Unmanned aerial vehicle cluster motion consistency evaluation method based on modified order parameter

Abstract

The application discloses a kind of based on correction order parameter's unmanned aerial vehicle cluster motion consistency evaluation method, this method includes: step one: establish unmanned aerial vehicle dynamics model;Step two: unmanned aerial vehicle dynamics model is mapped as particle model, realize the conversion between unmanned aerial vehicle dynamics model and particle model;Step three: unmanned aerial vehicle individual control law based on social force model;Step four: generate cluster steady-state motion and transition state data of transformation;Step five: calculate individual correction order parameter.The application can improve the evaluation mode of unmanned aerial vehicle cluster motion consistency, establish more scientific order parameter evaluation index for the possible surrounding, consistent turning and other motion modes of unmanned aerial vehicle cluster, improve the evaluation performance of unmanned aerial vehicle cluster consistent motion.

Description

Technical Field

[0001] This invention provides a method for evaluating the motion consistency of UAV swarms based on modified order parameters, and in particular, a method for evaluating the motion consistency of UAV swarms using order parameter indices based on localization and curvature correction, which belongs to the field of UAV swarm control. Background Technology

[0002] The consistency of motion in a drone swarm is a crucial aspect of drone swarm control. During collaborative tasks, the rapid achievement of motion consistency by the drone swarm can significantly improve task execution efficiency. To achieve consistent motion in a drone swarm, an effective evaluation metric for motion consistency is needed. Evaluation methods for system motion consistency, or system orderliness, generally include those based on statistical theory, entropy, and order parameter-based methods.

[0003] Evaluation methods based on statistical theory are data-driven approaches. They assess data consistency and correlation by calculating indicators such as correlation coefficients, Kappa consistency coefficients, and Kendall W. concordance coefficients. This data-driven approach, based on statistical theory, is not heavily reliant on the form of data correlation and is suitable for evaluating various forms of motion data. However, on the one hand, statistical evaluation methods require a large amount of data and a long time window. This means that evaluating drone swarm movements using statistical methods requires both collecting new data and preserving historical data. On the other hand, statistical theory can only obtain the correlation of swarm movements; the structural and temporal information implied by this correlation requires more complex evaluation methods.

[0004] Entropy-based evaluation methods construct entropy indices for systems. The concept of entropy originates from thermodynamics, reflecting the "inherent degree of disorder" of a system. As the temperature of a thermodynamic system increases, the randomness of the state of each microscopic particle increases, and the system's entropy also increases, meaning it becomes "more disordered." Shannon introduced the concept of thermodynamic entropy into communication channels, defining information entropy to describe the uncertainty in information transmission. High-information-content information has very low entropy, while lower information content results in higher randomness and thus higher entropy. Information entropy is not only applicable to communication channels; any activity that brings certainty, organization, regularity, or order can be measured by changes in information entropy. Similarly, structural entropy and cross-entropy also reflect the orderliness of a system in a certain property. Although the formula for entropy evaluation is simple in structure, its construction is very complex, and it is almost impossible to calculate for information with multiple preconditions. This leads to the fact that in practice, entropy-based indices are more suitable for evaluating more chaotic systems, while evaluating whether a system is more ordered requires constructing entropies for different levels of orderliness separately.

[0005] The order parameter was initially introduced as a thermodynamic parameter in Landau's phase transition theory to describe phase transitions. Within the Landau phase transition framework, the spontaneous symmetry breaking processes that emerge during phase transitions lead to symmetry-broken phases requiring more parameters to describe their states; these parameters are called order parameters. Simply put, it means that a change in molecular arrangement occurs between two states, and this change can be measured by a parameter—the order parameter. In synergetics, the order parameter refers to the ability of participants to coordinate and cooperate with each other in synergetics. Haken introduced the order parameter into synergetics because the object described by the order parameter in synergetics is similar to that in thermodynamics—the spatial arrangement structure of participants in a group between two states, i.e., "orderliness." The velocity polarization order parameter is a common order parameter in cluster systems. It assumes that the velocity magnitudes of all units in the system are the same, only their directions differ. The parameter obtained by summing all velocity vectors and taking the ratio of the modulus to the magnitude is the velocity polarization order parameter. This order parameter reflects the consistency of the cluster in the velocity direction. When all individuals are in the same direction, the order parameter is 1. When the velocity directions of individuals differ, the order parameter decreases, and when the system is disordered, the order parameter is almost 0. The velocity polarization order parameter is mainly used for velocity direction consistency. However, since the velocity magnitudes of unmanned systems cannot be completely consistent, and their motion consistency may also be reflected in other aspects, such as consistent orbiting motion or consistent turning, the velocity polarization order parameter cannot evaluate the consistency of unmanned system clusters in a broader sense.

