DJI drones, through swarm modeling and air-to-ground coordination technology, have achieved efficient information collection and real-time collaborative command, significantly improving the efficiency of flood control and disaster relief. As application scenarios expand to narrow environments such as indoor spaces and densely populated urban areas, multi-drone systems face new challenges due to space constraints, such as rapid formation, stable maintenance, and real-time obstacle avoidance.

[0003] While traditional multi-UAV swarm control algorithms can achieve basic coordination, they suffer from three major drawbacks: First, redundant communication resources. Traditional periodic communication mechanisms are prone to channel congestion when the UAV swarm size increases, leading to information transmission delays or loss. Equipping high-bandwidth communication equipment would significantly increase manufacturing costs. Second, insufficient consideration of system constraints. Most algorithms do not adequately adapt to the physical limitations of UAV speed, angular velocity, and changes in these parameters, making them prone to control misalignment. Third, weak adaptability to complex environments. In confined spaces, it is difficult to balance "formation maintenance" and "obstacle avoidance safety," failing to meet the requirements for high-precision coordination.

[0004] While existing event-triggered control strategies can reduce communication load to address the problem of limited communication resources, they still have shortcomings: some algorithms are designed for a single UAV, with the core objective of reducing actuator wear, which requires sacrificing control accuracy; some multi-UAV event-triggered strategies rely on the real-time status information of neighboring UAVs, which contradicts the core requirement of "reducing information interaction".

[0005] In summary, given the current problems of communication redundancy, lack of system constraints, and weak adaptability to narrow environments in multi-UAV formation control, there is an urgent need for a collaborative control method that can balance formation efficiency, obstacle avoidance safety, and resource conservation to meet the high-precision collaborative requirements in narrow scenarios. Summary of the Invention

[0006] This invention aims to provide a multi-UAV model predictive flight formation control method in confined spaces, addressing the difficulties in forming, maintaining, and avoiding obstacles in multi-UAV formations in narrow environments, as well as the problems of communication redundancy, insufficient constraints, and weak environmental adaptability in traditional algorithms. This method improves formation coordination accuracy, operational reliability, and resource utilization efficiency. To achieve the above objectives, this invention adopts the following technical solution:

[0007] The multi-UAV model predictive flight formation control method of the present invention in confined spaces includes the following steps:

[0008] The multi-drone system includes a navigator drone and multiple follower drones. It assumes that all drones operate in a two-dimensional plane with constant altitude, roll angle, and pitch angle, focusing on horizontal formation control and obstacle avoidance.

[0009] Based on the desired formation and the real-time pose of the leader drone, the desired pose of each follower is calculated in real time using the consensus algorithm to form and maintain the preset formation.

[0010] Construct a general objective function, including a formation consistency objective function and a static obstacle avoidance objective function, and solve for the optimal control sequence based on the general objective function.

[0011] Furthermore, a dynamic triggering function was designed. , Indicates the Navigator drone and static obstacles in The minimum distance at any given moment;

[0012] Inorganic organisms, when traversing narrow environments, rely on dynamic triggering functions. The value is used to perform the following formation transformation; the narrow environment refers to the Euclidean distance between two static obstacles. The value is less than a set threshold, which can be set as a positive number greater than or equal to twice the safe radius of the drone.

[0013] When the drone approaches a confined environment: Dynamically triggered function Triggering a linear formation, among which This indicates the first distance of the team switch, with each follower arranged sequentially along the flight axis of the navigator drone.

[0014] The drones passed between two static obstacles in a "line formation";

[0015] Drones moving away from confined environments: when Dynamically triggered function This triggers a diamond formation, with follower drones arranged in a diamond shape around the navigator drone, which is positioned at the center of the diamond. Dynamically triggered function Triggering a zigzag formation, in which This indicates the second distance of the team switching, with follower drones staggered along both sides of the navigator drone's trajectory; in, and These represent the Euclidean distances from the leader drone to the first and second static obstacles, respectively. This represents the Euclidean distance between two static obstacles. , Indicates the location of the first static obstacle in a confined environment; , This indicates the location of the second static obstacle in a confined environment, where the Navigator drone is positioned relative to the static obstacle. Minimum distance at time Pick and The minimum value in.

