有限领导者速度信息下的多机器人编队控制
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摘要
近二十年来,多机器人技术得到了广泛的关注,人们在此领域进行了大量的研究。和单机器人系统相比,多机器人系统具有更好的智能性、鲁棒性和自适应性。本文讨论多自主移动机器人在局部信息下的编队问题,主要围绕如何提高系统抗干扰能力和在领导者机器人速度信息有限甚至未知条件下的编队控制器设计问题来展开。文中采用领导者—跟随者(Leader-Follower)编队方法作为协调机制,为跟随者机器人设计适当的控制规律,使其和领导者机器人形成指定的队形。
现有机器人编队控制策略主要考虑理想环境下编队控制器的设计问题,控制器所需要的参数都是准确可测或者直接得到的。为了提高算法的可用性与机器人的适应性,还需要考虑更一般情况下的算法设计问题,如控制器所需参数无法通过传感器直接测量得到的情况。另外,为了降低机器人之间的耦合程度,也需要考虑控制器如何减少机器人间的相互依赖性。这些都是机器人编队控制器设计的重点与难点之所在。为了处理这些情况,本文从提高编队系统的鲁棒性着手,为多机器人系统设计编队控制器。接着讨论跟随者机器人不能得到领导者机器人部分速度信息时的控制器设计问题,再到跟随者机器人完全不能得到领导者机器人任何速度信息时控制器设计问题。论文利用所设计的控制规律,结合自适应切换控制策略来处理编队群体避障和队形切换问题,取得了很好的效果。最后用具体的实验来证明文中所提算法的有效性。整个论述层层递进,体现了理论与实际的有效结合。
论文首先回顾多机器人技术的发展历程及目前的研究现状。然后介绍单个机器人的运动学模型和控制方法,根据单个机器人的运动学规律推导两个机器人以距离—角度模型形成编队及三个机器人以距离—距离模型形成编队的动态方程。
论文的主要研究内容分为两个部分。第一个部分为控制算法的理论推导与MATLAB仿真,主要包括以下几个方面：
(1)在跟随者机器人完全可以得到领导者机器人速度信息的条件下,针对机器人编队系统(距离—角度模型和距离—距离模型)中存在不确定性因素(如传感器实际采样位置和理论期望位置不重合等原因而引起的不确定量)的情况,提出一种新颖的二阶滑模控制方法对传统滑模控制方法进行改进,以提高系统控制精度与抑制颤振现象。在不确定量变化率满足一定约束的条件下,将系统控制到指定的流形上,使得编队跟踪变量沿指定流形收敛到期望值,从而达到编队的目的。利用距离—距离编队模型来讨论跟随者机器人同时跟踪领导者机器人和躲避环境中障碍物的问题。
(2)在系统所有信息都已知或可检测的条件下,讨论机器人轮子有打滑现象时的运动规律,并据此推导出相应的编队方程,对现有编队模型进行补充与发展。通过补偿和归并的策略,将有打滑现象时的编队方程化成和没有打滑状况时的编队方程相似的形式,然后采用与后者相类似的方法进行控制器的设计
(3)受传感器或通信机制的制约,跟随者机器人可以完全得到领导者机器人速度信息的假设有时未必成立。针对此种情况,论文考虑领导者机器人线速度恒定,但跟随者机器人无法得到领导者线速度的情况。利用机器人的相对位置信息,采用自适应输出反馈的方法对领导者机器人的线速度进行在线实时估计,并将估计值引入到跟随者机器人控制器的设计当中。此算法结合输入输出反馈算法和自适应算法两者的优点,并对它们进行利用与发展,降低对系统参数采集的要求。在此算法中,控制器的设计过程由估计器的设计方法决定。为了增大控制器设计的灵活性,论文引入浸入和不变(Immersion and Invariance)法来估计领导者机器人的线速度,同时还对编队变量进行观测,最后采用二阶滑模控制算法对观测后的系统进行控制器设计,实现增强系统鲁棒性的同时降低系统各子部分之间的耦合程度。该设计方法弥补了二阶滑模控制算法需要系统中所有参数都能直接或间接得到的不足,是对二阶滑模控制算法的有效补充及对浸入和不变算法的后续升级。
(4)为了降低控制算法对传感器性能的依赖,进一步考虑领导者机器人的线速度和角速度时变,但跟随者机器人无法得到领导者机器人任何速度信息的情况。论文改造与提升传统的基于控制误差直接设计控制器方法,结合输入输出线性化方法的优点,构造自适应编队算法为系统设计控制器。首先根据期望的性能指标构造一个理想的控制器,随后采用自适应编队控制算法来拟合此理想控制器的输出,从而实现在领导者机器人速度信息未知情况下对编队系统控制的目的。自适应控制器的增益系数根据系统运行性能实时在线自动调整。适当选择控制器参数(除自适应增益系数外的其它参数),可以使编队误差足够小。控制器无需估计领导者机器人的速度信息,实现起来简单方便。
论文的第二部分为多机器人编队控制实验。为了检验理论算法在实际物理系统中的运行效果,论文以AmigoBot机器人为基础,搭建多机器人运动平台,对各编队算法进行实验验证和分析。实验结果说明文中所提算法是有效可行的。
最后,总结全文,并对后续工作进行展望。
Even since the last two decades, the multi-robot technology has been attractingwidespread attention, and people have done a lot of research in this area. Compared with asingle-robot system, a multi-robot system could achieve better performances in intelligence,robustness and adaptability. This paper discusses the problem of multiple autonomousmobile robots formation using local information, and mainly draws attention on how toimprove the capacity of attenuating disturbances of the system, and how to design propercontrollers using a limited or even totally no information of the leader robot’s velocity. Itdesigns some controllers to steer the follower robot to get into and maintain somepredesigned formation with the leader robot based on the leader-follower formationmethodology.
