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CN119758995A - A swarm robot affine formation control method based on hybrid measurement - Google Patents

A swarm robot affine formation control method based on hybrid measurement Download PDF

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Publication number
CN119758995A
CN119758995A CN202411736768.5A CN202411736768A CN119758995A CN 119758995 A CN119758995 A CN 119758995A CN 202411736768 A CN202411736768 A CN 202411736768A CN 119758995 A CN119758995 A CN 119758995A
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leader
robot
formation
follower
formation control
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李建祯
刘桂材
唐季叶
杨晓飞
王伟然
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Jiangsu University of Science and Technology
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Jiangsu University of Science and Technology
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Abstract

本发明公开了一种基于混合测量的群机器人编队控制方法，步骤如下：步骤1：选择一个主领导者和两个从领导者，构建以主领导者为根节点的通信拓扑图；步骤2：以主领导者的坐标作为原点建立全局坐标系，并获取环境地图；步骤3：基于环境地图获取从领导者的在全局坐标系中的坐标；步骤4：获取主领导者和从领导者各自的期望位置；步骤5：主领导者和从领导者基于优化后的领导者的控制律实时跟踪各自的期望位置；步骤6：计算当前跟随者与相邻机器人的理想距离；步骤7：基于跟随者编队控制率调节当前跟随者与相邻机器人之间的实时距离，实现队形控制。本发明不需要依赖GPS/GNSS获取全局坐标，可以采用不同的测量方式，提高系统构建的灵活性，成本降低。

The present invention discloses a group robot formation control method based on hybrid measurement, and the steps are as follows: Step 1: select a main leader and two slave leaders, and construct a communication topology diagram with the main leader as the root node; Step 2: establish a global coordinate system with the coordinates of the main leader as the origin, and obtain an environmental map; Step 3: obtain the coordinates of the slave leader in the global coordinate system based on the environmental map; Step 4: obtain the respective expected positions of the main leader and the slave leader; Step 5: the main leader and the slave leader track their respective expected positions in real time based on the control law of the optimized leader; Step 6: calculate the ideal distance between the current follower and the adjacent robot; Step 7: adjust the real-time distance between the current follower and the adjacent robot based on the follower formation control rate to realize formation control. The present invention does not need to rely on GPS/GNSS to obtain global coordinates, and can adopt different measurement methods, thereby improving the flexibility of system construction and reducing costs.

