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CN110750093A - Self-organizing cooperative tracking control method for extensible cluster particle robot - Google Patents

Self-organizing cooperative tracking control method for extensible cluster particle robot Download PDF

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CN110750093A
CN110750093A CN201911130970.2A CN201911130970A CN110750093A CN 110750093 A CN110750093 A CN 110750093A CN 201911130970 A CN201911130970 A CN 201911130970A CN 110750093 A CN110750093 A CN 110750093A
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余伶俐
况宗旭
王正久
周开军
霍淑欣
白宇
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Central South University
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Abstract

本发明公开了一种可扩展集群微粒机器人自组织协同跟踪控制方法，基于单点预瞄理论计算预瞄距离与预瞄点，驱动集群微粒机器人自组织地跟踪期望路径，并且当集群机器人出现横向位移偏差，可以重新回到期望路径。本发明提供的自组织协同跟踪控制方法无需对群体中的每个机器人进行编号，也不需要机器人集群保持固定的队形，并且不需要与特定个体进行通讯，因此在协同运动的过程中能扩展其他的微粒机器人加入集群。

Figure 201911130970

The invention discloses a self-organized cooperative tracking control method of an extensible swarm particle robot, which calculates a preview distance and a preview point based on a single-point preview theory, drives the swarm particle robot to track a desired path in a self-organized manner, and when the swarm robot appears horizontal Displacement deviation, you can return to the desired path. The self-organized cooperative tracking control method provided by the present invention does not need to number each robot in the group, nor does it need the robot group to maintain a fixed formation, and does not need to communicate with a specific individual, so it can be expanded in the process of cooperative movement. Other particle robots join the swarm.

Figure 201911130970

Description

可扩展集群微粒机器人自组织协同跟踪控制方法Self-organized cooperative tracking control method for scalable swarm particle robot

技术领域technical field

本发明涉及多机器人协同运动控制领域，特别是一种可扩展集群微粒机器人自组织协同跟踪控制方法。The invention relates to the field of multi-robot cooperative motion control, in particular to a self-organized cooperative tracking control method for scalable cluster particle robots.

背景技术Background technique

集群机器人协同控制是未来无人系统研究的重要内容之一，特别是创新机器人协同运动形式、简化机器人结构对于促进多机器人协同运动系统工程化具有重要意义。目前，集群机器人协同控制仍处于研究阶段，存在以下问题有待解决：Collaborative control of swarm robots is one of the important contents of future research on unmanned systems. In particular, it is of great significance to innovate the form of robot collaborative motion and simplify the robot structure to promote the engineering of multi-robot collaborative motion systems. At present, the collaborative control of swarm robots is still in the research stage, and there are the following problems to be solved:

(1)大多数的集群机器人系统都是采用具有自主运动能力的单机器人组合而成，机器人结构比较复杂，很难实现大规模集群；(1) Most of the swarm robot systems are composed of single robots with autonomous movement capabilities. The robot structure is relatively complex, and it is difficult to achieve large-scale swarms;

(2)大多数的集群机器人系统中每个机器人会有一个独立的身份，且需要通过特定的通讯结构进行信息交互，系统不具有可扩展性，在跟踪期望路径的过程中无法再加入其它机器人；(2) In most swarm robot systems, each robot has an independent identity and needs to exchange information through a specific communication structure. The system is not scalable, and other robots cannot be added in the process of tracking the desired path. ;

(3)大多数的集群机器人系统在跟踪期望路径的过程中，如果偏离期望路径，很难消除横向位移偏差、重新回到期望轨迹。(3) In the process of tracking the desired path of most swarm robot systems, if it deviates from the desired path, it is difficult to eliminate the lateral displacement deviation and return to the desired trajectory.

发明内容SUMMARY OF THE INVENTION

本发明所要解决的技术问题是，针对现有技术不足，提供一种可扩展集群微粒机器人自组织协同跟踪控制方法，实现机器人大规模集群，使集群机器人可扩展，并且当集群机器人出现横向位移偏差，可以重新回到期望路径。The technical problem to be solved by the present invention is to provide a self-organized collaborative tracking control method for scalable clustered particle robots, aiming at the deficiencies of the prior art, so as to realize a large-scale cluster of robots, so that the clustered robots can be expanded, and when the clustered robots have lateral displacement deviation , you can return to the desired path.

为解决上述技术问题，本发明所采用的技术方案是：一种可扩展集群微粒机器人自组织协同跟踪控制方法，包括以下步骤：In order to solve the above-mentioned technical problems, the technical solution adopted in the present invention is: a self-organized cooperative tracking control method of an extensible cluster particle robot, comprising the following steps:

1)初始化各微粒机器人的位置、膨胀收缩周期T、运动控制周期Tc、一组微粒机器人的数目n、距离更新周期

Figure BDA0002278272600000011
预瞄点更新周期并且选取一个机器人作为预瞄机器人，预瞄机器人需要预先存储需要跟踪的期望路径以及期望路径起点、终点坐标；1) Initialize the position of each particle robot, the expansion and contraction period T, the motion control period T c , the number n of a group of particle robots, and the distance update period
Figure BDA0002278272600000011
Preview point update cycle And select a robot as the preview robot. The preview robot needs to store the desired path to be tracked and the coordinates of the starting point and end point of the desired path;

2)预瞄机器人计算自身位置(xp,yp)与终点的距离DisToEnd；若DisToEnd＜ε，向群体广播已达到终点，程序终止；否则，预瞄机器人在期望路径上选取预瞄点(xpre,ypre)，并向群体广播预瞄点的坐标，同时设置预瞄机器人的0号计时器初始时间

Figure BDA0002278272600000021
0号计时器开始计时，并继续以下步骤；ε表示终止距离阈值，取值为机器人的最大预瞄距离lmax，即当预瞄机器人与终点的距离小于等于lmax，机器人群体停止运动；2) The preview robot calculates the distance DisToEnd between its own position (x p , y p ) and the end point; if DisToEnd < ε, the broadcast to the group has reached the end point, and the program terminates; otherwise, the preview robot selects the preview point on the desired path ( x pre , y pre ), broadcast the coordinates of the preview point to the group, and set the initial time of the timer 0 of the preview robot
Figure BDA0002278272600000021
Timer 0 starts timing and continues the following steps; ε represents the termination distance threshold, which is the maximum preview distance l max of the robot, that is, when the distance between the preview robot and the end point is less than or equal to l max , the robot group stops moving;

3)各微粒机器人计算自身的位置与预瞄点之间的距离Disi；各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin；各微粒机器人根据本机器人与预瞄点的距离Disi、最短距离Dismax，计算本机器人的响应序列Si；根据响应序列Si计算得到本机器人的唤醒时间并设置1号计时器初始时间

Figure BDA0002278272600000023
1号计时器开始计时；3) each particle robot calculates the distance Dis i between its own position and the preview point; each particle robot broadcasts distance information to the group, receives the distance information of other particle robots simultaneously, and compares the shortest distance Dis min ; each particle robot according to The distance Dis i and the shortest distance Dis max between the robot and the preview point , calculate the response sequence Si of the robot ; calculate the wake-up time of the robot according to the response sequence Si and set the initial time of timer 1
Figure BDA0002278272600000023
Timer 1 starts counting;

4)判断是否

Figure BDA0002278272600000024
如果是则执行以下步骤，否则该微粒机器人继续等待；4) Determine whether
Figure BDA0002278272600000024
If so, perform the following steps, otherwise the particle robot continues to wait;

5)设置2号计时器初始时间

Figure BDA0002278272600000025
2号计时器开始计时，当停止计时，继续以下操作：集群机器人中各微粒机器人根据其响应序列Si与1号计时器的计时时间
Figure BDA0002278272600000027
计算本机器人的驱动时间
Figure BDA0002278272600000028
根据微粒机器人的驱动时间
Figure BDA0002278272600000029
依次更新各机器人半径Ri，通过机器人膨胀收缩产生力的作用，驱动集群微粒机器人跟踪期望路径；5) Set the initial time of timer 2
Figure BDA0002278272600000025
Timer 2 starts counting, when Stop timing and continue the following operations: each particle robot in the swarm robot according to its response sequence S i and the timing time of the timer No. 1
Figure BDA0002278272600000027
Calculate the driving time of this robot
Figure BDA0002278272600000028
According to the driving time of the particle robot
Figure BDA0002278272600000029
The radius R i of each robot is updated in turn, and the force generated by the expansion and contraction of the robot is used to drive the swarm particle robot to track the desired path;

6)判断是否

Figure BDA00022782726000000210
若是则返回步骤2)，否则继续以下判断；判断是否
Figure BDA00022782726000000211
若是则返回步骤3)，否则返回步骤5)。6) Determine whether
Figure BDA00022782726000000210
If so, return to step 2), otherwise continue the following judgment; judge whether
Figure BDA00022782726000000211
If so, go back to step 3), otherwise go back to step 5).