[0006] This invention aims to address the motion consistency problem of UAV swarms. Based on statistical principles, it establishes localization and curvature correction methods to modify the fundamental velocity polarization order parameter, resulting in a consistency evaluation index more applicable to UAV swarm motion patterns, thereby evaluating the motion consistency of UAV swarms. Compared to entropy-based methods, this method does not require prior knowledge of the system, and compared to traditional order parameter-based methods, it is applicable to a wider range of consistent motion patterns in UAV swarms.

[0007] Localization methods limit the scope of an individual's assessment of the surrounding orderliness. When the group size is large, the influence between individuals that are far apart is small. If the scale of the assessment of orderliness is too large, the orderliness will be reduced due to these weakly influenced individuals. If the group moves in the same direction, such scale decay is negligible because all individuals move in the same way. However, this characteristic is only reflected in movement in the same direction, where the first-order features of the movement mode remain unchanged, thus it is suitable for large-scale orderliness assessment. If the group moves in a consistent circle around a certain point, the second-order features of the circle movement are invariant, so the differences between distant individuals are significant, requiring the use of localization methods to reduce the influence of distant individuals.

[0008] Curvature is a quantity calculated based on individual velocities and accelerations, utilizing both first-order and second-order information. Incorporating curvature into orderliness assessment allows for more comprehensive utilization of system information, enabling the determination of consistency in second-order information even in uniform circumferential motion, a form of motion where second-order characteristics remain invariant. Since uniform directional motion can be viewed as motion with degenerated second-order information, it is also suitable for evaluation methods incorporating curvature. By appropriately introducing curvature and combining it with velocity information to calculate order parameters, this approach is applicable not only to uniform directional motion but also to evaluating group motions with second-order information, such as uniform circumferential motion.

[0009] In summary, this invention proposes a method for evaluating the motion consistency of UAV swarms using order parameter evaluation indices based on localization and curvature correction. This method can obtain more effective order parameter evaluation results for possible motion patterns of UAV swarms, such as circling and uniform turning, thereby improving the efficiency and control performance of mining and evaluating the consistent motion of UAV swarms. Summary of the Invention

[0010] 1. Purpose of the invention:

[0011] This invention proposes a method for evaluating the motion consistency of UAV swarms based on modified order parameters. The purpose is to improve the evaluation method of UAV swarm motion consistency by establishing more scientific order parameter evaluation indicators for possible motion modes of UAV swarms, such as circling and uniform turning, thereby improving the evaluation performance of UAV swarm motion consistency.

[0012] 2. Technical Solution:

[0013] This invention addresses the problem of uniform motion in unmanned systems by constructing an order parameter evaluation index and a method for evaluating the orderliness of cluster motion based on localization and curvature correction. This evaluation method can accurately judge uniform directional motion applicable to conventional order parameter indices, and can also effectively evaluate motion modes that are still orderly but not applicable to conventional order parameters, such as uniform circling motion or uniform turning motion.

[0014] The indicator is constructed as follows:

[0015] Step 1: Establish the UAV dynamics model

[0016] Assuming each UAV is equipped with a three-channel autopilot for airspeed, heading, and trajectory, containing three translational degrees of freedom and two rotational degrees of freedom, the equivalent second-order system dynamic model of the UAV is established as follows:

[0017]

[0018] In the formula, (x i ,y i ,zi Let be the position vector of UAV i. Its derivative, V i ψ i and λ i These are horizontal speed, heading angle, and rate of change of altitude, respectively. and V is the corresponding derivative. i c ψ i c and z c Given the desired speed, heading angle, and altitude, τ v τ ψ and τ λ These are the time constants for the three control variables.

