This paper presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the Lagrangian form, is the use of the distributed stability and performance analysis tool, called contraction analysis that yields exact nonlinear stability proofs. The proposed decentralized tracking control law synchronizes the attitude of an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. Moreover, a decentralized translational tracking control law based on oscillator phase synchronization is presented, thus enabling coupled translational and rotational maneuvers. Although the translational dynamics can be adequately controlled by linear control laws, the proposed method permits highly nonlinear systems with nonlinearly coupled inertia matrices such as the attitude dynamics of spacecraft whose large and rapid slew maneuvers justify the nonlinear control approach. The proposed method integrates both the trajectory tracking and synchronization problems in a single control framework.

Satellite formation flying is an enabling technology for many space missions, especially for space-based telescopes. Usually there is a tight formation-keeping requirement that may need constant expenditure of fuel or at least fuel is required for formation reconfiguration. Electromagnetic Formation Flying (EMFF) is a novel concept that uses superconducting electromagnetic coils to provide forces and torques between different satellites in a formation which enables the control of all the relative degrees of freedom.With EMFF, the life-span of the mission becomes independent of the fuel available on board. Also the contamination of optics or sensitive formation instruments, due to thruster plumes, is avoided. This comes at the cost of coupled and nonlinear dynamics of the formation and makes the control problem a challenging one. In this thesis, the dynamics for a general N-satellite electromagnetic formation will be derived for both deep space missions and Low Earth Orbit (LEO) formations. Nonlinear control laws using adaptive techniques will be derived for general formations in LEO. Angular momentum management in LEO is a problem for EMFF due to interaction of the magnetic dipoles with the Earth's magnetic field. A solution of this problem for general Electromagnetic (EM) formations will be presented in the form of a dipole polarity switching control law. For EMFF, the formation reconfiguration problem is a nonlinear and constrained optimal time control problem as fuel cost for EMFF is zero. Two 3 different methods of trajectory generation, namely feedback motion planning using the Artificial Potential Function Method (APFM) and optimal trajectory generation using the Legendre Pseudospectral method, will be derived for general EM Formations. The results of these methods are compared for random EM Formations. This comparison shows that the artificial potential function method is a promising technique for solving the real-time motion planning problem of nonlinear and constrained systems, such as EMFF, with low computational cost. Specifically it is the purpose of this thesis to show that a fullyactuated N-satellite EM formation can be stabilized and controlled under fairly general assumptions, therefore showing the viability of this novel approach for satellite formation flying from a dynamics and controls perspective.

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This article presents a simple synchronization framework with application to synchronization control of formation flying spacecraft. A dynamical network of multiple Lagrangian systems is constructed by adding diffusive couplings to otherwise freely flying spacecraft. The proposed tracking control law synchronizes an arbitrary number of spacecraft into a common time-varying trajectory with global exponential convergence. The proposed strategy is much simpler than earlier work in terms of both the computational load and the required signals. Furthermore, in contrast with prior work which used simple double integrator models, the proposed method permits highly nonlinear systems and is further extended to adaptive synchronization, partial-state coupling, and time-delayed communications.

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