CN116819975A - Multi-target geometric center estimation method based on pure angle observation - Google Patents
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Abstract
The application relates to the technical field of multi-agent and sensor networks, in particular to a multi-target geometric center estimation method based on pure angle observation, which comprises the following steps: inputting initial information of the intelligent agent and the target into pure azimuth measurement; calculating the estimated position of the intelligent body on the target; inputting the estimated position of each target into a geometric center estimator to obtain the estimated position of the intelligent agent on the geometric center of the target; setting related parameters of the surrounding controller according to the corresponding geometric center estimation positions; inputting the related parameters into a surrounding controller to obtain a corresponding surrounding control law of each intelligent agent; according to the corresponding surrounding control law, a plurality of intelligent agents surround a plurality of targets and do circular motion around the geometric center of the targets at a certain speed, so as to realize the surrounding control of the plurality of intelligent agents on the plurality of targets; compared with the traditional azimuth measurement enclosure control, the method and the system are expanded to the enclosure between multiple targets and multiple intelligent agents, and the enclosure effect is obvious.
Description
Technical Field
The application relates to the technical field of multi-agent and sensor networks, in particular to a multi-target geometric center estimation method based on pure angle observation.
Background
A multi-agent system is a network system formed by a group of agents with sensing, communication, computing and execution capabilities that are interrelated. In the multi-agent system, the surrounding control refers to a control mode that an agent performs surrounding motion on a target or a target area according to obtained sensor data, and can be applied to the scenes of searching, rescuing, detecting, monitoring and the like of the target.
There are many studies on the control of the target enclosure at home and abroad. In the multi-agent system, there is a conventional method of acquiring the position information of the target by using a distance information design estimator and performing surrounding and surrounding control, the sensor required by acquiring the position information of the target by using the distance information design estimator is not easy to acquire data, has poor adaptability and low precision and efficiency, and compared with distance measurement, the sensor required by azimuth measurement is easier to acquire and is easier to be mounted on the robot; for azimuth measurement, researchers at home and abroad have a lot of related researches, and the researches are combined with a single target and a single intelligent agent, even combined with a multi-intelligent agent system; the direction information refers to that an onboard sensor of each intelligent body cannot directly obtain the position information of a target, and only the direction information of the target relative to the intelligent body can be obtained.
Disclosure of Invention
The application aims to provide a multi-target geometric center estimation method based on pure angle observation, which solves the problems that a sensor required by a distance information design estimator to acquire the position information of a target is difficult to acquire data, has poor adaptability and low precision and efficiency, and the problem that the on-board sensor of each intelligent body in azimuth measurement cannot directly acquire the position information of the target and only can acquire the direction information of the target relative to the intelligent body in the prior art.
In order to solve the technical problems, the application provides the following technical scheme: a multi-target geometric center estimation method based on pure angle observation comprises the following specific steps:
s1: constructing a topological structure of a multi-agent system, and inputting initial information of an agent i and a target j into pure azimuth measurement;
s2: estimating the positions of a plurality of targets j by calculating azimuth angles between the intelligent body i and the targets j, and calculating the estimated positions of the intelligent body i on the targets j；
S3: designing a geometric center estimator to obtain the estimated position of each target j by S2Inputting the estimated position of the geometric center of the object j to the geometric center estimator to obtain the estimated position of the geometric center of the object j>；
S4: designing an envelope controller to estimate a position based on a corresponding geometric centerSetting related parameters surrounding the controller;
s5: inputting the related parameters into a surrounding controller to obtain a corresponding surrounding control law of each intelligent agent i；
S6: according to corresponding surrounding control lawThe intelligent agent i surrounds the target j and performs circular motion around the geometric center of the target j at a certain speed, so that the surrounding control of the intelligent agent i on the target j is realized.
Further, in step S1The multi-agent system consists of n agents and m targets, wherein the agents and targets belong toKinetic model of the i-th agent:
；
wherein ：is the location of the i-th agent, < +.>Representing the control input of the ith agent, i.e., achieving the surrounding control law of the desired configuration.