[0019] Also considering the practical constraints of drones:

[0020]

[0021] In the formula, V max V min n max and λ max All are greater than 0, representing the maximum speed, minimum horizontal speed, maximum lateral overload, and maximum rate of change of height, respectively, λ. min Less than 0 indicates the minimum rate of change of height, where g is the acceleration due to gravity.

[0022] Step 2: Map the UAV dynamics model to a point mass model

[0023] The state variables of the particle model are the position and velocity of the particle, and the control variables are the forces acting on it. Its dynamic equations can be expressed as:

[0024]

[0025] Where, p i =(x i ,y i ,z i ) is the position vector of the point mass model. Its derivative, m is the mass of the particle model, and in this invention, the mass of the particle is taken as a unit mass of 1, v i =(v x ,v y ,v z ) is the velocity vector of the point mass model. Its derivative, u i =(u x ,u y ,u z ) represents the force acting on a point mass model.

[0026] Build mapping relationship

[0027]

[0028] This mapping relationship enables the conversion between the UAV dynamics model and the mass model.

[0029] Step 3: Individual Control Laws for Unmanned Aerial Vehicles Based on Social Force Model

[0030] In the social mechanics model, the fundamental interactions between individuals consist of position control forces and velocity control forces, and follow the three principles of "separation, aggregation, and consistency." The interaction forces between individual UAVs constructed based on the social force model are as follows:

[0031] u = u pos (p1,p2,...,p N )+u vel (v1,v2,...,v N (5)

[0032] Among them, u pos (·) represents positional control, which depends on the relative positions p between individuals. i (i=1,2,...,N), and u vel (·) represents the speed control force, which depends on the speed v of the individual members in the cluster. i (i = 1, 2, ..., N).

[0033] Based on the social force model, the control of individuals in this invention follows the following equation:

[0034]

[0035] in, It is the velocity vector of the individual, x ij The vector represents the distance between individuals i and j. v0 represents the magnitude of the expected convergent velocity. a and b are constants, representing the weights of the velocity convergence term and the repulsion-attraction factor, respectively. d0 represents the distance constant. α and β are variables, representing the negative powers of the weights affecting the radius of action of the individual and the repulsion-attraction factor, respectively, influencing the steady-state configuration of the system. σdξ represents the Gaussian noise term. Such a control law can ultimately form multiple steady states in a cyclic boundary, and the structure of the steady state is determined by the variables α and β. According to Newton's laws of motion, the control quantity is directly proportional to the velocity variable. In an open boundary environment, steady-state analysis of this system shows that the system will eventually tend towards open linear motion or closed circumferential motion.

[0036] Step 4: Generate cluster steady-state motion and transitional state data

[0037] Using specific parameters can stabilize a cluster in different motion states, and gradually changing the relevant parameters over a continuous period of time can also gradually change the shape of the system's motion state. By collecting steady-state motion data before parameter changes, transitional state data during parameter changes, and data after parameter changes to re-establish a steady state over a continuous period of time, data on multiple stable motion states can be collected simultaneously.

[0038] Step 5: Calculate the individual corrected order parameter

[0039] S51. Establish locality and calculate temporary correction copies based on the velocity directions of neighbors within the neighborhood.

[0040]

[0041] Among them, v x v y F represents the lateral and longitudinal velocities of an individual. x F y It indicates the horizontal and vertical forces acting on an individual.

[0042] The individual's orbital center (x) is calculated based on the radius of curvature, velocity, and individual position. center ,y center )

[0043]

[0044] Combining the radius parameter α of the repulsion-attraction ratio when an individual is under control in formula (6), the correction angle θ is first calculated for all "neighbor" individuals within a distance αd from the individual. i

[0045]

[0046] Where vec0 represents the distance vector between the main individual and the center, vec i This represents the distance vector between the neighboring individual and the center.

[0047] The correction velocity (v) of neighboring individuals is calculated based on the correction angle. xi ,v yi )

[0048]

[0049] The radius of curvature utilizes second-order information of the system, while locality limits the scale of individual interactive neighbors. The modified order parameter, compared to the velocity polarization order parameter, utilizes local second-order information and has a better evaluation effect on motion on smooth manifolds.