所述期望路径由三次多项式构成，记作y＝A3x3+A2x2+A1x1+A0；其中A3,A2,A1,A0为三次方系数，x为期望路径的横坐标且x∈[x0,xf]，(x0,y0)为期望路径起点，(xf,yf)为期望路径终点；The desired path is composed of a cubic polynomial, denoted as y=A 3 x 3 +A 2 x 2 +A 1 x 1 +A 0 ; where A 3 , A 2 , A 1 , and A 0 are cubic coefficients, and x is The abscissa of the desired path and x∈[x 0 ,x f ], (x 0 , y 0 ) is the starting point of the desired path, and (x f , y f ) is the end point of the desired path;

所述微粒机器人是指满足以下条件的一类机器人：The particle robot refers to a type of robot that satisfies the following conditions:

a)机器人可以在原地做径向膨胀收缩运动，机器人膨胀能达到的最大半径为Rmax，机器人收缩能达到的最小半径为Rmin；a) The robot can perform radial expansion and contraction movement in situ, the maximum radius that the robot can reach is R max , and the minimum radius that the robot can shrink is R min ;

b)机器人之间存在相互吸引力，吸引力大小与两个机器人之间的距离相关，机器人膨胀会产生膨胀力；b) There is a mutual attraction between the robots, the magnitude of the attraction is related to the distance between the two robots, and the expansion of the robots will generate expansion force;

c)机器人膨胀产生的膨胀力Fexpansion以及一定距离范围内机器人之间的吸引力Fattract必须大于机器人与地面之间的最大静摩擦力，但是小于其他机器人所受的摩擦力之和，表达式如下：c) The expansion force F expansion generated by the expansion of the robot and the attraction F attract between the robots within a certain distance must be greater than the maximum static friction force between the robot and the ground, but less than the sum of the friction forces experienced by other robots, the expression is as follows :

Figure BDA0002278272600000031
Figure BDA0002278272600000031

其中，Nstatic表示其他静态机器人个数，m表示单个机器人的质量，μstatic表示机器人接触平面的静摩擦系数，g表示重力加速度。Among them, N static represents the number of other static robots, m represents the mass of a single robot, μ static represents the static friction coefficient of the robot contacting the plane, and g represents the acceleration of gravity.

步骤1)中所述初始化各微粒机器人的位置应满足每个微粒机器人至少有2个机器人与之相切且不与任何机器人相交，而且每排机器人不少于3个、每列机器人不少于3个；预瞄机器人初始化放置在期望路径上的任意位置，其他机器人围绕预瞄机器人放置；所述膨胀收缩周期T为微粒机器人膨胀到最大半径再收缩到最小半径所需要的时间，运动控制周期Tc表示微粒机器人相邻两次动作的时间间隔，距离更新周期表示相邻两次更新各微粒机器人自身位置与预瞄点之间距离Disi的时间间隔，预瞄点更新周期

Figure BDA0002278272600000033
表示相邻两次预瞄点坐标更新的时间间隔。The position of initializing each particle robot described in step 1) should be such that each particle robot has at least 2 robots tangent to it and does not intersect with any robot, and there are not less than 3 robots in each row and not less than 3 robots in each column. 3; the preview robot is initially placed at any position on the desired path, and other robots are placed around the preview robot; the expansion and contraction period T is the time required for the particle robot to expand to the maximum radius and then shrink to the minimum radius, and the motion control period T c represents the time interval between two adjacent actions of the particle robot, and the distance update period Indicates the time interval between two adjacent updates of the distance Dis i between the position of each particle robot and the preview point, and the update cycle of the preview point
Figure BDA0002278272600000033
Indicates the time interval between two adjacent preview point coordinate updates.

步骤2)中所述计算自身位置(xp,yp)与终点的距离DisToEnd的计算公式为The calculation formula for calculating the distance DisToEnd between self-position (x p , y p ) and the end point described in step 2) is:

步骤2)中所述ε表示终止距离阈值，ε取值等于机器人的最大预瞄距离lmax，当预瞄机器人自身位置(xp,yp)与终点的距离DisToEnd＜ε，认为集群微粒机器人到达终点，预瞄机器人向群体广播已达到终点，所有机器人的程序终止，停止运动。In step 2), ε represents the termination distance threshold, and the value of ε is equal to the maximum preview distance l max of the robot. When the distance DisToEnd <ε between the robot's own position (x p , y p ) and the end point of the preview robot, it is considered that the swarm particle robot When the end point is reached, the preview robot broadcasts to the group that the end point has been reached, and the programs of all robots are terminated and the movement is stopped.

步骤2)中所述在期望路径上选取预瞄点(xpre,ypre)的具体过程如下：The specific process of selecting the preview point (x pre , y pre ) on the desired path described in step 2) is as follows:

(1)确定期望路径上距离机器人当前位置(xp,yp)的最近点(xnear,ynear)，具体做法为：(1) Determine the closest point (x near , y near ) on the desired path to the current position (x p , y p ) of the robot, the specific method is as follows:

首先，计算机器人当前位置(xp,yp)到期望路径的距离函数：First, calculate the distance function from the robot's current position (x p , y p ) to the desired path:

Figure BDA0002278272600000041
Figure BDA0002278272600000041

而后，取disp(x)关于x的一阶导，令一阶导

Figure BDA0002278272600000042
得到极值点；Then, take the first derivative of dis p (x) with respect to x, let the first derivative
Figure BDA0002278272600000042
get the extreme point;

最后，根据两点间的距离公式分别计算极值点、期望路径起点、期望路径终点与预瞄机器人自身位置的距离，其中最短距离对应的点即为最近点(xnear,ynear)，若存在多个最近点，则选择其中距离终点最远的点作为最近点；Finally, according to the distance formula between the two points, calculate the distance between the extreme point, the starting point of the desired path, the end point of the desired path and the position of the preview robot. The point corresponding to the shortest distance is the closest point (x near , y near ). If If there are multiple closest points, select the point farthest from the end point as the closest point;

(2)计算最近点(xnear,ynear)的曲率C，计算公式为

Figure BDA0002278272600000043
其中，
Figure BDA0002278272600000044
表示三次多项式的二阶导，
Figure BDA0002278272600000045
表示三次多项式的一阶导，令x＝xnear，代入曲率计算公式即可以计算得到最近点处的曲率；(2) Calculate the curvature C of the nearest point (x near , y near ), and the calculation formula is
Figure BDA0002278272600000043
in,
Figure BDA0002278272600000044
represents the second derivative of a cubic polynomial,
Figure BDA0002278272600000045
Represents the first-order derivative of the cubic polynomial, let x=x near , and substituting it into the curvature calculation formula can calculate the curvature at the nearest point;

(3)根据曲率C计算预瞄距离，计算公式其中，k为常数、表示预瞄距离的调整增益，lmax表示最大预瞄距离，lmin表示最小预瞄距离；该式表示随着曲率的增大，预瞄距离减小，即跟踪弯道路径时预瞄点距离机器人较近，以保证集群微粒机器人及时调整运动状态，准确跟踪期望路径；(3) Calculate the preview distance according to the curvature C, the calculation formula Among them, k is a constant, representing the adjustment gain of the preview distance, l max represents the maximum preview distance, and l min represents the minimum preview distance; this formula indicates that with the increase of the curvature, the preview distance decreases, that is, the tracking curve The preview point is close to the robot during the path to ensure that the swarm particle robot can adjust the motion state in time and accurately track the desired path;

(4)根据最近点(xnear,ynear)与预瞄距离l确定预瞄点(xpre,ypre)，计算公式为：(4) Determine the preview point (x pre , y pre ) according to the closest point (x near , y near ) and the preview distance l, and the calculation formula is:

Figure BDA0002278272600000047
Figure BDA0002278272600000047

求解该方程即可以得到预瞄点坐标(xpre,ypre)。Solving this equation can get the coordinates of the preview point (x pre , y pre ).