Further, in step S2, an estimated position of object j by agent i is calculatedThe calculation formula of (2) is as follows:
；
；
wherein ：representing the position estimate of agent i for object j, for example>Representing a unit array->Representing euclidean norms, +.>Is of normal number>Unit vector representing connection of agent i with target j +.>Representation->Is to be used in the present application,representing the position of object j->Is the location of the i-th agent, < +.>Representation vector->Is a binary norm of (c).
Further, step S2 also includes calculating an estimated error of agent i for target jThe expression is:
。
further, the geometric center estimator in step S3 is defined as follows:
；
；
；
wherein Representation geometryInternal state of the center estimator, and +.>；Estimated positions of entities i and j, respectively, to the geometric center,/, respectively>Error estimated for geometry center for agent i,/->For the actual geometric center of the object, +.>Is of normal number>Neighbor set representing agent i, +.>Representing a set of targets that can communicate with agent i,/->Representing the number of agents communicating with object j, wherein +.>For an element in the adjacency matrix, if in the node set, node i and node j belong to the set of edges, +.>Otherwise。
Further, based on the estimation errorDesign of Lyapunov function->The calculation formula is as follows:
；
wherein ：representation->Transpose of->And (3) deriving:
；
due to, and />Is a continuous excitation condition, so->Thereby get->。
Further, the definition of the surrounding controller in steps S4 to S6 is as follows:
；
；
；
wherein ,is the desired radius>Indicating tangential velocity of the agent, +.>By->Rotated 90 degrees anticlockwise, set->Representing vector +.>Is defined as the second norm of agent i to target physical geometric center->Distance of (1)/(2)>Representing vector +.>Is obtainable from a triangular geometry,
；
and because ofTherefore->Obtain->That is, the agent may encompass the geometric center of the multi-target and move circumferentially around it at a desired radius r.
By the technical scheme, the application provides a multi-target geometric center estimation method based on pure angle observation, which has at least the following beneficial effects:
the application introduces a pure angle measurement method into a multi-object geometric center position estimation method, and simultaneously designs a corresponding control law to force an intelligent object to surround the multi-object geometric center rapidly and do circular motion around the multi-object geometric center with a desired radius and a corresponding angular velocity, and the pure angle measurement-based multi-object geometric center estimation method is a new method compared with the traditional surrounding control method, and compared with the distance measurement method, the pure angle measurement-based multi-object geometric center estimation method has the advantages that the convergence and stability of a geometric center estimator and a surrounding controller are proved by the relevant theorem, finally, the multi-object can surround the multi-object geometric center with a certain angular velocity and a desired radius by setting parameters in the geometric center estimator and the surrounding controller, compared with the traditional surrounding control method, the surrounding effect of the multi-object geometric center estimation method based on the pure angle observation is more easy to obtain data, and is easier to guarantee that a machine is carried on the intelligent surrounding system and the multi-object surrounding system, and the surrounding control system is more complete, and the surrounding effect of the multi-object surrounding system is more remarkable.
Drawings
The accompanying drawings are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate the application and together with the embodiments of the application, serve to explain the application. In the drawings:
FIG. 1 is a flow chart of the control principle of the proposed method;
FIG. 2 is a graph of angular relationship of an agent of the present application using pure azimuth measurements;
FIG. 3 is a communication topology of an agent and a target in the present application;
FIG. 4 is a graph of the geometric relationship between the actual geometric center of the target and the location of the ith agent, as estimated by the geometric center of the target;
FIG. 5 is an error plot of the geometric center estimator of the present application;
FIG. 6 is a graph showing the effect of the intelligent agent in performing the surrounding control by using the multi-objective geometric center estimation method based on the pure angle observation.
Detailed Description
In order that the above-recited objects, features and advantages of the present application will become more readily apparent, a more particular description of the application will be rendered by reference to the appended drawings and appended detailed description. Therefore, the realization process of how to apply the technical means to solve the technical problems and achieve the technical effects can be fully understood and implemented.
