技术领域technical field
本发明属于智能机器人技术领域，具体涉及姿态未知条件下一种多移动机器人系统的自适应跟踪控制设计方法。The invention belongs to the technical field of intelligent robots, and in particular relates to an adaptive tracking control design method of a multi-mobile robot system under the condition of unknown postures.
背景技术Background technique
近年来，多移动机器人系统的跟踪控制与应用受到日益广泛的关注，逐渐成为复杂性科学研究的一个焦点问题。其中各移动机器人仅利用局部信息进行交互,并结合通信等手段发挥分布式资源的优势实现整体规划、解决局部冲突,从而达到整体预期目标。移动机器人系统是一个将环境感知、动态规划与决策、行为控制与执行等诸多功能融为一体的复杂智能系统。它将传感器技术、信息处理技术、电子工程技术、计算机技术、自动化控制以及人工智能技术等诸多前沿学科的研究成果集中起来，代表了机电控制领域以及电子工程领域内的最高成就，在目前众多科学技术研究领域中最为活跃的领域之一。随着智能机器人性能的不断发展，智能化水平不断提高，移动机器人的应用范围有了极大的扩展，不仅在工业、农业、医疗卫生行业、服务业等诸多行业中得到较为广泛的应用，同时也在安全防护、军工国防以及深空探测等对人体有害甚至有生命威胁的场合得到了极佳的应用。因此，移动机器人越来越受到当今学者的关注。In recent years, the tracking control and application of multi-mobile robot system has received more and more attention, and has gradually become a focus of complexity science research. Among them, each mobile robot only uses local information to interact, and combines the advantages of distributed resources with communication and other means to achieve overall planning and resolve local conflicts, so as to achieve the overall expected goal. The mobile robot system is a complex intelligent system that integrates many functions such as environment perception, dynamic planning and decision-making, behavior control and execution. It brings together the research results of many cutting-edge disciplines such as sensor technology, information processing technology, electronic engineering technology, computer technology, automation control and artificial intelligence technology, and represents the highest achievement in the field of electromechanical control and electronic engineering. One of the most active fields in the field of technical research. With the continuous development of the performance of intelligent robots and the continuous improvement of the level of intelligence, the application range of mobile robots has been greatly expanded, not only in industry, agriculture, medical and health industries, service industries and many other industries. It is also used in occasions that are harmful to the human body or even life-threatening, such as security protection, military industry and national defense, and deep space exploration. Therefore, mobile robots are getting more and more attention from scholars today.
在移动机器人系统中，所有机器人利用自身配置的多种传感器和执行器来感知环境并对环境的变化做出适当的反应，而整个移动机器人系统在某种程度上可以视为一个移动传感器网络和执行器网络；同时，整个移动机器人系统在控制过程中利用自身所配备的通信设备进行信息共享，使得整个系统在某种程度上又成为一个通信互联网络。由于移动机器人系统为实际情况下的真实系统，同时现实情况中往往环境较为复杂，突发情况较多，容易出现诸如传感器故障等情况，为了提高多智能体系统对环境的适应能力，减少多移动机器人系统在控制过程中所必需的信息量可以达到减少移动机器人配备的传感器数量，以此节约资源并提高多移动机器人系统对复杂环境的适应能力。In the mobile robot system, all robots use various sensors and actuators configured by themselves to perceive the environment and respond appropriately to changes in the environment, and the entire mobile robot system can be regarded as a mobile sensor network and network to some extent. At the same time, the entire mobile robot system uses its own communication equipment to share information during the control process, making the entire system a communication interconnection network to some extent. Since the mobile robot system is a real system in actual conditions, and the real environment is often complex, there are many unexpected situations, and it is prone to situations such as sensor failures, in order to improve the adaptability of the multi-agent system to the environment, reduce the number of mobile The amount of information necessary for the robot system in the control process can reduce the number of sensors equipped with mobile robots, thereby saving resources and improving the adaptability of multi-mobile robot systems to complex environments.
