Relative Information Based Distributed Control for Intrinsic Formations of Reduced Attitudes

Abstract: AbstractThis dissertation concerns the formation problems for multiple reduced at-titudes, which are extensively utilized in many pointing applications andunder-actuated scenarios for attitude maneuvers. In contrast to most exist-ing methodologies on formation control, the proposed method does not needto contain any formation errors in the protocol. Instead, the constructed for-mation 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 spaceS2, avoiding to use any attitude parame-terisations. At last but not least, along the studies, some elementary tools forreduced attitudes control are developed.In paper A, a continuous control law is provided for a reduced attitudesystems, by which a regular tetrahedron formation can achieve asymptoticstability under a quite large family of gain functions in the control. Then,with a further restriction on the control gain, almost global stability of thetetrahedron formation is also obtained. In this work, we introduce a novelcoordinates transformation that represents the relative reduced attitudes be-tween the agents. The proposed method is an intrinsic formation control thatdoes not need to involve any information of the desired formation before-hand. Another virtue of the method proposed is that only relative attitudemeasurement is required.Paper B further concerns the formation control of all regular polyhedralconfigurations (also called Platonic solids) for reduced attitudes. Accordingto the symmetries possessed by regular polyhedra, a unified framework isproposed for their formations. Via using the coordinates transformation pre-viously proposed, it is shown that the 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.Paper C considers the problem of tracking and encircling a moving targetby agents in 3-dimensional space. By this work, we show that similar designtechniques proposed for reduced attitudes formations can also be applied tothe formation control for point mass systems. Therein, a group of agentsare driven to some desired formation on a spherical surface and simultane-ously keep the center of this spherical formation coinciding with the targetto be tracked. By properly designing communication topology, the agentsconstitute a cyclic formation along the equator of an encircling sphere.