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CN113359432B - Control law design method for distributed self-adaptive state estimator of multi-rigid-body target system - Google Patents

Control law design method for distributed self-adaptive state estimator of multi-rigid-body target system Download PDF

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CN113359432B
CN113359432B CN202110778442.9A CN202110778442A CN113359432B CN 113359432 B CN113359432 B CN 113359432B CN 202110778442 A CN202110778442 A CN 202110778442A CN 113359432 B CN113359432 B CN 113359432B
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CN113359432A (en
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苏厚胜
李卓航
王晓玲
赵金
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Guangdong Intelligent Robotics Institute
Huazhong University of Science and Technology
Guangdong Hust Industrial Technology Research Institute
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Abstract

The invention discloses a control law design method of a distributed self-adaptive state estimator of a multi-rigid-body target system, which comprises the following steps: s1, determining the global state error of each rigid body, including leader dynamics, angular velocity and attitude error; s2, designing a distributed adaptive leader state estimator for each following rigid body; s3, giving sufficient conditions containing topology information and communication link faults to ensure the existence of the distributed state estimator; and S4, designing a fully distributed single rigid body control law by using a deterministic equivalence principle. The invention provides a distributed state estimator and a control law design of a multi-rigid system under the condition of communication link faults, eliminates the influence of the communication link faults on the consistency control law design of the multi-rigid system through a self-adaptive strategy, simultaneously reduces the requirements on communication topology connectivity, and has better universality and flexibility.

Description

多刚体目标系统分布式自适应状态估计器控制律设计方法Design method of distributed adaptive state estimator control law for multi-rigid-body target system

技术领域technical field

本发明属于多智能体分布式一致性控制领域，具体涉及一种多刚体目标系统分布式自适应状态估计器控制律设计方法。The invention belongs to the field of multi-agent distributed consistency control, in particular to a method for designing a control law of a distributed adaptive state estimator of a multi-rigid-body target system.

背景技术Background technique

协同控制是多智能体系统(MAS)控制中的一个重要研究内容，其在多个领域都用广泛的应用，例如卫星和航天器的姿态对准；飞行器的协同控制；无人机编队飞行等。分布式协同控制的一致性问题就是设计通信交换规则和控制律，指定双方的信息交换，使得所有的个体都可以收敛到统一的状态。Cooperative control is an important research content in multi-agent system (MAS) control, which is widely used in many fields, such as attitude alignment of satellites and spacecraft; cooperative control of aircraft; UAV formation flight, etc. . The consistency problem of distributed collaborative control is to design communication exchange rules and control laws, and specify the information exchange between the two parties, so that all individuals can converge to a unified state.

常规的一致性控制算法通常要求整个系统的通信拓扑具有以领导者为根节点的有向生成树，整个通信过程中拓扑不发生改变，并且通常假设通信权重是一个常数。在实际的应用中，由于存在通信链路故障(丢包、时延、量化误差、通信噪声等)，上述问题的存在增加了通信交互算法的指定困难。为了实现在通信链路故障情况下多刚体系统的一致性，对通信链路故障进行数学建模，引入自适应策略使得每个刚体在存在通信不确定性的情况下实现对于领导者状态的估计，进而将多刚体一致性问题转化为单刚体跟踪问题。Conventional consensus control algorithms usually require that the communication topology of the entire system has a directed spanning tree with the leader as the root node, the topology does not change during the entire communication process, and usually assumes that the communication weight is a constant. In practical applications, due to the existence of communication link failures (packet loss, time delay, quantization error, communication noise, etc.), the existence of the above problems increases the difficulty of specifying communication interaction algorithms. In order to achieve the consistency of the multi-rigid body system in the case of communication link failure, mathematical modeling of the communication link failure is carried out, and an adaptive strategy is introduced to make each rigid body realize the estimation of the leader state in the presence of communication uncertainty. , and then transform the multi-rigid body consistency problem into a single rigid body tracking problem.

本发明给出了一种完全分布式的自适应估计器及控制律的设计方法，避免了对通信拓扑的依赖，具有更好的灵活性。The invention provides a completely distributed self-adaptive estimator and a design method of the control law, which avoids the dependence on the communication topology and has better flexibility.

