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Intrinsic Formation and Macroscopic Intervention in Multi-agent Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this dissertation, we study two problems within the field of the multi-agent systems theory. One is the formation control for multiple reducedattitudes, which are extensively utilized in many pointing applications and under-actuated scenarios for attitude maneuvers. In contrast to most existing methodologies on the formation control, the proposed method does notneed to contain any formation errors in the protocol. Instead, the constructedformation is attributed to geometric properties of the configuration space andthe designed connection topology. We refer to this type of formation controlas intrinsic formation control. Besides, the control protocols proposed in thiswork are designed directly in space S^2 , avoiding to use any attitude parameterizations. Moreover, along the studies, some elementary tools for reducedattitudes control are developed.

Another problem is a moment-based methodology to modeling and ana-lyzing collective behavior of a group of agents. The theory is applicable fora wide range of applications, such as multi-agent systems with interactionsas well as with leaders and/or control input, and the use of this frameworkcan considerably reduce the computational burden for controlling and ana-lyzing such systems. We therefore propose to develop and use this theory forthe multi-agent applications such as crowd dynamics, opinion dynamics andother macroscopic problems.

Particularly, in paper A a continuous control law is provided for a reduced attitude system, by which a regular tetrahedron formation can achieveasymptotic stability under a quite large family of gain functions in the con-trol. Then, with a further restriction on the control gain, almost global stability of the tetrahedron formation is also obtained. In this work, we introducea novel coordinates transformation that represents the relative reduced atti-tudes between the agents. The proposed method is an intrinsic formationcontrol that does not need to involve any information of the desired formation beforehand. Another virtue of the method proposed is that only relativeattitude measurement is required.

Paper B further concerns the formation control of all regular polyhedralconfigurations (also called Platonic solids) for reduced attitudes. Accord-ing to the symmetries possessed by regular polyhedra, a unified frameworkis proposed for their formations. Via using the coordinates transformationpreviously proposed, it is shown that stability of the desired formations canbe provided by stabilizing a constrained nonlinear system. Then, a method-ology to investigate the stability of this type of constrained systems is alsopresented.

In paper C, we introduce an approach for modeling collective behaviorof a group of agents using moments. We represent the swarming via their dis-tribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distributionof the agents. In the latter an inverse problem is solved in order to reconstructa nominal distribution and to recover the macro-scale properties of the groupof agents. The proposed method is applicable for several types of multi-agent systems, including leader-follower systems.

Paper D considers the problem of tracking and encircling a moving target by agents in the 3-dimensional space. In this work, we show that similardesign techniques proposed for reduced attitudes formations can also be applied to the formation control for point mass systems. Therein, a group ofagents are driven to some desired formation on a spherical surface and simultaneously the center of this spherical formation is kept coinciding withthe target to be tracked. By properly designing communication topology, theagents constitute a cyclic formation along the equator of an encircling sphere.

In Paper E, a methodology based on differential geometry techniquesis proposed to investigate exponential stability of a formation for reducedattitudes. By such a method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formationproblem is evolving in a non-Euclidean space. In the paper, the desired formation is treated as an embedding submanifold in (S^2)^N and by using therotation symmetries owned by the attitude dynamics its stability is directlyexamined. Moreover, such a method turns out to be coordinates free, namely,exponential stability of a formation can be completely determined by just investigating any one equilibrium which can result in the formation under anylocal chart of (S^2 )^N . This greatly simplifies the stability analysis for theformation problems.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. , p. 31
Series
TRITA-SCI-FOU ; 2019:06
Keywords [en]
Attitude control, agents and autonomous systems, distributed control, formation control, nonlinear systems, moment based modelling, large- scale systems, reduced order modeling, nonlinear system identification
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-241369ISBN: 978-91-7873-090-2 (print)OAI: oai:DiVA.org:kth-241369DiVA, id: diva2:1280754
Public defence
2019-02-15, Kollegiesalen, Brinellvägen 8, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20190121

Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-01-21Bibliographically approved
List of papers
1. Intrinsic tetrahedron formation of reduced attitude
Open this publication in new window or tab >>Intrinsic tetrahedron formation of reduced attitude
Show others...
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 87, p. 375-382Article in journal (Refereed) Published
Abstract [en]

In this paper, formation control for reduced attitude is studied, in which a regular tetrahedron formation can be achieved and shown to be asymptotically stable under a large family of gain functions in the control. Moreover, by further restriction on the control gain, almost global stability of the desired formation is obtained. In addition, the control proposed is an intrinsic protocol that only uses relative information and does not need to contain any information of the desired formation beforehand. The constructed formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Besides, a novel coordinates transformation is proposed to represent the relative reduced attitudes in S2, which is shown to be an efficient approach to reduced attitude formation problems.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Attitude control, Distributed control, Formation control, Nonlinear systems
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-219636 (URN)10.1016/j.automatica.2017.10.023 (DOI)000423002400042 ()2-s2.0-85033383085 (Scopus ID)
Note

