Correctness Analysis and Optimality Bounds of Multi-spacecraft Formation Initialization Algorithms

This paper considers formation initialization for a class of autonomous spacecraft operating in deep space with arbitrary initial positions and velocities. Formation initialization is the task of getting a group of autonomous agents to obtain the relative and/or global dynamic state information necessary to begin formation control. We associate a "worst-case total angle traversed" optimality notion with the execution of any formation initialization algorithm, and present performance bounds valid for any correct algorithm. We design the spatial spacecraft localization algorithm and the wait and check algorithm, analyze their correctness properties and characterize their performance in terms of worst-case optimality and execution time