Description

Affine formation control method for group robot based on hybrid measurement
Technical Field
The invention relates to the technical field of group robot formation control, in particular to a group robot formation control method based on mixed measurement.
Background
With the development of technologies such as embedded, internet and artificial intelligence, mobile robot control technologies are becoming mature. In order to realize some large-scale tasks in a complex environment, multi-robot cooperation is an effective method. Through the mutual cooperation of a plurality of robots, the working efficiency can be improved, and tasks which cannot be completed by a single robot can be completed. Formation control is one of core technologies of group robot cooperation and is also a hot spot problem at present.
When robot formation passes through an obstacle-bearing area or a narrow passage, it is necessary to adjust the formation in real time according to the surrounding environment. The conventional formation control algorithm regards the whole formation as a rigid body, and cannot effectively realize the transformation of the formation. In recent years, affine formation control algorithms have been proposed by the academy in order to solve the formation transformation problem. The algorithm calculates the target position of the robot based on the stress matrix distribution, and can realize affine transformation of the formation, thereby realizing transformation such as formation expansion, rotation, translation and the like. But this algorithm requires that at least a part of the robots obtain absolute positions in the global coordinate system. In a GPS/GNSS rejection environment such as a tunnel, indoors, etc., it is difficult to obtain the absolute position of the robot.
As the price of lidar rapidly decreases, the range of application of lidar is becoming wider and wider. For a group robot system, if all robots use lidar, the total cost will also rise rapidly as the number of robots increases.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a group robot formation control method based on mixed measurement, which aims to solve the technical problems of difficult acquisition of absolute positions and high cost in the prior art.
The invention provides a group robot formation control method based on mixed measurement, which comprises the following steps:
Step 1, three robots provided with laser radars in a group of robots are respectively used as a master leader and two slave leaders, the other robots are used as followers, and a communication topological graph taking the master leader as a root node is constructed;
Step 2, a global coordinate system is established by taking the coordinates of a main leader as an origin, and an environment map is obtained through a laser radar of the main leader;
Step 3, acquiring a point cloud from a laser radar of a leader, and acquiring coordinates of the leader in a global coordinate system based on an environment map;
Step 4, acquiring respective expected positions of a master leader and a slave leader according to the environment map, the slave leader coordinates, the communication topological graph, the formed nominal formation and the affine formation stress coefficient;
Step 5, the master leader and the slave leader track the respective expected positions in real time based on the optimized control law of the leader;
Step 6, obtaining an affine transformation matrix of the adjacent robot of the current follower, and estimating the affine transformation matrix of the current follower; calculating the ideal distance between the current follower and the adjacent robot according to the estimated affine transformation matrix and the position difference of the adjacent robot in the nominal configuration;
and 7, acquiring the relative position of the adjacent robot under the own coordinate system of the current follower, and adjusting the real-time distance between the current follower and the adjacent robot according to the ideal distance based on the formation control rate of the follower to realize formation control.
Further, the desired positions in the steps 4 and 5 are:
wherein A (t) is an affine transformation matrix, B (t) is a translation matrix,R i is the nominal position of the leader robot node.
Further, in the step 5, the control law of the leader is:
Where a, b, k 1、k2 are control gains, p i is the actual position of the leader, μ (t) is a time-varying function; Is the target formation at time t, and omega ij is the stress coefficient.
Further, in the step 6, an affine transformation matrix of the current follower is estimated based on a consistency algorithm converged in a preset time.
Further, the specific formula of the estimation is:
In the formula, Is a matrixIs selected from the group consisting of the elements of the ith column,Is thatIs the set of adjacent robots of the current follower, a ij is the weight of the connection between the current follower and the adjacent robot, α, β is the control gain, μ 1 is the time-varying function.
Further, in the step 7, the follower formation control rate is as follows:
Wherein a is positive control gain, a >0; e ij is the distance error between follower i and the neighboring robot j, Sgn (·) is a sign function.
The invention has the beneficial effects that:
according to the invention, all robots do not need to rely on GPS/GNSS to acquire global coordinates, and a leader and a follower can adopt different measurement modes, so that the flexibility of system construction is improved, and the cost is reduced. The algorithm provided by the invention only needs to calculate the stress coefficients among three leaders in the implementation process, so that the implementation difficulty is reduced, the leaders can converge to the designated positions at the designated time, and the stress matrix is not required to be recalculated when the topological structure of the formation changes.
Drawings
The features and advantages of the present invention will be more clearly understood by reference to the accompanying drawings, which are illustrative and should not be construed as limiting the invention in any way, in which:
FIG. 1 is a flow chart of a method of an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The application will be further elucidated with reference to specific examples. It will be appreciated by those skilled in the art that these examples are intended to illustrate the application and not to limit the scope of the application, and that various equivalent modifications to the application fall within the scope of the application as defined by the appended claims.
As shown in fig. 1, the invention provides a group robot formation control method based on hybrid measurement, which comprises the following steps:
Step S1, three robots provided with laser radars in a group of robots are respectively used as a master leader and two slave leaders, the other robots are used as followers, and a communication topological graph with the master leader as a root node is constructed, wherein the specific steps are as follows:
Step S11, defining topological relation between robots as a graph Nominal formation is thenWherein, Represents a nominal configuration, andWherein, Representing a collection of nodes in the graph,Representing the collection of edges in the graph, when the graphIn which n l nodes are taken as leaders and marked asThe remaining nodes are followers, denoted asThe robot adjacent to the robot node i is denoted asIn formation of teamIs divided into leadersAnd followerThe state vector of robot i is denoted by p i.
Step S12, the dynamics model of N robot nodes can be represented by a first-order integrator model:
In the formula, U i is the control input to the robot.
Step S2, a global coordinate system is established by taking the coordinates of a main leader as an origin, and an environment map is acquired through a laser radar of the main leader, wherein the method comprises the following specific steps of:
Step S21, a main leader robot scans the surrounding environment by using a laser radar to acquire environment data of objects such as obstacles, walls and the like, the main leader converts the scanning data of the laser radar into a global map by using a SLAM algorithm, and the main leader acquires the position of the main leader by using a matching algorithm;
and S22, the master leader transmits the constructed map to the slave leader through the wireless communication module.
Step S3, acquiring a point cloud from a laser radar of a leader, and acquiring coordinates of the leader in a global coordinate system based on an environment map, wherein the coordinates are specifically as follows:
the method comprises the steps that a leader scans the surrounding environment of the leader through a laser radar to obtain the relative distance and the direction between the leader and a reference point in a global map, the leader matches the received map information with local environment information acquired by the laser radar of the leader, and the absolute position of the leader in the global map is calculated.
S4, acquiring respective expected positions of a master leader and a slave leader according to an environment map, slave leader coordinates, a communication topological graph, a nominal formation and stress coefficients of an affine formation;
Nominal formation of settings The following must be satisfied: At the position of Can be affine stretched to makeWith general rigidity and affine positioning,
Queuing the nominal valuesEach edge (i, j) in the nominal formation corresponds to a stress weightThis stress may be positive or negative, the stress matrix being:
Affine mapping of nominal formations is defined as:
the affine transformation matrix a (t) and the translation matrix b (t) of the leader can be obtained by affine mapping of the nominal formation.
Affine transformation is carried out on the nominal formation by the leader robot according to the latest topological information, the target position of the leader robot is adjusted in real time to control the position of the follower, the formation of the whole formation is further controlled, and the expected position of the leader i is as follows:
In the formula, For the affine transformation matrix, r i is the nominal position of the leader robot node,For the translation matrix, a (t) and b (t) are both continuous for time t. The master leader and the two slave leaders can acquire the respective expected positions through the expected position formulas.
The master leader calculates affine matrix parameters to be adjusted according to the environment and task requirements based on the position information of each robot in the formation, sends out instructions to control the formation to carry out affine transformation, and the leader coordinates the relative movement of the followers and helps to adjust the local structure of the formation.
Step 5, the master leader and the slave leader track the expected position of the target formation in real time based on the optimized control law of the leader;
when the leader robot tracks its own desired position, it is necessary to ensure that the system reaches the desired position of the formation within a specific time in consideration of the response speed and performance of the actual system. To ensure that the leader robot can reach the desired location within a specified time, a time-varying function is introduced, and the time T at which the control system converges to the desired location can be within a range of preset times [ T 0, T ], the time-varying function μ (T) being expressed as:
Where ρ >0 is the control gain.
After adding the time-varying function to the control law of the leader, the optimized control law of the leader is as follows:
Where a, b, k 1、k2 are control gains, p i is the actual position of the leader, μ (t) is a time-varying function; Is the target formation at time t, and omega ij is the stress coefficient.
Step 6, obtaining an affine transformation matrix of the adjacent robot of the current follower, and estimating the affine transformation matrix of the current follower based on a consistency algorithm converged in preset timeFrom estimated affine transformation matrixCalculating an ideal distance between the current follower and the adjacent robot according to the position difference between the current follower and the adjacent robot in the nominal configuration;
affine transformation matrix Dimension is m×n, affine transformation matrix is obtained by vectorization operationCan be expanded into column vectorsAt the same timeCan also be converted intoThe relationship is as follows
In the formula,Representation matrixIs the i-th column element of (c).
The follower robot adjusts the estimated value of the state variable through a consistency algorithm converged in preset timeAnd an estimate of the translation variableMaking it gradually trend to coincide with affine transformation and translation of the leader, the specific formula is as follows:
Wherein is of the formula Is the set of adjacent robots of the current follower, a ij is the weight of the connection between the current follower and the adjacent robot, α, β is the control gain, μ 1 is the time-varying function.
By combining the control law sum of the use-optimized leaderThe estimation method realizes the group robot system represented by the dynamics model and the affine transformation control motion of A (t), and can simultaneously enable the estimation value to be converged to the true value, namely, when t is in the range of [ t ]. Fwdarw ]
Will obtain convergence to a true valueConversion intoThe ideal distance between the follower and the adjacent robot p j can be obtained from the follower self position p i:
and 7, acquiring the relative position of the adjacent robot under the own coordinate system of the current follower, and adjusting the real-time distance between the current follower and the adjacent robot according to the ideal distance based on the formation control rate of the follower to realize formation control.
The follower i uses the sensor to measure the coordinates of the adjacent robot under the own coordinate system of the follower i, and the coordinates of the follower i are defined asThe coordinates of adjacent robots areThe distance error between follower i and the adjacent robot j is:
In the formula, Is the actual distance between two adjacent robots; the distance error between the robots is up and down limited as [ e min,emax ].
The square difference of the distance error between robots is expressed as:
In order to enable the formation to reach the target formation, the follower adopts the optimized follower formation control rate to control the relative distance between the follower formation control rate and the adjacent robots in real time, so that the relative distance between the robots is kept in a preset range [ e min,emax ],
The follower formation control rate is:
Wherein a is positive control gain, a >0; sgn (·) is a sign function.
Although embodiments of the present invention have been described in connection with the accompanying drawings, various modifications and variations may be made by those skilled in the art without departing from the spirit and scope of the invention, and such modifications and variations are within the scope of the invention as defined by the appended claims.

