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  • 1.
    Song, Wenjun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Markdahl, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Zhang, Silun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hong, Yiguang
    Intrinsic reduced attitude formation with ring inter-agent graph2017In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 85, p. 193-201Article in journal (Refereed)
    Abstract [en]

    This paper investigates the reduced attitude formation control problem for a group of rigid-body agents using feedback based on relative attitude information. Under both undirected and directed cycle graph topologies, it is shown that reversing the sign of a classic consensus protocol yields asymptotical convergence to formations whose shape depends on the parity of the group size. Specifically, in the case of even parity the reduced attitudes converge asymptotically to a pair of antipodal points and distribute equidistantly on a great circle in the case of odd parity. Moreover, when the inter-agent graph is an undirected ring, the desired formation is shown to be achieved from almost all initial states.

  • 2.
    Wei, Jieqiang
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zhang, Silun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Adaldo, Antonio
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Finite-time attitude synchronization with a discontinuous protocol2017In: 13th IEEE International Conference on Control and Automation, ICCA 2017, IEEE Computer Society, 2017, p. 192-197, article id 8003058Conference paper (Refereed)
    Abstract [en]

    A finite-time attitude synchronization problem is considered in this paper where the rotation of each rigid body is expressed using the axis-angle representation. One simple discontinuous and distributed controller using the vectorized signum function is proposed. This controller only involves the sign of the state differences of adjacent neighbors. In order to avoid the singularity introduced by the axis-angular representation, an extra constraint is added to the initial condition. It is proved that for some initial conditions, the control law achieves finite-time attitude synchronization. One simulated example is provided to verify the usage of the control protocol designed in this paper.

  • 3.
    Wei, Jieqiang
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Zhang, Silun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Adaldo, Antonio
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Johan, Thunberg
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Johansson, Karl H.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Finite-time attitude synchronization with distributed discontinuous protocols2018In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 63, no 10, p. 3608-3615Article in journal (Refereed)
    Abstract [en]

    The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and non-smooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper.

  • 4.
    Zhang, Silun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Intrinsic Formation and Macroscopic Intervention in Multi-agent Systems2019Doctoral 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.

  • 5.
    Zhang, Silun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Relative Information Based Distributed Control for Intrinsic Formations of Reduced Attitudes2017Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This dissertation concerns the formation problems for multiple reduced attitudes, which are extensively utilized in many pointing applications and under-actuated scenarios for attitude maneuvers. In contrast to most existing methodologies on formation control, the proposed method does not need to contain any formation errors in the protocol. Instead, the constructed formation is attributed to geometric properties of the configuration space and the designed connection topology. We refer to this type of formation control as intrinsic formation control. Besides, the control protocols proposed in this work are designed directly in space S2, avoiding to use any attitude parameterisations. At last but not least, along the studies, some elementary tools for reduced attitudes control are developed.In paper A, a continuous control law is provided for a reduced attitude systems, by which a regular tetrahedron formation can achieve asymptotic stability under a quite large family of gain functions in the control. Then, with a further restriction on the control gain, almost global stability of the tetrahedron formation is also obtained. In this work, we introduce a novel coordinates transformation that represents the relative reduced attitudes be-tween the agents. The proposed method is an intrinsic formation control that does not need to involve any information of the desired formation before-hand. Another virtue of the method proposed is that only relative attitude measurement is required.Paper B further concerns the formation control of all regular polyhedral configurations (also called Platonic solids) for reduced attitudes. According to the symmetries possessed by regular polyhedra, a unified framework is proposed for their formations. Via using the coordinates transformation previously proposed, it is shown that the stability of the desired formations can be provided by stabilizing a constrained nonlinear system. Then, a methodology to investigate the stability of this type of constrained systems is also presented. Paper C considers the problem of tracking and encircling a moving target by agents in 3-dimensional space. By this work, we show that similar design techniques proposed for reduced attitudes formations can also be applied to the formation control for point mass systems. Therein, 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. By properly designing communication topology, the agents constitute a cyclic formation along the equator of an encircling sphere.

  • 6.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Harbin Inst Technol, Control & Simulat Ctr, Harbin 150001, Heilongjiang, Peoples R China.
    He, Fenghua
    Hong, Yiguang
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Intrinsic Formation Control of Regular Polyhedra for Reduced Attitudes2017In: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, IEEE , 2017, p. 1002-1007Conference paper (Refereed)
    Abstract [en]

    This paper addresses formation control of reduced attitudes in which a continuous protocol is proposed for achieving and stabilizing all regular polyhedra (also known as Platonic solids) under a unified framework. The protocol contains only relative reduced attitude measurements and does not depend on any particular parametrization as is usually used in the literature. A key feature of the control proposed is that it is intrinsic in the sense that it does not need to incorporate any information of the desired formation. Instead, the achieved formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Using a novel coordinates transformation, asymptotic stability of the desired formations is proven by studying stability of a constrained nonlinear system. In addition, a methodology to investigate stability of such constrained systems is also presented.

  • 7.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    He, Fenghua
    Control and Simulation Center, Harbin Institute of Technology, Harbin, 150001, P. R. China.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Exponential Stability of Formations for Reduced Attitudes: A Coordinates Free Approach2018In: Proceedings of Chinese Control Conference, 2018, IEEE Computer Society, 2018, p. 7220-, article id 7215Conference 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 any one 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.

  • 8.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A moment-based approach to modeling collective behaviors2018In: 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 1681-1687, article id 8619389Conference paper (Refereed)
    Abstract [en]

    In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the occupation measure of the group of agents by their moments and show how the dynamics of the moments can be modeled. Then approximate trajectories of the moments can be computed and an inverse problem is solved to recover macro-scale properties of the group of agents. To illustrate the theory, a numerical example with interactions between the agents is given.

  • 9.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ringh, Axel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Modeling collective behaviors: A moment-based approachManuscript (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.

  • 10.
    Zhang, Silun
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. Harbin Institute of Technology, China.
    Song, Wenjun
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    He, Fenghua
    Control and Simulation Center, Harbin Institute of Technology, 150001 Harbin, China.
    Hong, Yiguang
    Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Intrinsic tetrahedron formation of reduced attitude2018In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 87, p. 375-382Article in journal (Refereed)
    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.

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