[0016] Furthermore, the present invention designs the first Variables for determining whether a drone has successfully completed obstacle avoidance ;

[0017] When the The real-time distance between the drone and all static obstacles meets the requirements. Furthermore, obstacle avoidance between individual drones meets the requirements. hour, This indicates that obstacle avoidance has been completed; otherwise... ;

[0018] in, For an additional safety margin, For the first The drone and the first The real-time Euclidean distance of the drone, and ;

[0019]

[0020] The minimum safe distance between individual drones in the formation is , Indicates any two drones in the formation and Dynamic safety margin between;

[0021] Furthermore, a second-order linear discrete model is used to describe the motion of the UAVs in the multi-UAV system, as shown in the following expression:

[0022]

[0023] in, , Indicates the first A drone in Position in the global coordinate system at any given time, when =0 indicates the Navigator drone, when... A value ≥1 indicates a follower drone. Indicates the solver for the first A drone in Constantly control the input speed. Indicates the first A drone in Yaw angle at any moment Indicates the time step. Indicates the solver for the first A drone in Constantly control the input angular velocity. Indicates the solver for the first A drone in Constantly control the input speed;

[0024] Set system constraints to limit the input speed. angular velocity Rate of change of velocity The rate of change of angular velocity is as follows:

[0025] (1).

[0026] Furthermore, the consensus algorithm update rule is as follows:

[0027]

[0028]

[0029]

[0030] in, , , They are respectively in At that moment, the The drone in , , The deviation between the desired position in the direction and its own state. The convergence coefficient is . , , It indicates the desired posture of the follower.

[0031] Furthermore, the overall objective function is expressed as:

[0032] ;

[0033] in, Describe the overall objective function. , Indicates the first The objective function for the horizontal position of the drone Indicates the first The objective function for the yaw angle of the UAV. This represents the objective function for static obstacle avoidance.

[0034] Furthermore, the consensus objective function is expressed as follows:

[0035]

[0036]

[0037]

[0038] in, , , All are positive numbers greater than zero;

[0039] The objective function for static obstacle avoidance is:

[0040]

[0041] Indicates the first A drone in Time and the The real-time Euclidean distance to the nth static obstacle, when the nth obstacle is... A drone in Time and the Euclidean distance of a static obstacle Less than When the objective function for static obstacles is active, it is active; otherwise, it is 0. Static obstacles at the edge in a narrow environment are equivalent to obstacles with a radius of... The cylindrical model, with the drone body simplified to a radius of... The regular sphere defines the obstacle avoidance safety threshold. ,in For an additional safety margin, For the static obstacle avoidance weights of the drone, This indicates the control time domain.

[0042] Furthermore, the leader drone in Time and the Real-time Euclidean distance of a static obstacle , is represented as:

[0043]

[0044] in, Indicates the first The location of a static obstacle.

[0045] Furthermore, the optimal control sequence is obtained by solving the overall objective function using IPOPT.

[0046]

[0047]

[0048] in To control the time domain, In order to be in Always Predicting the velocity output at any given time.

[0049] Beneficial Effects: This invention designs a multi-UAV formation control framework of "distributed model prediction + dynamic event triggering," specifically addressing the pain points of multi-UAV collaboration in confined spaces. Compared to traditional periodic communication algorithms, the dynamic event triggering mechanism only triggers communication and formation switching when the leader reaches a critical distance from an obstacle or when the formation deviation exceeds limits, significantly reducing communication redundancy. It eliminates the need for high-bandwidth communication equipment, effectively controlling hardware costs. Simultaneously, the consensus algorithm is transformed into objective functions of horizontal position and yaw angle, combined with a two-layer obstacle avoidance constraint between static obstacles and individual formation members. Furthermore, it clarifies the physical constraints on UAV speed, angular velocity, and their changes, avoiding control misalignment and improving adaptability to complex environments. The algorithm employs distributed parallel solution, with each UAV synchronously calculating locally optimal control quantities, shortening computation time and adapting to multi-UAV swarms. ROS + Gazebo simulation verification shows that it can achieve smooth switching from "diamond → straight line → diamond → zigzag" without collisions. This significantly improves the formation efficiency and operational reliability of multi-UAV formations.

[0050] This invention is specifically applied to the collaborative control of multiple drones in confined environments, such as indoor logistics platooning, search and rescue in narrow urban streets, and tunnel engineering monitoring. Through a control framework of "distributed model prediction + dynamic event triggering," it eliminates the need for complex, high-precision equipment, ensuring collaborative task execution even in space-constrained environments. Key features include the rapid formation and stable maintenance of multi-drone formations, real-time avoidance of static obstacles and collisions within the formation, and the ability of followers to track the leader with predetermined accuracy to achieve the control target. Attached Figure Description

[0051] Figure 1 This is a flowchart of the control method of the present invention;

[0052] Figure 2 This is a simulation scene diagram of the Gazebo of the present invention;

[0053] Figure 3 The drones transformed into a diamond formation.

