Collision avoidance for satellites in formation flight

Satellites in a formation might need to maneuver to avoid potential collisions that may occur when foreign objects enter the formation, or when a satellite within the formation drifts into the path of another. In either case we seek to determine the probability of a future collision based on current state knowledge and the uncertain dynamic environment, and further to determine a control strategy to reduce the collision probability to an acceptable level while minimizing the Delta V required for the maneuver. The approach taken in this paper is to propagate the uncertainty covariance using linear theory and determine the probability that the relative displacement between two objects is less than some "collision metric." This probability will be a function of the initial conditions, the uncertainty in the initial state and disturbing acceleration, and the time-to-go before closest approach. The intent of the paper is to examine the evolution of this probability and to determine an effective maneuver algorithm that can minimize the probability of collision while reducing the energy expenditure in the maneuver. Numerical values are used for satellites in a tightly spaced, low-Earth-orbit formation. For satellites in a close formation, it is demonstrated that the uncertain disturbance environment can make efficient A V maneuvers difficult to determine, as collision probabilities can vary rapidly (on the orbital timescale.) Remarks and some sample calculations on the total AV required for an evasion maneuver are presented.