步骤3)的具体步骤如下：The specific steps of step 3) are as follows:

(1)各微粒机器人计算自身的位置与预瞄点之间的距离Disi，计算公式为

Figure BDA0002278272600000048
其中i表示第i个微粒机器人，(xi,yi)表示第i个微粒机器人的坐标；(1) Each particle robot calculates the distance Dis i between its own position and the preview point, and the calculation formula is:
Figure BDA0002278272600000048
where i represents the ith particle robot, and (x i , y i ) represents the coordinates of the ith particle robot;

(2)各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin，具体做法为：首先，将本机器人与预瞄点之间的距离初始化为最短距离Dismin；然后，将接收到的距离信息Disj依次与最短距离Dismin进行比较，若接收到的距离信息小于Dismin，则将Disj更新为Dismin，即令Dismin＝Disj，否则不进行更新，最后直到未接收到其他新的距离信息，得到的Dismin即为集群机器人到预瞄点的最短距离。其中，j表示接收到的第j个机器人的信息j≠i且j∈[1,2,…,N-1，N]，N为微粒机器人的总个数；(2) Each particle robot broadcasts distance information to the group, and at the same time receives the distance information of other particle robots, and compares the shortest distance Dis min . The specific method is: first, initialize the distance between the robot and the preview point to the shortest distance Dis min ; Then, compare the received distance information Dis j with the shortest distance Dis min in turn, if the received distance information is less than Dis min , then update Dis j to Dis min , that is, make Dis min =Dis j , otherwise not Update, and finally until no other new distance information is received, the obtained Dis min is the shortest distance from the swarm robot to the preview point. Among them, j represents the received information of the jth robot j≠i and j∈[1,2,…,N-1,N], N is the total number of particle robots;

(3)根据本机器人与预瞄点的距离Disi、最短距离Dismax，计算本机器人的响应序列Si，计算公式为Si＝(Dismin-Disi)/(2*Rmin)*T/2，所述响应序列是指机器人进行膨胀收缩的先后次序，根据计算公式可知Si≤0并且越靠近预瞄点的机器人，响应序列Si较大并且机器人越先进行膨胀收缩运动；(3) Calculate the response sequence S i of the robot according to the distance Dis i and the shortest distance Dis max between the robot and the preview point. The calculation formula is S i =(Dis min -Dis i )/(2*R min )* T/2, the response sequence refers to the order in which the robot performs expansion and contraction. According to the calculation formula, it can be known that Si ≤ 0 and the robot closer to the preview point has a larger response sequence Si and the robot expands and contracts earlier;

(4)根据响应序列Si计算得到本机器人的唤醒时间

Figure BDA0002278272600000051
计算公式为
Figure BDA0002278272600000052
所述唤醒时间是指在一次距离更新周期内，机器人开始膨胀收缩运动的全局时间，全局时间是1号计时器计时的时间
Figure BDA0002278272600000053
步骤5)中各微粒机器人计算本机器人的驱动时间
Figure BDA0002278272600000054
的具体方法如下：首先根据响应序列Si与1号计时器的计时时间
Figure BDA0002278272600000055
将响应序列时序化，得到预驱动时间
Figure BDA0002278272600000056
计算公式为：(4) Calculate the wake-up time of the robot according to the response sequence S i
Figure BDA0002278272600000051
The calculation formula is
Figure BDA0002278272600000052
The wake-up time refers to the global time when the robot starts to expand and contract during a distance update period, and the global time is the time counted by the No. 1 timer.
Figure BDA0002278272600000053
In step 5), each particle robot calculates the driving time of the robot
Figure BDA0002278272600000054
The specific method is as follows: First, according to the response sequence S i and the timing time of the No. 1 timer
Figure BDA0002278272600000055
Timing the response sequence to get the pre-drive time
Figure BDA0002278272600000056
The calculation formula is:

Figure BDA0002278272600000057
Figure BDA0002278272600000057

而后，对预驱动时间

Figure BDA0002278272600000058
进一步进行处理，按照组别计算得到微粒机器人的驱动时间
Figure BDA0002278272600000059
计算公式为：Then, for the pre-drive time
Figure BDA0002278272600000058
After further processing, the driving time of the particle robot is calculated according to the group
Figure BDA0002278272600000059
The calculation formula is:

Figure BDA0002278272600000061
Figure BDA0002278272600000061

其中，floor表示向下取整，n表示一组微粒机器人的数目；所述驱动时间是指机器人从唤醒时间开始，以n*T/2为周期的周期循环时间，n*T/2表示一组机器人均完成膨胀收缩所需要的时间。即从唤醒时间开始计时，计时到n*T/2之后又重新开始计时，以n*T/2为周期循环，该计时时间即为驱动时间。Among them, floor represents rounding down, and n represents the number of a group of particle robots; the driving time It refers to the cycle time of the robot starting from the wake-up time, with n*T/2 as the period, n*T/2 represents the time required for a group of robots to complete the expansion and contraction. That is to say, start timing from the wake-up time, and start timing again after the timing reaches n*T/2, with n*T/2 as the cycle, and the timing time is the driving time.

步骤5)中根据微粒机器人的驱动时间

Figure BDA0002278272600000063
依次更新各机器人半径Ri的具体过程如下：In step 5), according to the driving time of the particle robot
Figure BDA0002278272600000063
The specific process of sequentially updating the radius R i of each robot is as follows:

a)根据驱动时间

Figure BDA0002278272600000064
计算机器人的期望半径；计算方法如下：首先判断是否若是则认为机器人需要进行径向膨胀，膨胀后的期望半径为
Figure BDA0002278272600000066
否则继续判断是否
Figure BDA0002278272600000067
若是则认为机器人需要进行径向收缩，收缩后的期望半径为
Figure BDA0002278272600000068
否则认为机器人既不膨胀也不收缩，期望半径为
Figure BDA0002278272600000069
Ri为机器人此时的半径。a) According to the driving time
Figure BDA0002278272600000064
Calculate the expected radius of the robot; the calculation method is as follows: first determine whether If so, it is considered that the robot needs to expand radially, and the expected radius after expansion is
Figure BDA0002278272600000066
Otherwise, continue to judge whether
Figure BDA0002278272600000067
If so, it is considered that the robot needs to perform radial contraction, and the expected radius after contraction is
Figure BDA0002278272600000068
Otherwise, the robot is considered neither expanding nor contracting, and the expected radius is
Figure BDA0002278272600000069
R i is the radius of the robot at this time.

b)机器人根据期望半径计算电机驱动力矩Torquei，通过电机正反转驱动机器人膨胀/收缩，更新机器人半径Ri，驱动力矩计算公式为

Figure BDA00022782726000000610
对驱动力矩进行限幅，判断是否Torquei＞Constra int，若是则令Torquei＝Constra int，其中Constra int表示最大驱动力矩，Speed表示机器人膨胀收缩的速度。b) The robot calculates the motor driving torque Torque i according to the desired radius, drives the robot to expand/contract through the forward and reverse rotation of the motor, and updates the robot radius R i . The driving torque calculation formula is:
Figure BDA00022782726000000610
Limit the driving torque to determine whether Torque i > Constra int, if so, set Torque i =Constra int, where Constra int represents the maximum driving torque, and Speed represents the speed of expansion and contraction of the robot.

与现有技术相比，本发明所具有的有益效果为：Compared with the prior art, the present invention has the following beneficial effects:

1、本发明提供的自组织协同跟踪控制方法无需对群体中的每个机器人进行编号，也不需要机器人集群保持固定的队形，并且不需要与特定个体进行通讯，因此在协同运动的过程中能扩展其他的微粒机器人加入集群；1. The self-organized cooperative tracking control method provided by the present invention does not need to number each robot in the group, nor does it require the robot cluster to maintain a fixed formation, and does not need to communicate with a specific individual, so in the process of coordinated movement Can expand other particle robots to join the cluster;

2、应用单点预瞄理论，将集群机器人跟踪期望路径的问题转换为跟踪预瞄点的问题，机器人在控制的过程中只需要关注机器人本身的位置和预瞄点坐标，无需关注其他机器人的状态，可以降低控制难度、减少计算量；2. Apply the single-point preview theory to convert the problem of tracking the desired path of the swarm robot into the problem of tracking the preview point. The robot only needs to pay attention to the position of the robot itself and the coordinates of the preview point during the control process, without paying attention to other robots. state, which can reduce the difficulty of control and reduce the amount of calculation;

3、基于最近点来计算预瞄点的位置，可以保证预瞄点在机器人前方并且在期望路径上。因此，当出现横向位移偏差时，机器人一定是朝向消除横向位移偏差的方向运动，直到重新回到期望轨迹。3. Calculate the position of the preview point based on the closest point, which can ensure that the preview point is in front of the robot and on the desired path. Therefore, when the lateral displacement deviation occurs, the robot must move in the direction of eliminating the lateral displacement deviation until it returns to the desired trajectory.

