Relative Information Based Distributed Control for Intrinsic Formations of Reduced Attitudes

Abstract: 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.