Unmanned aerial vehicle formation distributed model predictive control method based on field of view constraint

Abstract

The application provides a UAV formation distributed model predictive control method based on field of view constraints, and belongs to the technical field of UAV cooperative control. The method comprises the following steps: S1, a double-integrator particle kinematics model is established; S2, a predicted state sequence is received; S3, it is judged whether it falls into a conical field of view; S4, it is dynamically decided whether to add a field of view constraint in a local optimization problem; S5, an optimal control sequence is solved; S6, the double-integrator particle kinematics model is updated; and S7, steps S2 to S6 are repeated until all UAVs complete a target tracking task. The application aims to overcome the defects of single field of view constraint processing mode and limited formation mobility in the existing UAV formation target tracking technology, and can simultaneously guarantee global target continuous coverage and individual UAV obstacle avoidance and flexible formation maintenance in a complex obstacle environment.

Description

Technical Field

[0001] This invention relates to the field of collaborative control technology for unmanned aerial vehicles (UAVs), and in particular to a distributed model predictive control method for UAV formations based on field-of-view constraints. Background Technology

[0002] Multi-UAV collaborative formation tracking has significant application value in fields such as military reconnaissance, environmental monitoring, and disaster early warning. Compared with single-UAV tracking, formation tracking can achieve multi-angle collaborative imaging, improve target positioning accuracy, and has stronger mission robustness—when one UAV fails, the others can still continue to perform the mission.

[0003] Existing single-UAV target tracking technologies mainly include fuzzy control-based, visual servoing-based, and predictive methods with obstacle avoidance capabilities. Some schemes mitigate occlusion effects through dedicated filters, but single-UAV tracking still struggles to avoid tracking failures due to temporary target loss. For multi-UAV formation tracking, existing research primarily employs centralized or distributed control frameworks, with Distributed Model Predictive Control (DMPC) attracting widespread attention due to its low computational burden and minimal communication requirements. However, most DMPC formation tracking schemes only focus on trajectory tracking, formation maintenance, and obstacle avoidance, failing to incorporate the field-of-view (FOV) constraints of the airborne cameras into a unified optimization framework. Some studies involving FOV constraints typically require each UAV to independently meet the FOV coverage requirement; this static constraint limits the flexibility of the formation when performing obstacle avoidance or maneuvers.

[0004] Furthermore, existing technologies fall short in addressing the paradoxical problem of "how to maximize the maneuver freedom of individual machines while ensuring continuous coverage of the global target." There is a lack of a distributed cooperative control method capable of utilizing formation redundancy coverage capabilities and dynamically switching individual field-of-view constraints. Summary of the Invention

[0005] This invention provides a distributed model predictive control method for UAV formation based on field-of-view constraints, which aims to overcome the shortcomings of existing UAV formation target tracking technologies, such as the single field-of-view constraint processing method and limited formation maneuverability. It can simultaneously ensure continuous global target coverage and obstacle avoidance for individual UAVs and maintain formation flexibility in complex obstacle environments.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A distributed model predictive control method for UAV formation based on field-of-view constraints includes: Step S1: Establish a dual integrator mass kinematic model for each UAV in the formation and discretize it into a linear state equation; set the communication topology between UAVs as a ring neighbor relationship, and each UAV only exchanges predicted trajectories with its neighboring UAVs; Step S2: At the current moment, each drone receives from each of its neighboring drones the predicted state sequence broadcast by that neighboring drone at the previous moment, which covers each prediction step in the prediction time domain. Step S3: Each UAV determines, based on the received predicted state sequence of neighboring UAVs, whether there exists at least one neighboring UAV in the predicted time domain that can cause the ground target to fall into its downward-pointing conical field of view; if so, the global coverage flag of that UAV is set to valid; otherwise, it is set to invalid. Step S4: Each UAV dynamically decides whether to add field of view constraints to the local optimization problem based on the state of the global coverage flag: if the global coverage flag is invalid, the UAV is forced to satisfy the field of view constraints; if the global coverage flag is valid, the UAV skips the field of view constraints, allowing ground targets not to fall within its field of view during the current optimization cycle. Step S5: For each UAV, with the objective function as the goal, a convex optimization problem is constructed and solved under the conditions including physical constraints and inter-UAV collision avoidance constraints to obtain the optimal control sequence; the objective function includes at least a trajectory tracking term, a formation maintenance term, an input penalty term, and an obstacle avoidance penalty term; Step S6: Each UAV takes the first control variable from the optimal control sequence, applies it to the dual integrator mass kinematic model of the UAV to update its state, and broadcasts the newly generated predicted state sequence of the UAV in the prediction time domain to all neighboring UAVs. Step S7: Repeat steps S2 to S6 until all drones have completed the target tracking task.