Most of the existed researches of mobile robot formation control are mainly dealingwith how to design a formation controller under an idea environment, that all of theparameters needed for the controller can be detected or obtained directly. In order toenhance the usability for the algorithm and applicability for the robots, a more commonsituation should be considered for the algorithm design, such as the parameters neededcannot be detected directly according to the sensors. Furthermore, in order to reduce thedegree of coupling among robots, there should also consider how to reduce the dependencewith each other. All of these are not only the focal point but also the difficulty for the robotformation controller design. To deal with these cases, this dissertation starts with discussinghow to improve the system’s robustness and designing some controllers for the multi-robotsystem. Following, the controller design method via a situation that the follower robotcannot obtain part information of the leader robot’s velocity, and then to discuss thecontroller design method via a situation that the follower robot cannot obtain anyinformation of the leader robot’s velocity. Combining the controllers designed with theadaptive switching strategies, the obstacle avoidance and formation switching problems arediscussed for the formation system, and a good result is obtained. Finally, some experiments are provided to verify the effectiveness of the algorithms proposed. The wholediscussion is layer progressive and demonstrates an effective combination of theory andapplication.
Firstly, this paper reviews the development and current research status of themulti-robot technology. Secondly, it introduces the dynamic model and control method of asingle robot system, and deduces the dynamic formation equations of a two-robot systembased on the distance-bearing model and a three-robot system based on thedistance-distance model according to the single robot’s dynamic equation.
The dissertation is divided into two parts. The former part is the control algorithmdeduction and MATLAB simulation in theory, which mainly includes
(1) Due to the fact that some uncertainties may occur in the formation system (such asdue to the sensor’s real position does not coincide with it’s expected position, which maycause some uncertainties), under the condition that the follower robot can obtain completeinformation of the leader robot (for both distance-bearing model and distance-distancemodel), a novel second order sliding mode control algorithm is proposed to improve theperformance of the standard sliding mode control method and to increase the controlaccuracy and restrain chatting phenomenon for the system. Under the condition that theuncertainties are satisfied some constraints, the system is driven to some assigned surfaceof the manifold and the formation tracking variables are forced to converge to their desiredvalues to obtain a desired formation along the manifold. The problem of obstacle avoidanceduring the follower robot tracking to the leader robot is discussed based on thedistance-distance formation model.
(2) Under the condition that all information of the system is known or can be detected,it discusses the dynamic motion of the robot in a slipping situation, and deduces the relativeformation equations, that complements and delvelops the existed formation models.According to the compensation and merging methods, the dynamic formation equationsunder slipping condition are transformed into the style similar to the formation equationswithout slipping, and then the controller is designed similarly to the case without slipping.