[0054] Figure 4 It is a picture of drones approaching a narrow area and forming a straight line formation;

[0055] Figure 5 The image shows drones partially leaving a narrow area to form a single-line formation.

[0056] Figure 6 The image shows drones leaving a narrow area and forming a diamond-shaped formation.

[0057] Figure 7 The image shows drones leaving a narrow area and forming a zigzag formation. Detailed Implementation

[0058] The invention will now be further explained with reference to the accompanying drawings.

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0060] The present invention will be further described below with reference to embodiments.

[0061] This embodiment is based on the Ubuntu 20.04 operating system, using the ROS Noetic framework and the Gazebo simulation platform to build the experimental environment. A quadcopter drone model is selected, with the leader drone labeled UAV0 and the four follower drones labeled UAV1, UAV2, UAV3, and UAV4 respectively. The experimental parameters are configured as shown in Table 1, and the core parameters are as follows:

[0062] Navigator UAV0 initial pose: preset initial x and y coordinates and yaw angle in the global coordinate system; Follower UAVs UAV1-UAV4 initial pose: set to initial discrete positions around the navigator to ensure no collision in the initial state; Static obstacle positions: two wall obstacles are set to... , The wall is only wide enough for a single drone to pass through; weighting factor: The target function weights for direction, yaw angle, and obstacle avoidance are all set according to experimental requirements to ensure that the formation maintains a balance between priority and obstacle avoidance.

[0063] like Figure 1 As shown, the present invention provides a multi-UAV model predictive flight formation control method in a confined space, comprising the following steps:

[0064] Step 1: Establish the kinematic model and system constraints of the UAV;

[0065] Step 1.1, System Composition Definition: The multi-UAV system is defined as "1 leader + 4 followers". All UAVs operate in a two-dimensional plane, with constant altitude, roll angle, and pitch angle, focusing only on horizontal formation control and obstacle avoidance;

[0066] Kinematic modeling: A second-order linear discrete model is used to describe the motion of the UAV, as shown in the following expression:

[0067]

[0068] in, , Indicates the first A drone in Position in the global coordinate system at any given time, when =0 indicates the Navigator drone, when... A value ≥1 indicates a follower drone. Indicates the solver for the first A drone in Constantly control the input speed. Indicates the first A drone in Yaw angle at any moment Indicates the time step. Indicates the solver for the first A drone in Constantly control the input angular velocity.

[0069] Step 1.2, System Constraint Setting: To avoid control misalignment, limits are set on velocity, angular velocity, velocity change, and angular velocity change. The relationship between them is shown in the following formula:

[0070] (1)

[0071] , Indicates the solver for the first A drone in The control input at time t, in a physical sense, represents the first... The desired speed and desired angular velocity of the drone. For time step. Horizontal speed and angle control input. , and rate of change of velocity and rate of change of angular velocity .

[0072] Step 2: Design the formation consensus algorithm and formation;

[0073] The steps involved in designing a formation consensus algorithm include:

[0074] The consensus algorithm is implemented using a "distance-angle navigation-following" strategy, with the following consensus update rules:

[0075]

[0076]

[0077]

[0078] in, , , They are respectively in At that moment, the The drone in , , The deviation between the desired position in the direction and its own state. As a convergence coefficient, the logic for determining the formation is based on the preset formation requirements and the real-time pose of the Navigator UAV during its flight. , , Calculate the desired pose of each follower. , , The follower drones iteratively adjust their own motion state through a consensus algorithm, track the desired pose of the follower, and ultimately form and maintain a preset formation. Furthermore, the adjustment process relies only on local information interaction and does not require global state data. , , In order to be in At that moment, the The deviation between the desired position of the drone and its own state forms a feedback adjustment mechanism of "catching up with the high and making up for the low".

[0079] Step 3: Define the objective function and design the dynamic trigger function;

[0080] Step 3.1: First, design the objective function of the consensus algorithm for the UAV.

[0081]

[0082]

[0083]

[0084] in, , , All are positive numbers greater than zero. , Indicates the first The objective function for the horizontal position of the drone Indicates the first Objective function for the yaw angle of a drone.

