Adaptive radius encircling tracking control method for UAV formation in narrow space

Abstract

The present application relates to a kind of narrow space under unmanned aerial vehicle formation adaptive radius encircling tracking control method, using the relative kinematics model between unmanned aerial vehicle and target, and based on the interconnection system theorem, the encircling tracking guidance law of unmanned aerial vehicle formation to mobile target is designed.Simultaneously, considering the flyable area constraint and target maneuverability, adaptive radius control algorithm is designed, so that unmanned aerial vehicle formation can dynamically adjust the encircling radius when crossing narrow space, improve adaptability and effectiveness, realize safe navigation.

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:

[0006] 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.

[0007] Furthermore, the relative error kinematic model is as follows:

[0008]

[0009] 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 represents the UAV a relative angular velocity between the target and the UAV; and respectively represent and an error value of the target relative to the desired state, represents the UAV an error of the relative heading angle between the UAV and the adjacent UAV, represents a desired target orbit radius, and a first derivative and a second derivative of the target orbit radius exist, represents a desired linear velocity of the UAV.

[0010] 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.

[0011] The calculation formula of the optimal orbit radius is as follows:

[0012]

[0013] wherein, represents the target position at this moment, represents the lowest boundary corresponding to the longitudinal coordinate value of the channel collected at this moment in the direction of the axis, represents the highest boundary corresponding to the longitudinal coordinate value of the channel in the direction of the axis.

[0014] Further, the and are calculated by safety margin constraint:

[0015]

[0016] wherein, represents the longitudinal coordinate value of the upper boundary of the channel collected at this moment, represents the longitudinal coordinate value of the lower boundary of the channel, is defined as a physical safety margin parameter.

[0017] Further, a safety buffer distance is set at the entrance and the exit of the narrow space;

[0018] Before entering the entrance of the narrow space, the circumferential radius of the UAV is set to ;

[0019] After leaving the entrance of the narrow space, the circumferential radius of the UAV is set to ;

[0020] wherein,​​ This represents the x-coordinate value at the entrance of the passage. This represents the x-coordinate value at the exit of the channel.

[0021] Furthermore, the orbital tracking guidance law is as follows:

[0022]

[0023] in, All are normal numbers.

[0024] The beneficial effects of this invention are as follows: This invention considers the potentially confined spaces that may exist in complex environments. To improve orbital tracking accuracy, a UAV formation orbital tracking guidance law is designed based on a relative error kinematic model. In this guidance law, an adaptive radius controller is introduced. This controller comprehensively considers the constraints of the flyable area and the target's maneuverability, effectively improving the adaptability and flexibility of the UAV formation through real-time dynamic adjustment of the orbital radius. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of a drone formation coordinating and orbiting to track a target.

[0026] Figure 2 This is a diagram showing the geometric relationship between the drone and the target.

[0027] Figure 3 A two-dimensional trajectory diagram for drone formation encirclement and tracking in confined spaces.

[0028] Figure 4 A 3D trajectory diagram for drone formation encirclement and tracking in confined spaces.

[0029] Figure 5 The results show the relative heading angle error between each UAV and the target.

[0030] Figure 6 This represents the result of the tracking radius error.

[0031] Figure 7 The relative heading angle between each pair of drones. Detailed Implementation

[0032] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0033] I. Kinematic Model of Unmanned Aerial Vehicles

[0034] Considering a scenario where N drones move in space, a diagram illustrating the drone formation's encirclement and tracking of a target is shown below. Figure 1 As shown, the kinematic model of the UAV is described as follows:

[0035] (1)

[0036] in, This indicates the current position coordinates of the drone. Indicates the current heading angle of the drone. This represents the linear velocity of the drone's motion. This represents the angular velocity of the drone's motion.

[0037] 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.

[0038] The kinematic model of the UAV relative to the target is represented as follows:

[0039] (2)

[0040] 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.

[0041] Meanwhile, the linear velocity of the drone With angular velocity Subject to physical constraints.

[0042] (3)

[0043] (4)

[0044] 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.

[0045] II. Interconnected Systems Theorem

[0046] The interconnected systems theorem decomposes a complex system into two subsystems and proves their stability. The following analysis will cover nonlinear combined systems:

[0047] (5)

[0048] in, In this system, Indicates an isolated subsystem. Indicates interconnected items.