(3) Due to the sensor or transmission mechanism limitations, the assumption that thefollower robot can obtain complete information of the leader robot may not hold in somesituations. For this problem, it considers that the leader robot has a constant velocity, butthe follower robot cannot obtain this velocity in any away. The leader robot’s linear velocityis estimated dynamically by the adaptive output feedback method using relative positioninformation, and the estimated value is added into the controller designed. This algorithmreduces the requiment of paramets detecting via using and delveloping the advantagies ofboth of the input and out feedback algorithm and adptive algorithm. For this algorithm, thecontroller designed followers the procedures of the estimation design method. In order toenhance the flexibility for the controller design, the immersion and invariance algorithm isemployed to estimate the linear velocity of the leader robot, and the formation variables areobserved at the same time, at last the second order sliding mode control algorithm is chosento design a control law for the observed system, it achieves the objective of increasing thesystem robustness and decreasing the couping among the subparts simultaneously. Thedeficiency of needing a complete known paramets for the second order sliding mode controlmethodology is made up by the immersion and invariance based second order sliding modecontrol algorithm, and this algorithm is also an effective complement and updating for theimmersion and invariance algorithm.
(4) Furthermore, in order to reduce the restrictions depending on the sensor’sperformance for the control algorithm, it considers that the follower robot has totally noinformation of the leader robot’s dynamic velocities, including linear velocity and angularvelocity. The traditional control error directly based algorithm is changed and upgraded inthis dissertation, and an adaptive formation algorithm is constructed for the formationsystem by conbinding the advantagies of the input and output linearization method. Firstly,an ideal controller is designed to satisfy the performance required. Secondly, the adaptiveformation control algorithm is used to approach the output of the ideal controller to obtainthe goal of forming a formation without knowing any information of the leader robot’svelocity. The adaptive gain parameters are adjusted according to the system’s performance dynamically. And the formation error can be reduced to small enough by selecting thecontrol parameters (the parameters excluding the adaptive gains) properly. The proposedcontroller does not need to estimate the leader robot’s velocity, and is rather simple andconvenient in realization.
The latter part of this dissertation is the multi-robot formation experiments. Amulti-robot moving platform is set up based on the AmigoBot robots to check theeffectiveness of the theoretical algorithms running on the physical system, and each of theformation algorithms is verified and analyzed through the relative experiment. Theexperiment results validae the effectiveness of the algorithms proposed.
Finally, some conclusions and prospects are given.
现有机器人编队控制策略主要考虑理想环境下编队控制器的设计问题,控制器所需要的参数都是准确可测或者直接得到的。为了提高算法的可用性与机器人的适应性,还需要考虑更一般情况下的算法设计问题,如控制器所需参数无法通过传感器直接测量得到的情况。另外,为了降低机器人之间的耦合程度,也需要考虑控制器如何减少机器人间的相互依赖性。这些都是机器人编队控制器设计的重点与难点之所在。为了处理这些情况,本文从提高编队系统的鲁棒性着手,为多机器人系统设计编队控制器。接着讨论跟随者机器人不能得到领导者机器人部分速度信息时的控制器设计问题,再到跟随者机器人完全不能得到领导者机器人任何速度信息时控制器设计问题。论文利用所设计的控制规律,结合自适应切换控制策略来处理编队群体避障和队形切换问题,取得了很好的效果。最后用具体的实验来证明文中所提算法的有效性。整个论述层层递进,体现了理论与实际的有效结合。
论文首先回顾多机器人技术的发展历程及目前的研究现状。然后介绍单个机器人的运动学模型和控制方法,根据单个机器人的运动学规律推导两个机器人以距离—角度模型形成编队及三个机器人以距离—距离模型形成编队的动态方程。
