CN115711603A - Coordinate-free distributed control algorithm in multi-agent system - Google Patents
Coordinate-free distributed control algorithm in multi-agent system Download PDFInfo
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- CN115711603A CN115711603A CN202211387475.1A CN202211387475A CN115711603A CN 115711603 A CN115711603 A CN 115711603A CN 202211387475 A CN202211387475 A CN 202211387475A CN 115711603 A CN115711603 A CN 115711603A
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Abstract
The invention discloses a coordinate-free distributed control algorithm in a multi-agent system. The method relates to the field of distributed control in multi-agent system control, and aims at a pure orientation surrounding control algorithm. The invention provides a coordinate-free distributed positioning and surrounding control algorithm for a vehicle cluster. A multi-target center estimator algorithm is designed for center estimation, and a controller algorithm is designed according to the estimated target center to control a plurality of trolleys to move in a surrounding manner. The distributed positioning and surrounding algorithm provided by the invention is in a coordinate-free form and does not need any position information, so that a unified global coordinate system is not needed any more, and the local coordinates of different vehicles are not aligned. The present invention considers only a portion of the vehicles to measure the relative bearing with respect to the target. Nevertheless, the distributed positioning algorithm provided by the invention still ensures that all vehicles accurately position the target through cooperation.
Description
Technical Field
The invention relates to the field of distributed control in multi-agent system control, and aims at a pure orientation surrounding control algorithm.
Background
With the continuous development of robotics and computer communication technologies, the formation control of multi-agent systems has also been widely studied and applied. Formation control of a multi-agent system refers to performing certain commands, such as changing the formation shape, enclosing a target object, co-transporting an item, etc., in accordance with a given formation shape by controlling the individual agents within the system. The surrounding control of the multi-agent system is also a popular subject of current research, and meanwhile, the system has great research potential, and the existing research results bring beneficial significance and value in practice. The research on the enclosure control is carried out in the environment of a second-order multi-agent system, mainly by controlling the motion speed and the motion direction of the agents in the multi-agent system, one or more objects can be enclosed in a surrounding way according to a specified bypassing way, and after the objects are successfully enclosed, all the agents in the agent system can still move according to the specified bypassing way.
The multi-agent system can realize surrounding control without global information through information interaction between agents, and has wide prospect. In real life, the surrounding control of the multi-agent system is based on a Global Positioning System (GPS) for positioning an object, but in some special environments, the multi-agent in the multi-agent system may lose global positioning information, so that the global information cannot be reused to determine the object, and under the condition that the global information is no longer available, the research of the object positioning based on incomplete information is particularly important because the object can be precisely surrounded and controlled only when the object(s) are precisely positioned. At present, the incomplete target information of the hot is mainly based on the surrounding control of distance or azimuth information, and how to accurately position the target (center) according to the incomplete information is the key of research. The invention positions the targets only by using incomplete information of the targets measured in azimuth and controls the surrounding of circular formation according to the estimated position information of the targets.
Disclosure of Invention
The invention provides a coordinate-free distributed positioning and surrounding control algorithm for a vehicle cluster. A multi-target center estimator algorithm is designed for center estimation, and a controller algorithm is designed according to the estimated target center to control a plurality of trolleys to move in a surrounding manner.
The technical scheme adopted by the invention is as follows:
step 1: each trolley measures the azimuth information of the corresponding target;
step 2: each trolley also accesses orientation information related to its neighbors;
and 3, step 3: converting the positions of the targets corresponding to all the target estimation into a local coordinate system of a trolley, and estimating the geometric center positions of a plurality of targets;
and 4, step 4: sharing the geometric center position estimated by one trolley with a neighbor trolley to carry out surrounding control on a target center;
and 5: the Lyapunov stability analysis verifies that the proposed algorithm realizes multi-target positioning and surrounding control without depending on a global unified coordinate system.
The algorithm designed by the invention has the following advantages:
1. compared with a positioning algorithm based on an absolute target position and a positioning algorithm based on a relative target position, the invention provides a distributed pure azimuth algorithm which is used for positioning and surrounding control of cluster vehicles without any position information.
2. Unlike the pure orientation algorithm that relies on a unified global coordinate system, the distributed positioning and surround algorithm proposed by the present invention is coordinate-free, thus eliminating the need for a unified global coordinate system and the local coordinates of different vehicles are not aligned.
3. Unlike projects where all vehicles independently locate an object by their respective orientation measurements, the present invention considers only a portion of the vehicles to measure the relative orientation with respect to the object. Nevertheless, the distributed positioning algorithm provided by the invention still ensures that all vehicles accurately position the target through cooperation.
Drawings
FIG. 1 is a diagram: and (5) estimating a target schematic diagram of the trolley.
FIG. 2 is a diagram of: and (5) coordinate transformation schematic diagram.
FIG. 3 is a diagram: theta ij And delta ij And (4) relationship.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
In order to enable a vehicle cluster to estimate a plurality of target geometric centers and drive counterclockwise around the geometric centers according to given detour distances and speeds, a comprehensive distributed algorithm is designed, the algorithm is mainly divided into two parts, and the positions of a single target, a trolley and the geometric centers of the plurality of targets are estimated by using knowledge of coordinate changes and matrixes. And then performing envelope control based on the estimated position.
If each trolley can measure the relative position of the corresponding target, that is, each trolley is provided with a corresponding target position measuring sensor, fig. 1 schematically illustrates the situation that the trolley tracks the target and acquires target information. Wherein P is i Representing the distance, alpha, of the corresponding target measured by the trolley in its own coordinate system i Represents the coordinate system sigma of the trolley i With the global coordinate system sigma g Angle of rotation after counter-clockwise, theta i Representing the angle of the corresponding target measured by the trolley in its own coordinate system. And (3) representing the position and angle information of all the targets in the self coordinate system of a trolley, and estimating the geometric center of the targets.
