A direct solution for fuel-optimal reactive collision avoidance of collaborating spacecraft

We develop a reactive collision avoidance (RCA) algorithm for multiple spacecraft collaborating in deep space. The RCA algorithm calculates a fuel-optimal trajectory for a host spacecraft to avoid multiple colliding spacecraft subject to acceleration limits. Additionally, collisions with other spacecraft are not induced. A direct optimization method is used to obtain an algorithm implementable in real-time. The RCA algorithm focuses on planar spacecraft formations such as the Terrestrial Planet Finder Interferometer (TPF-I) and Stellar Imager. The algorithm is compared to a numerical nonlinear programming approach and applied to five-spacecraft TPF-I and nine-spacecraft Stellar Imager-based scenarios