发明内容SUMMARY OF THE INVENTION

发明目的：本发明提供一种多刚体目标系统分布式自适应状态估计器控制律设计方法，放宽了多刚体系统姿态一致性对于通信权重的要求，排除了通信网络对全局信息的依赖，具有更强的鲁棒性和更好的灵活性。Purpose of the invention: The present invention provides a distributed adaptive state estimator control law design method for a multi-rigid-body target system, which relaxes the requirements for the communication weight of the attitude consistency of the multi-rigid-body system, eliminates the dependence of the communication network on global information, and has more advantages. Strong robustness and better flexibility.

发明内容：本发明提出一种多刚体目标系统分布式自适应状态估计器控制律设计方法，包括以下步骤：SUMMARY OF THE INVENTION The present invention proposes a method for designing a control law of a distributed adaptive state estimator for a multi-rigid-body target system, including the following steps:

S1、确定每一个刚体的全局状态误差，包括领导者动力学、角速度、姿态误差；S1. Determine the global state error of each rigid body, including leader dynamics, angular velocity, and attitude error;

S2、为每一个跟随刚体设计分布式的自适应领导者状态估计器；S2. Design a distributed adaptive leader state estimator for each follower rigid body;

S3、给出包含拓扑信息和通信链路故障的充分条件来保证分布式状态估计器的存在性；S3. Provide sufficient conditions including topology information and communication link failures to ensure the existence of the distributed state estimator;

S4、利用确定性等价原理设计出全分布的单刚体控制律。S4, using the deterministic equivalence principle to design a fully distributed single rigid body control law.

具体的，所述步骤S1包括以下步骤：Specifically, the step S1 includes the following steps:

S11、对每一个刚体进行全局误差建模，得出每一个刚体相对于其邻居的误差总和；S11. Perform global error modeling on each rigid body to obtain the sum of the errors of each rigid body relative to its neighbors;

首先对每一个刚体定义角速度和姿态估计器

Figure BDA0003155212690000021
其中姿态估计器属于单位四元数空间，角速度估计器属于三维欧氏空间，得出每一个刚体的分布式估计误差：First define angular velocity and attitude estimator for each rigid body
Figure BDA0003155212690000021
The attitude estimator belongs to the unit quaternion space, and the angular velocity estimator belongs to the three-dimensional Euclidean space, and the distributed estimation error of each rigid body is obtained:

Figure BDA0003155212690000022
Figure BDA0003155212690000022

Figure BDA0003155212690000023
Figure BDA0003155212690000023

其中Hi是每个刚体与其邻居刚体的分布式姿态误差，Γi是每个刚体与其邻居刚体的分布式角速度误差；where H i is the distributed attitude error of each rigid body and its neighbor rigid bodies, and Γ i is the distributed angular velocity error of each rigid body and its neighbor rigid bodies;

S12、制定领导者的动力学；S12. Develop the dynamics of the leader;

刚体系统的领导者动力学包括基于四元数表示的姿态动力学和角速度动力学：Leader dynamics for rigid body systems include attitude dynamics and angular velocity dynamics based on quaternion representation:

Figure BDA0003155212690000024
Figure BDA0003155212690000024

Figure BDA0003155212690000025
Figure BDA0003155212690000025

其中

Figure BDA0003155212690000026
表示领导者的角速度，
Figure BDA0003155212690000027
表示领导者的姿态。in
Figure BDA0003155212690000026
represents the angular velocity of the leader,
Figure BDA0003155212690000027
Indicates the gesture of a leader.

具体的，所述步骤S2包括以下步骤：Specifically, the step S2 includes the following steps:

S21、根据步骤S1中所建立的单刚体分布式估计误差，设计估计器的动力学，具体形式如下：S21. According to the single rigid body distributed estimation error established in step S1, the dynamics of the estimator is designed, and the specific form is as follows:

Figure BDA0003155212690000031
Figure BDA0003155212690000031

Figure BDA0003155212690000032
Figure BDA0003155212690000032

Figure BDA0003155212690000033
Figure BDA0003155212690000033

Figure BDA0003155212690000034
Figure BDA0003155212690000034

Figure BDA0003155212690000035
Figure BDA0003155212690000035

其中α，β＞0，且为常数，每个刚体的自适应参数的初始值都大于1，aξi(0)，aηi(0)≥1。Where α, β>0, and are constants, the initial value of the adaptive parameters of each rigid body is greater than 1, a ξi (0), a ηi (0) ≥ 1.