论文的主要研究内容分为两个部分。第一个部分为控制算法的理论推导与MATLAB仿真,主要包括以下几个方面：
(1)在跟随者机器人完全可以得到领导者机器人速度信息的条件下,针对机器人编队系统(距离—角度模型和距离—距离模型)中存在不确定性因素(如传感器实际采样位置和理论期望位置不重合等原因而引起的不确定量)的情况,提出一种新颖的二阶滑模控制方法对传统滑模控制方法进行改进,以提高系统控制精度与抑制颤振现象。在不确定量变化率满足一定约束的条件下,将系统控制到指定的流形上,使得编队跟踪变量沿指定流形收敛到期望值,从而达到编队的目的。利用距离—距离编队模型来讨论跟随者机器人同时跟踪领导者机器人和躲避环境中障碍物的问题。
(2)在系统所有信息都已知或可检测的条件下,讨论机器人轮子有打滑现象时的运动规律,并据此推导出相应的编队方程,对现有编队模型进行补充与发展。通过补偿和归并的策略,将有打滑现象时的编队方程化成和没有打滑状况时的编队方程相似的形式,然后采用与后者相类似的方法进行控制器的设计
(3)受传感器或通信机制的制约,跟随者机器人可以完全得到领导者机器人速度信息的假设有时未必成立。针对此种情况,论文考虑领导者机器人线速度恒定,但跟随者机器人无法得到领导者线速度的情况。利用机器人的相对位置信息,采用自适应输出反馈的方法对领导者机器人的线速度进行在线实时估计,并将估计值引入到跟随者机器人控制器的设计当中。此算法结合输入输出反馈算法和自适应算法两者的优点,并对它们进行利用与发展,降低对系统参数采集的要求。在此算法中,控制器的设计过程由估计器的设计方法决定。为了增大控制器设计的灵活性,论文引入浸入和不变(Immersion and Invariance)法来估计领导者机器人的线速度,同时还对编队变量进行观测,最后采用二阶滑模控制算法对观测后的系统进行控制器设计,实现增强系统鲁棒性的同时降低系统各子部分之间的耦合程度。该设计方法弥补了二阶滑模控制算法需要系统中所有参数都能直接或间接得到的不足,是对二阶滑模控制算法的有效补充及对浸入和不变算法的后续升级。
(4)为了降低控制算法对传感器性能的依赖,进一步考虑领导者机器人的线速度和角速度时变,但跟随者机器人无法得到领导者机器人任何速度信息的情况。论文改造与提升传统的基于控制误差直接设计控制器方法,结合输入输出线性化方法的优点,构造自适应编队算法为系统设计控制器。首先根据期望的性能指标构造一个理想的控制器,随后采用自适应编队控制算法来拟合此理想控制器的输出,从而实现在领导者机器人速度信息未知情况下对编队系统控制的目的。自适应控制器的增益系数根据系统运行性能实时在线自动调整。适当选择控制器参数(除自适应增益系数外的其它参数),可以使编队误差足够小。控制器无需估计领导者机器人的速度信息,实现起来简单方便。
论文的第二部分为多机器人编队控制实验。为了检验理论算法在实际物理系统中的运行效果,论文以AmigoBot机器人为基础,搭建多机器人运动平台,对各编队算法进行实验验证和分析。实验结果说明文中所提算法是有效可行的。
最后,总结全文,并对后续工作进行展望。
Even since the last two decades, the multi-robot technology has been attractingwidespread attention, and people have done a lot of research in this area. Compared with asingle-robot system, a multi-robot system could achieve better performances in intelligence,robustness and adaptability. This paper discusses the problem of multiple autonomousmobile robots formation using local information, and mainly draws attention on how toimprove the capacity of attenuating disturbances of the system, and how to design propercontrollers using a limited or even totally no information of the leader robot’s velocity. Itdesigns some controllers to steer the follower robot to get into and maintain somepredesigned formation with the leader robot based on the leader-follower formationmethodology.
Most of the existed researches of mobile robot formation control are mainly dealingwith how to design a formation controller under an idea environment, that all of theparameters needed for the controller can be detected or obtained directly. In order toenhance the usability for the algorithm and applicability for the robots, a more commonsituation should be considered for the algorithm design, such as the parameters neededcannot be detected directly according to the sensors. Furthermore, in order to reduce thedegree of coupling among robots, there should also consider how to reduce the dependencewith each other. All of these are not only the focal point but also the difficulty for the robotformation controller design. To deal with these cases, this dissertation starts with discussinghow to improve the system’s robustness and designing some controllers for the multi-robotsystem. Following, the controller design method via a situation that the follower robotcannot obtain part information of the leader robot’s velocity, and then to discuss thecontroller design method via a situation that the follower robot cannot obtain anyinformation of the leader robot’s velocity. Combining the controllers designed with theadaptive switching strategies, the obstacle avoidance and formation switching problems arediscussed for the formation system, and a good result is obtained. Finally, some experiments are provided to verify the effectiveness of the algorithms proposed. The wholediscussion is layer progressive and demonstrates an effective combination of theory andapplication.