注意到在实际环境中突发情况较多，针对系统的姿态未知以及控制输入存在非线性扰动的问题，通过利用观测器理论对未知智能体的姿态进行估计可以有效地减少系统对状态信息的依赖程度，同时针对系统控制输入存在非线性扰动的问题，可以利用自适应控制律对扰动进行逼近，可以使系统更具有鲁棒性，是系统能够更好地在复杂的环境适应，也为大规模移动机器人系统的实际应用提供了一种有效地解决方法。It is noticed that there are many unexpected situations in the actual environment. In view of the unknown attitude of the system and the nonlinear disturbance of the control input, the estimation of the attitude of the unknown agent by using the observer theory can effectively reduce the dependence of the system on the state information. At the same time, for the problem of nonlinear disturbance in the system control input, the adaptive control law can be used to approximate the disturbance, which can make the system more robust, enable the system to better adapt to complex environments, and provide large-scale The practical application of the mobile robot system provides an effective solution.
姿态未知条件下多移动机器人系统的自适应跟踪控制在国内外均处于探索研究阶段，针对姿态未知的问题，目前很多成果都是利用滑模控制使系统的误差逐渐收敛于滑模面上，但是滑模控制往往容易出现抖振现象，同时很多成果针对的控制系统也主要为较为理想的二阶积分器系统，这就使得成果在实际的移动机器人系统中无法适用。The adaptive tracking control of multi-mobile robot system under the condition of unknown attitude is in the exploratory research stage both at home and abroad. For the problem of unknown attitude, many achievements at present are to use sliding mode control to make the system error gradually converge on the sliding mode surface, but Sliding mode control is often prone to chattering. At the same time, the control system of many achievements is mainly a relatively ideal second-order integrator system, which makes the achievements unapplicable in the actual mobile robot system.
发明内容Contents of the invention
有鉴于此，本发明提供了一种姿态未知的多移动机器人系统自适应跟踪控制方法，能够在姿态未知条件下实现对多移动机器人系统的跟踪控制，且该方法为基于观测器的自适应控制方法，可以使系统在演化的过程中实现跟随者机器人对领航者机器人的跟踪控制。In view of this, the present invention provides an adaptive tracking control method for a multi-mobile robot system with an unknown attitude, which can realize tracking control for a multi-mobile robot system under the condition of an unknown attitude, and the method is an adaptive control method based on an observer The method can make the system realize the tracking control of the leader robot by the follower robot in the process of evolution.
为了达到上述目的，本发明的技术方案为：该方法包括如下步骤：In order to achieve the above object, the technical solution of the present invention is: the method comprises the steps:
步骤一：针对多移动机器人系统中的每个移动机器人，均进行如下建模，首先建立全局坐标系O-xy：选取平面空间内任意一点O点为原点，并选取过O点的相互正交的两个方向分别为x轴和y轴；然后建立当前移动机器人的局部坐标系C-xRyR：选取当前移动机器人的轴心点C点为原点，选取过C点的相互正交的两个方向分别为xR轴和yR轴；其中C点在全局坐标系O-xy中的坐标为(xC，yC)，局部坐标系相对于全局坐标系的旋转角为θ。Step 1: For each mobile robot in the multi-mobile robot system, the following modeling is carried out. First, the global coordinate system O-xy is established: select any point O in the plane space as the origin, and select the mutually orthogonal points passing through O The two directions are the x-axis and the y-axis; then establish the local coordinate system CxR yR of the current mobile robot: select the pivot point C of the current mobile robot as the origin, and select two mutually orthogonal The directions are xR axis and yR axis respectively; the coordinates of point C in the global coordinate system O-xy are (xC , yC ), and the rotation angle of the local coordinate system relative to the global coordinate system is θ.
步骤二：在多移动机器人系统中，单个移动机器人依据其轨迹跟踪分为领航者与跟随者，其中领航者r的轴心点在全局坐标系O-xy中的坐标为(xr，yr)，r的局部坐标系相对于全局坐标系O-xy的旋转角度为θr，平动的线速度为vr，转动的角速度为ωr。Step 2: In a multi-robot system, a single mobile robot is divided into a leader and a follower according to its trajectory tracking, where the coordinates of the pivot point of the leader r in the global coordinate system O-xy are (xr , yr ), the rotation angle of the local coordinate system of r relative to the global coordinate system O-xy is θr , the linear velocity of translation is vr , and the angular velocity of rotation is ωr .
