SSCI is proposing to develop, test and deliver a set of topology control algorithms and software for a formation flying spacecraft that can be used to design and evaluate candidate formation architectures. Properties of these topology control algorithms include: (a) Preserving the connectivity of the underlying state-dependent sensing graph during reconfiguration and re-targeting of the formation; (b) Achieving a balanced interplay between performance and robustness to communication delays; and (c) Using only local information to make local decisions that collectively guarantee global properties such as the network connectivity for formation flying. Phase I effort resulted in the development of a unified framework for the design and analysis of many topology control problems associated with formation flying spacecraft. A novel game-theoretic approach to network topology control was successfully applied to key trajectory design problems such as formation initialization and reconfiguration in the presence of local and global constraints. Phase II effort will deliver a complete set of algorithms and software tools to help the NASA TPF-I team plan and evaluate missions for candidate TPF-I architectures. In order to achieve these objectives, we plan to carry out the following tasks: (i) Further refinements and testing of the game-theoretic approach to state-dependent network synthesis problems and trajectory-following in the absence of centralization, (ii) Development and testing of convex parameterization of path-planning problems for multiple spacecraft formations, (iii) Demonstration of the application of the developed novel methods to TPF-I baseline mission. These algorithms and software will be tested on high fidelity formation flying testbeds at JPL such as FAST or FCT. Professor Mehran Mesabhi of University of Washington will provide technical support under the project.