[0049] 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.

[0050] (6)

[0051] Ignore interconnected items The system can be decomposed into An isolated subsystem .

[0052] [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.

[0053] (7)

[0054] (8)

[0055] (9)

[0056] (10).

[0057] [C2] The domain is A positive definite continuous function, For positive integers, It is a non-negative constant.

[0058] [C3] S is a A matrix, whose elements are defined as follows:

[0059] (11)

[0060] And S is an M matrix.

[0061] 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.

[0062] III. Adaptive Radius Control Algorithm Design

[0063] 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.

[0064] To ensure the safety and stability of drone formations flying in confined spaces, the safety margin constraint is designed as follows:

[0065] (12)

[0066] in, This represents the ordinate value of the upper boundary of the channel collected at this moment. This represents the ordinate value of the lower boundary of the channel. Defined as a physical safety margin parameter.

[0067] So, the radius of circumference The calculation formula can be derived as follows:

[0068] (13)

[0069] in, This indicates the target location at this moment. This represents the channel that was collected at this moment. The ordinate value corresponding to the lowest boundary along the axis. This means that the channel is in The ordinate value corresponding to the highest boundary along the axis. The optimal encirclement radius is calculated in real-time. It enables drone formations to safely circle and track moving targets in confined spaces.

[0070] To effectively mitigate flight instability caused by sudden changes in radius when drones enter confined spaces and to avoid collision risks at passageway entrances and exits, a safety buffer zone was designed with a reserved buffer distance. .

[0071] Before entering the passage, the circumference radius of the drone within the buffer zone is set to... To achieve a smooth transition; after leaving the channel, the radius is adjusted to This reduces the risk of subsequent collisions. Among them, This represents the x-coordinate value at the entrance of the passage. This represents the x-coordinate value at the exit of the passage. By calculating the optimal orbital radius in real time, the safe orbiting and tracking of moving targets by the UAV formation within a narrow space was achieved.

[0072] IV. Design of Unmanned Aerial Vehicle Guidance Laws

[0073] drones The relative error kinematic model is as follows:

[0074] (14)

[0075] in, This represents the angle between the relative heading angles of each pair of drones. Represents the distance to the target. Defined as pointing from target to drone Direction and drones The angle between the headings, 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.

[0076] According to the expected goals , , The orbital tracking control error is defined as:

[0077] (15)

[0078] 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.

[0079] By utilizing model (2) and differentiating the above expression, the following relative error kinematic model can be derived:

[0080] (16).

[0081] To achieve precise control of UAV formation tracking based on the adaptive radius control algorithm, the following guidance law is designed:

[0082] (17)

[0083] 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.

[0084] V. Proof of the stability of the guidance law

[0085] By substituting the guidance law into the relative error kinematic model, the following nonlinear composite closed-loop system can be obtained:

[0086] (18)

[0087] in, .

[0088] According to the interconnected systems theorem, the combined system can be decomposed into two isolated subsystems and two interconnected terms as shown below:

[0089] (19)

[0090] (20)

[0091] in, , Indicates the current moment.

[0092] For the entire drone formation system, its subsystems can be described as follows:

[0093] (twenty one)

[0094] (twenty two)

[0095] For the first subsystem, the constructed Lyapunov function is: ,in .

[0096] (1) The derivative of the Lyapunov function of the first subsystem with respect to time is obtained as follows:

[0097] (twenty three)

[0098] In isolated subsystems Down, right The derivative:

[0099] (twenty four)

[0100] By combining equations (23) and (24), the following inequality can be derived:

[0101] (25)

[0102] in, , .

[0103] (2) right Norm of the derivative:

[0104] (26)

[0105] in, .

[0106] (3) The 2-norm:

[0107] (27)

[0108] in, , , .

[0109] For the second subsystem, the constructed Lyapunov function is: .

[0110] (4) The derivative of the Lyapunov function of the second subsystem with respect to time is obtained as follows:

[0111] (28)

[0112] In isolated subsystems Down, right The derivative:

[0113] (29)

[0114] Combining equations (28) and (29), the following inequality can be derived:

[0115] (30)

[0116] in, .