[0007] In this specification, the trajectory tracking term in the objective function calculates the reference trajectory of the UAV by superimposing the future position of the ground target with the desired formation offset, and minimizes the weighted deviation between the predicted state of the UAV and the reference trajectory; the formation maintaining term calculates the weighted deviation between the actual relative position and the desired relative position between the UAV and each neighboring UAV using the predicted state sequence received from neighboring UAVs; the input penalty term applies a weighted sum of squares penalty to the amplitude of each control variable in the control sequence; and the obstacle avoidance penalty term applies a penalty to the predicted position where the distance between the UAV and the obstacle is less than a safe distance in the prediction time domain, based on the equivalent model of the circumcircle of the obstacle.

[0008] In this specification, the specific method for determining whether a neighboring UAV can bring a ground target into its conical field of view in step S3 is as follows: based on the horizontal position in the predicted state sequence of the neighboring UAV, calculate the horizontal distance between the horizontal position of the ground target and the horizontal position; if the horizontal distance is less than or equal to the product of the flight altitude of the neighboring UAV and the tangent of the half-apex angle of the conical field of view, then it is determined that the neighboring UAV can cover the ground target in the corresponding prediction step; if the above condition is met in any prediction step in the prediction time domain, it is determined that the neighboring UAV can cover the ground target.

[0009] In this specification, the mandatory satisfaction of the field of view constraint means that, in the constraints of the local optimization problem, the horizontal distance between the horizontal position of the UAV and the horizontal position of the ground target in each prediction step in the prediction time domain does not exceed the product of the UAV's flight altitude and the tangent of the half-apex angle of the conical field of view.

[0010] In this specification, the physical constraint means that the absolute value of the component of each axis of the acceleration vector of this UAV does not exceed the preset maximum acceleration value; the inter-UAV collision avoidance constraint means that the distance between the horizontal position of this UAV at each prediction step in the prediction time domain and the horizontal position of the corresponding prediction step in the previous prediction state sequence received from the neighboring UAV is not less than the preset UAV safety distance.

[0011] In this specification, the equivalent model of the circumcircle of the obstacle is as follows: each obstacle is equivalent to an infinitely tall cylinder, and the radius of its base circle is the radius of the circumcircle of the obstacle; in the obstacle avoidance penalty term, the distance between the UAV and the obstacle is defined as the distance from the horizontal position of the UAV to the center of the circumcircle of the obstacle minus the radius of the circumcircle; when the distance is less than the preset obstacle safety distance, a quadratic penalty function is used to calculate the penalty value; in order to maintain the convexity of the optimization problem, a second-order Taylor expansion of the penalty function is performed based on the current predicted position in each optimization to obtain a quadratic form with respect to the control sequence.

[0012] In this specification, the number of drones in the formation is three, and the desired formation is a triangle formation with equal side lengths; the desired relative position vector is the position vector corresponding to the side of the triangle.

[0013] In this specification, the prediction time domain and control time domain adopt a rolling time domain strategy. After each sampling period, all UAVs execute steps S2 to S6 in parallel. All UAVs use the predicted state sequence received from their neighbors at the previous moment within the same sampling period to achieve distributed parallel optimization.

[0014] In this specification, the predicted state sequence includes the position and velocity information of the current UAV at each prediction step in the prediction time domain; the predicted state sequence of the previous moment broadcast by the neighboring UAV is used by the current UAV to detect the risk of inter-UAV collision at future moments and to determine whether the ground target has been covered by the neighboring UAV.

[0015] In this specification, at each sampling time, each UAV sequentially performs the following steps: receiving the predicted state sequence broadcast by all neighbors; calculating the neighbor coverage flag based on the received predicted state sequence, thereby obtaining the local global coverage flag; determining whether to add field-of-view constraints to the optimization problem based on the global coverage flag; constructing an objective function that includes trajectory tracking, formation maintenance, input penalty, and obstacle avoidance penalty, and combining physical constraints, inter-UAV collision avoidance constraints, and if added field-of-view constraints to form a convex optimization problem; calling the convex optimization solver to obtain the optimal control sequence; applying the first control variable to the UAV; and broadcasting the local new predicted state sequence to all neighbors.

[0016] In summary, the present invention has at least the following beneficial effects: Coordinated optimization of global field-of-view coverage and individual maneuverability: Through a dynamic field-of-view constraint switching mechanism, as long as one UAV in the formation covers the target, the other UAVs can temporarily break free from field-of-view limitations, thus enabling more flexible obstacle avoidance maneuvers or formation adjustments. This significantly improves the overall maneuverability and adaptability of the formation while ensuring that the target is not lost.

[0017] Efficient solution under a unified multi-constraint framework: Trajectory tracking, formation keeping, input smoothing, obstacle avoidance and field of view constraints are integrated into the same distributed model predictive control optimization problem, avoiding the performance loss caused by multi-module cascade design, and the convexity processing ensures that the problem can be solved quickly to meet the real-time control requirements.