具体的，所述步骤S3实现过程如下：Specifically, the implementation process of step S3 is as follows:

S31、确定包含通信拓扑和通信链路故障的充分条件，具体条件如下：S31. Determine sufficient conditions including communication topology and communication link failures, the specific conditions are as follows:

(1)整个多刚体系统的通信拓扑初始状态包含一簇以领导者为根节点的有向生成树；(1) The initial state of the communication topology of the entire multi-rigid-body system contains a cluster of directed spanning trees with the leader as the root node;

(2)领导者的角速度系统矩阵是临界稳定的；(2) The angular velocity system matrix of the leader is critically stable;

(3)通信链路故障体现在对于通信权重的影响，这种影响及其导数是有界的；(3) The communication link failure is reflected in the influence on the communication weight, and the influence and its derivative are bounded;

(4)通信链路故障可以使得任意两个刚体之间的通信权重为0，即无通信。(4) The communication link failure can make the communication weight between any two rigid bodies to be 0, that is, no communication.

(5)通信链路故障造成的通信拓扑改变，其有限时间内子图的并集存在一簇以领导者为根节点的有向生成树；(5) The communication topology changes caused by the failure of the communication link, the union of the subgraphs in a limited time has a cluster of directed spanning trees with the leader as the root node;

S32、根据以上提出的5点条件，根据Lyapunov稳定性理论，建立如下李雅普诺夫函数：S32. According to the five conditions proposed above, according to the Lyapunov stability theory, the following Lyapunov function is established:

Figure BDA0003155212690000036
Figure BDA0003155212690000036

具体的，所述步骤S4包括以下步骤：Specifically, the step S4 includes the following steps:

S41、建立每个刚体的自身动力学，具体形式如下：S41, establish the own dynamics of each rigid body, the specific form is as follows:

Figure BDA0003155212690000037
Figure BDA0003155212690000037

Figure BDA0003155212690000038
Figure BDA0003155212690000038

其中

Figure BDA0003155212690000039
是表示每个刚体自身参考系相对于惯性参考系的单位四元数，
Figure BDA00031552126900000310
表示每个刚体相对于自身参考系的惯性张量，
Figure BDA00031552126900000311
表示每个刚体的控制扭矩；in
Figure BDA0003155212690000039
is the unit quaternion representing each rigid body's own reference frame relative to the inertial reference frame,
Figure BDA00031552126900000310
represents the inertia tensor of each rigid body relative to its own frame of reference,
Figure BDA00031552126900000311
represents the control torque of each rigid body;

S42、建立每个刚体的误差系统，具体形式如下：S42, establish the error system of each rigid body, the specific form is as follows:

Figure BDA0003155212690000041
Figure BDA0003155212690000041

Figure BDA0003155212690000042
Figure BDA0003155212690000042

其中

Figure BDA0003155212690000043
它们的动力学如下：in
Figure BDA0003155212690000043
Their dynamics are as follows:

Figure BDA0003155212690000044
Figure BDA0003155212690000044

S43、根据步骤S3建立的包含通信拓扑和通信链路故障的状态估计器收敛充分条件，与步骤S2建立的基于自适应的状态估计器，运用确定性等价原理，重新建立如下的误差系统：S43, according to the sufficient condition of convergence of the state estimator including the communication topology and communication link failure established in step S3, and the self-adaptive state estimator established in step S2, using the deterministic equivalence principle, re-establish the following error system:

Figure BDA0003155212690000045
Figure BDA0003155212690000045

Figure BDA0003155212690000046
Figure BDA0003155212690000046

它们的动力学具有如下形式：Their dynamics have the following form:

Figure BDA0003155212690000047
Figure BDA0003155212690000047

Figure BDA0003155212690000048
Figure BDA0003155212690000048

其中

Figure BDA0003155212690000049
具有如下形式：in
Figure BDA0003155212690000049
has the following form:

Figure BDA00031552126900000410
Figure BDA00031552126900000410

Figure BDA00031552126900000411
Figure BDA00031552126900000411

其中：in:

Figure BDA00031552126900000412
Figure BDA00031552126900000412

S44、设计临时变量，重新建立步骤S43中的误差系统：S44, design temporary variables, and re-establish the error system in step S43:

Figure BDA00031552126900000413
Figure BDA00031552126900000413

Figure BDA00031552126900000414
Figure BDA00031552126900000414

Figure BDA00031552126900000415
Figure BDA00031552126900000415

Figure BDA00031552126900000416
Figure BDA00031552126900000416

其中

Figure BDA00031552126900000417
in
Figure BDA00031552126900000417

S45、完成上述系统建模后，设计如下控制律：S45. After the above system modeling is completed, the following control law is designed:

Figure BDA0003155212690000051
Figure BDA0003155212690000051

其中ki2是一个大于0的常数。where k i2 is a constant greater than 0.

