Unmanned aerial vehicle formation adaptive radius surrounding tracking control method in narrow space

Abstract

The invention relates to an adaptive radius surrounding tracking control method for an unmanned aerial vehicle formation in a narrow space, and the method employs a relative kinematics model between an unmanned aerial vehicle and a target, and designs a surrounding tracking guidance law of the unmanned aerial vehicle formation for a moving target based on an interconnection system theorem. Meanwhile, in consideration of the flight area constraint and the target maneuverability, a self-adaptive radius control algorithm is designed, so that the unmanned aerial vehicle formation can automatically and dynamically adjust the surrounding radius when passing through the narrow space, the adaptability and effectiveness are improved, and safe navigation is realized.

Description

Technical Field

[0001] This invention relates to drone formation tracking and control technology, specifically to a drone formation adaptive radius orbiting tracking and control method in confined spaces. Background Technology

[0002] In recent years, illegal activities by low-altitude, slow-moving, and small aircraft have frequently occurred in the field of urban low-altitude airspace security, posing a threat to core urban infrastructure and public safety. These targets can evade the monitoring of traditional defense systems, highlighting the limitations of existing security mechanisms. Currently, multi-UAV swarm tracking and control methods are a research hotspot, providing intelligent and highly maneuverable solutions for various application scenarios.

[0003] It is worth noting that dynamic encirclement and autonomous tracking control of multi-UAV systems, due to their ability to continuously monitor low-observability and low-maneuverability targets and subsequently implement intelligent countermeasures, has become one of the core research directions in this field in recent years, attracting many scholars to explore it in depth. Existing research shows that UAVs often adopt a fixed-radius encirclement control strategy. This static control method makes it difficult for formations to achieve real-time adaptive adjustments in the narrow spaces of cities, failing to meet the application requirements of flexibility and adaptability. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive radius orbiting tracking control method for UAV formations in confined spaces that effectively improves the adaptability and flexibility of UAV formations.

[0005] The present invention adopts the following technical solution: An adaptive radius orbiting tracking control method for UAV formations in confined spaces is proposed. This method employs a kinematic model of the relative error between the UAV and the target, and designs an orbiting tracking guidance law for the UAV formation to a moving target based on an adaptive radius control algorithm.

[0006] Furthermore, the relative error kinematic model is as follows: in, Indicates drone The current position coordinates, Indicates drone Distance to the target Indicates pointing from the target to the drone Direction and drones The angle between the headings, Indicates drone The relative linear velocity with respect to the target Indicates drone Relative angular velocity with respect to the target; and respectively represent and error values from the desired state, represents a UAV error of the relative heading angle between adjacent UAVs, represents a desired target orbit radius, and first and second derivatives of represents a desired linear velocity of the UAV.

[0007] Further, the adaptive radius control algorithm is: based on the collected channel boundary position data, the optimal orbit radius in the narrow space is calculated in real time by using an orbit radius calculation formula.

[0008] The calculation formula of the optimal orbit radius is: wherein, represents the target position at this moment, represents the lowest boundary of the collected channel at this moment in the axis direction corresponding to the longitudinal coordinate value, represents the highest boundary of the channel in the axis direction corresponding to the longitudinal coordinate value.

[0009] Further, the and are calculated by safety margin constraints: wherein, represents the longitudinal coordinate value of the upper boundary of the collected channel at this moment, represents the longitudinal coordinate value of the lower boundary of the channel, defined as a physical safety margin parameter.

[0010] Further, safety buffer distances are set at the entrances and exits of the narrow space; Before entering the entrance of the narrow space, the circumferential radius of the UAV is set to ; After leaving the entrance of the narrow space, the circumferential radius of the UAV is set to ; wherein, represents the longitudinal coordinate value of the channel entrance, represents the longitudinal coordinate value of the channel exit.

[0011] Further, the orbit tracking guidance law is: wherein, are all normal numbers.

