System and Method of Tracking a Spacecraft Trajectory for Orbital Transfer

Patent metadata

Field	Value
Publication number	US-2020055617-A1
Application number	US-201916299300-A
Country	US
Kind code	A1
Filing date	Mar 12, 2019
Priority date	Aug 17, 2018
Publication date	Feb 20, 2020
Grant date	—

Abstract

A system for optimizing a low-thrust trajectory of a spacecraft trajectory for orbital transfer includes an interface to receive data, a memory to store scheduled geostationary transfer orbit (GTO) data and scheduled geostationary Earth orbit (GEO) data and computer-executable programs, and a processor. The processor is configured to provide a two-dimensional (2D) averaged trajectory consisting of a predetermined revolutions by executing the optimal control program using the GTO data and GEO data, arrange N equidistant points on the 2D averaged trajectory to form segments on the 2D averaged trajectory, obtain osculating elements corresponding to the segments by solving optimization problems for the segments, estimate initial guesses of the segments under continuous thrusting conditions in tangential directions at the N equidistant points, solve a minimum energy optimization problem to obtain a minimum energy 2D osculating trajectory by using as initial guess the concatenation of segments, compute a minimum energy three-dimensional (3D) osculating trajectory by linearly decreasing an inclination of the minimum energy 2D osculating trajectory to zero, and generating a minimum fuel 3D osculating trajectory by iteratively solving a cost function while changing a parameter from one to zero.

First claim

1 . A system for optimizing a low-thrust trajectory of a spacecraft trajectory for orbital transfer, comprising:
an interface to receive data via a network; a memory to store scheduled geostationary transfer orbit (GTO) data and scheduled geostationary Earth orbit (GEO) data and computer-executable programs including an optimal control program; a processor, in connection with the memory, configured to:
provide a two-dimensional (2D) averaged trajectory consisting of a predetermined revolutions by executing the optimal control program using the GTO data and GEO data;
arrange N equidistant points on the 2D averaged trajectory to form segments on the 2D averaged trajectory;
obtain osculating elements corresponding to the segments by solving optimization problems for the segments, wherein each of the optimization problems is solved by minimizing a distance between an end-point of a current segment and a next point of a next segment on the 2D averaged trajectory;
estimate initial guesses of the segments under continuous thrusting conditions in tangential directions at the N equidistant points;
use the minimum energy 2D averaged trajectory to solve for a minimum energy 2D osculating trajectory by applying the initial guesses to the segments;
compute a minimum energy three-dimensional (3D) osculating trajectory by starting with a trajectory obtained by linearly decreasing the inclination of the minimum energy 2D osculating trajectory from that GTO to zero; and
generating a minimum fuel 3D osculating trajectory by iteratively solving a cost function while changing a parameter from one to zero.

2 . The system of claim 1 , wherein the N equidistant points are arranged to divide the revolutions by 2π radian.

3 . The system of claim 1 , wherein the parameter is a homotopy parameter α of a function represented by
J=∫ 0 T |u ( t )|(α| u ( t )|+(1−α)) dt

wherein J, T and u(t) are the cost function, total time of mission and control input.

4 . The system of claim 1 , wherein the distance is measured in (a,ex,ey) coordinates.

5 . The system of claim 1 , wherein the data include measured trajectory data of the spacecraft from an online satellite operation control system via the network.

6 . A method for optimizing a low-thrust trajectory of a spacecraft trajectory for orbital transfer, comprising:
receiving data via a network using an interface; providing, using a processor, a two-dimensional (2D) averaged trajectory consisting of a predetermined revolutions by executing the optimal control program using scheduled geostationary transfer orbit (GTO) data and scheduled geostationary Earth orbit GEO data stored in a memory;
arranging N equidistant points on the 2D averaged trajectory to form segments on the 2D averaged trajectory;
obtaining osculating elements corresponding to the segments by solving optimization problems for the segments, wherein each of the optimization problems is solved by minimizing a distance between an end-point of a current segment and a next point of a next segment on the 2D averaged trajectory;
estimating initial guesses of the segments under continuous thrusting conditions in tangential directions at the N equidistant points;
using the minimum energy 2D averaged trajectory to solve for a minimum energy 2D osculating trajectory by applying the initial guesses to the segments;
computing a minimum energy three-dimensional (3D) osculating trajectory by starting with a trajectory obtained by linearly decreasing the inclination of the minimum energy 2D osculating trajectory from that GTO to zero; and
generating a minimum fuel 3D osculating trajectory by iteratively solving a cost function while changing a parameter from one to zero.

7 . The method of claim 6 , wherein the N equidistant points are arranged to divide the revolutions by 2π radian.

8 . The method of claim 6 , wherein the parameter is a homotopy parameter α of a function represented by
J=∫ 0 T |u ( t )|(α| u ( t )|+(1−α)) dt

wherein J, T and u(t) are the cost function, total time of mission and control input.

9 . The method of claim 6 , wherein the distance is measured in (a,ex,ey) coordinates.

10 . The method of claim 6 , wherein the data include measured trajectory data of the spacecraft from an online satellite operation control system via the network.

Assignees

• Mitsubishi Electric Res Laboratories Inc

Inventors

• Grover Piyush
• Kalabic Uros
• Weiss Avishai

Classifications

• G06F17/13 Primary

  Differential equations (using digital differential analysers G06F7/64) · CPC title

• B64G1/44

  using radiation, e.g. deployable solar arrays · CPC title

• B64G1/363

  using sun sensors · CPC title

• B64G1/283

  using reaction wheels · CPC title

• B64G1/007 Primary

  Operations & Transport · mapped topic