If only one dolly can observe all targets, namely only one dolly is provided with a target direction measurement sensor, the geometric centers of a plurality of targets can be estimated easily, because the dolly provided with the target direction sensor establishes a local coordinate system, and all targets can be represented in one local coordinate system, so that the geometric centers of the plurality of targets can be directly estimated, the situation is definitely simple for the estimation of the target centers, but is simple only for the dolly provided with the target direction sensor, and the other dollies without the target direction sensor need to obtain the geometric centers of the plurality of targets for comparison, so that a positioning algorithm is designed based on the situation, and the other dollies estimate the geometric centers of the targets by means of the direction information of the neighboring dollies.
FIG. 2 is a schematic diagram of coordinate transformation analysis, wherein P point is assumed to be represented as (P) in the coordinate system A x ,P y ) The point P can be represented as (P ') under the coordinate system C' x ,P' y ) The relationship between the coordinate system A and the coordinate system C is as follows: the coordinate system A is firstly rotated by alpha along the anticlockwise direction to obtain a coordinate system B, and the coordinate system B is respectively towards X A Direction translation dotX to X B The coordinate system C is obtained by carrying out directional translation on dotY
The distributed control algorithm is mainly divided into two parts, one part is used for positioning algorithm, including positioning between a trolley and a neighboring trolley, and positioning between the trolley and a corresponding target, and the other part is used for surrounding control.
Positioning algorithm
Formula 1 is used for the location between dolly and the neighbour's dolly. In the formula
Is the relative position p of trolley i to trolley j ij Taking cart i as an example, cart j is a neighbor cart of cart i because there are two carts adjacent to cart i (assuming eventually all carts converge on a circular trajectory of a given radius and the number n of carts in a cluster of carts>2) Thus the possible values for dolly j are j = i-1 or j = i +1. The values of i and j are 1,2, …, n, j = i-1=n when i =1, and j = i +1=1 when i = n. The last bit feedback term in the equation is used to cancel the estimation error, k 1 、k 2 Are values of the parameter to be determined and are all positive. Theta ij The included angle between the two trolley speed directions is the included angle between the two trolleys in the x-axis direction of the local coordinate system established by taking the two trolleys as the original points respectively. Further analysis of the included angle theta between the two car speed directions ij Previously, an angle quantity delta was introduced to represent the relationship between the speed direction of the cart and the angle between the two cart distance lines, e.g. theta in fig. 3 i And theta j Respectively the angle of counterclockwise rotation of the trolley i and the trolley j around the x axis under the global coordinate system, delta ij Indicating the speed direction v of the vehicle i 1 Angle delta to the straight line of the connection line between the two carriages ji Indicating the speed direction v of the trolley j 2 And the included angle of the straight line of the distance connecting line between the two trolleys.
Each car only needs to know the identity of its own front and rear neighbors and does not need to touch other vehicles. Thus, each trolley forms a central angle of 2 pi/n relative to the front and rear adjacent trolleys, and further equidistant circumambulation motion around the target is ensured. Meanwhile, the positioning formula algorithm is actually composed of two parts, the first two terms of the formula form a feedforward component which plays a role in counteracting the inherent component of the corresponding estimation error dynamic state, and the second two terms of the formula form a feedback component, so that the corresponding estimation error is effectively guaranteed to be converged to zero, namely the positioning accuracy is guaranteed.
Whether positioning or surround controlThe algorithm is only dependent on the information measured locally except the information of the number of vehicles, and the information measured locally can be processed by information exchange between adjacent trolleys, which is necessary information exchange. In particular, in order to implement the proposed distributed algorithm under a given cyclic interaction network, each vehicle will have its own angular velocity ω i Transmitting the speed direction of the trolley to other adjacent trolleys, and forming an included angle delta between the speed direction of the trolley and a straight line on which a distance connecting line of the two trolleys is positioned ij And delta ji And estimating an error of the target center in the local coordinate system
And its own velocity magnitude v i Interacting with its forward and backward neighbors.
While the invention has been described with reference to specific embodiments, any feature disclosed in this specification may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise; all of the disclosed features, or all of the method or process steps, may be combined in any combination, except combinations where mutually exclusive features or/and steps are present.
Claims (2)
1. A coordinate-free distributed control algorithm in a multi-agent system, comprising the steps of:
step 1: each trolley measures the azimuth information of the corresponding target;
step 2: each trolley also accesses orientation information related to its neighbors;
and step 3: converting the positions of the targets corresponding to all the target estimation into a local coordinate system of a trolley, and estimating the geometric center positions of a plurality of targets;
and 4, step 4: sharing the geometric center position estimated by one trolley with a neighbor trolley to carry out surrounding control on a target center;
and 5: the Lyapunov stability analysis verifies that the proposed algorithm realizes multi-target positioning and surrounding control without depending on a global unified coordinate system.
2. The method of claim 1, wherein the coordinate transformation method in step 3 is as follows, assuming that the point P can be represented as (P) in the coordinate system a x ,P y ) The point P can be represented as (P ') in the coordinate system C' x ,P' y ) The relationship between coordinate system a and coordinate system C is: the coordinate system A is firstly rotated by alpha along the anticlockwise direction to obtain a coordinate system B, and the coordinate system B is respectively towards X A Direction translation dotX to X B And performing directional translation dotY to obtain a coordinate system C.
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| CN116819975A (en) * | 2023-08-30 | 2023-09-29 | 安徽大学 | Multi-target geometric center estimation method based on pure angle observation |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116819975A (en) * | 2023-08-30 | 2023-09-29 | 安徽大学 | Multi-target geometric center estimation method based on pure angle observation |
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