相对于现有技术，本发明的有益效果在于：本发明提出了存在通信链路故障情况下多刚体系统的分布式状态估计器及控制律设计，通过自适应策略消除了通信链路故障对于多刚体系统一致性控制律设计的影响，同时降低了对于通信拓扑连通性的要求，具有更好的普适性和灵活性。Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention proposes a distributed state estimator and a control law design for a multi-rigid body system in the presence of communication link failures, and eliminates communication link failures for multiple rigid bodies through adaptive strategies. The rigid body system has the influence of the consistent control law design, and reduces the requirements for the connectivity of the communication topology, and has better universality and flexibility.

附图说明Description of drawings

为了更清楚地说明本发明实施例中的技术方案，下面将对实施例或现有技术描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to illustrate the technical solutions in the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only for the present invention. In some embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

图1为本发明的流程图。FIG. 1 is a flow chart of the present invention.

具体实施方式Detailed ways

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

为了说明本发明所述的技术方案，下面通过具体实施例来进行说明。In order to illustrate the technical solutions of the present invention, the following specific embodiments are used for description.

实施例Example

如图1所示，本实施例提出一种多刚体目标系统分布式自适应状态估计器控制律设计方法，包括以下步骤：As shown in FIG. 1 , this embodiment proposes a method for designing a control law of a distributed adaptive state estimator for a multi-rigid-body target system, including the following steps:

步骤S1、确定每一个刚体的全局状态误差，包括领导者动力学、角速度、姿态误差，具体包括以下步骤：Step S1, determine the global state error of each rigid body, including leader dynamics, angular velocity, and attitude error, specifically including the following steps:

S11、对每一个刚体进行全局误差建模，得出每一个刚体相对于其邻居(包括领导者)的误差总和；S11. Perform global error modeling for each rigid body, and obtain the sum of the errors of each rigid body relative to its neighbors (including the leader);

首先对每一个刚体定义角速度和姿态估计器

Figure BDA0003155212690000052
其中姿态估计器属于单位四元数空间，角速度估计器属于三维欧氏空间，得出每一个刚体的分布式估计误差：First define angular velocity and attitude estimator for each rigid body
Figure BDA0003155212690000052
The attitude estimator belongs to the unit quaternion space, and the angular velocity estimator belongs to the three-dimensional Euclidean space, and the distributed estimation error of each rigid body is obtained:

Figure BDA0003155212690000061
Figure BDA0003155212690000061

Figure BDA0003155212690000062
Figure BDA0003155212690000062

其中Hi是每个刚体与其邻居刚体(包括领导者)的分布式姿态误差，Γi是每个刚体与其邻居刚体(包括领导者)的分布式角速度误差，之后定义其全局形式：where H i is the distributed attitude error of each rigid body and its neighbor rigid bodies (including the leader), Γ i is the distributed angular velocity error of each rigid body and its neighbor rigid bodies (including the leader), and then its global form is defined:

Figure BDA0003155212690000063
Figure BDA0003155212690000063

进一步地，全局领导者状态估计误差定义为：Further, the global leader state estimation error is defined as:

Figure BDA0003155212690000064
Figure BDA0003155212690000064

根据每个刚体的分布式姿态估计误差与全局领导者状态估计误差，得出全局领导者误差可以表示为According to the distributed attitude estimation error of each rigid body and the global leader state estimation error, the global leader error can be expressed as

Figure BDA0003155212690000065
Figure BDA0003155212690000065

在通信拓扑存在一簇以领导者为根节点的有向生成树时，LG(t)一定是一个可逆的矩阵，那么得出如下的不等式：When there is a cluster of directed spanning trees with the leader as the root node in the communication topology, L G (t) must be an invertible matrix, then the following inequality is obtained:

Figure BDA0003155212690000066
Figure BDA0003155212690000066

运用同样的定义方式，还可以得到如下不等式：Using the same definition, the following inequality can also be obtained:

Figure BDA0003155212690000067
Figure BDA0003155212690000067

其中

Figure BDA0003155212690000068
in
Figure BDA0003155212690000068

上述两个不等式为步骤S3建立包含拓扑信息和通信链路故障的充分条件保证估计器的存在性提供了证明前件；The above two inequalities provide proof preconditions for the existence of the estimator for establishing sufficient conditions including topology information and communication link failures in step S3;

S12、制定领导者的动力学(跟随者未知)；S12, formulate the dynamics of the leader (the follower is unknown);

刚体系统的领导者动力学包括基于四元数表示的姿态动力学和角速度动力学：Leader dynamics for rigid body systems include attitude dynamics and angular velocity dynamics based on quaternion representation:

Figure BDA0003155212690000071
Figure BDA0003155212690000071

Figure BDA0003155212690000072
Figure BDA0003155212690000072

其中

Figure BDA0003155212690000073
表示领导者的角速度，
Figure BDA0003155212690000074
表示领导者的姿态，
Figure BDA0003155212690000075
是一个常数矩阵，并且其表示的角速度动力学系统需要满足临界稳定的条件；in
Figure BDA0003155212690000073
represents the angular velocity of the leader,
Figure BDA0003155212690000074
the gesture of a leader,
Figure BDA0003155212690000075
is a constant matrix, and the angular velocity dynamic system it represents needs to satisfy the critical stability condition;

步骤S2、为每一个刚体设计分布式的自适应状态估计器，具体包括以下步骤：Step S2: Design a distributed adaptive state estimator for each rigid body, which specifically includes the following steps:

S21、根据步骤S1中所建立的单刚体分布式估计误差，设计估计器的动力学，具体形式如下：S21. According to the single rigid body distributed estimation error established in step S1, the dynamics of the estimator is designed, and the specific form is as follows:

Figure BDA0003155212690000076
Figure BDA0003155212690000076

Figure BDA0003155212690000077
Figure BDA0003155212690000077

Figure BDA0003155212690000078
Figure BDA0003155212690000078

Figure BDA0003155212690000079
Figure BDA0003155212690000079

Figure BDA00031552126900000710
Figure BDA00031552126900000710

其中α，β＞0，且为常数，每个刚体的自适应参数的初始值都大于1，aξi(0)，aηi(0)≥1；其中领导者系统矩阵估计器采用一阶滑膜估计器，保证其在有限时间内收敛；Where α, β>0, and are constants, the initial value of the adaptive parameters of each rigid body is greater than 1, a ξi (0), a ηi (0) ≥ 1; the leader system matrix estimator adopts a first-order sliding A membrane estimator, which is guaranteed to converge in finite time;

步骤S3、给出包含拓扑信息和通信链路故障的充分条件来保证分布式自适应估计器的存在性，具体实现过程如下：Step S3, providing sufficient conditions including topology information and communication link faults to ensure the existence of the distributed adaptive estimator, and the specific implementation process is as follows:

S31、确定包含通信拓扑和通信链路故障的充分条件，具体条件如下：S31. Determine sufficient conditions including communication topology and communication link failures, the specific conditions are as follows:

(1)整个多刚体系统的通信拓扑初始状态包含一簇以领导者为根节点的有向生成树；(1) The initial state of the communication topology of the entire multi-rigid-body system contains a cluster of directed spanning trees with the leader as the root node;

(2)领导者的角速度系统矩阵是临界稳定的；(2) The angular velocity system matrix of the leader is critically stable;

(3)通信链路故障体现在对于通信权重的影响，这种影响及其导数是有界的；(3) The communication link failure is reflected in the influence on the communication weight, and the influence and its derivative are bounded;

(4)通信链路故障可以使得任意两个刚体之间的通信权重为0，即无通信。(4) The communication link failure can make the communication weight between any two rigid bodies to be 0, that is, no communication.

(5)通信链路故障造成的通信拓扑改变，其有限时间内子图的并集存在一簇以领导者为根节点的有向生成树。(5) The communication topology changes caused by the failure of the communication link, the union of the subgraphs in a limited time has a cluster of directed spanning trees with the leader as the root node.

