An adaptive risk-aware multi-target tracking method with network repair

Abstract

An adaptive risk-aware multi-target tracking method with network repair relates to the technical field of drone trajectory planning. The beneficial effects of the present invention are as follows: the method is a two-stage strategy: in the first stage, the entire team is checked to see if repair is necessary. If necessary, the observability of the team is quantified using the trace of the Grammian matrix, and a new network structure that satisfies one-hop observability is given; while in the second stage, the coordinates of the drone at the next moment are given by quantifying security and accuracy, using the sensing margin as a dynamic weight. The present method is not only used for trajectory generation after an adaptive trade-off between accuracy and security, but also has the function of automatically repairing the communication network.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) trajectory planning, and in particular to an adaptive risk-aware multi-target tracking method with network repair. Background Art

[0002] Target tracking technology uses a variety of sensors to detect targets and obtain their status, including but not limited to position and velocity. This technology is widely used in both civilian and military applications. However, with the increasing diversity and complexity of application scenarios, traditional target tracking theory based on single-point target models no longer meets the requirements of these tasks. Consequently, research has begun on multi-target tracking theory. To reduce costs and improve resource utilization, this technology is often applied to heterogeneous drone fleets.

[0003] Given the complexity of multi-target tracking tasks and scenarios, multi-robot systems performing these tasks are inevitably subject to external interference and even high-intensity attacks. These external interference and attacks can arise from harsh environments, such as fires and magnetic fields, or from unavoidable issues during the measurement process, such as angular glint, limited sensing areas, or tracked targets with offensive capabilities. To address these challenges, research typically focuses on three key metrics: robustness, resilience, and flexibility.

[0004] Risk-aware target tracking (also known as safety-aware target tracking) often requires modeling and estimating known or unknown hazards. Hazards may arise from adversarial tracking objects, complex task execution environments, interference within a multi-robot team, or unknown external disturbances. One of the most fundamental requirements in these tasks is collision avoidance, which involves three types of constraints: within the tracker, between the tracker and the environment, and between the tracker and the target. One approach is to use a control obstacle function, leveraging its forward invariance to constrain the control policy of the robot team to achieve collision avoidance. However, control obstacle functions have limitations in collision avoidance control, including reliance on an accurate system model, high computational complexity, policy conservatism, difficulty in parameter tuning, compatibility issues with other control methods, insufficient robustness, and the potential for entrapment in local minima. These shortcomings can affect the collision avoidance effectiveness and efficiency in practical applications.

[0005] Another approach is to use artificial potential fields to achieve safe behavior. In practical applications, risk-aware target tracking, in addition to meeting collision avoidance requirements, must also consider other objectives, such as observation accuracy, safety, and energy consumption. It is important to note that these objectives may conflict or even contradict each other. To achieve this balance between these multiple objectives, numerous researchers have conducted research in related fields. One approach employs a cascade control strategy: first, balancing perception performance and energy consumption when generating trajectories; second, when generating control policies, a trade-off is made between closeness to the nominal control policy and response speed. To address these issues, one approach linearly combines the two objective functions and uniformly optimizes them. Alternatively, a cascade control strategy can be employed, sequentially optimizing the two objectives to obtain the final control policy. However, this approach also suffers from local minima, target unreachability, oscillation, difficulty in parameter adjustment, and high computational complexity, limiting its effectiveness and efficiency in practical applications.

[0006] In addition, reinforcement learning based on composite artificial potential fields can be used to obtain equilibrium control strategies. However, using reinforcement learning for decision-making has problems such as long training time, high consumption of computing resources, strong dependence on the environment, difficult to explain the decision-making process, low sample efficiency, and stability during training. Summary of the Invention