附图说明Description of drawings

图1为所述方法的流程图；Fig. 1 is the flow chart of described method;

图2为微粒机器人间相互吸引力与距离的关系；Figure 2 shows the relationship between the mutual attraction and distance between particle robots;

图3为微粒机器人移动示意图；Figure 3 is a schematic diagram of the movement of the particle robot;

图4为微粒机器人协同跟踪运动过程，图4(a)为集群微粒机器人协同跟踪运动初始化状态，图4(b)为集群微粒机器人协同跟踪运动开始第一次膨胀，图4(c)为集群微粒机器人协同跟踪运动预瞄点坐标更新，图4(d)为集群微粒机器人协同跟踪运动达到终点；Figure 4 is the process of the cooperative tracking movement of the particle robot, Figure 4(a) is the initial state of the cooperative tracking movement of the cluster particle robot, Figure 4(b) is the first expansion of the cooperative tracking movement of the cluster particle robot, and Figure 4(c) is the cluster The coordinates of the preview point of the cooperative tracking movement of the particle robots are updated. Figure 4(d) shows that the cooperative tracking movement of the group particle robots reaches the end point;

图5为微粒机器人消除横向位移偏差示意图；Figure 5 is a schematic diagram of the particle robot eliminating lateral displacement deviation;

图6为微粒机器人协同跟踪控制的可扩展性示意图；图6(a)为集群微粒机器人系统初始化，图6(b)为集群微粒机器人系统完成扩展。Figure 6 is a schematic diagram of the scalability of the cooperative tracking control of the particle robot; Figure 6(a) is the initialization of the cluster particle robot system, and Figure 6(b) is the completion of the expansion of the cluster particle robot system.

具体实施方式Detailed ways

本发明所述的一种可扩展集群微粒机器人自组织协同跟踪控制方法，如图1所示，包括以下步骤：A self-organized cooperative tracking control method of an extensible cluster particle robot according to the present invention, as shown in FIG. 1 , includes the following steps:

步骤一：初始化各微粒机器人的位置、膨胀收缩周期T、运动控制周期Tc、一组微粒机器人的数目n、距离更新周期

Figure BDA0002278272600000071
预瞄点更新周期
Figure BDA0002278272600000072
并且选取一个机器人作为预瞄机器人，预瞄机器人需要预先存储需要跟踪的期望路径以及期望路径起点、终点坐标；Step 1: Initialize the position of each particle robot, the expansion and contraction period T, the motion control period T c , the number n of a group of particle robots, and the distance update period
Figure BDA0002278272600000071
Preview point update cycle
Figure BDA0002278272600000072
And select a robot as the preview robot. The preview robot needs to store the desired path to be tracked and the coordinates of the starting point and end point of the desired path;

步骤二：预瞄机器人计算自身位置(xp,yp)与终点的距离DisToEnd；若DisToEnd＜ε，向群体广播已达到终点，程序终止；否则，预瞄机器人在期望路径上选取预瞄点(xpre,ypre)，并向群体广播预瞄点的坐标，同时设置预瞄机器人的0号计时器初始时间0号计时器开始计时，并继续以下步骤；Step 2: The preview robot calculates the distance DisToEnd between its own position (x p , y p ) and the end point; if DisToEnd < ε, the broadcast to the group has reached the end point, and the program terminates; otherwise, the preview robot selects the preview point on the desired path (x pre , y pre ), broadcast the coordinates of the preview point to the group, and set the initial time of the timer 0 of the preview robot Timer 0 starts and continues with the following steps;

步骤三：各微粒机器人计算自身位置与预瞄点之间的距离Disi；各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin；各微粒机器人根据本机器人与预瞄点的距离Disi、最短距离Dismax，计算本机器人的响应序列Si；根据响应序列Si计算得到本机器人的唤醒时间

Figure BDA0002278272600000081
并设置1号计时器初始时间
Figure BDA0002278272600000082
1号计时器开始计时；Step 3: each particle robot calculates the distance Dis i between its own position and the preview point; each particle robot broadcasts distance information to the group, simultaneously receives the distance information of other particle robots, and compares and obtains the shortest distance Dis min ; The distance Dis i and the shortest distance Dis max between the robot and the preview point , calculate the response sequence Si of the robot ; calculate the wake-up time of the robot according to the response sequence Si
Figure BDA0002278272600000081
and set the initial time of timer 1
Figure BDA0002278272600000082
Timer 1 starts counting;

步骤四：判断是否

Figure BDA0002278272600000083
如果是则执行以下步骤，否则该微粒机器人继续等待；Step 4: Determine whether
Figure BDA0002278272600000083
If so, perform the following steps, otherwise the particle robot continues to wait;

步骤五：设置2号计时器初始时间

Figure BDA0002278272600000084
2号计时器开始计时，当
Figure BDA0002278272600000085
停止计时，继续以下操作：集群机器人中各微粒机器人根据其响应序列Si与1号计时器的计时时间
Figure BDA0002278272600000086
计算本机器人的驱动时间根据微粒机器人的驱动时间
Figure BDA0002278272600000088
依次更新各机器人半径Ri，通过机器人膨胀收缩产生力的作用，驱动集群微粒机器人跟踪期望路径；Step 5: Set the initial time of timer 2
Figure BDA0002278272600000084
Timer 2 starts counting, when
Figure BDA0002278272600000085
Stop timing and continue the following operations: each particle robot in the swarm robot according to its response sequence S i and the timing time of the timer No. 1
Figure BDA0002278272600000086
Calculate the driving time of this robot According to the driving time of the particle robot
Figure BDA0002278272600000088
The radius R i of each robot is updated in turn, and the force generated by the expansion and contraction of the robot is used to drive the swarm particle robot to track the desired path;

步骤六：判断是否

Figure BDA0002278272600000089
若是则返回步骤2)，否则继续以下判断；判断是否
Figure BDA00022782726000000810
若是则返回步骤3)，否则返回步骤5)。Step 6: Determine whether
Figure BDA0002278272600000089
If so, return to step 2), otherwise continue the following judgment; judge whether
Figure BDA00022782726000000810
If so, go back to step 3), otherwise go back to step 5).

所述期望路径由三次多项式构成，记作y＝A3x3+A2x2+A1x1+A0；其中A3,A2,A1,A0为三次方系数，x为期望路径的横坐标且x∈[x0,xf]，(x0,y0)为期望路径起点，(xf,yf)为期望路径终点，设定的期望路径如图4所示；The desired path is composed of a cubic polynomial, denoted as y=A 3 x 3 +A 2 x 2 +A 1 x 1 +A 0 ; where A 3 , A 2 , A 1 , and A 0 are cubic coefficients, and x is The abscissa of the desired path and x∈[x 0 ,x f ], (x 0 , y 0 ) is the starting point of the desired path, (x f , y f ) is the end point of the desired path, and the set desired path is shown in Figure 4 ;

所述微粒机器人是指满足以下条件的一类机器人：The particle robot refers to a type of robot that satisfies the following conditions:

a)机器人可以在原地做径向膨胀收缩运动，机器人膨胀能达到的最大半径为Rmax，机器人收缩能达到的最小半径为Rmin；a) The robot can perform radial expansion and contraction movement in situ, the maximum radius that the robot can reach is R max , and the minimum radius that the robot can shrink is R min ;

b)机器人之间存在相互吸引力，吸引力大小与两个机器人之间的距离相关，机器人膨胀会产生膨胀力；b) There is a mutual attraction between the robots, the magnitude of the attraction is related to the distance between the two robots, and the expansion of the robots will generate expansion force;

c)机器人膨胀产生的膨胀力Fexpansion以及一定距离范围内机器人之间的吸引力Fattract必须大于机器人与地面之间的最大静摩擦力，但是小于其他机器人所受的摩擦力之和，表达式如下：c) The expansion force F expansion generated by the expansion of the robot and the attraction F attract between the robots within a certain distance must be greater than the maximum static friction force between the robot and the ground, but less than the sum of the friction forces experienced by other robots, the expression is as follows :

Figure BDA0002278272600000091
Figure BDA0002278272600000091

其中，Nstatic表示其他静态机器人个数，m表示单个机器人的质量，μstatic表示机器人接触平面的静摩擦系数，g＝9.8N/kg表示重力加速度。本实例中m＝0.5kg，摩擦系数μstatic＝0.5。Among them, N static represents the number of other static robots, m represents the mass of a single robot, μ static represents the static friction coefficient of the contact plane of the robot, and g=9.8N/kg represents the acceleration of gravity. In this example, m = 0.5 kg, and the friction coefficient μ static = 0.5.