[0018] Enhanced system robustness and reliability: The distributed architecture ensures that a single point of failure will not cause the entire system to fail; at the same time, the dynamic switching mechanism of the field of view constraint naturally has redundant coverage characteristics. Even if individual UAVs deviate from the formation due to obstacle avoidance, other UAVs can still take over to maintain target coverage, greatly improving mission reliability.

[0019] Excellent adaptability to complex environments: After the obstacle is treated as an equivalent circumcircle and combined with the obstacle avoidance penalty, the UAV can detect and avoid obstacles in advance; the formation maintenance item uses local neighbor information to maintain a triangular formation, and can quickly restore the desired formation after obstacle avoidance, adapting to static and regular dynamic obstacle environments.

[0020] Reduced communication and computational burden: Each drone only needs to broadcast its predicted trajectory to its neighbors, without the need for global information exchange or a centralized solver. This results in low communication overhead and distributed computational load, making it suitable for real-time applications of large-scale drone formations. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the distributed model predictive control method for UAV formation based on field-of-view constraints involved in this invention.

[0023] Figure 2 This is an equivalent schematic diagram of the circumscribed ball of the obstacle involved in this invention.

[0024] Figure 3 This is a schematic diagram of the FOV model of the unmanned aerial vehicle involved in this invention.

[0025] Figure 4 This is a top-view schematic diagram of the trajectory involved in this invention.

[0026] Figure 5 This is a schematic diagram of the trajectory side view involved in the present invention.

[0027] Figure 6 This is a schematic diagram of the formation error involved in this invention.

[0028] Figure 7 This is a schematic diagram of the field of view coverage ratio involved in this invention.

[0029] Figure 8 This is a schematic diagram of the machine-to-machine distance involved in this invention.

[0030] Figure 9 This is a schematic diagram of the nearest obstacle involved in this invention. Detailed Implementation

[0031] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0032] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0033] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0034] like Figure 1 As shown, this embodiment provides a distributed model predictive control method for UAV formation based on field-of-view constraints, including: Step S1: Establish a dual integrator mass kinematic model for each UAV in the formation and discretize it into a linear state equation; set the communication topology between UAVs as a ring neighbor relationship, and each UAV only exchanges predicted trajectories with its neighboring UAVs; Step S2: At the current moment, each drone receives from each of its neighboring drones the predicted state sequence broadcast by that neighboring drone at the previous moment, which covers each prediction step in the prediction time domain. Step S3: Each UAV determines, based on the received predicted state sequence of neighboring UAVs, whether there exists at least one neighboring UAV in the predicted time domain that can cause the ground target to fall into its downward-pointing conical field of view; if so, the global coverage flag of that UAV is set to valid; otherwise, it is set to invalid. Step S4: Each UAV dynamically decides whether to add field of view constraints to the local optimization problem based on the state of the global coverage flag: if the global coverage flag is invalid, the UAV is forced to satisfy the field of view constraints; if the global coverage flag is valid, the UAV skips the field of view constraints, allowing ground targets not to fall within its field of view during the current optimization cycle. Step S5: For each UAV, with the objective function as the goal, a convex optimization problem is constructed and solved under the conditions including physical constraints and inter-UAV collision avoidance constraints to obtain the optimal control sequence; the objective function includes at least a trajectory tracking term, a formation maintenance term, an input penalty term, and an obstacle avoidance penalty term; Step S6: Each UAV takes the first control variable from the optimal control sequence, applies it to the dual integrator mass kinematic model of the UAV to update its state, and broadcasts the newly generated predicted state sequence of the UAV in the prediction time domain to all neighboring UAVs. Step S7: Repeat steps S2 to S6 until all drones have completed the target tracking task.

[0035] In some embodiments, the trajectory tracking term in the objective function calculates the reference trajectory of the UAV by superimposing the future position of the ground target with the desired formation offset, and minimizes the weighted deviation between the predicted state of the UAV and the reference trajectory; the formation maintaining term calculates the weighted deviation between the actual relative position and the desired relative position between the UAV and each neighboring UAV using the predicted state sequence received from neighboring UAVs; the input penalty term applies a weighted sum of squares penalty to the amplitude of each control variable in the control sequence; and the obstacle avoidance penalty term applies a penalty to the predicted position where the distance between the UAV and the obstacle is less than a safe distance in the prediction time domain, based on the equivalent model of the circumcircle of the obstacle.

[0036] In some embodiments, the specific method for determining whether a neighboring UAV can bring a ground target into its conical field of view in step S3 is as follows: based on the horizontal position in the predicted state sequence of the neighboring UAV, calculate the horizontal distance between the horizontal position of the ground target and the horizontal position; if the horizontal distance is less than or equal to the product of the flight altitude of the neighboring UAV and the tangent of the half-apex angle of the conical field of view, it is determined that the neighboring UAV can cover the ground target in the corresponding prediction step; if the above condition is met in any prediction step in the prediction time domain, it is determined that the neighboring UAV can cover the ground target.