[0117] (5) right Norm of the derivative:

[0118] (31)

[0119] in, .

[0120] (6) The 2-norm:

[0121] (32)

[0122] in, , .

[0123] From the parameter values ​​calculated in the above proof process, the matrix S can be derived as follows:

[0124] (33)

[0125] Clearly, all the principal minors of matrix S are positive, indicating that matrix S is an M-matrix. Furthermore, the Lyapunov functions V1 and V2 are radially unbounded. According to Lemma 1, the guidance system at the equilibrium point... It achieves globally consistent asymptotic stability.

[0126] VI. Simulation Experiment

[0127] Design a quadcopter formation system consisting of four unmanned aerial vehicles (designated as agents A, B, C, and D) to collaboratively orbit and track a maneuvering target. Equation (34) defines the trajectory followed by the maneuvering target:

[0128] (34).

[0129] To simulate real urban combat constraints, two narrow spaces were set as the flight environment boundaries. All physical parameters were strictly implemented using the International System of Units (SI). The location information of the two narrow spaces is shown in Table 1. The guidance law parameters were set as follows: , , .

[0130] Table 1 Geometric parameters of narrow spaces

[0131] .

[0132] This simulation was performed using the MATLAB R2023b platform. The total simulation duration was set to 230 seconds, with a time step of 0.01 seconds.

[0133] Figure 3 and Figure 4 This demonstration showcases the 2D and 3D surround tracking trajectories of a drone formation in confined spaces, visually illustrating the dynamic changes in the encirclement radius as the drone formation traverses two narrow spaces. Under normal circumstances, the drone formation maintains an encirclement radius of 3 meters. When encountering a narrow space, the system calculates the desired encirclement radius in real-time based on channel position information fed back by sensors, and uses this desired radius to safely surround and track the target. Simultaneously, by setting the buffer zone to 3 meters, i.e., the drone's maximum encirclement radius, the system ensures that the drone formation avoids obstacles when entering and exiting narrow passages, guaranteeing safe passage. The control error of the drone formation during the encirclement and tracking process is shown below. Figures 5 to 7 As shown.

[0134] Figure 5 The relative heading angle error between the UAV and the target eventually converges to , Figure 6 The encirclement tracking radius error of the UAV, Figure 7 The heading angle interval between adjacent UAVs eventually converges to The results show that changes in the enclosing radius did not affect the convergence state of the UAV when entering a narrow space.

Claims

1. A method for adaptive radius-based orbiting tracking control of UAV formations in confined spaces, characterized in that, A kinematic model of the relative error between the UAV and the target is adopted, and an adaptive radius control algorithm is used to design the orbital tracking guidance law of the UAV formation for the moving target; The relative error kinematic model is as follows: in, This indicates the current position coordinates of the drone. Represents the distance to the target. Defined as pointing from target to drone Direction and drones The angle between the headings, 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; and They represent and Error value from the desired state, This represents the error in the relative heading angle between each pair of drones. 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 adaptive radius control algorithm is as follows: based on the collected channel boundary position data, the optimal surrounding radius in the narrow space is calculated in real time using the surrounding radius calculation formula; The circumference The calculation formula is: in, This indicates the target location at this moment. This represents the channel that was collected at this moment. The ordinate value corresponding to the lowest boundary along the axis. This means that the channel is in The ordinate value corresponding to the highest boundary along the axis; The orbital tracking guidance law is as follows: in, , All are normal numbers.

2. The UAV formation adaptive radius orbiting tracking control method in a narrow space according to claim 1, characterized in that, The and Calculated using safety margin constraints: in, This represents the ordinate value of the upper boundary of the channel collected at this moment. This represents the ordinate value of the lower boundary of the channel. Defined as a physical safety margin parameter.

3. The UAV formation adaptive radius orbiting tracking control method in a narrow space according to claim 2, characterized in that, Safety buffer distances should be set at the entrance and exit of narrow spaces; Before entering the narrow space entrance, the drone's circumference radius is set to... ; After exiting the confined space, the drone's circumference radius is set to... ; in, This represents the x-coordinate value at the entrance of the passage. This represents the x-coordinate value at the exit of the channel.

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