本实例中，所述机器人膨胀产生的膨胀力Fexpansion＝4.5N，满足m×g×μstatic＜Fexpansion＜Nstatic×m×g×μstatic。In this example, the expansion force F expansion generated by the expansion of the robot is 4.5N, which satisfies m×g×μ static <F expansion <N static ×m×g×μ static .

所述机器人之间的吸引力Fattract与距离的关系，如图2所示。当微粒机器人之间的距离小于2cm或大于5cm时，微粒间的吸引力小于最大静摩擦力，距离在2cm与5cm之间时，微粒间的吸引力大于最大静摩擦力，即满足m×g×μstatic＜Fattract＜Nstatic×m×g×μstatic。The relationship between the attraction force F attract and the distance between the robots is shown in FIG. 2 . When the distance between the particle robots is less than 2cm or greater than 5cm, the attractive force between the particles is less than the maximum static friction force, and when the distance is between 2cm and 5cm, the attractive force between the particles is greater than the maximum static friction force, that is, m×g×μ static <F attract <N static ×m × g × μ static .

步骤1)中所述初始化各微粒机器人的位置应满足每个微粒机器人至少有2个机器人与之相切且不与任何机器人相交，而且每排机器人不少于3个、每列机器人不少于3个；如图4(a)所示，预瞄机器人初始化放置在期望路径上的起点，其他机器人围绕预瞄机器人放置；本实例中，取膨胀收缩周期T＝2s，运动控制周期Tc＝100ms，一组微粒的数目n＝3，距离更新周期

Figure BDA0002278272600000092
预瞄点更新周期 The position of initializing each particle robot described in step 1) should be such that each particle robot has at least 2 robots tangent to it and does not intersect with any robot, and there are not less than 3 robots in each row and not less than 3 robots in each column. 3; as shown in Figure 4(a), the preview robot is initially placed at the starting point on the desired path, and other robots are placed around the preview robot; in this example, the expansion and contraction period T = 2s, and the motion control period T c = 100ms, the number of particles in a group n=3, the distance update period
Figure BDA0002278272600000092
Preview point update cycle

如图3所示，集群微粒机器人移动的过程如下，排在前面的微粒机器人先膨胀，由于产生的膨胀力大于微粒机器人自身的最大静摩擦力小于其他微粒机器人所受的最大静摩擦力之和，因此机器人个体的重心会向前移动Δs。当该微粒机器人收缩时，后续的微粒机器人开始膨胀，使该微粒机器人保持在原来的位置，后续微粒机器人的重心也会向前移动Δs。如此循环，直到最后一个微粒机器人收缩时，由于机器人个体间的吸引力确保最后一个微粒机器人不会脱离集群。As shown in Figure 3, the movement process of the clustered particle robot is as follows. The particle robot in the front expands first. Since the expansion force generated is greater than the maximum static friction force of the particle robot itself, it is smaller than the sum of the maximum static friction forces suffered by other particle robots. Therefore, The center of gravity of the individual robot moves forward by Δs. When the particle robot shrinks, the subsequent particle robot begins to expand, so that the particle robot remains in the original position, and the center of gravity of the subsequent particle robot also moves forward by Δs. This cycle is repeated until the last particle robot shrinks, due to the attraction between the robot individuals to ensure that the last particle robot will not leave the swarm.

步骤2)中所述计算自身位置(xp,yp)与终点的距离DisToEnd的计算公式为

Figure BDA0002278272600000094
The calculation formula for calculating the distance DisToEnd between self-position (x p , y p ) and the end point described in step 2) is:
Figure BDA0002278272600000094

步骤2)中所述ε表示终止距离阈值，ε取值等于机器人的最大预瞄距离lmax，如图4(d)所示，当预瞄机器人自身位置(xp,yp)与终点的距离DisToEnd＜ε，认为集群微粒机器人到达终点，预瞄机器人向群体广播已达到终点，所有机器人的程序终止，停止运动。In step 2), ε represents the termination distance threshold, and the value of ε is equal to the maximum preview distance l max of the robot. When the distance DisToEnd < ε, it is considered that the swarm particle robot has reached the end point, the preview robot has reached the end point of broadcasting to the group, and the programs of all robots are terminated and the movement is stopped.

步骤2)中所述在期望路径上选取预瞄点(xpre,ypre)如图4(b)所示，具体过程如下：As described in step 2), selecting the preview point (x pre , y pre ) on the desired path is shown in Figure 4(b), and the specific process is as follows:

(1)确定期望路径上距离机器人当前位置(xp,yp)的最近点(xnear,ynear)，具体做法为：(1) Determine the closest point (x near , y near ) on the desired path to the current position (x p , y p ) of the robot, the specific method is as follows:

首先，计算机器人当前位置(xp,yp)到期望路径的距离函数：First, calculate the distance function from the robot's current position (x p , y p ) to the desired path:

Figure BDA0002278272600000101
Figure BDA0002278272600000101

而后，取disp(x)关于x的一阶导，令一阶导

Figure BDA0002278272600000102
得到极值点；Then, take the first derivative of dis p (x) with respect to x, let the first derivative
Figure BDA0002278272600000102
get the extreme point;

最后，根据两点间的距离公式分别计算极值点、期望路径起点、期望路径终点与预瞄机器人自身位置的距离，其中最短距离对应的点即为最近点(xnear,ynear)，若存在多个最近点，则选择其中距离终点最远的点作为最近点；Finally, according to the distance formula between the two points, calculate the distance between the extreme point, the starting point of the desired path, the end point of the desired path and the position of the preview robot. The point corresponding to the shortest distance is the closest point (x near , y near ). If If there are multiple closest points, select the point farthest from the end point as the closest point;

(2)计算最近点(xnear,ynear)的曲率C，计算公式为

Figure BDA0002278272600000103
其中，
Figure BDA0002278272600000104
表示三次多项式的二阶导，
Figure BDA0002278272600000105
表示三次多项式的一阶导，令x＝xnear，代入曲率计算公式即可以计算得到最近点处的曲率；(2) Calculate the curvature C of the nearest point (x near , y near ), and the calculation formula is
Figure BDA0002278272600000103
in,
Figure BDA0002278272600000104
represents the second derivative of a cubic polynomial,
Figure BDA0002278272600000105
Represents the first-order derivative of the cubic polynomial, let x=x near , and substituting it into the curvature calculation formula can calculate the curvature at the nearest point;

(3)根据曲率C计算预瞄距离，计算公式

Figure BDA0002278272600000106
其中，k为常数、表示预瞄距离的调整增益，lmax表示最大预瞄距离，lmin表示最小预瞄距离；该式表示随着曲率的增大，预瞄距离减小，即跟踪弯道路径时预瞄点距离机器人较近，以保证集群微粒机器人及时调整运动状态，准确跟踪期望路径；(3) Calculate the preview distance according to the curvature C, the calculation formula
Figure BDA0002278272600000106
Among them, k is a constant, representing the adjustment gain of the preview distance, l max represents the maximum preview distance, and l min represents the minimum preview distance; this formula indicates that with the increase of the curvature, the preview distance decreases, that is, the tracking curve The preview point is close to the robot during the path to ensure that the swarm particle robot can adjust the motion state in time and accurately track the desired path;

(4)根据最近点(xnear,ynear)与预瞄距离l确定预瞄点(xpre,ypre)，计算公式为：(4) Determine the preview point (x pre , y pre ) according to the closest point (x near , y near ) and the preview distance l, and the calculation formula is:

Figure BDA0002278272600000111
Figure BDA0002278272600000111

求解该方程即可以得到预瞄点坐标(xpre,ypre)。Solving this equation can get the coordinates of the preview point (x pre , y pre ).