[0085] Step 3.2, for static obstacle avoidance, the edge static obstacle in the narrow environment is equivalent to a radius of... The cylindrical model, with the drone body simplified to a radius of... The regular sphere defines the obstacle avoidance safety threshold. (in (For additional safety margin to compensate for sensor errors and control delays); assuming a drone... exist The real-time location at any given moment is Given the first The locations of the static obstacles are: Then the first A drone in Time and the The real-time Euclidean distance between the static obstacles is:

[0086]

[0087] When the Euclidean distance between the drone and the obstacle is less than When the obstacle avoidance condition is met, the static obstacle avoidance objective function takes effect; otherwise, it is zero, to avoid excessive interference with normal movement within the safe area. Therefore, the static obstacle avoidance objective function is designed as follows:

[0088]

[0089] in, For the static obstacle avoidance weights of the drone, This refers to the distance at which the drone reaches the static obstacle.

[0090] Overall objective function for:

[0091]

[0092] Step 3.3, for obstacle avoidance between individual drones in a formation, define any two drones within the formation. and The dynamic safety margin between them is The minimum safe distance between individuals within a formation is defined as follows: For any two drones and Constructing inter-individual obstacle avoidance constraints as

[0093]

[0094]

[0095] in, This represents the real-time Euclidean distance between the two drones.

[0096] Step 3.4, Define the obstacle avoidance completeness index

[0097] Choose a dual indicator of "distance threshold + formation status" to determine obstacle avoidance completion, and define the obstacle avoidance completion judgment variable. , If the drone indicates obstacle avoidance is complete, otherwise it indicates it is incomplete. Real-time distances to all static obstacles satisfy hour, This represents an additional safety margin, indicating that obstacle avoidance has been successfully achieved. Static obstacle avoidance judgment stator variables. Otherwise, the value is 0. Inter-individual obstacle avoidance must satisfy... That is, the drone can only succeed if both static obstacle avoidance and inter-individual obstacle avoidance meet the completion conditions. Once obstacle avoidance is deemed complete, the optimization intervention of the obstacle avoidance objective function on the overall objective function is stopped, and the system reverts to normal formation tracking mode.

[0098] Step 3.5 Trigger Function Definition

[0099] The minimum real-time distance between the Navigator drone and obstacles Dynamic trigger function as the triggering basis The return value directly corresponds to the desired formation of the formation, and the specific rules are as follows:

[0100] When the Navigator drone encounters obstacles Minimum distance at time hour, This triggers a zigzag formation, with followers staggered left and right along the navigator's trajectory, improving lateral search coverage; when hour, This triggers a diamond formation, with each follower drone arranged in a diamond shape around the navigator, expanding the environmental detection range and adapting to open areas without spatial constraints, thus ensuring a smooth transition to a straight line formation in the next step. hour, Trigger a single-file formation, with each follower arranged in sequence along the navigator's flight axis, minimizing the lateral width to ensure the formation can safely traverse narrow passages that only allow a single drone to pass at a time;

[0101]

[0102]

[0103]

[0104] in, and These represent the Euclidean distances from the leader drone to the first and second static obstacles, respectively. This represents the Euclidean distance between two static obstacles. , Indicates the location of the first static obstacle; , This indicates the location of the second static obstacle.

[0105] Only during formation switching, the navigator broadcasts the desired pose offset to the followers; no communication occurs outside of switching times.

[0106] Step 4: Solve the distributed objective function using IPOPT (Interior Point OPTimizer).

[0107] Step 4.1 Solver Selection: Predicting the overall objective function of the distributed model using IPOPT. Solve the following: The drones were respectively based on The system continuously monitors the drone's own state, the navigator's state, and the positions of static obstacles. It then calculates the overall objective function from step 3. Finally, it sets physical constraints for the drone to ensure its output remains within physical limits.

[0108] The output physics constraints of the UAV are as follows:

[0109]

[0110] Find the optimal control sequence

[0111]

[0112]

[0113] in To control the time domain, In order to be in Always Predicting the velocity output at any given time.

[0114] In one embodiment, taking the navigator drone UAV0 and four follower drones UAV1, UAV2, UAV3, and UAV4 as an example, the initial positions of the drones and the positions of the obstacles are shown in Table 1.

[0115] Table 1 Parameters of the Example

[0116]

[0117] like Figure 2 As shown, the initial stage: a simulation scene diagram of the Gazebo of this invention;

[0118] like Figure 3 As shown, in the initial stage: the navigator drone is activated, and the followers form a diamond formation through a consensus algorithm;

[0119] like Figure 4 As shown, approaching a narrow area: Navigator This triggers a linear formation.

[0120] like Figure 5 As shown, during the crossing phase: the formation passes through the wall obstacles in a straight line without collision;

[0121] like Figure 6 As shown, the separation phase: Restore the diamond formation;

[0122] like Figure 7 As shown, the search phase: This triggers a zigzag formation, expanding the search coverage area.

