Recursive Polynomial Method for Fast Collision Avoidance Maneuver Design

TL;DR

This paper introduces a polynomial-based algorithm for rapid collision avoidance maneuver design that efficiently handles complex dynamics and safety metrics, providing accurate solutions in under a second.

Contribution

It presents a novel polynomial approximation approach for collision probability, enabling fast and accurate maneuver planning across various dynamical models.

Findings

Computes collision avoidance maneuvers in under 1 second.

Handles complex nonlinear safety metrics effectively.

Applicable to diverse orbital dynamics including Keplerian and three-body problems.

Abstract

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.