[0050] S52. Calculating Individual Local Order Parameters Based on Modified Velocity Copy

[0051] After calculating the corrected velocity vectors for all neighbors, the local order parameter P of the individual is calculated. i

[0052]

[0053] Among them, v i v j Let i represent the velocity vectors of the main individual i and its neighboring individual j, respectively. dis(·,·) is the velocity distance function, calculating the difference between the two velocity vectors. This can be achieved using...

[0054]

[0055] The calculation methods are as follows. This distance function reflects the difference in velocity vectors. The dis1 function uses the exponential distance of the normalized vector difference. Because it uses an exponent, it is more gentle than a direct weighted sum. The difference only approaches 0 when the velocity vector difference is huge, which also makes the lower limit of the improved order parameter calculated by this distance formula higher. dis2 is similar to dis1, but it does not consider the difference in the magnitude of the velocity vectors. Instead, it takes the angle between the velocity vectors as a power of the natural constant. Since the angle between the velocity vectors has a range of values, this index is more gentle than dis1. dis3 takes the imaginary power of the natural constant for the angular difference of the velocities. This index is 1 if and only if the two velocities are in the same direction.

[0056] S53. Calculate the local order parameters of all individuals and the cluster order parameters.

[0057] The local order parameters of all individuals are statistically analyzed and averaged. This average value is used to evaluate the orderliness of the system. When the value of this value is close to 1, it indicates that the cluster system is ordered, while when the value is close to 0, it indicates that the cluster system does not have good orderliness.

[0058]

[0059] 3. Beneficial effects: The method of the present invention can improve the evaluation of the motion consistency of UAV swarms, and establish more scientific order parameter evaluation indicators for the motion modes that UAV swarms may have, such as circling and uniform turning, thereby improving the evaluation performance of the motion consistency of UAV swarms. Attached Figure Description

[0060] Figure 1 This is a flowchart of the modified sequence parameter evaluation method of the present invention.

[0061] Figure 2 It is a consistent directional motion pattern generated.

[0062] Figure 3 It is a generated, consistent, circling motion pattern.

[0063] Figure 4 It refers to the stable and transitional trajectories of the generated uniform directional motion and circumferential motion.

[0064] Figure 5 It is a comparison between the corrected order parameter and the velocity polarization order parameter when the cluster moves in the same direction.

[0065] Figure 6 It is a comparison between the corrected order parameter and the velocity polarization order parameter when the cluster moves in a consistent orbit. Detailed Implementation

[0066] The invention will be further described below with reference to the accompanying drawings. The experimental computer was configured with an Intel Core i7-10700 processor, 2.90GHz clock speed, 16GB of memory, and MATLAB R2017b software. Specific steps are as follows: Figure 1 As shown, it includes the following steps:

[0067] Step 1: Establish the UAV dynamics model

[0068] Initialize and set the various parameters of the drone, including the airspeed and time constant τ. v =3, heading angle time constant τ ψ =0.1, altitude time constant τ λ =0.3,τ h =1, minimum speed limit V min =0m / s, maximum speed limit V max =5m / s, maximum lateral overload n max =5,λ max =5, minimum track inclination angle λ min = -5.

[0069] Step 2: Map the UAV dynamics model to a point mass model

[0070] Set the cluster size to 100 and the initial density to 5, then calculate the rectangular range of the initial location. Generate random position information within a rectangle with side length l and random velocity information of size 10 with direction angle in the range (0, 2π] for all individuals.

[0071] Step 3: Design individual control laws for UAVs based on a social force model

[0072] In the social mechanics model, the fundamental interactions between individuals consist of position control forces and velocity control forces, and follow the three principles of "separation, aggregation, and consistency." The interaction forces between individual UAVs constructed based on the social force model are as follows:

[0073] u = u pos (p1,p2,...,pN )+u vel (v1,v2,...,v N (5)

[0074] Among them, u pos (·) represents positional control, which depends on the relative positions p between individuals. i (i=1,2,...,N), and u vel (·) represents the speed control force, which depends on the speed v of the individual members in the cluster. i (i = 1, 2, ..., N).