[0012] The present application has the beneficial effect that the present application considers the narrow space that may exist in a complex environment. In order to improve the surround tracking accuracy, the unmanned aerial vehicle formation surround tracking guidance law is designed based on the relative error kinematics model. In the guidance law, an adaptive radius controller is introduced, which comprehensively considers the flyable area constraint and the target maneuvering characteristics, and through real-time dynamic adjustment of the surround radius, the adaptability and flexibility of the unmanned aerial vehicle formation are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 is a schematic diagram of the unmanned aerial vehicle formation surrounding and tracking the target.

[0014] Figure 2 is a geometric relationship diagram between the unmanned aerial vehicle and the target.

[0015] Figure 3 is a two-dimensional trajectory diagram of the unmanned aerial vehicle formation surrounding and tracking considering the narrow space.

[0016] Figure 4 is a three-dimensional trajectory diagram of the unmanned aerial vehicle formation surrounding and tracking considering the narrow space.

[0017] Figure 5 is the relative heading angle error result between each unmanned aerial vehicle and the target.

[0018] Figure 6 is the surround tracking radius error result.

[0019] Figure 7 is the relative heading angle between each pair of unmanned aerial vehicles. DETAILED DESCRIPTION

[0020] The technical solutions of the present application will be described in detail below with the specific embodiments and the accompanying drawings.

[0021] I. Unmanned aerial vehicle kinematics model Considering the scenario of N unmanned aerial vehicles moving in space, the schematic diagram of the unmanned aerial vehicle formation surrounding and tracking the target is shown in Figure 1 The kinematics model of the unmanned aerial vehicle is described as follows: (1) wherein, represents the current position coordinates of the unmanned aerial vehicle, represents the current heading angle of the unmanned aerial vehicle, represents the linear velocity of the unmanned aerial vehicle movement, represents the angular velocity of the unmanned aerial vehicle movement.

[0022] Considering the impact of the target's dynamic characteristics on encirclement tracking accuracy, this invention employs a relative error kinematic model between the UAV and the target. This model, by describing the state error between the UAV and the moving target, can capture the target's motion trend in real time.

[0023] The kinematic model of the UAV relative to the target is represented as follows: (2) in, Indicates the first The relative linear velocity between the drone and the target. Indicates the first The relative angular velocity between the drone and the target. Indicates by the first The angle between the linear velocity directions of the drone and the target. The geometric relationship between the drone and the target on the horizontal plane is as follows: Figure 2 As shown, where Represents the distance to the target. This represents the desired radius of the target orbit, and Both the first and second derivatives exist. Relative heading angle relative azimuth The angle between them.

[0024] Meanwhile, the linear velocity of the drone With angular velocity Subject to physical constraints. (3) (4) in, This indicates the minimum linear velocity constraint for the drone. This indicates the maximum linear velocity constraint for the drone. This indicates the minimum angular velocity constraint for the drone. This indicates the maximum angular velocity constraint for the drone.

[0025] II. Interconnected Systems Theorem The interconnected systems theorem decomposes a complex system into two subsystems and proves their stability. The following analysis will cover nonlinear combined systems: (5) in, In this system, Indicates an isolated subsystem. Indicates interconnected items.

[0026] Theorem 1: Hypothesis Function and It possesses sufficient smoothness and ensures that, under all initial conditions, the system's solution within the domain is locally existent and unique. The origin of the coordinate system is the equilibrium point of the entire system and its subsystems. (6) Ignore interconnected items The system can be decomposed into An isolated subsystem .

[0027] [C1] For each isolated subsystem, construct a positive definite and decreasing Lyapunov function. The derivative of this function along the trajectory of its isolated subsystem is negative definite. (7) (8) (9) (10).

[0028] [C2] The domain is A positive definite continuous function, For positive integers, It is a non-negative constant.

[0029] [C3] S is a A matrix, whose elements are defined as follows: (11) And S is an M matrix.

[0030] If conditions [C1], [C2], and [C3] are all satisfied, then the origin is uniformly asymptotically stable. Furthermore, if all assumptions hold globally, and the Lyapunov function... If it has radial unboundedness, then the origin of the coordinate system is globally uniformly asymptotically stable.

[0031] III. Adaptive Radius Control Algorithm Design UAV-borne detectors can accurately detect and acquire location information in narrow spaces within complex urban environments. Based on the collected channel boundary location data, an adaptive radius controller is designed.