跟随者f的轴心点在全局坐标系O-xy中的坐标为(xf，yf)，跟随者f的局部坐标系相对于全局坐标系O-xy的旋转角度为θf，平动的线速度为vf，转动的角速度为ωf。The coordinates of the pivot point of the follower f in the global coordinate system O-xy are (xf , yf ), the rotation angle of the local coordinate system of the follower f relative to the global coordinate system O-xy is θf , and the translation The linear velocity is vf , and the angular velocity of rotation is ωf .
则跟随者f与领航者r的误差模型为：Then the error model of follower f and leader r is:
其中为跟随者f沿xR轴方向的速度，为跟随者f沿yR轴方向的速度，为跟随者f的转动角速度；其中xe为f与r的在x轴方向上的误差，ye为f与r的在y轴方向上的误差，θe为f与r的局部坐标系相对于全局坐标系的旋转角的误差，和分别为xe、ye以及θe的导数。in is the velocity of the follower f along the xR axis direction, is the speed of the follower f along the yR axis direction, is the rotational angular velocity of the follower f; where xe is the error between f and r in the x-axis direction, ye is the error between f and r in the y-axis direction, and θe is the relative local coordinate system of f and r The error of the rotation angle of the global coordinate system, and are the derivatives of xe , ye and θe , respectively.
其中σ为非线性扰动，该非线性扰动σ局部光滑并最终能够趋近于一个紧集Ωi∈R，R为实数集。Where σ is a nonlinear disturbance, which is locally smooth and can eventually approach a compact set Ωi ∈ R, where R is a set of real numbers.
步骤三：在多移动机器人系统中，每个移动机器人均获取其他移动机器人的信息进行非线性扰动评估，获得该移动机器人的非线性扰动的估计值其中是对该移动机器人的扰动系数W的估计值，为扰动函数，Rv'为v’维度的欧式空间，其中v’为基础函数。Step 3: In the multi-robot system, each mobile robot obtains the information of other mobile robots for nonlinear disturbance evaluation, and obtains the estimated value of the nonlinear disturbance of the mobile robot in is the estimated value of the disturbance coefficient W of the mobile robot, is the perturbation function, Rv' is the Euclidean space of dimension v', where v' is the basis function.
建立非线性扰动系数的自适应律为：The adaptive law for establishing the nonlinear disturbance coefficient is:
其中c4和c5为自适应参数，是的导数，φ＝sinθe，ψ＝cosθe，和分别为φ和ψ的估计值。where c4 and c5 are adaptive parameters, yes The derivative of φ=sinθe , ψ=cosθe , and are the estimated values of φ and ψ, respectively.
步骤四：建立针对θe的三角函数值的二阶观测器，建立二阶观测器状态中间量f和g的导数：则该二阶观测器具体为：Step 4: Establish a second-order observer for the trigonometric function value of θe , and establish the derivatives of the state intermediate quantities f and g of the second-order observer: then the second-order observer is specifically:
和分别为f和g的估计值；和分别为f和g的估计值的导数；由该二阶观测器，获得为vr的导数。 and are estimated values of f and g, respectively; and are the derivatives of estimates of f and g, respectively; from this second-order observer, one obtains is the derivative of vr .
步骤五：跟随者的控制律设置为：Step 5: The control law of the follower is set as:
vf＝vr+c2xe-c3ωryevf ＝vr +c2 xe -c3 ωr ye
其中，c2,c3,c6均为固定参数，此时领航者r的vr和ωr为持续的外部输入，且c2＞0，c3＞-1，c4＜0，c5＜0，1＞c6＞0，k＞0为固定参数，WM表示扰动参数W的上界。Among them, c2 , c3 , and c6 are all fixed parameters. At this time, vr and ωr of the navigator r are continuous external inputs, and c2 >0, c3 >-1, c4 <0, c5 < 0, 1 > c6 > 0, k>0 is a fixed parameter, and WM represents the upper bound of the disturbance parameter W.
根据该控制律，对跟随者进行跟踪控制。According to the control law, the follower is tracked and controlled.