[0075] Based on the social force model, the control of individuals in this invention follows the following equation:

[0076]

[0077] in, This is the velocity vector of each individual, where v0 represents the magnitude of the expected convergent velocity. a and b are constants, both set to 1, representing the weights of the velocity convergence term and the repulsion-attraction factor. d0 is the distance constant, set to 0.5. α and β are variables, representing the negative powers of the influence on the radius of influence of the individual's action force and the repulsion-attraction factor, respectively, affecting the steady-state configuration of the system. When α = 10 and β = 2, the cluster has a larger range of influence and smaller force attenuation, eventually moving in a uniform direction at stability. The overall system shape is as follows: Figure 2 As shown; when α=2 and β=1, the cluster has a small effective range, and when it finally stabilizes, it exhibits a uniform, circling motion as the overall shape of the system. Figure 3 As shown.

[0078] Step 4: Generate cluster steady-state motion and transitional state data

[0079] Using specific parameters can stabilize the cluster in different motion states, and gradually changing the relevant parameters over a continuous time can also gradually change the shape of the system's motion state. By continuously collecting steady-state motion data before parameter changes, transitional state data during parameter changes, and data after the parameter changes re-establish a steady state, data from multiple stable motion states can be collected simultaneously. When generating data, the steady-state parameters are consistent with those in step three, while the parameters in the transitional state are gradually changed. When the system changes from a uniform directional motion state to a uniform circling motion state...

[0080]

[0081] Where t trans The transition time is set to 3, where t0 is the start time of the transition state and t is the actual time.

[0082] When the system changes from a uniform orbital motion state to a uniform directional motion state...

[0083]

[0084] The meaning of the parameters is consistent with that of equation (7). During the transition state, the cluster will exhibit a short period of disorder, but eventually the system will enter a steady state as the parameters stabilize. Figure 4 This represents the trajectory that transitions multiple times between two states.

[0085] Step 5: Calculate the individual corrected order parameter

[0086] S51. Establish locality and calculate temporary correction copies based on the velocity directions of neighbors within the neighborhood.

[0087] Calculate the radius of curvature of a single individual by combining its force state and velocity information.

[0088]

[0089] Among them, v x v y F represents the lateral and longitudinal velocities of an individual. x F y It indicates the horizontal and vertical forces acting on an individual.

[0090] The individual's orbital center (x) is calculated based on the radius of curvature, velocity, and individual position. center ,y center )

[0091]

[0092] Based on the radius parameter α of the repulsion-attraction relationship when an individual is under control, the correction angle θ is first calculated for all "neighbor" individuals within a distance αd from the individual. i

[0093]

[0094] Where vec0 represents the distance vector between the main individual and the center, vec i This represents the distance vector between the neighboring individual and the center.

[0095] The correction velocity (v) of neighboring individuals is calculated based on the correction angle. xi ,v yi )

[0096]

[0097] S52. Calculating Individual Local Order Parameters Based on Modified Velocity Copy

[0098] After calculating the corrected velocity vectors for all neighbors, the local order parameter P of the individual is calculated. i

[0099]

[0100] Among them, v i v j Let represent the velocity vectors of the main individual i and its neighboring individual j, respectively. `dis(·,·)` is the velocity distance function, which calculates the difference between the two velocity vectors. It employs...

[0101]

[0102] The three ordinal parameters are calculated and recorded using the three calculation methods respectively.

[0103] S53. Calculate the local order parameters of all individuals, calculate the cluster order parameters, and draw conclusions.

[0104] The local order parameters of all individuals are statistically analyzed and their average values ​​are calculated. This average value is the final evaluation index. When the index value is close to 1, it indicates that the cluster system is ordered, while when the index value is close to 0, it indicates that the cluster system does not have good order.