Those of ordinary skill in the art will appreciate that all or a portion of the steps in a method of implementing an embodiment described above may be implemented by a program to instruct related hardware, and thus, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Referring to fig. 1-6, a specific implementation manner of this embodiment is shown, the present application estimates the geometrical center position of the multi-object from time to time by introducing a pure angle measurement method into the multi-object system, and designs a corresponding control law to force the intelligent object to quickly surround the geometrical center of the multi-object and make circular motion around the intelligent object with a desired radius and a corresponding angular velocity, and by introducing a fixed time convergence lyapunov function method and related theorem, the convergence and stability of the estimator and the controller are proved, finally the intelligent object can surround the geometrical center of the multi-object with a certain angular velocity and a desired radius by setting parameters in the estimator and the controller, compared with the distance measurement, compared with the conventional azimuth measurement surround control, the present application expands the intelligent object to surround between the multi-object and the plurality of intelligent objects, and the surround effect is remarkable.
Referring to fig. 1, the present embodiment provides a multi-objective geometric center estimation method based on pure angle observation, which includes the following specific steps:
s1: constructing a multi-agent system topology structure, and inputting initial information of an agent i and a target j into a pure azimuth measurement, wherein the initial information comprises initial positions of all agents and targets，FIG. 3 is a communication topology diagram of the agent and the target in the present application;
specifically, the multi-agent system in S1 is composed of n agents and m targets, wherein the agents and targets belong toKinetic model of the i-th agent:
；（1）
wherein ：is the location of the i-th agent, < +.>Representing the control input of the ith agent, i.e., achieving the surrounding control law of the desired configuration.
S2: in order to realize the position estimation of a plurality of targets, the positions of a plurality of targets j are estimated by calculating the azimuth angle between the intelligent body i and the targets j, and the estimated positions of the intelligent body i and the targets j are calculated；
Specifically, for stationary target S2, the estimated position of object j by agent i is calculatedIs defined as follows：
；（2）
；（3）
wherein ：representing the position estimate of agent i for object j, for example>Representing a unit array->Representing euclidean norms, +.>Is of normal number>Unit vector representing connection of agent i with target j +.>Representation->Is to be used in the present application,representing the position of object j->Is the location of the i-th agent, < +.>Representation vector->Is a binary norm of (c).
Specifically, S2 further comprises calculating an estimated error of agent i to target jThe expression is:
；（4）
we assume that each target can be observed by at least one agent through azimuth angles measured by pure azimuth measurements, and now construct a geometric center estimator based on azimuth information to estimate the geometric centers of multiple targets.
S3: designing a geometric center estimator to obtain the estimated position of each target j by S2Inputting the estimated position of the geometric center of the object j to the geometric center estimator to obtain the estimated position of the geometric center of the object j>；
Specifically, the geometric center estimator in S3 is defined as follows:
；（5）
；（6）
；（7）
wherein Represents the internal state of the geometric center estimator and +.>；Estimation of geometric centers by agents i and j, respectivelyGauge position->Error estimated for geometry center for agent i,/->For the actual geometric center of the object, +.>Is of normal number>Neighbor set representing agent i, +.>Representing a set of targets that can communicate with agent i,/->Representing the number of agents communicating with object j, wherein +.>For an element in the adjacency matrix, if in the node set, node i and node j belong to the set of edges, +.>Otherwise；
Assuming that the target is stationary, combining the pairs of formulas (2) (3) and (4)The derivation can be obtained:；（8）
wherein ,is of normal number>By->Rotated 90 degrees counterclockwise to obtain->Representation->Is a transpose of (a).