进一步地，对步骤五建立的二阶观测器进行误差分析：Further, error analysis is performed on the second-order observer established in step five:
该二阶观测器的误差分别为则该二阶观测器误差的动态方程分别为：The errors of the second-order observer are Then the dynamic equations of the second-order observer error are:
其中和分别为和的导数，当和近似为0时，该多移动机器人系统保持稳定。in and respectively and The derivative of when and When is approximately 0, the multi-mobile robot system remains stable.
有益效果：Beneficial effect:
本发明针对姿态未知条件下多移动机器人系统的跟踪控制问题，提出了一种基于观测器的自适应控制方法，针对多移动机器人系统中跟随者无法获取自身姿态的问题，对跟随者与领航者误差角的三角函数设计观测器，以此间接实现了对跟随者与领航者误差角的观测，同时针对系统控制输入存在非线性扰动的问题，在对该扰动进行建模后，设计了自适应控制律，最后将观测器与自适应律相结合设计了一种基于观测器的自适应控制方法，成功实现了多移动机器人系统中跟随者对领航者的跟踪控制，使跟随者能够实现对领航者的跟踪控制。本发明提出的控制方法可以适用于实际的移动机器人系统，为复杂环境下移动机器人出现传感器故障等突发情况时的跟踪控制问题提供了一种行之有效的解决方法，同时该方法也可以减少移动机器人对姿态传感器的依赖，使移动机器人可以以较低的负载，较少的能耗实现控制目标。Aiming at the problem of tracking control of a multi-mobile robot system under the condition of unknown attitude, the present invention proposes an adaptive control method based on an observer. Aiming at the problem that the follower in a multi-mobile robot system cannot obtain its own attitude, the follower and the leader The trigonometric function of the error angle is used to design the observer, which indirectly realizes the observation of the error angle of the follower and the leader. At the same time, for the problem of nonlinear disturbance in the system control input, after modeling the disturbance, an adaptive Finally, an observer-based adaptive control method was designed by combining the observer with the adaptive law, which successfully realized the tracking control of the leader by the follower in the multi-mobile robot system, enabling the follower to control the leader. Follow-up control of the user. The control method proposed by the present invention can be applied to the actual mobile robot system, and provides an effective solution to the tracking control problem when the mobile robot has a sensor failure and other emergencies in a complex environment, and the method can also reduce The dependence of the mobile robot on the attitude sensor enables the mobile robot to achieve the control goal with a lower load and less energy consumption.
附图说明Description of drawings
图1—移动机器人运动学模型；Figure 1—Mobile robot kinematics model;
图2—多移动机器人系统轨迹跟踪控制模型；Figure 2—Track tracking control model of multi-mobile robot system;
图3—MobileSim仿真实验多移动机器人系统的初始状态；Figure 3—MobileSim simulation experiment initial state of multi-mobile robot system;
图4—MobileSim仿真实验多移动机器人系统的最终状态。Figure 4—MobileSim simulation experiment with the final state of the multi-mobile robot system.
具体实施方式Detailed ways
下面结合附图并举实施例，对本发明进行详细描述。The present invention will be described in detail below with reference to the accompanying drawings and examples.
本发明针对姿态未知条件下多移动机器人系统跟踪控制问题提出了一种基于观测器的自适应控制方法，使多移动机器人系统中跟随者能够实现对领航者的跟踪控制。The invention proposes an observer-based self-adaptive control method aiming at the tracking control problem of the multi-mobile robot system under the condition of unknown posture, so that the follower in the multi-mobile robot system can realize the tracking control of the leader.