[0105] Figure 5 To apply the correction order parameter based on localization and curvature correction to the data of consistent motion extracted from the trajectory data generated in step two, the curve of the correction order parameter transformation is obtained. Figure 6 To apply the corrected order parameter based on localization and curvature correction to the uniform circling motion data extracted from the trajectory data generated in step two, the curves of the corrected order parameter transformation are obtained. It can be seen that when the cluster moves in a uniform direction, both the corrected order parameter index and the velocity polarization order parameter index are close to 1, indicating that the cluster system is ordered. However, when the cluster system enters a transition state, both indices drop, indicating that the cluster system enters a disordered state. When the cluster system re-establishes stable uniform circling motion, the corrected order parameter index again approaches 1, while the velocity polarization order parameter remains at a low level. The uniform circling motion state determined by this method is still highly ordered.

Claims

1. A method for evaluating the motion consistency of UAV swarms based on modified order parameters, characterized in that: The method includes: Step 1: Establish the UAV dynamics model Assuming each UAV is equipped with an autopilot with three channels for airspeed, heading, and trajectory, including three translational degrees of freedom and two rotational degrees of freedom, establish an equivalent second-order system dynamic model of the UAV. Step 2: Map the UAV dynamics model to a point mass model to achieve the conversion between the UAV dynamics model and the point mass model; Step 3: Individual Control Laws for Unmanned Aerial Vehicles Based on Social Force Model In the social mechanics model, the basic interaction forces between individuals consist of position control force and velocity control force, and follow the three principles of "separation, aggregation, and consistency" to construct the interaction forces between individual UAVs; Step 4: Generate cluster steady-state motion and transitional state data The system collects steady-state motion data before parameter changes, transitional state data during parameter changes, and steady-state data after parameter changes within a continuous time period, so as to simultaneously collect data of multiple stable motion states. Step 5: Calculate the individual corrected order parameter; specifically: S51. Establish locality and calculate temporary correction copies based on the velocity directions of neighbors within the neighborhood. (7) in, , Indicates the horizontal and vertical speeds of an individual. , This indicates the horizontal and vertical forces acting on an individual. The individual's orbital center is calculated based on the radius of curvature, velocity, and individual position. ; ； Combining the radius parameter of repulsion-attraction when the individual is under control in formula (6) For the distance to that individual within The correction angle is calculated first for all "neighbor" individuals within the calculation. ; ； in, The distance vector between the main individual and the center. This represents the distance vector between the neighboring individual and the center; The correction speed of neighboring individuals is calculated based on the correction angle. ; ； S52. Calculating Individual Local Order Parameters Based on Modified Velocity Copy After calculating the corrected velocity vectors for all neighbors, the local order parameters of the individual are then calculated. ; ； in, , Representing the main individual and neighbor individuals The velocity vector, It is a velocity-distance function that calculates the difference between two velocity vectors; S53. Calculate the local order parameters of all individuals and the cluster order parameters. The local order parameters of all individuals are statistically analyzed and the average value is calculated. This index is used to evaluate the orderliness of the system. When the index value is close to 1, it indicates that the cluster system is ordered, while when the index value is close to 0, it indicates that the cluster system does not have good orderliness. (13)。 2. The method for evaluating the motion consistency of UAV swarms based on modified order parameters according to claim 1, characterized in that: The interaction forces between individual drones described in step three are in the following form: (5) in, This represents positional control, which depends on the relative positions of individuals. ,and This represents speed control, which depends on the speed of the individual members in the cluster. in, .

3. The method for evaluating the motion consistency of UAV swarms based on modified order parameters according to claim 2, characterized in that: Based on the social force model, the control of the individual drone follows the equations below: (6) in, It is the velocity vector of an individual. Represents the individual With individuals The distance vector, This represents the magnitude of the expected convergence speed. and The constant represents the weights of the velocity convergence term and the repulsion-attraction term. It represents the distance constant. and Let be variables, representing the negative powers of the radius weights of individual forces and the repulsive-attractive forces, respectively, which affect the steady-state configuration of the system. This represents the Gaussian noise term; such a control law can eventually form multiple steady states within the loop boundary, and the structure of the steady state is determined by the variables. and The decision is based on Newton's laws of motion, which state that the control quantity is directly proportional to the velocity variable. In an open-boundary environment, steady-state analysis of the system shows that it will eventually tend towards either open linear motion or closed circular motion.

4. The method for evaluating the motion consistency of UAV swarms based on modified order parameters according to claim 1, characterized in that: Calculate the difference between the two velocity vectors, specifically as follows: (12)。

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