Distributed Attitude Control Of Satellite Formation Flying

In recent years, spacecraft formation flying has been well studied. By havingmultiple simple rigid bodies working together, the formation control gains lots ofadvantages, such as low cost, good performance as well as high stability. For someapplications, numerous rigid bodies should keep their attitudes consistent with eachother in order to accomplish the given task. This coordination control problem ofcomplex system belongs to the advanced research topic in coordination ofmulti-agent system. Besides, cooperative attitude control algorithms in mostliterature require the system to be equipped with tachometers, thus algorithmswithout angular velocity measurement is needy. Therefore, attitude consensuscontrol and velocity-free attitude cooperative control is discussed in this paper.This paper first briefly introduces related fundamental mathmatical knowledgeand attitude kinematic equations. The preliminaries include graph(used to modelinformation exchange among satellites) theory, matrix theory, stability theorems ofsystems, and attitude dynamic equations using description method named ModifiedRodriguez Parameters(MRPs) and Lagrange equation.Secondly, results of consensus in linear multi-agent systems are applied in thispaper to the nonlinear attitude kinematics of rigid bodies. Three different attitudeconsensus algorithms are proposed, the goal of which is to guarantee simply attitudeconsensus between rigid bodies in the formation, attitude synchronization to adesired constant state, attitude agreement with bounded control input, respectively.Then the global stability of the system under each proposed control law isdemonstrated by Lasalle’s invariance principle. Also, through simulation based onMATLAB, the effectiveness of the proposed law is further demonstrated.Lastly, a new velocity free attitude synchronization control law based onsliding mode method is proposed. By using the Lagrange equations to denote theattitude dynamics, a terminal sliding mode observer using only attitudemeasurement is constructed to estimate the velocity state of each rigid body in finitetime. Using the estimated states of velocity, the proposed control law can ensureattitude agreement between rigid bodies in the team and time-varying referenceattitude tracking.