  A simple and reliable algorithm for collision avoidance maneuvers (CAMs),
capable of computing impulsive, multi-impulsive, and low-thrust maneuvers, is
proposed. The probability of collision (PoC) is approximated by a polynomial of
arbitrary order as a function of the control, transforming the CAM designinto a
polynomial program. The solution procedure is initiated by computing the CAM
via a first-order greedy optimization approach, wherein the control action is
applied in the direction of the gradient of PoC to maximize its change.
Successively, the polynomial is truncated at higher orders, and the solution of
the previous order is used to linearize the constraint. This enables achieving
accurate solutions even for highly nonlinear safety metrics and dynamics. Since
the optimization process comprises only polynomial evaluations, the method is
computationally efficient, with run times typically below 1 s. Moreover, no
restrictions on the considered dynamics are necessary; therefore, results are
shown for Keplerian, J2, and circular restricted three-body problem dynamics.