Specifically, according to the estimation errorDesign of Lyapunov function->The calculation formula is as follows:
；
wherein ：representation->Transpose of->And (3) deriving:
；
therefore, it isIs bounded because->Is a unit vector, so->Is bounded, combined with formula (4) to obtain +.>Is bounded, thereby get->Also bounded, therefore, < >> and />Is bounded;
is provided with, wherein />Representing vector +.>I.e. the distance of agent i from its estimated geometric center, +.>R represents the desired radius, derived in combination with the above: /> ；（9）
The solution to equation (9) is obtained as:；（10）
due toBounded, let->B is a constant, so that；
Therefore, it isBounded, so->Is bounded. Is available from triangle relations>Bounded, i.e.)>, wherein Is of normal number>Representation vector->And only when +.>Error for the duration of the excitation condition>Trend to 0, i.e. for any +.>There are three positive integers +.>，/>T is such that：；（11）
wherein ,transpose of U, U being the unit vector. Set U and->The included angle is->，/>The included angle between the horizontal direction is->，/>The included angle between the horizontal direction is->As shown in FIG. 2, the intelligent agent of the application adopts the angle relation diagram of pure azimuth measurement, and we assume the angle +.>，/> and />Is positive counterclockwise and negative, and is derived from the geometric relationship: />；（12）
And because ofTherefore->Exists, and is obtained by geometric relationship:；（13）
thus obtaining；（14）
Therefore, continuous functionAlways increasing with time, it cannot converge to a constant value, so that a certain +.>And T, so that the left inequality of formula (11) is satisfied, thus +.>For the continuous excitation condition, the error ∈>Trend towards 0, i.e.)>；
Assume that the distance from the target to the actual geometric center of the target is bounded, again because，Therefore, it isTherefore, getI.e. +.>The error map of geometric center estimator agent i to geometric center estimation in the present application as shown in FIG. 5, therefore proposes true azimuthThe measurement method and the geometric center estimation method meet the requirements.
S4: designing an envelope controller to estimate a position based on a corresponding geometric centerSetting relevant parameters in the surrounding controller, including +.>，/>Isoparametric parameters;
s5: inputting the related parameters into a surrounding controller to obtain a corresponding surrounding control law of each intelligent agent i；
S6: according to corresponding surrounding control lawThe intelligent agent i surrounds the target j and performs circular motion around the geometric center of the target j at a certain speed, so that the surrounding control of the intelligent agent i on the target j is realized.
Specifically, the definition formula of the surrounding controller in S4-S6 is as follows:
；（15）
；（16）
； （17）
wherein ,is the desired radius>Indicating tangential velocity of the agent, +.>By->Rotated 90 degrees counterclockwise to obtain->A control input representing an ith agent, i.e., a surrounding control law that achieves a desired configuration, "control input" for the robot, "surrounding control law" for the surrounding task;
as shown in FIG. 4, the position of the object j in the present applicationGeometric center estimated position +.>The actual geometric center of the object->And the position of the ith agent +.>A geometrical relationship diagram between, whereinRepresentation vector->I.e. the distance of agent i from its estimated geometric center; is provided with->Representing vector +.>Is defined as the second norm of agent i to target physical geometric center->Distance of (2)，/>Representation vector->Is a binary norm of (2);
is provided withRepresenting vector +.>Is obtainable from the triangular geometry:
；（18）
and because ofTherefore->Can be obtained by combining (10) and the related theoremThat is, the intelligent agent can surround the multi-target geometric center and make circular motion around the multi-target geometric center with a desired radius r, as shown in fig. 6, the effect diagram of the intelligent agent for completing the surrounding control by adopting the multi-target geometric center estimation method based on the pure angle observation in the application is shown, and it can be seen that the multi-target geometric center estimation method based on the pure angle observation provided in the application can well realize the task of surrounding control of the multi-intelligent agent surrounding a plurality of target geometric centers in a two-dimensional space.
The application designs a multi-target geometric center estimator based on pure azimuth information, and designs a corresponding surrounding controller, so that the multi-intelligent system is ensured to complete surrounding and surrounding control, and a surrounding and surrounding control method of a group of multi-intelligent bodies to a group of target areas is obtained; compared with the traditional surrounding control, the multi-target geometric center estimation method based on the pure angle measurement is a new method, compared with the distance measurement, the sensor required by the pure angle measurement is easier to obtain and is easier to load on a robot, the multi-intelligent system is guaranteed to complete the surrounding and surrounding control, and the surrounding effect is obvious.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present application, and the present application is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present application has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (7)
1. A multi-target geometric center estimation method based on pure angle observation is characterized in that: the method comprises the following specific steps:
s1: constructing a multi-agent system topological structure, and inputting initial information of an agent i and a target j into pure azimuth measurement;
s2: estimating the positions of a plurality of targets j by calculating azimuth angles between the intelligent body i and the targets j, and calculating the estimated positions of the intelligent body i on the targets j；
S3: designing a geometric center estimator to obtain the estimated position of each target j by S2Inputting the estimated position of the geometric center of the object j to the geometric center estimator to obtain the estimated position of the geometric center of the object j>；
S4: designing an envelope controller to estimate a position based on a corresponding geometric centerSetting related parameters surrounding the controller;
s5: inputting the related parameters into a surrounding controller to obtain a corresponding surrounding control law of each intelligent agent i；
S6: according to corresponding surrounding control lawThe intelligent agent i surrounds the target j and performs circular motion around the geometric center of the target j at a certain speed, so that the surrounding control of the intelligent agent i on the target j is realized.