[0032] To ensure the safety and stability of drone formations flying in confined spaces, the safety margin constraint is designed as follows: (12) in, This represents the ordinate value of the upper boundary of the channel collected at this moment. a longitudinal coordinate value representing a lower boundary of the channel, is defined as a physical safety margin parameter.

[0033] Then, the calculation formula of the optimal circumradius can be derived as follows: (13) wherein, represents the target position at this moment. represents a longitudinal coordinate value corresponding to the lowest boundary of the channel in the axis direction at this moment, represents a longitudinal coordinate value corresponding to the highest boundary of the channel in the axis direction. By calculating the optimal circumradius in real time, the safe circumnavigation and tracking of the mobile target by the UAV formation in the narrow space can be realized.

[0034] To effectively alleviate the flight instability problem caused by the sudden change of the radius when the UAV enters the narrow space, and to avoid the collision risk at the entrance and exit of the channel, a safety buffer zone is designed, and a reserved buffer distance is set.

[0035] Before entering the channel, the circumradius of the UAV in the buffer zone is set to to realize smooth transition; after leaving the channel, the radius is adjusted to , thereby reducing the subsequent collision risk. Wherein, represents the longitudinal coordinate value at the entrance of the channel, represents the longitudinal coordinate value at the exit of the channel. By calculating the optimal circumradius in real time, the safe circumnavigation and tracking of the mobile target by the UAV formation in the narrow space can be realized.

[0036] IV. UAV guidance law design The relative error kinematic model of the UAV is as follows: (14) wherein, represents the included angle between the relative heading angles of each pair of UAVs, represents the distance to the target, is defined as the included angle between the direction from the target pointing to the UAV and the heading of the UAV , represents the relative linear velocity between the th UAV and the target, represents the relative angular velocity between the th UAV and the target.

[0037] According to the expected goals , , The orbital tracking control error is defined as: (15) in, and They represent drones Expected state and The error, and Indicates drone Error in relative heading angle between the drone and its neighboring drone. This represents the desired radius of the target orbit, and Both the first and second derivatives exist. This represents the expected linear velocity of the drone. This represents the actual number of drones.

[0038] By utilizing model (2) and differentiating the above expression, the following relative error kinematic model can be derived: (16).

[0039] To achieve precise control of UAV formation tracking based on the adaptive radius control algorithm, the following guidance law is designed: (17) in, All are positive numbers. Indicates drone Distance to the target Defined as pointing from target to drone Direction and drones The angle between the headings, Indicates drone The relative linear velocity with respect to the target Indicates drone The relative angular velocity between the target and the target. and They represent and The error value between the expected state and the actual state. Indicates drone The error in the relative heading angle between the drone and its neighboring drone. This represents the desired radius of the target orbit, and Both the first and second derivatives exist. This represents the expected linear velocity of the drone. The radius of circumference is calculated using the adaptive radius algorithm.

[0040] V. Stability proof of the guidance law By substituting the guidance law into the relative error kinematic model, the following nonlinear compound closed-loop system is obtained: (18) where .

[0041] According to the interconnection system theorem, the compound system can be decomposed into two isolated subsystems and two interconnection terms as follows: (19) (20) where , denotes the current time.

[0042] For the whole UAV formation system, its subsystems can be expressed as: (21) (22) For the first subsystem, the constructed Lyapunov function is where .

[0043] (1) The derivative of the Lyapunov function of the first subsystem with respect to time is as follows: (23) Under the isolated subsystem , the derivative of is: (24) By combining (23) and (24), the following inequality can be derived: (25) where , .

[0044] (2) the norm of the derivative of : (26) where .

[0045] (3) the two-norm of : (27) , , .

[0046] For the second subsystem, the constructed Lyapunov function is .

[0047] (4) The derivative of the Lyapunov function of the second subsystem with respect to time is as follows: (28) Under the isolated subsystem , the derivative of : (29) By combining equation (28) with equation (29), the following inequality can be derived: (30) where .

[0048] (5) The norm of the derivative of : (31) where .

[0049] (6) The two-norm of : (32) where , .