Firstly, this paper reviews the development and current research status of themulti-robot technology. Secondly, it introduces the dynamic model and control method of asingle robot system, and deduces the dynamic formation equations of a two-robot systembased on the distance-bearing model and a three-robot system based on thedistance-distance model according to the single robot’s dynamic equation.
The dissertation is divided into two parts. The former part is the control algorithmdeduction and MATLAB simulation in theory, which mainly includes
(1) Due to the fact that some uncertainties may occur in the formation system (such asdue to the sensor’s real position does not coincide with it’s expected position, which maycause some uncertainties), under the condition that the follower robot can obtain completeinformation of the leader robot (for both distance-bearing model and distance-distancemodel), a novel second order sliding mode control algorithm is proposed to improve theperformance of the standard sliding mode control method and to increase the controlaccuracy and restrain chatting phenomenon for the system. Under the condition that theuncertainties are satisfied some constraints, the system is driven to some assigned surfaceof the manifold and the formation tracking variables are forced to converge to their desiredvalues to obtain a desired formation along the manifold. The problem of obstacle avoidanceduring the follower robot tracking to the leader robot is discussed based on thedistance-distance formation model.
(2) Under the condition that all information of the system is known or can be detected,it discusses the dynamic motion of the robot in a slipping situation, and deduces the relativeformation equations, that complements and delvelops the existed formation models.According to the compensation and merging methods, the dynamic formation equationsunder slipping condition are transformed into the style similar to the formation equationswithout slipping, and then the controller is designed similarly to the case without slipping.
(3) Due to the sensor or transmission mechanism limitations, the assumption that thefollower robot can obtain complete information of the leader robot may not hold in somesituations. For this problem, it considers that the leader robot has a constant velocity, butthe follower robot cannot obtain this velocity in any away. The leader robot’s linear velocityis estimated dynamically by the adaptive output feedback method using relative positioninformation, and the estimated value is added into the controller designed. This algorithmreduces the requiment of paramets detecting via using and delveloping the advantagies ofboth of the input and out feedback algorithm and adptive algorithm. For this algorithm, thecontroller designed followers the procedures of the estimation design method. In order toenhance the flexibility for the controller design, the immersion and invariance algorithm isemployed to estimate the linear velocity of the leader robot, and the formation variables areobserved at the same time, at last the second order sliding mode control algorithm is chosento design a control law for the observed system, it achieves the objective of increasing thesystem robustness and decreasing the couping among the subparts simultaneously. Thedeficiency of needing a complete known paramets for the second order sliding mode controlmethodology is made up by the immersion and invariance based second order sliding modecontrol algorithm, and this algorithm is also an effective complement and updating for theimmersion and invariance algorithm.
(4) Furthermore, in order to reduce the restrictions depending on the sensor’sperformance for the control algorithm, it considers that the follower robot has totally noinformation of the leader robot’s dynamic velocities, including linear velocity and angularvelocity. The traditional control error directly based algorithm is changed and upgraded inthis dissertation, and an adaptive formation algorithm is constructed for the formationsystem by conbinding the advantagies of the input and output linearization method. Firstly,an ideal controller is designed to satisfy the performance required. Secondly, the adaptiveformation control algorithm is used to approach the output of the ideal controller to obtainthe goal of forming a formation without knowing any information of the leader robot’svelocity. The adaptive gain parameters are adjusted according to the system’s performance dynamically. And the formation error can be reduced to small enough by selecting thecontrol parameters (the parameters excluding the adaptive gains) properly. The proposedcontroller does not need to estimate the leader robot’s velocity, and is rather simple andconvenient in realization.
The latter part of this dissertation is the multi-robot formation experiments. Amulti-robot moving platform is set up based on the AmigoBot robots to check theeffectiveness of the theoretical algorithms running on the physical system, and each of theformation algorithms is verified and analyzed through the relative experiment. Theexperiment results validae the effectiveness of the algorithms proposed.
Finally, some conclusions and prospects are given.
引文
[1]董炀斌.多机器人系统的协作研究[D].杭州：浙江大学,2006
[2]焦平平.基于通信的多机器人编队系统[D].北京：北京交通大学,2008：30-32
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