[0123] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-UAV model predictive flight formation control method, characterized in that, Includes the following steps: The multi-drone system consists of one navigator drone and multiple follower drones, assuming that all drones operate in a two-dimensional plane, maintaining altitude, roll angle, and pitch angle. Based on the desired formation and the real-time pose of the leader drone, the desired pose of each follower is calculated in real time using the consensus algorithm to form and maintain the preset formation. Construct a general objective function, including a formation consistency objective function and a static obstacle avoidance objective function, and solve for the optimal control sequence based on the general objective function.

2. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, A dynamic trigger function was designed. , Indicates the Navigator drone and static obstacles in The minimum distance at any given moment; Inorganic organisms, when traversing narrow environments, rely on dynamic triggering functions. The value is used to perform the following formation transformation; the narrow environment refers to the Euclidean distance between two static obstacles. The value is less than the set threshold; When the drone approaches a confined environment: hour, Triggering a diamond formation, the follower drones are arranged in a diamond shape around the navigator, with the navigator located at the center of the diamond; when Dynamically triggered function Triggering a linear formation, among which This indicates the first distance of the team switch, with each follower arranged sequentially along the flight axis of the navigator drone. The drones passed between two static obstacles in a "line formation"; Drones moving away from confined environments: when Dynamically triggered function This triggers a diamond formation, with follower drones arranged in a diamond shape around the navigator drone, which is positioned at the center of the diamond. Dynamically triggered function Triggering a zigzag formation, in which This indicates the second distance of the team switching, with follower drones staggered along both sides of the navigator drone's trajectory; ； ； ； in, and These represent the Euclidean distances from the leader drone to the first and second static obstacles, respectively. This represents the Euclidean distance between two static obstacles. , Indicates the location of the first static obstacle in a confined environment; , This indicates the location of the second static obstacle in a confined environment, where the Navigator drone is positioned relative to the static obstacle. Minimum distance at time Pick and The minimum value in.

3. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The design of the first Variables for determining whether a drone has successfully completed obstacle avoidance ; When the The real-time distance between the drone and all static obstacles meets the requirements. Furthermore, obstacle avoidance between individual drones meets the requirements. hour, This indicates that obstacle avoidance has been completed; otherwise... ; in, For an additional safety margin, For the first The drone and the first The real-time Euclidean distance of the drone, and ; ； The minimum safe distance between individual drones in the formation is , Indicates any two drones in the formation and The dynamic safety margin between them.

4. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The motion of UAVs in a multi-UAV system is described using a second-order linear discrete model, as shown in the following expression: ； in, , Indicates the first A drone in Position in the global coordinate system at any given time, when =0 indicates the Navigator drone, when... A value ≥1 indicates a follower drone. Indicates the solver for the first A drone in Constantly control the horizontal speed of input. Indicates the first A drone in Yaw angle at any moment Indicates the time step. Indicates the solver for the first A drone in Constantly control the input angular velocity. Indicates the first A drone in Constantly control the input speed; Set system constraints to limit input speed angular velocity Rate of change of velocity and rate of change of angular velocity ,as follows: (1)。 5. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The consensus algorithm update rule is as follows: ； ； ； in, , , They are respectively in At that moment, the The drone in , , The deviation between the desired position in the direction and its own state. The convergence coefficient is . , , It indicates the desired posture of the follower.

6. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The overall objective function is expressed as: ； in, Describe the overall objective function. , Indicates the first The objective function for the horizontal position of the drone Indicates the first The objective function for the yaw angle of the UAV. This represents the objective function for static obstacle avoidance.

7. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The consistency objective function is expressed as follows: ； ； ； in, , , All are positive numbers greater than zero; The objective function for static obstacle avoidance is: ； Indicates the first A drone in Time and the The real-time Euclidean distance to the nth static obstacle, when the nth obstacle is... A drone in Time and the Euclidean distance of a static obstacle Less than When the objective function for static obstacles is active, it is active; otherwise, it is 0. Static obstacles at the edge in a narrow environment are equivalent to obstacles with a radius of... The cylindrical model, with the drone body simplified to a radius of... The regular sphere defines the obstacle avoidance safety threshold. ,in For an additional safety margin, For the static obstacle avoidance weights of the drone, This indicates the control time domain.

8. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, Leader drones in Time and the Real-time Euclidean distance of a static obstacle , is represented as: ； in, Indicates the first The location of a static obstacle.

9. The multi-UAV model predictive flight formation control method according to claim 1, characterized in that, The optimal control sequence is obtained by solving the overall objective function using IPOPT. ； ； in To control the time domain, In order to be in Always Predicting the velocity output at any given time.

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