步骤3)的具体步骤如下：The specific steps of step 3) are as follows:

(1)各微粒机器人计算自身的位置与预瞄点之间的距离Disi，计算公式为

Figure BDA0002278272600000112
其中i表示第i个微粒机器人，(xi,yi)表示第i个微粒机器人的坐标；(1) Each particle robot calculates the distance Dis i between its own position and the preview point, and the calculation formula is:
Figure BDA0002278272600000112
where i represents the ith particle robot, and (x i , y i ) represents the coordinates of the ith particle robot;

(2)各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin，具体做法为：首先，将本机器人与预瞄点之间的距离初始化为最短距离Dismin；然后，将接收到的距离信息Disj依次与最短距离Dismin进行比较，若接收到的距离信息小于Dismin，则将Disj更新为Dismin，即令Dismin＝Disj，否则不进行更新，最后直到未接收到其他新的距离信息，得到的Dismin即为集群机器人到预瞄点的最短距离。其中，j表示接收到的第j个机器人的信息j≠i且j∈[1,2,…,N-1，N]，N为微粒机器人的总个数；本实例中微粒机器人向群体广播自信息，或者接收其他微粒机器人广播的信息是采用XBee S1无线模块，通讯波特率为9600；(2) Each particle robot broadcasts distance information to the group, and at the same time receives the distance information of other particle robots, and compares the shortest distance Dis min . The specific method is: first, initialize the distance between the robot and the preview point to the shortest distance Dis min ; Then, compare the received distance information Dis j with the shortest distance Dis min in turn, if the received distance information is less than Dis min , then update Dis j to Dis min , that is, make Dis min =Dis j , otherwise not Update, and finally until no other new distance information is received, the obtained Dis min is the shortest distance from the swarm robot to the preview point. Among them, j represents the received information of the jth robot j≠i and j∈[1,2,…,N-1,N], N is the total number of particle robots; in this example, the particle robots broadcast to the group Self-information, or receiving information broadcast by other particle robots uses XBee S1 wireless module, the communication baud rate is 9600;

(3)根据本机器人与预瞄点的距离Disi、最短距离Dismax，计算本机器人的响应序列Si，计算公式为Si＝(Dismin-Disi)/(2*Rmin)*T/2，所述响应序列是指机器人进行膨胀收缩的先后次序，根据计算公式可知Si≤0并且越靠近预瞄点的机器人，响应序列Si较大并且机器人越先进行膨胀收缩运动；(3) Calculate the response sequence S i of the robot according to the distance Dis i and the shortest distance Dis max between the robot and the preview point. The calculation formula is S i =(Dis min -Dis i )/(2*R min )* T/2, the response sequence refers to the order in which the robot performs expansion and contraction. According to the calculation formula, it can be known that Si ≤ 0 and the robot closer to the preview point has a larger response sequence Si and the robot expands and contracts earlier;

(4)根据响应序列Si计算得到本机器人的唤醒时间

Figure BDA0002278272600000113
计算公式为
Figure BDA0002278272600000114
所述唤醒时间是指在一次距离更新周期内，机器人开始膨胀收缩运动的全局时间，全局时间是1号计时器计时的时间
Figure BDA0002278272600000121
所述各微粒机器人计算自身的位置采用如下定位方法计算：(4) Calculate the wake-up time of the robot according to the response sequence S i
Figure BDA0002278272600000113
The calculation formula is
Figure BDA0002278272600000114
The wake-up time refers to the global time when the robot starts to expand and contract during a distance update period, and the global time is the time counted by the No. 1 timer.
Figure BDA0002278272600000121
The position of each particle robot is calculated by the following positioning method:

其中，

Figure BDA0002278272600000123
分别表示为微粒机器人真实的横、纵坐标；xi、yi分别表示为微粒机器人的横、纵坐标计算值；xm、ym分别表示为该微粒机器人的邻近单体机器人中的第m个微粒机器人的横、纵坐标计算值；Dm表示为该微粒机器人与其通讯范围内第m微粒机器人之间的测量距离。in,
Figure BDA0002278272600000123
respectively represent the real horizontal and vertical coordinates of the particle robot; x i and y i represent the calculated values of the horizontal and vertical coordinates of the particle robot respectively; x m and y m represent the mth of the particle robot's neighboring single robots, respectively The calculated values of the horizontal and vertical coordinates of each particle robot; D m represents the measured distance between the particle robot and the mth particle robot within its communication range.

所述微粒机器人均安装红外发射器通过红外发射器计算其与通讯范围内其他机器人之间的距离。The particle robots are equipped with infrared emitters to calculate the distance between them and other robots within the communication range through the infrared emitters.

步骤5)中各微粒机器人计算本机器人的驱动时间

Figure BDA0002278272600000124
的具体方法如下：In step 5), each particle robot calculates the driving time of the robot
Figure BDA0002278272600000124
The specific method is as follows:

首先根据响应序列Si与1号计时器的计时时间

Figure BDA0002278272600000125
将响应序列时序化，得到预驱动时间
Figure BDA0002278272600000126
计算公式为：First, according to the response sequence S i and the timing time of the No. 1 timer
Figure BDA0002278272600000125
Timing the response sequence to get the pre-drive time
Figure BDA0002278272600000126
The calculation formula is:

Figure BDA0002278272600000127
Figure BDA0002278272600000127

而后，对预驱动时间

Figure BDA0002278272600000128
进一步进行处理，按照组别计算得到微粒机器人的驱动时间
Figure BDA0002278272600000129
计算公式为：Then, for the pre-drive time
Figure BDA0002278272600000128
After further processing, the driving time of the particle robot is calculated according to the group
Figure BDA0002278272600000129
The calculation formula is:

其中，floor表示向下取整，n表示一组微粒机器人的数目；所述驱动时间

Figure BDA00022782726000001211
是指机器人从唤醒时间开始，以n*T/2为周期的周期循环时间，n*T/2表示一组机器人均完成膨胀收缩所需要的时间。即从唤醒时间开始计时，计时到n*T/2之后又重新开始计时，以n*T/2为周期循环，该计时时间即为驱动时间。Among them, floor represents rounding down, and n represents the number of a group of particle robots; the driving time
Figure BDA00022782726000001211
It refers to the cycle time of the robot starting from the wake-up time, with n*T/2 as the period, n*T/2 represents the time required for a group of robots to complete the expansion and contraction. That is to say, start timing from the wake-up time, and start timing again after the timing reaches n*T/2, with n*T/2 as the cycle, and the timing time is the driving time.

微粒机器人协同运动过程中关键参数如表1所示。The key parameters in the cooperative motion process of the particle robot are shown in Table 1.

表1 微粒机器人协同运动过程中关键参数Table 1 The key parameters in the cooperative motion of the particle robot

Figure BDA00022782726000001212
Figure BDA00022782726000001212

Figure BDA0002278272600000131
Figure BDA0002278272600000131

Figure BDA0002278272600000141
Figure BDA0002278272600000141

步骤5)中根据微粒机器人的驱动时间

Figure BDA0002278272600000142
依次更新各机器人半径Ri的具体过程如下：In step 5), according to the driving time of the particle robot
Figure BDA0002278272600000142
The specific process of sequentially updating the radius R i of each robot is as follows:

a)根据驱动时间

Figure BDA0002278272600000143
计算机器人的期望半径；计算方法如下：首先判断是否
Figure BDA0002278272600000144
若是则认为机器人需要进行径向膨胀，膨胀后的期望半径为
Figure BDA0002278272600000145
否则继续判断是否
Figure BDA0002278272600000146
若是则认为机器人需要进行径向收缩，收缩后的期望半径为否则认为机器人既不膨胀也不收缩，期望半径为
Figure BDA0002278272600000148
Ri为机器人此时的半径。a) According to the driving time
Figure BDA0002278272600000143
Calculate the expected radius of the robot; the calculation method is as follows: first determine whether
Figure BDA0002278272600000144
If so, it is considered that the robot needs to expand radially, and the expected radius after expansion is
Figure BDA0002278272600000145
Otherwise, continue to judge whether
Figure BDA0002278272600000146
If so, it is considered that the robot needs to perform radial contraction, and the expected radius after contraction is Otherwise, the robot is considered neither expanding nor contracting, and the expected radius is
Figure BDA0002278272600000148
R i is the radius of the robot at this time.

b)机器人根据期望半径计算电机驱动力矩Torquei，通过电机正反转驱动机器人膨胀/收缩，更新机器人半径Ri，驱动力矩计算公式为

Figure BDA0002278272600000151
对驱动力矩进行限幅，判断是否Torquei＞Constra int，若是则令Torquei＝Constra int，其中Constra int表示最大驱动力矩，Speed表示机器人膨胀收缩的速度。本实例中，Constra int＝2.5N*m，Speed＝0.5m/s。b) The robot calculates the motor driving torque Torque i according to the desired radius, drives the robot to expand/contract through the forward and reverse rotation of the motor, and updates the robot radius R i . The driving torque calculation formula is:
Figure BDA0002278272600000151
Limit the driving torque to determine whether Torque i > Constra int, if so, set Torque i =Constra int, where Constra int represents the maximum driving torque, and Speed represents the speed of expansion and contraction of the robot. In this example, Constraint=2.5N*m, Speed=0.5m/s.