2. The multi-objective geometric center estimation method based on pure angle observation according to claim 1, wherein the method comprises the following steps: the multi-agent system in S1 is composed of n agents and m targets, wherein the agents and the targets belong toKinetic model of the i-th agent:
；
wherein ：is the location of the i-th agent, < +.>Representing the control input of the ith agent, i.e., achieving the surrounding control law of the desired configuration.
3. The multi-objective geometric center estimation method based on pure angle observation according to claim 1, wherein the method comprises the following steps: the estimated position of the object j of the intelligent agent i is calculated in the S2The calculation formula of (2) is as follows:
；
；
wherein ：representing the position estimate of agent i for object j, for example>Representing a unit array->Representing euclidean norms, +.>Is of normal number>Unit vector representing connection of agent i with target j +.>Expressed +.>The device is transposed and the device is used for the treatment of the surface,representing the position of object j->Is the location of the i-th agent, < +.>Representation vector->Is a binary norm of (c).
4. The multi-objective geometric center estimation method based on pure angle observation according to claim 1, wherein the method comprises the following steps: the S2 also comprises calculating the estimated error of the intelligent agent i to the target jThe expression is:
。
5. the multi-objective geometric center estimation method based on pure angle observation according to claim 1, wherein the method comprises the following steps: the geometric center estimator in S3 is defined as follows:
；
；
；
wherein Represents the internal state of the geometric center estimator and +.>；/>Respectively are provided withIs the estimated position of agent i and j to the geometric center,/, for>Error estimated for geometry center for agent i,/->For the actual geometric center of the object, +.>Is of normal number>Neighbor set representing agent i, +.>Representing a set of targets that can communicate with agent i,/->Representing the number of agents communicating with object j, wherein +.>For an element in the adjacency matrix, if in the node set, node i and node j belong to the set of edges, +.>Otherwise->。
6. The method for estimating the geometric center of the multiple targets based on the pure angle observation according to claim 5, wherein the method comprises the following steps: based on the estimation errorDesign of Lyapunov function->The calculation formula is as follows:
；
wherein ：representation->Transpose of->And (3) deriving:
；
due to, and />Is a continuous excitation condition, soThereby get->。
7. The multi-objective geometric center estimation method based on pure angle observation according to claim 1, wherein the method comprises the following steps: the definition formula of the surrounding controller in S4-S6 is as follows:
；
；
；
wherein ,is the desired radius>Indicating tangential velocity of the agent, +.>By->Rotated 90 degrees anticlockwise, set->Representing vector +.>Is defined as the second norm of agent i to target physical geometric center->Distance of (1)/(2)>Representing vector +.>Is obtainable from a triangular geometry,
；
and because ofTherefore->Obtain->That is, the agent may encompass the geometric center of the multi-target and move circumferentially around it at a desired radius r.
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| 张丽: "多智能体系统有限时间环绕控制问题研究", 《中国优秀硕士学位论文全文数据库 信息科技辑》, pages 22 - 23 * |
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| 邵敬平: "多自主体系统的协作目标定位与巡航控制", 《中国博士学位论文全文数据库 信息科技辑》, pages 1 - 75 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117093021A (en) * | 2023-10-19 | 2023-11-21 | 西北工业大学深圳研究院 | Distributed formation surrounding method applied to group intelligent system |
| CN117093021B (en) * | 2023-10-19 | 2024-01-30 | 西北工业大学深圳研究院 | Distributed formation surrounding method applied to group intelligent system |
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