步骤一：单个移动机器人建模Step 1: Modeling a single mobile robot
如图1所示，在平面空间内任意选定一点，将该点设置为原点O，在该点建立全局坐标系并选取互相正交的两个方向作为x轴与y轴。为了局部坐标系在全局坐标系的映射情况，选择机器人轴心点C点作为局部坐标轴的原点，在通常情况认为C点也即是机器人的重心所在。在局部坐标系中，使用{xR,yR}坐标机器人局部坐标系上的两条轴线，这样就完成了机器人局部坐标系的定义。考虑到机器人所在的全局坐标系，C点的位置可以用全局坐标系(x,y)来表示，同时局部坐标系可以看作是全局坐标系旋转了θ而得到，同时假定移动机器人平动的线速度为v(t)，转动的角速度为ω(t)，这样则可以得到移动机器人在全局坐标系上的运动模型。As shown in Figure 1, a point is arbitrarily selected in the plane space, and this point is set as the origin O. A global coordinate system is established at this point and two mutually orthogonal directions are selected as the x-axis and y-axis. For the mapping of the local coordinate system to the global coordinate system, point C, the axis point of the robot, is selected as the origin of the local coordinate axis. In general, point C is considered to be the center of gravity of the robot. In the local coordinate system, use {xR , yR } to coordinate the two axes on the local coordinate system of the robot, thus completing the definition of the local coordinate system of the robot. Considering the global coordinate system where the robot is located, the position of point C can be represented by the global coordinate system (x, y), and the local coordinate system can be regarded as obtained by rotating the global coordinate system by θ. At the same time, it is assumed that the translation of the mobile robot is The linear velocity is v(t), and the rotational angular velocity is ω(t), so that the motion model of the mobile robot on the global coordinate system can be obtained.
从系统模型中可以看出，模型的状态信息共有3个，分布式xR,yR,θ，但是控制量只有2个，分别是v(t),ω(t)，这就使得系统模型是非完整约束模型，同时状态量与控制量存在乘积形式的耦合，这都极大地提高了处理移动机器人模型的难度。It can be seen from the system model that there are three state information of the model, distributed xR , yR , θ, but there are only two control variables, namely v(t), ω(t), which makes the system model It is a non-holonomic constrained model, and there is a coupling between the state quantity and the control quantity in the form of a product, which greatly increases the difficulty of dealing with the mobile robot model.
步骤二：多移动机器人系统轨迹跟踪控制建模Step 2: Modeling the trajectory tracking control of a multi-mobile robot system
考虑到本专利主要研究的是多移动机器人系统的轨迹跟踪问题，因而需要对跟随者与领航者之间的状态误差进行研究，因此需要对模型做出一定的变化。假定领航者同为移动机器人模型，它的状态信息用(xr,yr,θr)来表示，相对应的，控制输入用(vr,ωr)表示，为了将领航者与跟随者进行区分，跟随者的状态信息以及控制输入则为(x,y,θ)以及(v,ω)。跟随者与领航者的误差坐标如图2所示。Considering that this patent mainly studies the trajectory tracking problem of a multi-mobile robot system, it is necessary to study the state error between the follower and the leader, so certain changes need to be made to the model. Assuming that the leader is also a mobile robot model, its state information is represented by (xr , yr , θr ), and correspondingly, the control input is represented by (vr , ωr ), in order to connect the leader and follower To distinguish, the state information and control input of the follower are (x, y, θ) and (v, ω). The error coordinates of the follower and the leader are shown in Figure 2.
根据图中的坐标系，就可以得到跟随者与领航者的误差模型为According to the coordinate system in the figure, the error model between the follower and the leader can be obtained as
将(1)式代入，可以得到式(3)，该式则是本章节主要的研究对象。Substituting formula (1) into formula (3) can be obtained, which is the main research object of this chapter.
步骤三：非线性扰动建模Step 3: Nonlinear Disturbance Modeling
式(2)以及(3)已经给出了移动机器人运动学模型以及轨迹跟踪控制的基本形式，但两式属于理想条件下控制输入不存在扰动的模型，由于姿态角控制器存在非线性扰动，式(3)中移动机器人模型需要改写为Equations (2) and (3) have given the mobile robot kinematics model and the basic form of trajectory tracking control, but the two equations belong to the model with no disturbance in the control input under ideal conditions. Due to the nonlinear disturbance in the attitude angle controller, The mobile robot model in formula (3) needs to be rewritten as
假定该非线性扰动局部光滑并最终能够趋近于一个紧集Ωi∈R，则非线性扰动σ可以被定义为其中是每个节点i对应的vi函数，而Wi则是一系列未知参数且有界，即|Wi|＜WM。vi函数的可以选择多种基础函数，比如符号函数，高斯函数等。文中，被视为神经网络触发矩阵而则是神经网络权重矩阵同时被假定为未知量。Assuming that the nonlinear disturbance is locally smooth and can eventually approach a compact set Ωi ∈ R, the nonlinear disturbance σ can be defined as in is the vi function corresponding to each node i, and Wi is a series of unknown parameters and bounded, that is, |Wi |<WM . Thevi function can choose a variety of basic functions, such as symbolic functions, Gaussian functions, etc. In the text, considered as a neural network trigger matrix and is the neural network weight matrix and is assumed to be an unknown quantity.