步骤6)中,判断是否若是则返回步骤2),是判断预瞄机器人0号计时器计时是否超过预瞄点更新周期，若是则更新预瞄点，如图4(b)～图4(c)所示。In step 6), determine whether If so, return to step 2), which is to judge whether the timer of the preview robot No. 0 exceeds the preview point update period, and if so, update the preview point, as shown in Figure 4(b) to Figure 4(c).

当集群微粒机器人出现横向位移偏差时，如图5所示，机器人一定是朝向消除横向位移偏差的方向运动，直到重新回到期望轨迹。When the swarm particle robot has a lateral displacement deviation, as shown in Figure 5, the robot must move in the direction of eliminating the lateral displacement deviation until it returns to the desired trajectory.

关于集群机器人可扩展性的示意图如图6所示。图6(a)为集群微粒机器人系统初始化，图6(b)为集群微粒机器人系统完成扩展。A schematic diagram of the scalability of the swarm robot is shown in Figure 6. Fig. 6(a) is the initialization of the swarm particle robot system, and Fig. 6(b) is the expansion of the swarm particle robot system.

Claims (10)

1.一种可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，包括以下步骤：1. A self-organized collaborative tracking control method for an extensible cluster particle robot, characterized in that, comprising the following steps: 1)初始化各微粒机器人的位置、膨胀收缩周期T、运动控制周期Tc、一组微粒机器人的数目n、距离更新周期预瞄点更新周期
Figure FDA0002278272590000012
选取一个微粒机器人作为预瞄机器人，预瞄机器人需要预先存储需要跟踪的期望路径以及期望路径起点、终点坐标；1) Initialize the position of each particle robot, the expansion and contraction period T, the motion control period T c , the number n of a group of particle robots, and the distance update period Preview point update cycle
Figure FDA0002278272590000012
Select a particle robot as the preview robot. The preview robot needs to store the desired path to be tracked and the coordinates of the starting point and end point of the desired path; 2)预瞄机器人计算自身位置(xp,yp)与终点的距离DisToEnd；若DisToEnd＜ε，向群体广播已达到终点，结束；否则，预瞄机器人在期望路径上选取预瞄点(xpre,ypre)，并向群体广播预瞄点的坐标，同时设置预瞄机器人的0号计时器初始时间
Figure FDA0002278272590000013
0号计时器开始计时；ε表示终止距离阈值；2) The preview robot calculates the distance DisToEnd between its own position (x p , y p ) and the end point; if DisToEnd < ε, the broadcast to the group has reached the end point and ends; otherwise, the preview robot selects the preview point (x pre ,y pre ), broadcast the coordinates of the preview point to the group, and set the initial time of the timer 0 of the preview robot
Figure FDA0002278272590000013
Timer 0 starts timing; ε represents the termination distance threshold; 3)各微粒机器人计算自身的位置与预瞄点之间的距离Disi；各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin；对于某一微粒机器人，根据该微粒机器人与预瞄点的距离Disi、最短距离Dismax，计算该微粒机器人的响应序列Si，根据响应序列Si计算得到该微粒机器人的唤醒时间
Figure FDA0002278272590000014
并设置1号计时器初始时间
Figure FDA0002278272590000015
1号计时器开始计时；判断
Figure FDA0002278272590000016
是否满足，如果是则进入步骤4)，否则该微粒机器人继续等待；3) each particle robot calculates the distance Dis i between its own position and the preview point; each particle robot broadcasts distance information to the group, receives the distance information of other particle robots simultaneously, and compares the shortest distance Dis min ; for a certain particle The robot calculates the response sequence S i of the particle robot according to the distance Dis i and the shortest distance Dis max between the particle robot and the preview point, and calculates the wake-up time of the particle robot according to the response sequence S i
Figure FDA0002278272590000014
and set the initial time of timer 1
Figure FDA0002278272590000015
Timer 1 starts counting; judgment
Figure FDA0002278272590000016
Whether it is satisfied, if so, go to step 4), otherwise the particle robot continues to wait; 4)设置2号计时器初始时间
Figure FDA0002278272590000017
2号计时器开始计时，当停止计时，继续以下操作：集群机器人中各微粒机器人根据其响应序列Si与1号计时器的计时时间
Figure FDA0002278272590000019
计算本机器人的驱动时间
Figure FDA00022782725900000110
根据微粒机器人的驱动时间
Figure FDA00022782725900000111
依次更新各微粒机器人半径Ri，通过微粒机器人膨胀收缩产生力的作用，驱动微粒机器人跟踪期望路径；4) Set the initial time of timer 2
Figure FDA0002278272590000017
Timer 2 starts counting, when Stop timing and continue the following operations: each particle robot in the swarm robot according to its response sequence S i and the timing time of the timer No. 1
Figure FDA0002278272590000019
Calculate the driving time of this robot
Figure FDA00022782725900000110
According to the driving time of the particle robot
Figure FDA00022782725900000111
The radius Ri of each particle robot is updated in turn, and the particle robot is driven to track the desired path through the action of the force generated by the expansion and contraction of the particle robot; 5)判断
Figure FDA0002278272590000021
是否满足，若是则返回步骤2)；否则判断是否
Figure FDA0002278272590000022
若是则返回步骤3)，否则返回步骤4)。5) Judgment
Figure FDA0002278272590000021
Whether it is satisfied, if so, return to step 2); otherwise, judge whether
Figure FDA0002278272590000022
If so, go back to step 3), otherwise go back to step 4). 2.根据权利要求1所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，所述期望路径y＝A3x3+A2x2+A1x1+A0；其中A3,A2,A1,A0为三次方系数，x为期望路径的横坐标且x∈[x0,xf]，(x0,y0)为期望路径起点，(xf,yf)为期望路径终点。2 . The self-organized cooperative tracking control method of the scalable swarm particle robot according to claim 1 , wherein the desired path y=A 3 x 3 +A 2 x 2 +A 1 x 1 +A 0 ; wherein A 3 , A 2 , A 1 , A 0 are cubic coefficients, x is the abscissa of the desired path and x∈[x 0 ,x f ], (x 0 ,y 0 ) is the starting point of the desired path, (x f , y f ) is the desired path end point. 3.根据权利要求1所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，步骤1)中，初始化后的各微粒机器人的位置满足如下条件：每个微粒机器人至少有2个微粒机器人与之相切，且不与任何微粒机器人相交,且每行微粒机器人不少于3个、每列机器人不少于3个；预瞄机器人初始化放置在期望路径上的非终点的任意位置，其他微粒机器人围绕预瞄机器人放置。3. The self-organized collaborative tracking control method for scalable cluster particle robots according to claim 1, wherein in step 1), the position of each particle robot after initialization satisfies the following conditions: each particle robot has at least 2 The particle robot is tangent to it, and does not intersect with any particle robot, and there are no less than 3 particle robots in each row and no less than 3 robots in each column; the preview robot is initialized and placed at any position other than the end point on the desired path , other particle robots are placed around the preview robot. 4.根据权利要求2所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，步骤2)中，预瞄机器人在期望路径上选取预瞄点(xpre,ypre)的具体过程包括：4. The self-organized cooperative tracking control method of the scalable cluster particle robot according to claim 2, wherein in step 2), the preview robot selects the specific details of the preview point (x pre , y pre ) on the desired path The process includes: 1)确定期望路径上距离预瞄机器人当前位置(xp,yp)最近的点(xnear,ynear)；1) Determine the closest point (x near , y near ) on the desired path to the current position (x p , y p ) of the preview robot; 2)计算最近的点(xnear,ynear)的曲率C；2) Calculate the curvature C of the nearest point (x near , y near ); 3)根据曲率C计算预瞄距离l；3) Calculate the preview distance l according to the curvature C; 4)根据最近点(xnear,ynear)与预瞄距离l确定预瞄点(xpre,ypre)：4) Determine the preview point (x pre , y pre ) according to the closest point (x near , y near ) and the preview distance l:
Figure FDA0002278272590000023
Figure FDA0002278272590000023