QC 20171211

Available from: 2017-12-11 Created: 2017-12-11 Last updated: 2019-01-21Bibliographically approved
2. An Intrinsic Approach to Formation Control of Regular Polyhedra for Reduced Attitudes
Open this publication in new window or tab >>An Intrinsic Approach to Formation Control of Regular Polyhedra for Reduced Attitudes
(English)Manuscript (preprint) (Other academic)
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-202350 (URN)
Note

QC 20170303

Available from: 2017-02-21 Created: 2017-02-21 Last updated: 2019-01-21Bibliographically approved
3. Modeling collective behaviors: A moment-based approach
Open this publication in new window or tab >>Modeling collective behaviors: A moment-based approach
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Abstract—In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the group of agents via their distribution and derive a method to estimate the dynamics of the moments. We use this to predict the evolution of the distribution of agents by first computing the moment trajectories and then use this to reconstruct the distribution of the agents. In the latter an inverse problem is solved in order to reconstruct a nominal distribution and to recover the macro-scale properties of the group of agents. The proposed method is applicable for several types of multi-agent systems, e.g., leader-follower systems. We derive error bounds for the moment trajectories and describe how to take these error bounds into account for computing the moment dynamics. The convergence of the moment dynamics is also analyzed for cases with monomial moments. To illustrate the theory, two numerical examples are given. In the first we consider a multi-agent system with interactions and compare the proposed methods for several types of moments. In the second example we apply the framework to a leader-follower problem for modeling pedestrian crowd dynamics.

National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-241259 (URN)
Note

QC 20190117

Available from: 2019-01-17 Created: 2019-01-17 Last updated: 2019-01-21Bibliographically approved
4. Spherical cyclic formation control
Open this publication in new window or tab >>Spherical cyclic formation control
Show others...
2016 (English)In: Proceedings of the 35th Chinese Control Conference 2016, IEEE Computer Society, 2016, Vol. 2016, p. 8207-8212, article id 7554663Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, we study the problem of tracking and encircling a moving target by agents in 3D. Specifically, a group of agents are driven to some desired formation on a spherical surface and simultaneously keep the center of this spherical formation coinciding with the target to be tracked. In our control design, the desired formation is not used as a reference signal for tracking. Rather by designing communication topology for the agents we can achieve the desired formation using relative positions only. We can also place the desired cyclic formation on the equator if the north pole is specified.

Place, publisher, year, edition, pages
IEEE Computer Society, 2016
Series
Chinese Control Conference, ISSN 2161-2927
Keywords
encircling control, formation control, Multi-agent systems, nonlinear feedback control
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-194928 (URN)10.1109/ChiCC.2016.7554663 (DOI)000400282204081 ()2-s2.0-84987899171 (Scopus ID)9789881563910 (ISBN)
Conference
35th Chinese Control Conference, CCC 2016, Chengdu, China, 27 July 2016 through 29 July 2016
Note

QC 20161129

Available from: 2016-11-29 Created: 2016-11-01 Last updated: 2019-01-21Bibliographically approved
5. Exponential Stability of Formations for Reduced Attitudes: A Coordinates Free Approach
Open this publication in new window or tab >>Exponential Stability of Formations for Reduced Attitudes: A Coordinates Free Approach
2018 (English)In: Proceedings of Chinese Control Conference, 2018, IEEE Computer Society, 2018, p. 7220-, article id 7215Conference paper, Published paper (Refereed)
Abstract [en]

In this work, a methodology based on differential geometry techniques is proposed to investigate exponential stability of a formation for reduced attitudes. By the proposed method, there is no need in finding any relative coordinates, which is typically needed but shown to be difficult when the formation problem is evolving in a non-Euclidean space. In this paper, the desired formation is treated as an embedding submanifold in (S 2 ) N and by using the rotation symmetries owned by the attitude dynamics its stability is directly examined. Moreover, such a method turns out to be coordinates free, namely, exponential stability of a formation can be completely determined by just investigating anyone equilibrium which can result in the formation under any local chart of (S 2 ) N . This greatly simplifies the stability analysis for the formation problems.

Place, publisher, year, edition, pages
IEEE Computer Society, 2018
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-241260 (URN)10.23919/ChiCC.2018.8482861 (DOI)2-s2.0-85056133917 (Scopus ID)9789881563941 (ISBN)
Conference
37th Chinese Control Conference, CCC 2018; Wuhan; China; 25 July 2018 through 27 July 2018
Note

QC 20190117

Available from: 2019-01-17 Created: 2019-01-17 Last updated: 2019-01-21Bibliographically approved

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