步骤四：针对非线性扰动的自适应律设计Step 4: Adaptive law design for nonlinear disturbance
为了对非线性扰动进行补偿，每个智能体都必须对该扰动进行估计补偿，对这一问题，主要的思路是将智能体i所获取到的其他智能体的信息来评估控制器的控制效果，因此，非线性扰动的估计值为In order to compensate for the nonlinear disturbance, each agent must estimate and compensate the disturbance. For this problem, the main idea is to use the information of other agents acquired by agent i to evaluate the control effect of the controller , so the estimated nonlinear perturbation is
其中是对每个智能体i的扰动系数Wi的估计值。非线性扰动系数的自适应律可以设计为：in is the estimated value of the perturbation coefficient Wi for each agent i. The adaptive law of the nonlinear disturbance coefficient can be designed as:
步骤五：姿态观测器设计Step 5: Attitude Observer Design
从式(4)可以看出，直接对θe进行估计需要进行三角函数的运算，求导之后运算较为复杂，本专利的观测器将直接对θe的三角函数值进行观测，首先引入二阶观测器状态中间量为：It can be seen from formula (4) that directly estimating θe requires the operation of trigonometric functions, and the operation after derivation is more complicated. The observer of this patent will directly observe the value of the trigonometric function of θe . Firstly, the second-order The observer state intermediate quantity is:
f＝sinθe+c4vryef＝sinθe +c4 vr ye
(7)(7)
g＝cosθe+c5vrxeg＝cosθe + c5 vr xe
其中f和g只是中间量，并不具备实际的物理意义，c4,c5分别为两个固定参数，对式(6)进行求导并将式(4)代入可得：Among them, f and g are only intermediate quantities and do not have actual physical meaning. c4 and c5 are two fixed parameters respectively. Deriving formula (6) and substituting formula (4) can be obtained:
假设φ＝sinθe,ψ＝cosθe，则对θe的三角的函数的估计值可以写成本专利的观测器形式设计如下所示：Assuming φ=sinθe , ψ=cosθe , the estimated value of the trigonometric function of θe can be written as The observer form design of this patent is as follows:
步骤六：姿态观测器误差分析Step 6: Error Analysis of Attitude Observer
假定观测器的误差分别为对其求导可得观测器误差的动态方程分别为Assume that the observer errors are The dynamic equations of the observer error obtained by deriving it are
将式(7)-(9)代入上式可得Substituting formulas (7)-(9) into the above formula can be obtained
将上式中各项两两正负相抵，可以得到化简的观测器误差动态方程为：By offsetting the positive and negative values of each item in the above formula, the simplified observer error dynamic equation can be obtained as:
对第一个式子，由于分别为未知量的乘积与估计量的乘积之和，并不能直接消除，故作下述的数学处理For the first formula, since are respectively the sum of the product of the unknown quantity and the product of the estimated quantity, which cannot be eliminated directly, so the following mathematical treatment
将上式代入观测器的误差动态方程中，则可以得到：Substituting the above formula into the error dynamic equation of the observer, we can get:
步骤七：基于观测器的自适应控制律设计Step 7: Observer-Based Adaptive Control Law Design
假定欧式空间中存在2个智能体，其中1个智能体为跟随者，另1个智能体为领航者，智能体的动力学方程均由公式(3)描述，轨迹跟踪控制模型由公式(4)描述，跟随者的控制律由公式(11)描述。当跟随者的控制律满足公式(12)且领航者的线速度满足持续激励条件时，系统将实现局部渐进稳定，跟随者也将能够对领航者进行跟踪。Assume that there are two agents in the Euclidean space, one of which is a follower and the other is a leader. The dynamic equations of the agents are described by formula (3), and the trajectory tracking control model is given by formula (4 ), the control law of the follower is described by formula (11). When the control law of the follower satisfies formula (12) and the linear velocity of the leader satisfies the continuous excitation condition, the system will achieve local asymptotic stability, and the follower will also be able to track the leader.