Claims (6)

1.一种基于混合测量的群机器人编队控制方法，其特征在于，包括如下步骤：1. A group robot formation control method based on hybrid measurement, characterized in that it includes the following steps: 步骤1：将群机器人中配备激光雷达的三个机器人分别作为一个主领导者和两个从领导者，其余机器人作为跟随者，构建以主领导者为根节点的通信拓扑图；Step 1: The three robots equipped with laser radar in the group of robots are respectively used as a main leader and two slave leaders, and the remaining robots are used as followers, and a communication topology graph with the main leader as the root node is constructed; 步骤2：以主领导者的坐标作为原点建立全局坐标系，并通过主领导者的激光雷达获取环境地图；Step 2: Establish a global coordinate system with the coordinates of the main leader as the origin, and obtain the environment map through the laser radar of the main leader; 步骤3：通过从领导者的激光雷达获取点云，并基于环境地图获取从领导者的在全局坐标系中的坐标；Step 3: Obtain the point cloud from the leader's lidar and obtain the leader's coordinates in the global coordinate system based on the environment map; 步骤4：根据环境地图、从领导者坐标以及通信拓扑图、编队的标称队形以及仿射编队的应力系数，获取主领导者和从领导者各自的期望位置；Step 4: Obtain the expected positions of the master leader and the slave leader according to the environment map, the slave leader coordinates, the communication topology map, the nominal formation of the formation, and the stress coefficient of the affine formation; 步骤5：主领导者和从领导者基于优化后的领导者的控制律实时跟踪各自的期望位置；Step 5: The master leader and the slave leader track their respective desired positions in real time based on the optimized leader's control law; 步骤6：获取当前跟随者相邻机器人的仿射变换矩阵，并估计当前跟随者的仿射变换矩阵；根据估计的仿射变换矩阵与相邻机器人在标称构型中的位置差计算当前跟随者与相邻机器人的理想距离；Step 6: Obtain the affine transformation matrix of the current follower's adjacent robot and estimate the affine transformation matrix of the current follower; calculate the ideal distance between the current follower and the adjacent robot according to the estimated affine transformation matrix and the position difference of the adjacent robot in the nominal configuration; 步骤7：获取当前跟随者自身坐标系下相邻机器人的相对位置，并基于跟随者编队控制率根据理想距离调节当前跟随者与相邻机器人之间的实时距离，实现队形控制。Step 7: Obtain the relative position of the adjacent robot in the current follower's own coordinate system, and adjust the real-time distance between the current follower and the adjacent robot according to the ideal distance based on the follower formation control rate to achieve formation control. 2.如权利要求1所述的基于混合测量的群机器人编队控制方法，其特征在于，所述步骤4、5中的期望位置为：2. The group robot formation control method based on hybrid measurement according to claim 1, characterized in that the desired position in steps 4 and 5 is: 式中，A(t)为仿射变换矩阵，b(t)为平移矩阵，ri为领导者机器人节点的标称位置。Where A(t) is the affine transformation matrix, b(t) is the translation matrix, ri is the nominal position of the leader robot node. 3.如权利要求1或2所述的基于混合测量的群机器人编队控制方法，其特征在于，所述步骤5中，领导者的控制律为：3. The group robot formation control method based on hybrid measurement according to claim 1 or 2, characterized in that in step 5, the control law of the leader is: 式中，a、b、k1、k2为控制增益；pi为领导者的实际位置；μ(t)为时变函数；为t时刻的目标队形；ωij为应力系数。Where a, b, k 1 , k 2 are control gains; p i is the actual position of the leader; μ(t) is a time-varying function; is the target formation at time t; ω ij is the stress coefficient. 4.如权利要求1所述的基于混合测量的群机器人编队控制方法，其特征在于，所述步骤6中，基于预设时间收敛的一致性算法估计当前跟随者的仿射变换矩阵。4. The group robot formation control method based on hybrid measurement as described in claim 1 is characterized in that in step 6, the affine transformation matrix of the current follower is estimated based on a consistency algorithm that converges within a preset time. 5.如权利要求4所述的基于混合测量的群机器人编队控制方法，其特征在于，所述估计的具体公式为：5. The group robot formation control method based on hybrid measurement according to claim 4, characterized in that the specific formula of the estimation is: 式中，为矩阵的第i列元素，是是当前跟随者的相邻机器人的集合；aij是当前跟随者与相邻机器人之间连接的权重；α、β为控制增益；μ1为时变函数。In the formula, For the matrix The i-th column element of yes is the set of neighboring robots of the current follower; aij is the weight of the connection between the current follower and the neighboring robots; α and β are control gains; μ1 is a time-varying function. 6.如权利要求1所述的基于混合测量的群机器人编队控制方法，其特征在于，所述步骤7中跟随者编队控制率为：6. The group robot formation control method based on hybrid measurement according to claim 1, characterized in that the follower formation control rate in step 7 is: 式中，a为正控制增益，a>0； eij为跟随者i与相邻机器人j之间的距离误差，sgn(·)为正负号函数。Where a is the positive control gain, a>0; e ij is the distance error between follower i and adjacent robot j, sgn(·) is a sign function.
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