 5.根据权利要求4所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，最近的点(xnear,ynear)的计算过程包括：5. The self-organized cooperative tracking control method of the scalable cluster particle robot according to claim 4, wherein the calculation process of the nearest point (x near , y near ) comprises: A)计算机器人当前位置(xp,yp)到期望路径的距离函数：A) Calculate the distance function from the robot's current position (x p , y p ) to the desired path: B)根据两点间的距离公式分别计算极值点、期望路径起点、期望路径终点与预瞄机器人自身位置的距离，其中最短距离对应的点即为最近点(xnear,ynear)。B) Calculate the distance between the extreme point, the starting point of the desired path, the end point of the desired path and the position of the preview robot according to the distance formula between the two points, wherein the point corresponding to the shortest distance is the closest point (x near , y near ). 6.根据权利要求4所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，
Figure FDA0002278272590000032
其中
Figure FDA0002278272590000033
表示三次多项式y的二阶导，
Figure FDA0002278272590000034
表示三次多项式的一阶导。6. The scalable cluster particle robot self-organized cooperative tracking control method according to claim 4, characterized in that:
Figure FDA0002278272590000032
in
Figure FDA0002278272590000033
represents the second derivative of the cubic polynomial y,
Figure FDA0002278272590000034
represents the first derivative of a cubic polynomial. 7.根据权利要求4所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，
Figure FDA0002278272590000035
其中，k为常数，表示预瞄距离的调整增益，lmax表示最大预瞄距离，lmin表示最小预瞄距离。7. The self-organized cooperative tracking control method of the scalable cluster particle robot according to claim 4, characterized in that:
Figure FDA0002278272590000035
Among them, k is a constant, which represents the adjustment gain of the preview distance, l max represents the maximum preview distance, and l min represents the minimum preview distance. 8.根据权利要求1所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，步骤3)的具体实现过程包括：8. The self-organized cooperative tracking control method of the scalable cluster particle robot according to claim 1, wherein the specific implementation process of step 3) comprises: 1)各微粒机器人计算自身的位置与预瞄点之间的距离Disi，计算公式为
Figure FDA0002278272590000036
其中i表示第i个微粒机器人，(xi,yi)表示第i个微粒机器人的坐标；1) Each particle robot calculates the distance Dis i between its own position and the preview point, and the calculation formula is
Figure FDA0002278272590000036
where i represents the ith particle robot, and (x i , y i ) represents the coordinates of the ith particle robot; 2)各微粒机器人向群体广播距离信息，同时接收其他微粒机器人的距离信息，比较得出最短距离Dismin，具体实现过程包括：首先，将本微粒机器人与预瞄点之间的距离初始化为最短距离Dismin；然后，将接收到的距离信息Disj依次与最短距离Dismin进行比较，若接收到的距离信息小于Dismin，则将Disj更新为Dismin，即令Dismin＝Disj，否则不进行更新，最后直到未接收到其他新的距离信息，得到的Dismin即为集群机器人到预瞄点的最短距离；其中，j表示接收到的第j个机器人的信息j≠i且j∈[1,2,…,N-1，N]，N为微粒机器人的总个数；2) Each particle robot broadcasts distance information to the group, receives the distance information of other particle robots at the same time, and compares the shortest distance Dis min . The specific implementation process includes: first, initialize the distance between the particle robot and the preview point to the shortest distance Dis min ; then, compare the received distance information Dis j with the shortest distance Dis min in turn, if the received distance information is less than Dis min , then update Dis j to Dis min , that is, make Dis min =Dis j , otherwise No update is performed, and finally until no other new distance information is received, the obtained Dis min is the shortest distance from the swarm robot to the preview point; where j represents the received information of the jth robot j≠i and j∈ [1,2,…,N-1,N], N is the total number of particle robots; 3)根据本微粒机器人与预瞄点的距离Disi、最短距离Dismax，计算本微粒机器人的响应序列Si，计算公式为Si＝(Dismin-Disi)/(2*Rmin)*T/2；3) Calculate the response sequence S i of the particle robot according to the distance Dis i and the shortest distance Dis max between the particle robot and the preview point, and the calculation formula is S i =(Dis min -Dis i )/(2*R min ) *T/2; 4)根据响应序列Si计算得到本机器人的唤醒时间
Figure FDA0002278272590000041
计算公式为
Figure FDA0002278272590000042
4) Calculate the wake-up time of the robot according to the response sequence S i
Figure FDA0002278272590000041
The calculation formula is
Figure FDA0002278272590000042
 9.根据权利要求1所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，步骤4)中，驱动时间的具体计算方法包括：首先根据响应序列Si与1号计时器的计时时间
Figure FDA0002278272590000044
将响应序列时序化，得到预驱动时间
Figure FDA0002278272590000045
计算公式为9. The self-organized cooperative tracking control method of the scalable cluster particle robot according to claim 1, characterized in that, in step 4), the driving time The specific calculation method includes: first, according to the response sequence S i and the timing time of the No. 1 timer
Figure FDA0002278272590000044
Timing the response sequence to get the pre-drive time
Figure FDA0002278272590000045
The calculation formula is
Figure FDA0002278272590000046
Figure FDA0002278272590000046
 而后，对预驱动时间
Figure FDA0002278272590000047
进一步进行处理，按照组别计算得到微粒机器人的驱动时间计算公式为：Then, for the pre-drive time
Figure FDA0002278272590000047
After further processing, the driving time of the particle robot is calculated according to the group The calculation formula is: 。 . 10.根据权利要求1所述的可扩展集群微粒机器人自组织协同跟踪控制方法，其特征在于，步骤4)中，更新各微粒机器人半径Ri的具体实现过程包括：10. The self-organized collaborative tracking control method for scalable cluster particle robots according to claim 1, wherein in step 4), the specific implementation process for updating the radius R i of each particle robot comprises: 1)根据驱动时间
Figure FDA00022782725900000410
计算机器人的期望半径；计算方法如下：首先判断是否若是则认为机器人需要进行径向膨胀，膨胀后的期望半径为否则继续判断是否
Figure FDA0002278272590000051
若是则认为微粒机器人需要进行径向收缩，收缩后的期望半径为否则认为微粒机器人既不膨胀也不收缩，期望半径为
Figure FDA0002278272590000053
Ri为微粒机器人此时的半径；1) According to the driving time
Figure FDA00022782725900000410
Calculate the expected radius of the robot; the calculation method is as follows: first determine whether If so, it is considered that the robot needs to expand radially, and the expected radius after expansion is Otherwise, continue to judge whether
Figure FDA0002278272590000051
If so, it is considered that the particle robot needs to perform radial contraction, and the expected radius after contraction is Otherwise, it is considered that the particle robot neither expands nor contracts, and the expected radius is
Figure FDA0002278272590000053
R i is the radius of the particle robot at this time; 2)微粒机器人根据期望半径计算电机驱动力矩Torquei，通过电机正反转驱动机器人膨胀/收缩，更新机器人半径Ri，驱动力矩计算公式为
Figure FDA0002278272590000054
对驱动力矩进行限幅，判断是否Torquei＞Constraint，若是则令Torquei＝Constraint，其中Constraint表示最大驱动力矩，Speed表示机器人膨胀收缩的速度。2) The particle robot calculates the motor driving torque Torque i according to the desired radius, drives the robot to expand/contract through the forward and reverse rotation of the motor, and updates the robot radius R i . The driving torque calculation formula is:
Figure FDA0002278272590000054
Limit the driving torque to determine whether Torque i > Constraint, if so, set Torque i =Constraint, where Constraint represents the maximum driving torque, and Speed represents the speed of expansion and contraction of the robot.
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