[0037] In some embodiments, the forced satisfaction of the field of view constraint means that, in the constraints of the local optimization problem, the horizontal distance between the horizontal position of the UAV and the horizontal position of the ground target in each prediction step in the prediction time domain does not exceed the product of the UAV's flight altitude and the tangent of the half-apex angle of the conical field of view.

[0038] In some embodiments, the physical constraint means that the absolute value of the component of each axis of the acceleration vector of the UAV does not exceed a preset maximum acceleration value; the inter-UAV collision avoidance constraint means that the distance between the horizontal position of the UAV at each prediction step in the prediction time domain and the horizontal position of the corresponding prediction step in the previous prediction state sequence received from the neighboring UAV is not less than a preset UAV safety distance.

[0039] In some embodiments, the equivalent model of the circumcircle of the obstacle is: each obstacle is equivalent to an infinitely tall cylinder, the radius of its base circle being the radius of the circumcircle of the obstacle; in the obstacle avoidance penalty term, the distance between the UAV and the obstacle is defined as the distance from the horizontal position of the UAV to the center of the circumcircle of the obstacle minus the radius of the circumcircle; when the distance is less than the preset obstacle safety distance, a quadratic penalty function is used to calculate the penalty value; to maintain the convexity of the optimization problem, a second-order Taylor expansion of the penalty function is performed based on the current predicted position during each optimization to obtain a quadratic form with respect to the control sequence.

[0040] In some embodiments, the number of drones in the formation is three, and the desired formation is a triangle formation with equal side lengths; the desired relative position vector is the position vector corresponding to the side of the triangle.

[0041] In some embodiments, the prediction time domain and control time domain adopt a rolling time domain strategy. After each sampling period, all UAVs execute steps S2 to S6 in parallel. All UAVs use the predicted state sequence received from their neighbors at the previous moment within the same sampling period to achieve distributed parallel optimization.

[0042] In some embodiments, the predicted state sequence includes the position and velocity information of the local UAV at each prediction step in the prediction time domain; the predicted state sequence of the previous moment broadcast by the neighboring UAV is used by the local UAV to detect the risk of inter-UAV collision at future moments and to determine whether the ground target has been covered by the neighboring UAV.

[0043] In some embodiments, at each sampling time, each UAV sequentially performs the following steps: receiving the predicted state sequence broadcast by all neighbors; calculating the neighbor coverage flag based on the received predicted state sequence, thereby obtaining the local global coverage flag; determining whether to add field-of-view constraints to the optimization problem based on the global coverage flag; constructing an objective function including trajectory tracking, formation keeping, input penalty, and obstacle avoidance penalty, and combining physical constraints, inter-UAV collision avoidance constraints, and if added field-of-view constraints to form a convex optimization problem; calling the convex optimization solver to obtain the optimal control sequence; applying the first control variable to the UAV; and broadcasting the local new predicted state sequence to all neighbors.

[0044] The technical concept of this invention is as follows: This invention proposes a distributed model predictive control method for UAV formation based on field-of-view constraints, used for multiple UAVs to collaboratively track ground targets in obstacle environments. The core scheme is as follows: Each UAV employs a dual integrator point mass model, discretized into a linear state-space equation. A ring-neighbor communication topology is used between UAVs, with each UAV exchanging predicted trajectory information only with its local neighbors.

[0045] The objective function for the local optimization problem consists of four parts: Trajectory tracking: Guides the UAV to track the overall movement of the target and superimposes the desired formation offset; Formation maintenance: Using neighbor-predicted trajectories, the relative positions of the drones are made closer to the desired triangular formation; Input penalty term: Limit the acceleration amplitude to ensure a smooth trajectory; Obstacle avoidance penalty: Based on the equivalent model of the circumcircle of the obstacle, a penalty is imposed on the predicted position where the distance from the obstacle is less than the safe distance.

[0046] The constraints include: Physical constraints (maximum acceleration limit); Inter-drone collision avoidance constraints (maintaining a safe distance between drones); Field of view constraint: The downward-pointing sensor field of view of the UAV is modeled as a conical region, requiring that the projected distance of the target in the horizontal direction be less than the radius of the field of view.

[0047] The core feature of this invention lies in its dynamic switching mechanism for field-of-view constraints based on neighbor coverage status. When solving the local optimization problem, each UAV determines, based on the predicted trajectory received from its neighbors at the previous moment, whether there exists at least one neighbor within the prediction time domain that can cause the target to fall within its field-of-view cone. If such a neighbor exists (global coverage flag is 1), the UAV can temporarily relax or skip its own field-of-view constraints, thereby gaining greater maneuver freedom. If all neighbors cannot cover the target (global coverage flag is 0), the UAV must forcibly satisfy the field-of-view constraints to ensure that the global target is always covered by at least one UAV.

[0048] All constraints and the objective function constitute a convex optimization problem, which is solved using quadratic programming to obtain the optimal control sequence and execute the first control input. This process is repeated in each sampling period until the task is completed.