S32、根据以上提出的5点条件，根据Lyapunov稳定性理论，建立如下李雅普诺夫函数：S32. According to the five conditions proposed above, according to the Lyapunov stability theory, the following Lyapunov function is established:

Figure BDA0003155212690000081
Figure BDA0003155212690000081

该李雅普诺夫是基于条件1所建立，保证了全局存在通信的情况下S2设计的自适应状态估计器的存在性；The Lyapunov is established based on condition 1, which ensures the existence of the adaptive state estimator designed by S2 in the case of global communication;

在条件5的情况下，建立如下的李雅普诺夫函数：In the case of condition 5, the following Lyapunov function is established:

Figure BDA0003155212690000082
Figure BDA0003155212690000082

Figure BDA0003155212690000083
Figure BDA0003155212690000083

上述李雅普诺夫函数确保了通信链路故障将整个系统分为数个子图时，每个子图的自适应状态估计器的领导者估计误差不变的性质；The above Lyapunov function ensures that when the communication link failure divides the whole system into several subgraphs, the leader of the adaptive state estimator of each subgraph estimates the invariant property;

步骤S4、在步骤S3的基础上，利用确定性等价原理设计出完全分布的控制律，具体包括以下步骤：Step S4, on the basis of step S3, using the deterministic equivalence principle to design a fully distributed control law, which specifically includes the following steps:

S41、建立每个刚体的自身动力学，具体形式如下：S41, establish the own dynamics of each rigid body, the specific form is as follows:

Figure BDA0003155212690000084
Figure BDA0003155212690000084

Figure BDA0003155212690000085
Figure BDA0003155212690000085

其中

Figure BDA0003155212690000086
是表示每个刚体自身参考系相对于惯性参考系的单位四元数，
Figure BDA0003155212690000087
表示每个刚体相对于自身参考系的惯性张量，
Figure BDA0003155212690000088
表示每个刚体的控制扭矩；in
Figure BDA0003155212690000086
is the unit quaternion representing each rigid body's own reference frame relative to the inertial reference frame,
Figure BDA0003155212690000087
represents the inertia tensor of each rigid body relative to its own frame of reference,
Figure BDA0003155212690000088
represents the control torque of each rigid body;

S42、建立每个刚体的误差系统，具体形式如下：S42, establish the error system of each rigid body, the specific form is as follows:

Figure BDA0003155212690000089
Figure BDA0003155212690000089

Figure BDA00031552126900000810
Figure BDA00031552126900000810

其中

Figure BDA00031552126900000811
它们的动力学如下：in
Figure BDA00031552126900000811
Their dynamics are as follows:

Figure BDA00031552126900000812
Figure BDA00031552126900000812

S43、根据步骤S3建立的包含通信拓扑和通信链路故障的状态估计器收敛充分条件，与步骤S2建立的基于自适应的状态估计器，运用确定性等价原理，重新建立如下的误差系统：S43, according to the sufficient condition of convergence of the state estimator including the communication topology and communication link failure established in step S3, and the self-adaptive state estimator established in step S2, using the deterministic equivalence principle, re-establish the following error system:

Figure BDA0003155212690000091
Figure BDA0003155212690000091

Figure BDA0003155212690000092
Figure BDA0003155212690000092

它们的动力学具有如下形式：Their dynamics have the following form:

Figure BDA0003155212690000093
Figure BDA0003155212690000093

Figure BDA0003155212690000094
Figure BDA0003155212690000094

其中

Figure BDA0003155212690000095
具有如下形式：in
Figure BDA0003155212690000095
has the following form:

Figure BDA0003155212690000096
Figure BDA0003155212690000096

Figure BDA0003155212690000097
Figure BDA0003155212690000097

其中：in:

Figure BDA0003155212690000098
Figure BDA0003155212690000098

S44、设计临时变量，重新建立S43中的误差系统。S44, design temporary variables, and re-establish the error system in S43.

Figure BDA0003155212690000099
Figure BDA0003155212690000099

Figure BDA00031552126900000910
Figure BDA00031552126900000910

Figure BDA00031552126900000911
Figure BDA00031552126900000911

Figure BDA00031552126900000912
Figure BDA00031552126900000912

其中

Figure BDA00031552126900000913
in
Figure BDA00031552126900000913

S45、完成上述系统建模后，设计如下控制律：S45. After the above system modeling is completed, the following control law is designed:

Figure BDA00031552126900000914
Figure BDA00031552126900000914

其中ki2是一个大于0的常数。where k i2 is a constant greater than 0.

以上仅为本发明的较佳实施例而已，并不用于限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention. Inside.

