Optimal range observability maneuvers of a spacecraft formation using angles-only navigation

Abstract

The work presented in this paper leverages existing progress in angles-only navigation to develop optimal range observability maneuvers and trajectory planning methods for spacecraft formations under constrained relative orbital motion. Relative motion is modeled in the Clohessy-Wiltshire frame for proximity operations of multiple chaser spacecraft about a non-cooperative resident-space-object (RSO).The objective of the optimization is to maximize range observability of the RSO from each of the chaser spacecraft in the formation. Each chaser spacecraft transfers between an initial and a final trajectory with respect to the RSO on an intermediate trajectory. Optimal range observability is sought during the transfer. A two-burn impulsive maneuver pair is used to 1) take the chaser spacecraft from the initial to the transfer trajectory and 2) to acquire the final trajectory. By parameterizing the relative states of each chaser using relative orbit elements, the system of equations governing the optimization problem is expressed in terms of a single time varying relative orbital element per spacecraft, per target trajectory. The free parameters are constrained in terms of the fuel used per burn, collision avoidance with the RSO, and collision avoidance with other members of the formation. Lighting (eclipse) and field of view (optical) obstructions by neighboring celestial bodies are considered as well.A representative scenario for a single spacecraft is presented for ease of visualization and to illustrate the cost and constraints in a single 3D map. The method presented hereafter has been extended to a formation of arbitrary cardinality; however, the results shown are those of a three-spacecraft formation. Examples are then given for distinctive formations of three spacecraft. For each example, the optimal burns are determined given the initial and target trajectories of each member in the formation.