Satellite Formation Mission Optimization with a Multi-Impulse Design

Abstract

Satellite formation flight has emerged as a method to increase science return and enable missions that had been impossible with a single spacecraft. Formations often must maintain a precise geometry, which complicates mission design, given natural orbit dynamics. This paper presents a multi-impulse formation design strategy that is a compromise between active control and drift solutions. This design formulation is applied to optimize the magnetospheric multiscale tetrahedron mission using two optimization algorithms, a hierarchical strategy, and a particle swarm approach. Results are presented for a variety of multi-impulse problem specifications, including formation attitude, demonstrating that a multi-impulse solution is a viable strategy that can dramatically improve formation accuracy and longevity at minimal fuel cost. The impact of perturbing forces on optimal designs and their costs is also characterized. Nomenclature a = semimajor axis of the T frame, km c = constant coefficient to determine weight of cognitive c 1 and social c 2 influence D = amount of delay after firing thrusters before data can be collected, s e = eccentricity of the T frame g best = vector location and cost of best candidate solution so far investigated by any particle i = inclination of the T frame, rad J = value of the cost function L = tetrahedron vertices vector (L 1 , L 2 , L 3 , and L 4 ) n = number of design variables, number of orbits p best;i = vector location and cost of best candidate solution investigated by a specific particle P i = position of impulsive thruster firing (i 1, 2) P A 2;j = actual position of satellite j when the virtual satellite is at location P 2 (j 1; . . . ; 4), km P D 2;j = desired position of satellite j when the virtual satellite is at location P 2 (j 1; . . . ; 4), km P 2;j = correct position of satellite j when the virtual satellite is at location P 2 (j 1; . . . ; 4), km Q dt = integrated quality factor, s Q G = Glassmeier quality factor Q R = Robert-Roux tetrahedron quality factor (1 regular tetrahedron) r i = random number to vary search (i 1, 2) R ij = Euler rotation angles (i x, y, z and j 1, 2), rad T obs = observation time, s v = velocity of a particle for the particle swarm optimization algorithm w = weights applied to the terms of the cost function x = position of a particle for the particle swarm optimization algorithm P 2j = difference between P2; j D , and P A 2;j , km r = two-norm magnitude of x, y, and z, km t = time step, s V = velocity change used as a measure of fuel used, km/s V x = velocity change along the inertial x axis, km/s V y = velocity change along the inertial y axis, km/s V z = velocity change along the inertial z axis, km/s x = position error along the inertial x axis, km y = position error along the inertial y axis, km z = position error along the inertial z axis, km = angle between burn application sites, rad c = angle from perigee to the center of , rad ! = inertial weight factor to determine the influence of the current state on the next statẽ ! true = true longit...

Satellite constellation design for forest fire monitoring via a stochastic programing approach

“…Researchers have examined the general problem of task scheduling for satellites after a natural disaster using heuristics (Wang, Dai, & Vasile, ) as well as robust methods (Zhai, Niu, Tang, Wu, & Shen, ). There have been works that investigated the tradeoff between observation time and fuel usage (Zhu, Li, & Baoyin, ) after a disaster and as part of mission design (Hoskins & Atkins, ), but these works assumed prior knowledge about the state of the system that would not be known before a disaster occurs.…”

“…Other research has also investigated the optimization of a constellation through reconfigurable maneuvers (Appel, Guelman, & Mishne, ) with other work focusing on the selection of maneuvers based on technological constraints (Co, Zagaris, & Black, ). Another study did not consider the groundtrack of the satellite constellation, but considered the relative spacing between satellites to maximize the collection of scientific data (Hoskins & Atkins, ). In addition, researchers have investigated the concept of maneuvering satellites in response to a natural disaster such as an earthquake (Kim, Bang, & Hung, ).…”