[0049] This invention studies a method of... A formation system of quadcopter drones collaboratively tracks a ground target moving along a known trajectory. Each drone is equipped with downward-pointing sensors, and its field of view (FOV) is modeled as a cone-shaped area with its axis vertically downwards. During tracking, the drones must maintain a triangular formation to ensure the target remains within the FOV of at least one drone and avoid obstacles encountered during flight. To simplify the problem, this invention makes the following assumptions: a) Assume the drone can detect obstacles in the environment from a sufficiently long distance and avoid them by circumventing them. Treat the obstacles as infinitely tall cylinders, with the size of the base circle equivalent to the obstacle's circumcircle, such as... Figure 2 As shown.

[0050] b) Assuming the UAV flies in an ideal environment, the UAV can be simplified into a kinematic model of a point mass with a dual integrator, which is beneficial for fast calculation.

[0051] c) Assume that the communication topology between UAVs is fixed as a ring neighbor relationship, with no communication delay, packet loss or noise.

[0052] System Model: a) UAV modeling. The UAV state equation is: (1) in Indicates the first The position of the drone in the ground coordinate system. and It indicates its speed and control input (acceleration). This represents which drone. Indicates a collection of drones. Represent a constant. express The first derivative, express The first derivative, Indicates the first The positional components of the drone Indicates the first The velocity component of the drone Indicates the first The acceleration component of the drone. T represents the transpose.

[0053] Discretizing the state equations yields: (2) Among them, the state variables of the drone System matrix Input matrix , Sampling time. The number of discrete time steps. It is a 3rd order identity matrix. It is a 3rd order zero matrix.

[0054] b) Physical constraints. To meet the physical characteristics of the UAV, its acceleration needs to be constrained.

[0055] (3) in This is the maximum acceleration.

[0056] d) Collision avoidance constraints. Collision avoidance constraints were designed to ensure the safe flight of the UAV.

[0057] (4) in for Current drones Location, for Proximity drones The predicted location, To maintain a safe distance for drones.

[0058] e) Field of View (FOV) Constraints. This invention proposes a constraint switching method based on neighbor coverage status. When solving the local optimization problem, each UAV uses the predicted trajectory received from its neighbors at the previous time step to determine whether other UAVs will satisfy the FOV constraints at future time steps. If at least one neighbor can cover the target, the UAV can temporarily relax its own FOV constraints to enhance maneuverability; if all neighbors cannot cover the target, the UAV must satisfy the FOV constraints. The UAV FOV model is as follows: Figure 3 As shown.

[0059] Define a neighbor overlay flag function For drones Each neighbor The present invention is based on the neighbor information received at the previous moment. The predicted position is used to determine: at a future prediction step, the neighbor... Whether the target can be brought into its field of view cone.

[0060] (5) in for The target location at any given time The altitude at which the drone flies. The semi-apex angle of the field of view cone. To predict the number of time-domain steps, It means neighbors In the previous moment's planning, it was believed that the goal could be achieved at some point in the future.

[0061] Define a global override flag function , This means that at least one neighbor can cover the target, otherwise .

[0062] (6) For drones The set of neighbors. The constraint switching mechanism is: if Then drone Field of view constraints must be enforced to ensure global coverage. Then drone The field of view constraint can be temporarily ignored in exchange for greater maneuverability. It is a large operator that represents a logical OR operation.

[0063] Controller design: Distributed Model Predictive Control: The method of this invention is based on distributed model predictive control. Each UAV independently constructs a local optimization problem in parallel iterations using the predicted state sequence shared by its neighbors from the previous time step, and achieves cooperative coverage through dynamic field-of-view constraint switching. At each discrete time point, each UAV sequentially executes the following steps: a) Receive the predicted state sequence broadcast by all neighboring drones at the previous moment, and use these sequences to detect the risk of inter-drone collision at future moments and whether the target has been covered by other drones.

[0064] b) Constructing the local optimization problem: The objective function includes the tracking cost of the desired formation position, the cost of relative position deviation with neighbors, the cost of control variables, and the cost of obstacle avoidance penalties; constraints include acceleration limits and inter-machine collision avoidance. Specifically, based on the coverage status of neighbors in step a, it is dynamically decided whether to add a field-of-view constraint to the local optimization: if all neighbors do not cover the target in the prediction time domain, the local machine must be forced to satisfy the field-of-view constraint; otherwise, the constraint is skipped, allowing the local machine to flexibly adjust to optimize the formation.

[0065] c) Solve the optimization problem to obtain the optimal control sequence. Apply the first control variable to the UAV model to update its state, and broadcast the newly generated predicted state sequence to all neighbors in the cluster. Repeat the above process until all UAVs have completed the tracking task.

[0066] This strategy ensures that at least one drone covers the target by imposing field-of-view constraints only on "uncovered" drones, while giving other drones greater freedom to maintain formation and avoid obstacles.