[0007] This invention aims to address the shortcomings and deficiencies of existing technologies by providing an adaptive, risk-aware multi-target tracking method with network repair. This method employs a two-stage strategy: In the first stage, the entire team is checked to see if repair is necessary. If necessary, the team's observability is quantified using the Grammian matrix trace, resulting in a new network structure that satisfies one-hop observability. In the second stage, the next-step coordinates of the drone are determined by quantifying safety and accuracy, using sensor margins as dynamic weights. This method not only generates trajectories that adaptively balance accuracy and safety, but also enables automatic repair of the communication network.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: an adaptive risk-aware multi-target tracking method with network repair, in which a heterogeneous drone team tracks a group of dynamic targets, and the motion of each target can be represented by the following state-space equation: Where Z is the robot coordinate, A is the state transition matrix, B is the input matrix, u is the input control variable, and w is the zero-mean independent Gaussian noise matrix with covariance matrix Q; the formula written in compact form is as follows: Although each drone tracker only tracks its own target, it still observes all targets. Therefore, for each drone, there is the following linear observation model: Among them, y is the observation value of the target state, H is the output matrix, and v is the observation noise; considering the one-hop community where the drone is located in the communication network Therefore, the linear observation model is as follows: in, The community-based measurement noise takes the following form: in, Based on the above observation model, the Gaussian function danger field of the j-th tracking target is defined as follows. It can be seen that it is exponentially related to the square of the distance; Correspondingly, the safety field function is defined as follows: Then, for the target state measured by the sensor, the Kalman filter is used for data fusion, which is divided into the prediction step and the update step: In order to quantify the task performance, an evaluation index is given and a one-hop observable Gramian matrix is ​​defined. The specific formula is as follows: Among them, T o is a pre-selected time interval, Π i,t is a positive definite matrix used to quantify the security of closed community i, based on the previously defined security field, the security weight π i,t The definition is as follows: Among them, π k (x j,t ) represents the safety field between UAV j and target k; sensor margin is selected as another indicator to evaluate mission performance. A distributed UAV is observable in its community, which means that its is observable, corresponding to The rank of is φ, φ = Md, and the sensing margin under distributed conditions is defined as follows: First, based on the above dynamic model, observation model, and two performance indicators, the following optimization-based adaptive risk-aware target tracking algorithm is proposed:

[0009] When the drone is subjected to a tolerable attack, the above solution is no longer effective. Therefore, an edge repair strategy is introduced. When performing edge repair, it is not necessary to consider the observation performance, but only the one-hop observable Gramian matrix. The observable Gramian matrix of sensor j is as follows:

[0010] The one-hop observable Gram matrix of drone i is as follows:

[0011] in, is a closed connection matrix, and the compressed form of the observable Gram matrix of the entire team is as follows: Then use vector To record which drone individuals do not meet one-hop observability: For individuals that are not satisfied, the repair weight is increased. The updated weight is as follows: W = I + Diag(l). Based on the above content, the following repair algorithm is given:

[0012]

[0013] in, Then, seven drones track seven targets with attack intentions. At the beginning, when resources are sufficient, the drones will track the targets closely, but maintain a certain distance. After being attacked, the distance will increase. When irreparable resources are encountered, the communication map will be repaired by adding edges.

[0014] Furthermore, the sensor is one-dimensional, so the sensor output matrix is ​​as follows Among them, h is the output vector of the sensor, and As a combination of the column indices of the non-empty entries in the i-th row of the resource matrix Γ, for a given resource matrix and sensor output matrix, the output matrix of drone i for target j is as follows:

[0015] Furthermore, the measurement noise is defined as the covariance R ij,t The zero-mean and independent Gaussian noise is a distance-related function. As the observation distance increases, the observation noise increases exponentially: in: Among them, λ s and w s is the shape parameter of the Gaussian distribution.

[0016] Furthermore, considering that a heterogeneous drone team may be attacked when performing distributed tracking of multiple targets, the attacks are divided into the following three categories based on the changes in observability status before and after the attack: 1. Mild attack (the individuals satisfy one-hop observability before and after the attack); 2. Tolerable attack (one-hop observability is satisfied before the attack, but not after the attack, but one-hop observability can be restored by acquiring the sensor resources of new members); 3. Intolerable attack (one-hop observability is satisfied before the attack, but not after the attack, but one-hop observability can be restored by acquiring the sensor resources of new members and one-hop observability cannot be re-satisfied by sharing resources).

[0017] Furthermore, the In the algorithm, the first constraint is the UAV's dynamic constraint, which limits the displacement of a single iteration. The second constraint is the collision avoidance constraint between different UAVs, which limits the minimum distance between UAVs. The third constraint is the scaling of the UAV's measurement accuracy. The fourth constraint is the scaling of the UAV's safety. The objective function is a linear combination of the scaling of the two indicators based on the sensor margin. In the observation task, when observability is met, the accuracy of tracking observation is improved as much as possible. When the UAV makes a slight attack, the observability decreases, and the focus is on improving safety first, and then optimizing the tracking accuracy.