其中，ωr,vr分别为领航者的角速度以及线速度，c2,c3,c6均为固定参数。Among them, ωr and vr are the angular velocity and linear velocity of the navigator respectively, and c2 , c3 , and c6 are all fixed parameters.
对于式(12)，由于括号内的数均有界，k＞0为固定参数，这样可以通过调节k值的大小来尽可能大的扩大系统局部稳定的范围，同时当k值足够大时，其中WM表示扰动参数W的上界。For formula (12), since the numbers in the brackets are bounded, k>0 is a fixed parameter, so that the range of local stability of the system can be expanded as much as possible by adjusting the value of k, and when the value of k is large enough, where WM represents the upper bound of the disturbance parameter W.
对于欧式空间中存在的2个智能体，假定其中1个智能体为跟随者，另1个智能体为领航者，智能体的动力学方程均由公式(1)描述，轨迹跟踪控制模型由公式(4)描述，跟随者的控制律由公式(11)描述。当跟随者的控制律满足公式(12)且领航者的线速度满足持续激励条件时，系统将实现局部稳定，跟随者将实验对领航者的跟踪控制。For two agents in the Euclidean space, it is assumed that one agent is a follower and the other agent is a leader, the dynamic equations of the agents are described by formula (1), and the trajectory tracking control model is given by the formula (4), the control law of the follower is described by formula (11). When the control law of the follower satisfies formula (12) and the linear velocity of the leader satisfies the continuous excitation condition, the system will achieve local stability, and the follower will experiment with the tracking control of the leader.
本实施例通过实验验证控制方法的有效性和可行性：This embodiment verifies the validity and feasibility of the control method by experiment:
仿真实验主要基于移动机器人仿真测试平台MobileSim，仿真中的机器人模型为P3-DX型移动机器人。The simulation experiment is mainly based on the mobile robot simulation test platform MobileSim, and the robot model in the simulation is a P3-DX mobile robot.
图3给出了MobileSim仿真平台上移动机器人系统的初始位置，，图中1号和2号机器人分别为跟随者，领航者机器人则用leader进行标记，其中1号机器人的扰动系数较小，2好机器人的扰动系数较大。Figure 3 shows the initial position of the mobile robot system on the MobileSim simulation platform. Robots No. 1 and No. 2 in the figure are followers respectively, and the leader robot is marked with a leader. The disturbance coefficient of No. 1 robot is small, and No. 2 A good robot has a large disturbance coefficient.
图4给出了MobileSim仿真平台上移动机器人系统的最终状态，其中领航者的轨迹为一弧形轨迹，由于与领航者的相对距离不同，各个跟随者的轨迹不尽相同，但最终都实现了对领航者的跟踪控制。尽管从该图中并无法分辨不同的扰动对控制效果的影响，但该图已经成功测试了所提出控制算法可以对于实际移动机器人系统的适用性，下一步将使用相同的程序在实际的移动机器人上运行并对比实验结果。Figure 4 shows the final state of the mobile robot system on the MobileSim simulation platform. The trajectory of the leader is an arc trajectory. Due to the different relative distances from the leader, the trajectories of each follower are different, but they are all realized in the end. Tracking control of the Navigator. Although the influence of different disturbances on the control effect cannot be distinguished from this figure, the figure has successfully tested the applicability of the proposed control algorithm to the actual mobile robot system, and the next step will be to use the same program in the actual mobile robot Run and compare the experimental results.
综上，以上仅为本发明的较佳实施例而已，并非用于限定本发明的保护范围。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。To sum up, the above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.
| Application Number | Priority Date | Filing Date | Title |
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| CN201510319327.XACN104881044B (en) | 2015-06-11 | 2015-06-11 | The adaptive tracking control method of the multiple-mobile-robot system that a kind of attitude is unknown |
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| CN201510319327.XACN104881044B (en) | 2015-06-11 | 2015-06-11 | The adaptive tracking control method of the multiple-mobile-robot system that a kind of attitude is unknown |
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| CN104881044B CN104881044B (en) | 2016-12-21 |
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| CN201510319327.XAActiveCN104881044B (en) | 2015-06-11 | 2015-06-11 | The adaptive tracking control method of the multiple-mobile-robot system that a kind of attitude is unknown |
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