Intrinsic Formation and Macroscopic Intervention in Multi-agent Systems

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.QC 20190121