[0050] From the parameter values calculated in the above proof process, the matrix S can be derived as follows: (33) Obviously, all the principal minors of the matrix S are positive, which indicates that the matrix S is a M matrix. In addition, the Lyapunov functions V1 and V2 have radial unboundedness. According to Lemma 1, the guidance system achieves global uniform asymptotic stability at the equilibrium point .

[0051] Sixth, simulation experiment A quad-rotor formation system consisting of four unmanned aerial vehicles (designated as agents A, B, C, and D, respectively) is designed to cooperatively track a maneuvering target. Equation (34) defines the motion trajectory followed by the maneuvering target: (34).

[0052] To simulate the real urban combat constraints, two narrow spaces are set as the flight environment boundaries. All physical parameters are strictly in the International System of Units (SI units). The location information of the two narrow spaces is shown in Table 1. The guidance law parameters are set as , , .

[0053] Table 1. Geometry parameters of narrow spaces .

[0054] The simulation is based on the MATLAB R2023b platform. The total simulation time is set to 230 seconds, and the time step is 0.01 seconds.

[0055] Figure 3 and Figure 4 shows the two-dimensional and three-dimensional surround tracking trajectories of the UAV formation in the presence of narrow spaces, which intuitively presents the dynamic change process of the surround radius when the UAV formation passes through the two narrow spaces. Normally, the UAV formation maintains a surround radius of 3 meters. When encountering a narrow space, the system will calculate the expected surround radius in real time based on the channel position information feedback by the sensor, and complete the safe surround tracking of the target with the expected radius. At the same time, by setting the buffer zone to 3 meters, which is the maximum surround radius of the UAV, it can ensure that the UAV formation avoids obstacles when entering and exiting the narrow channel, and ensures the safety of traffic. The control error of the UAV formation during the surround tracking process is shown in Figures 5 to 7 .

[0056] Figure 5 For the relative heading angle error between the UAV and the target, it finally converges to , Figure 6 is the surround tracking radius error of the UAV, Figure 7 is the heading angle interval between adjacent UAVs, and finally converges to . The results show that the change of the surround radius does not affect the convergence state of the UAV when entering the narrow space.

Claims

1. A method for adaptive radius encirclement tracking control of UAV formation in narrow space, characterized in that, The relative error kinematic model between the unmanned aerial vehicle and the target is adopted, and a surround tracking guidance law of the unmanned aerial vehicle formation to the moving target is designed based on an adaptive radius control algorithm.

2. The method of claim 1, wherein, The relative error kinematic model is: in, Indicates drone The current position coordinates, Indicates drone Distance to the target Indicates pointing from the target to the drone Direction and drones The angle between the headings, Indicates drone The relative linear velocity with respect to the target Indicates drone Relative angular velocity with respect to the target; and They represent and Error value from the desired state, Indicates drone The error in the relative heading angle between the drone and its neighboring drone. This represents the desired radius of the target orbit, and Both the first and second derivatives exist. This represents the expected linear velocity of the drone.

3. The method of claim 2, wherein, The adaptive radius control algorithm is that based on the collected channel boundary position data, an optimal surround radius in the narrow space is calculated in real time by using a surround radius calculation formula; the optimal wrap radius The formula for calculating the optimal wrap radius is: wherein, represents the target position at this moment, represents the lowest boundary of the channel in the axis direction corresponding to the ordinate value, represents the highest boundary of the channel in the axis direction corresponding to the ordinate value.

4. The method of claim 3, wherein, The And By safety margin constraint calculation: wherein, represents the ordinate value of the upper boundary of the channel at this moment, represents the ordinate value of the lower boundary of the channel, defined as a physical safety margin parameter.

5. The method of claim 4, wherein, A safety buffer distance is arranged at the entrance and the exit of the narrow space; The drone's circumradius is set to before entering the narrow space entrance. After exiting the narrow space exit, the drone circumferential radius is set to ; wherein represents the x-coordinate value at the entrance of the channel, represents the x-coordinate value at the exit of the channel.

6. The method of claim 5, wherein, The surround tracking guidance law is: wherein are all normal numbers.

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