[0018] Furthermore, the In the example, the decision variable L represents the new Laplacian graph, where the first constraint ensures the properties of the Laplacian graph; the second constraint ensures that the graph is connected; the sixth constraint strictly defines that each diagonal element of L is greater than 0; the seventh constraint ensures that the off-diagonal elements in L are the opposite values ​​of the corresponding elements in π; the ninth constraint determines that at least one edge is added; the third constraint strictly defines the form of the one-hop observable Gram matrix; the fourth and fifth elements ensure the property of π as a closed connected matrix; and the eighth constraint limits the maximum number of added edges.

[0019] By adopting the above technical solution, the present invention has the following beneficial effects: This method is a two-stage strategy: In the first stage, the entire team is checked to see if repair is necessary. If necessary, the team's observability is quantified using the trace of the Grammian matrix, and a new network structure that satisfies one-hop observability is derived. In the second stage, the next coordinates of the drone are determined by quantifying safety and accuracy, using the sensor margin as a dynamic weight. This method not only generates trajectories with an adaptive trade-off between accuracy and safety, but also has the ability to automatically repair the communication network. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0021] Figure 1 It is a schematic flow diagram of the present invention.

[0022] Figure 2 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 1 .

[0023] Figure 3 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 2 .

[0024] Figure 4 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 3 .

[0025] Figure 5 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 4 .

[0026] Figure 6 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 5 .

[0027] Figure 7 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 6 .

[0028] Figure 8 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 7 .

[0029] Figure 9 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 8 .

[0030] Figure 10 This is a schematic diagram of 7 to 7 multi-target tracking in the present invention Figure 9 . DETAILED DESCRIPTION

[0031] See Figure 1 As shown, the technical solution adopted in this specific embodiment is: a heterogeneous drone team tracks a group of dynamic targets, and the motion of each target can be expressed by the following state space equation:

[0032]

[0033] Where Z is the robot coordinate, A is the state transfer matrix, B is the input matrix, u is the input control variable, and w is the independent Gaussian noise matrix with zero mean and covariance matrix Q;

[0034] The formula written in compact form is as follows:

[0035]

[0036] Although each drone tracker only tracks its own target, it still observes all targets. Therefore, for each drone, there is the following linear observation model:

[0037]

[0038] Where y is the observed value of the target state, H is the output matrix, and v is the observation noise;

[0039] The sensor is one-dimensional, so the sensor output matrix is ​​as follows Among them, h is the output vector of the sensor, and As a combination of the column indices of the non-empty entries in the i-th row of the resource matrix Γ, for a given resource matrix and sensor output matrix, the output matrix of drone i for target j is as follows:

[0040]

[0041] The measurement noise is defined as the covariance R ij,t The zero-mean and independent Gaussian noise is a distance-related function. As the observation distance increases, the observation noise increases exponentially:

[0042]

[0043] in:

[0044]

[0045] Among them, λ s and w s is the shape parameter of the Gaussian distribution.

[0046] Considering the one-hop community of the drone in the communication network Therefore, the linear observation model is as follows:

[0047]

[0048] in,

[0049] The community-based measurement noise takes the following form:

[0050] in,

[0051] Based on the above observation model, the Gaussian function danger field of the j-th tracking target is defined as follows. It can be seen that it is exponentially related to the square of the distance:

[0052]

[0053] Correspondingly, the safety field function is defined as follows:

[0054]

[0055] Then, for the target state measured by the sensor, the Kalman filter is used for data fusion, which is divided into the prediction step and the update step:

[0056]

[0057] In order to quantify the task performance, an evaluation index is given and a one-hop observable Gramian matrix is ​​defined. The specific formula is as follows:

[0058]

[0059] Among them, T o is a pre-selected time interval, Π i,t is a positive definite matrix used to quantify the security of closed community i, based on the previously defined security field, the security weight π i,t The definition is as follows:

[0060]

[0061] Among them, π k (x j,t ) represents the safety field between UAV j and target k;

[0062] Sensor margin is selected as another indicator to evaluate mission performance. A distributed UAV is observable within its community, which means that its is observable, corresponding to The rank of is φ, φ = Md, and the sensing margin under distributed conditions is defined as follows:

[0063]

[0064] Considering that a heterogeneous drone team may be attacked when performing distributed tracking of multiple targets, we divide attacks into the following three categories based on the changes in observability before and after the attack:

[0065] 1) Minor attack (both individuals before and after the attack satisfy one-hop observability);

[0066] 2) Tolerable attacks (one-hop observability is satisfied before the attack, but not after the attack, but one-hop observability can be restored by acquiring the sensing resources of new members);

[0067] 3) Intolerable attacks (one-hop observability is satisfied before the attack, but not after the attack. However, one-hop observability can be restored by acquiring the sensing resources of new members, and one-hop observability cannot be re-satisfied by sharing resources).

[0068] First, based on the above dynamic model, observation model, and two performance indicators, the following optimization-based adaptive risk-aware target tracking algorithm is proposed:

[0069]

[0070] Among them, the first constraint is the dynamic constraint of the UAV, which limits the displacement of a single iteration. The second constraint is the collision avoidance constraint between different UAVs, which limits the minimum distance between UAVs. The third constraint is the scaling of the UAV measurement accuracy. The fourth constraint is the scaling of the UAV safety. The objective function is a linear combination of the scaling of the two indicators based on the sensor margin. In the observation task, when observability is met, the accuracy of tracking observation is improved as much as possible. When the UAV makes a slight attack, the observability decreases, and the focus is on improving safety first, and then optimizing the tracking accuracy.

[0071] When the drone is subjected to a tolerable attack, the above solution is no longer effective. Therefore, an edge repair strategy is introduced. When performing edge repair, it is not necessary to consider the observation performance, but only the one-hop observable Gramian matrix. The observable Gramian matrix of sensor j is as follows:

[0072]

[0073] The one-hop observable Gram matrix of drone i is as follows:

[0074]

[0075] in, is a closed connection matrix, and the compressed form of the observable Gram matrix of the entire team is as follows:

[0076]

[0077] Then use vector To record which drone individuals do not meet one-hop observability:

[0078]

[0079] For individuals who are not satisfied, the repair weight is increased, and the updated weight is as follows:

[0080] W=I+Diag(l) (17)

[0081] Based on the above content, the following repair algorithm is given:

[0082]

[0083] in, The decision variable L represents the new Laplacian graph, where the first constraint ensures the properties of the Laplacian graph; the second constraint ensures that the graph is connected; the sixth constraint strictly defines that each diagonal element of L is greater than 0; the seventh constraint ensures that the off-diagonal elements in L are the opposite values ​​of the corresponding elements in π; the ninth constraint determines that at least one edge is added; the third constraint strictly defines the form of the one-hop observable Gram matrix; the fourth and fifth elements ensure the property of π as a closed connected matrix; the eighth constraint limits the maximum number of added edges

[0084] See Figure 2-Figure 10 As shown, 7 drones are then used to track 7 targets with attack intentions. At the beginning, when resources are sufficient, the drones will track the targets closely, but maintain a certain distance. After being attacked, the distance will increase. When irreparable resources are encountered, the communication diagram will be repaired by adding edges.