Claims (4)

1. A control law design method for a distributed self-adaptive state estimator of a multi-rigid-body target system is characterized by comprising the following steps:
s1, determining the global state error of each rigid body, including leader dynamics, angular velocity and attitude error;
s2, designing a distributed adaptive leader state estimator for each following rigid body;
s3, giving sufficient conditions containing topology information and communication link faults to ensure the existence of the distributed state estimator;
step S3 is implemented as follows:
s31, determining sufficient conditions including communication topology and communication link faults, wherein the specific conditions are as follows:
(1) the communication topology initial state of the whole multi-rigid body system comprises a cluster of directed spanning trees taking a leader as a root node;
(2) the leader's angular velocity system matrix is critically stable;
(3) communication link failure is reflected in the effect on the communication weights, which effect and its derivatives are bounded;
(4) communication link failure can make the communication weight between any two rigid bodies be 0, i.e. no communication;
(5) the communication topology changes caused by communication link faults, and a union of subgraphs in limited time has a cluster of directed spanning trees with a leader as a root node;
s32, establishing the following Lyapunov function according to the 5-point condition and the Lyapunov stability theory:
Figure FDA0003753395990000011
and S4, designing a fully distributed single rigid body control law by using a deterministic equivalence principle.
2. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S1 comprises the steps of:
s11, carrying out global error modeling on each rigid body to obtain the error sum of each rigid body relative to the neighbor of the rigid body;
first, an angular velocity and attitude estimator is defined for each rigid body
Figure FDA0003753395990000021
Wherein the attitude estimator belongs to a unit quaternion space, the angular velocity estimator belongs to a three-dimensional Euclidean space, and a distributed estimation error of each rigid body is obtained:
Figure FDA0003753395990000022
Figure FDA0003753395990000023
wherein H i Is the distributed attitude error, Γ, of each rigid body with its neighbor rigid bodies i Is the distributed angular velocity error of each rigid body with its neighbor rigid bodies；
S12, establishing the dynamics of the leader;
the leader dynamics of the rigid body system include attitude dynamics and angular velocity dynamics based on quaternion representations:
Figure FDA0003753395990000024
Figure FDA0003753395990000025
wherein
Figure FDA0003753395990000026
The angular velocity of the leader is represented,
Figure FDA0003753395990000027
representing the pose of the leader.
3. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S2 comprises the steps of:
s21, designing the dynamics of the estimator according to the single rigid body distributed estimation error established in the step S1, wherein the specific form is as follows:
Figure FDA0003753395990000031
Figure FDA0003753395990000032
Figure FDA0003753395990000033
Figure FDA0003753395990000034
Figure FDA0003753395990000035
wherein alpha and beta are more than 0 and are constants, and the initial value of the adaptive parameter of each rigid body is more than 1, a ξi (0)，a ηi (0)≥1。
4. The distributed adaptive state estimator control law design method for multi-rigid body target system according to claim 1, wherein said step S4 comprises the steps of:
s41, establishing the self-dynamics of each rigid body, wherein the specific form is as follows:
Figure FDA0003753395990000036
Figure FDA0003753395990000037
wherein
Figure FDA0003753395990000038
Is a unit quaternion representing the reference frame of each rigid body per se relative to the inertial reference frame,
Figure FDA0003753395990000039
representing the inertia tensor of each rigid body relative to its own frame of reference,
Figure FDA00037533959900000310
representing the control torque of each rigid body;
s42, establishing an error system of each rigid body, wherein the specific form is as follows:
Figure FDA00037533959900000311
Figure FDA00037533959900000312
wherein
Figure FDA00037533959900000313
Their kinetics are as follows:
Figure FDA00037533959900000314
s43, according to the state estimator containing communication topology and communication link failure established in step S3, converging sufficient conditions, and the state estimator based on self-adaption established in step S2, applying the principle of determinism equivalence, reestablishing the following error system:
Figure FDA0003753395990000041
Figure FDA0003753395990000042
their kinetics have the following form:
Figure FDA0003753395990000043
Figure FDA0003753395990000044
wherein
Figure FDA0003753395990000045
Has the following form:
Figure FDA0003753395990000046
Figure FDA0003753395990000047
wherein:
Figure FDA0003753395990000048
s44, designing temporary variables, and reestablishing the error system in the step S43:
Figure FDA0003753395990000049
Figure FDA00037533959900000410
Figure FDA00037533959900000411
Figure FDA00037533959900000412
wherein
Figure FDA00037533959900000413
S45, after the system modeling is completed, designing the following control law:
Figure FDA0003753395990000051
wherein k is i2 Is a constant greater than 0.
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