[0067] Objective function: To compute the optimal input sequence and thus minimize the objective function, there are four parts: a) Trajectory tracking. Guides the UAV to follow the overall movement of the target. By adding a fixed formation offset to the target's future position, it ensures that the UAV maintains target tracking in the global coordinate system.

[0068] (7) in For reference, its position portion consists of the target position plus an offset, while the velocity portion is set to 0. As the reference trajectory tracking weight matrix, ; For the trajectory tracking term of the objective function, This is a MATLAB function used to construct a block diagonal matrix. It is a 3rd order zero matrix. As the reference trajectory position weight matrix, It is a MATLAB function used to construct diagonal matrices.

[0069] b) Formation Preservation Term. Using neighbor-predicted trajectories, the relative positions of the UAVs are brought closer to the desired triangular formation. This term reduces the complexity of the solution by making formation control rely solely on local communication.

[0070] (8) For the desired drone Compared to drones The position vector, To maintain the weight matrix for the formation, ; To maintain the position weight matrix for the formation, This is the formation preservation term of the objective function.

[0071] c) Input penalty term. Penalize the acceleration amplitude to ensure a smooth trajectory and compliance with physical constraints.

[0072] (9) in To control the number of steps in the time domain, the weight matrix... ; This is the input penalty term for the objective function.

[0073] d) Obstacle avoidance penalty. Definition of the first... unmanned aerial vehicles and obstacles The distance is: (10) in Let the center of the circumcircle of the obstacle be... For the radius. When Imposing punishment The safe distance from the obstacle. The penalty function is defined as: (11) in It is the penalty weight.

[0074] The total obstacle avoidance penalty is the sum of all obstacles and all prediction steps: (12) in Number the obstacles, because It is a non-convex function of the predicted position. To maintain the convexity of the problem, in each optimization, the current predicted position is used as the basis for... Performing a second-order Taylor expansion yields information about the control sequence. The quadratic form. This is the obstacle avoidance penalty term in the objective function.

[0075] Therefore, the optimization problem can be constructed as follows: (13) This indicates that formulas (3), (4), (5), and (6) are used as constraint terms.

[0076] Simulation Experiment and Analysis: To verify the effectiveness of the proposed control algorithm, a simulation scenario of multiple UAVs collaboratively tracking a ground target was set up. Three UAVs formed a formation with sides of length 3... An equilateral triangle formation with a fixed height of 5 m m is flying, and the target is moving on the ground.

[0077] During the simulation, the three drones successfully tracked the target, exhibiting smooth flight trajectories without any violent maneuvers. They also quickly returned to the desired triangular formation after safely avoiding obstacles.

[0078] Figure 4 and Figure 5 The images show the relative positions of the drone trajectories and obstacles, and it can be seen that each drone adjusted its course in advance when approaching the obstacle, and no collisions occurred.

[0079] Figure 6 The curve showing the change in formation error over time is presented. Formation error is an indicator that measures the difference between the actual formation of UAVs and the desired formation. Formation error is defined as: (14) That is, to calculate the distance between each pair of the three drones. , , Then calculate their values ​​and the expected side length. The root mean square error was [value missing]. Throughout the entire process, the maximum formation error was only approximately 0.8 [value missing]. m, and after avoiding obstacles, it can quickly converge and accurately maintain the formation shape.

[0080] Figure 7 The curve showing the change of field of view coverage ratio over time is presented. Field of view coverage ratio is an indicator of the target's deviation from the field of view range. The field of view coverage ratio is defined as: (15) That is, the actual horizontal distance of the target divided by the field of view radius, where This is the actual horizontal distance. This indicates that the target is within the field of view.

[0081] Figure 8 This demonstrates the distance between drones, with an expected formation side length of 3m and the distance between drones. The distance between a drone and its neighbor fluctuates when the drone deviates due to obstacle avoidance, but remains much greater than 1 meter. This indicates that the inter-machine collision avoidance constraints were fully satisfied, the formation remained well maintained, and no collision occurred.

[0082] Figure 9 The diagram shows the distance between the drone and the nearest obstacle. As can be seen from the curve, when the drone approaches an obstacle, the minimum distance is about 0.2m and the duration is extremely short, which is acceptable in a real system. Overall, the drone successfully avoided all obstacles.

[0083] This invention addresses the task of multi-UAV cooperative tracking of ground targets by proposing a distributed model predictive control (MPC) method for UAV formation based on field-of-view constraints. Each UAV independently constructs a local optimization problem, and cooperation is achieved by exchanging predicted trajectories, avoiding the excessive time complexity of centralized control. By introducing a dynamic field-of-view constraint switching strategy, the problem of single-UAVs easily losing targets is solved. Simulation results demonstrate that the proposed distributed MPC framework can achieve cooperative tracking of multi-UAV formations in complex obstacle environments, balancing formation maintenance, field-of-view coverage, and obstacle avoidance safety, exhibiting good robustness and promising engineering applications.