[0085] The above description is only used to illustrate the technical solution of the present invention and is not intended to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. An adaptive risk-aware multi-target tracking method with network repair, characterized by: A heterogeneous drone fleet is tracking a set of dynamic targets. The motion of each target can be represented by the following state-space equation: Where Z is the robot coordinate, A is the state transfer matrix, B is the input matrix, u is the input control variable, and w is the independent Gaussian noise matrix with zero mean and covariance matrix Q; The formula written in compact form is as follows: Although each drone tracker only tracks its own target, it still observes all targets. Therefore, for each drone, there is the following linear observation model: Where y is the observed value of the target state, H is the output matrix, and v is the observation noise; Considering the one-hop community of the drone in the communication network Therefore, the linear observation model is as follows: in, The community-based measurement noise takes the following form: in, Based on the above observation model, the Gaussian function danger field of the j-th tracking target is defined as follows. It can be seen that it is exponentially related to the square of the distance; Correspondingly, the safety field function is defined as follows: Then, for the target state measured by the sensor, Kalman filtering is used for data fusion. It is divided into prediction step and update step: In order to quantify the task performance, an evaluation index is given and a one-hop observable Gramian matrix is ​​defined. The specific formula is as follows: Among them, T o is a pre-selected time interval, Π i,t is a positive definite matrix used to quantify the security of closed community i, based on the previously defined security field, the security weight π i,t The definition is as follows: Among them, π k (x j,t ) represents the safety field between UAV j and target k; Sensor margin is selected as another indicator to evaluate mission performance. A distributed UAV is observable within its community, which means that its is observable, corresponding to The rank of is φ, φ = Md, and the sensing margin under distributed conditions is defined as follows: First, based on the above dynamic model, observation model, and two performance indicators, the following optimization-based adaptive risk-aware target tracking algorithm is proposed: When the drone is subjected to a tolerable attack, the above solution is no longer effective. Therefore, an edge repair strategy is introduced. When performing edge repair, it is not necessary to consider the observation performance, but only the one-hop observable Gramian matrix. The observable Gramian matrix of sensor j is as follows: The one-hop observable Gram matrix of drone i is as follows: in, is a closed connection matrix, and the compressed form of the observable Gram matrix of the entire team is as follows: Then use vector To record which drone individuals do not meet one-hop observability: For individuals who are not satisfied, the repair weight is increased, and the updated weight is as follows: W=I+Diag(l) (17) Based on the above content, the following repair algorithm is given: in, Then, seven drones track seven targets with attack intentions. At the beginning, when resources are sufficient, the drones will track the targets closely, but maintain a certain distance. After being attacked, the distance will increase. When irreparable resources are encountered, the communication map will be repaired by adding edges.

2. The adaptive risk-aware multi-target tracking method with network repair according to claim 1, characterized in that: The sensor is one-dimensional, so the sensor output matrix is ​​as follows Among them, h is the output vector of the sensor, and As a combination of the column indices of the non-empty entries in the i-th row of the resource matrix Γ, for a given resource matrix and sensor output matrix, the output matrix of drone i for target j is as follows:

3. The adaptive risk-aware multi-target tracking method with network repair according to claim 1, characterized in that: The measurement noise is defined as the covariance R ij,t The zero-mean and independent Gaussian noise is a distance-related function. As the observation distance increases, the observation noise increases exponentially: in: Among them, λ s and w s is the shape parameter of the Gaussian distribution.

4. The adaptive risk-aware multi-target tracking method with network repair according to claim 1, characterized in that: Considering that a heterogeneous drone team may be attacked when performing distributed tracking of multiple targets, we divide attacks into the following three categories based on the changes in observability before and after the attack: 1) Minor attack: the individual before and after the attack satisfies one-hop observability; 2) Tolerable attacks: one-hop observability is satisfied before the attack but not after the attack, but one-hop observability can be restored by acquiring the sensing resources of new members; 3) Intolerable attack: one-hop observability is satisfied before the attack but not after the attack. However, one-hop observability can be restored by acquiring the sensor resources of new members and one-hop observability cannot be satisfied again by sharing resources.

5. The adaptive risk-aware multi-target tracking method with network repair according to claim 1, characterized in that: In Formula 12, the first constraint is the UAV's dynamic constraint, which limits the displacement of a single iteration. The second constraint is the collision avoidance constraint between different UAVs, which limits the minimum distance between UAVs. The third constraint is the scaling of the UAV's measurement accuracy. The fourth constraint is the scaling of the UAV's safety. The objective function is a linear combination of the scaling of the two indicators based on the sensor margin. In the observation task, when observability is met, the accuracy of tracking observation is improved as much as possible. When the UAV makes a slight attack and observability decreases, the focus is first on improving safety and then optimizing tracking accuracy.

6. The adaptive risk-aware multi-target tracking method with network repair according to claim 1, characterized in that: In Formula 18, the decision variable L represents the new Laplacian graph, where the first constraint ensures the properties of the Laplacian graph; the second constraint ensures that the graph is connected; the sixth constraint strictly defines that each diagonal element of L is greater than 0; the seventh constraint ensures that the off-diagonal elements in L are the opposite values ​​of the corresponding elements in π; the ninth constraint determines that at least one edge is added; the third constraint strictly defines the form of the one-hop observable Gram matrix; the fourth and fifth elements ensure the property of π as a closed connection matrix; and the eighth constraint limits the maximum number of added edges.

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