[0084] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0085] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

[0086] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention. The above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

[0087] It should be noted that the above description of the process is for illustrative purposes only and does not limit the scope of this specification. Those skilled in the art can make various modifications and changes to the process under the guidance of this specification. However, these modifications and changes remain within the scope of this specification.

[0088] The basic concepts have been described above. Obviously, for those skilled in the art who have read this application, the above disclosure is merely illustrative and does not constitute a limitation of this application. Although not explicitly stated herein, those skilled in the art may make various modifications, improvements, and corrections to this application. Such modifications, improvements, and corrections are suggested in this application, and therefore, such modifications, improvements, and corrections still fall within the spirit and scope of the exemplary embodiments of this application.

[0089] Furthermore, this application uses specific terms to describe its embodiments. For example, "an embodiment," "one embodiment," and / or "some embodiments" refer to a particular feature, structure, or characteristic related to at least one embodiment of this application. Therefore, it should be emphasized and noted that "an embodiment," "one embodiment," or "an alternative embodiment" mentioned twice or more in different positions in this specification do not necessarily refer to the same embodiment. In addition, certain features, structures, or characteristics in one or more embodiments of this application can be appropriately combined.

[0090] Furthermore, those skilled in the art will understand that aspects of this application can be described and illustrated through several patentable types or situations, including any new and useful combination of processes, machines, products, or substances, or any new and useful improvements thereof. Therefore, aspects of this application can be implemented entirely in hardware, entirely in software (including firmware, resident software, microcode, etc.), or a combination of hardware and software. All of the above hardware or software can be referred to as a “unit,” “module,” or “system.” Furthermore, aspects of this application can take the form of a computer program product embodied in one or more computer-readable media, wherein computer-readable program code is contained therein.

[0091] The computer program code required for the operation of each part of this application can be written in any one or more programming languages, including object-oriented programming languages ​​such as Java, Scala, Smalltalk, Eiffel, JADE, Emerald, C++, C#, VB.NET, and Python; general programming languages ​​such as C; Visual Basic, Fortran2103, Perl, COBOL2102, PHP, and ABAP; dynamic programming languages ​​such as Python, Ruby, and Groovy; or other programming languages. This program code can run entirely on the user's computer, or as a standalone software package on the user's computer, or partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer can be connected to the user's computer via any network, such as a local area network (LAN) or wide area network (WAN), or connected to an external computer (e.g., via the Internet), or in a cloud computing environment, or used as a service such as Software as a Service (SaaS).

[0092] Furthermore, unless expressly stated in the claims, the order of processing elements and sequences, the use of numbers and letters, or other names described in this application are not intended to limit the order of the processes and methods of this application. Although some currently considered useful embodiments of the invention have been discussed in the foregoing disclosure by way of various examples, it should be understood that such details are for illustrative purposes only, and the appended claims are not limited to the disclosed embodiments; rather, the claims are intended to cover all modifications and equivalent combinations that conform to the substance and scope of the embodiments of this application. For example, although the implementation of the various components described above can be embodied in a hardware device, it can also be implemented as a purely software solution, such as an installation on an existing server or mobile device.

[0093] Similarly, it should be noted that, in order to simplify the description of the present application and thus aid in the understanding of one or more embodiments of the invention, the foregoing description of the embodiments of the present application sometimes combines multiple features into a single embodiment, drawing, or description thereof. However, this approach of the present application should not be construed as reflecting an intention that the claimed subject matter requires more features than expressly recited in each claim. Rather, the subject of the invention should possess fewer features than in any single embodiment described above.

Claims

1. A distributed model predictive control method for UAV formation based on field-of-view constraints, characterized in that, include: Step S1: Establish a dual integrator mass kinematic model for each UAV in the formation and discretize it into a linear state equation; set the communication topology between UAVs as a ring neighbor relationship, and each UAV only exchanges predicted trajectories with its neighboring UAVs; Step S2: At the current moment, each drone receives from each of its neighboring drones the predicted state sequence broadcast by that neighboring drone at the previous moment, which covers each prediction step in the prediction time domain. Step S3: Each UAV determines, based on the received predicted state sequence of neighboring UAVs, whether there is at least one neighboring UAV in the predicted time domain that can cause the ground target to fall into its downward-pointing conical field of view. If it exists, then set the global coverage flag of the drone to an active state; otherwise, set it to an inactive state. Step S4: Each UAV dynamically decides whether to add field of view constraints to the local optimization problem based on the state of the global coverage flag: if the global coverage flag is invalid, the UAV is forced to satisfy the field of view constraints; if the global coverage flag is valid, the UAV skips the field of view constraints, allowing ground targets not to fall within its field of view during the current optimization cycle. Step S5: For each UAV, with the objective function as the goal, a convex optimization problem is constructed and solved under the conditions including physical constraints and inter-UAV collision avoidance constraints to obtain the optimal control sequence; the objective function includes at least a trajectory tracking term, a formation maintenance term, an input penalty term, and an obstacle avoidance penalty term; Step S6: Each UAV takes the first control variable from the optimal control sequence, applies it to the dual integrator mass kinematic model of the UAV to update its state, and broadcasts the newly generated predicted state sequence of the UAV in the prediction time domain to all neighboring UAVs. Step S7: Repeat steps S2 to S6 until all drones have completed the target tracking task.

2. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, The trajectory tracking term in the objective function calculates the reference trajectory of the UAV by superimposing the future position of the ground target with the desired formation offset, and minimizes the weighted deviation between the predicted state of the UAV and the reference trajectory. The formation maintaining term calculates the weighted deviation between the actual relative position and the desired relative position between the UAV and each neighboring UAV using the predicted state sequence received from neighboring UAVs. The input penalty term applies a weighted sum of squares penalty to the amplitude of each control variable in the control sequence. The obstacle avoidance penalty term applies a penalty to the predicted position where the distance between the UAV and the obstacle is less than the safe distance in the prediction time domain, based on the equivalent model of the circumcircle of the obstacle.

3. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, The specific method for determining whether a neighboring UAV can bring a ground target into its conical field of view in step S3 is as follows: based on the horizontal position in the predicted state sequence of the neighboring UAV, calculate the horizontal distance between the horizontal position of the ground target and the horizontal position; if the horizontal distance is less than or equal to the product of the flight altitude of the neighboring UAV and the tangent of the half-apex angle of the conical field of view, it is determined that the neighboring UAV can cover the ground target in the corresponding prediction step; if the above condition is met in any prediction step in the prediction time domain, it is determined that the neighboring UAV can cover the ground target.

4. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, The mandatory field-of-view constraint means that, in the constraints of the local optimization problem, the horizontal distance between the horizontal position of the UAV and the horizontal position of the ground target in each prediction step in the prediction time domain does not exceed the product of the UAV's flight altitude and the tangent of the half-apex angle of the conical field of view.

5. The distributed model predictive control method for UAV formation based on field-of-view constraints according to claim 1, characterized in that, The physical constraint means that the absolute value of the component of each axis of the acceleration vector of this UAV does not exceed the preset maximum acceleration value; the inter-UAV collision avoidance constraint means that the distance between the horizontal position of this UAV at each prediction step in the prediction time domain and the horizontal position of the corresponding prediction step in the prediction state sequence received from the neighboring UAV at the previous moment is not less than the preset UAV safety distance.

6. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 2, characterized in that, The equivalent model of the circumcircle of the obstacle is as follows: each obstacle is equivalent to an infinitely tall cylinder, and the radius of its base circle is the radius of the circumcircle of the obstacle; in the obstacle avoidance penalty term, the distance between the UAV and the obstacle is defined as the distance from the horizontal position of the UAV to the center of the circumcircle of the obstacle minus the radius of the circumcircle; when the distance is less than the preset obstacle safety distance, a quadratic penalty function is used to calculate the penalty value; in order to maintain the convexity of the optimization problem, a second-order Taylor expansion of the penalty function is performed based on the current predicted position in each optimization to obtain a quadratic form with respect to the control sequence.

7. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, The formation consists of three drones, and the desired formation is a triangle with equal side lengths; the desired relative position vector is the position vector corresponding to the side of the triangle.

8. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, The prediction and control time domains adopt a rolling time domain strategy. After each sampling period, all UAVs execute steps S2 to S6 in parallel. All UAVs use the predicted state sequence received from their neighbors in the previous sampling period to achieve distributed parallel optimization.

9. The distributed model predictive control method for UAV formation based on field-of-view constraints according to claim 1, characterized in that, The predicted state sequence includes the position and velocity information of the current UAV at each prediction step in the prediction time domain; the predicted state sequence of the previous moment broadcast by the neighboring UAV is used by the current UAV to detect the risk of inter-UAV collision at future moments and to determine whether the ground target has been covered by the neighboring UAV.

10. The UAV formation distributed model predictive control method based on field-of-view constraints according to claim 1, characterized in that, At each sampling time, each UAV sequentially performs the following steps: receiving the predicted state sequence broadcast by all neighbors; calculating the neighbor coverage flag based on the received predicted state sequence, and then obtaining the global coverage flag of the local machine; The decision to add field-of-view constraints to the optimization problem is based on the global coverage flag; an objective function is constructed that includes trajectory tracking, formation keeping, input penalty, and obstacle avoidance penalty, and a convex optimization problem is formed by combining physical constraints, inter-machine collision avoidance constraints, and if added field-of-view constraints; the optimal control sequence is obtained by calling the convex optimization solver; the first control variable is applied to the UAV; and the new predicted state sequence of the UAV is broadcast to all neighbors.

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