Electromagnetic Formation Flight Progress Report: January 2003 Submitted to: Lt. Col. John Comtois Technical Scientific Officer National Reconnaissance Office Contract Number: NRO-000-02-C0387-CLIN0001 MIT WBS Element: 6893087 Submitted by: Prof. David W. Miller Space Systems Laboratory Massachusetts Institute of TechnologyOVERVIEW Description of the Effort The Massachusetts Institute of Technology Space Systems Lab (MIT SSL) and the Lockheed Martin Advanced Technology Center (ATC) are collaborating to explore the potential for an Electro-Magnetic Formation Flight (EMFF) system applicable to Earth-orbiting satellites flying in close formation. Progress Overview At MIT, work on EMFF has been pursued on two fronts: the MIT conceive, design, implement and operate (CDIO) class, and the MIT SSL research group. While all of the progress reports to date have focused on the work completed at MIT, this report summarizes recent progress made at the Lockheed Martin ATC.INTRODUCTION The possibility of controlling the relative positions and orientations of a number of satellites flying in close formation by means of applied magnetic fields has been addressed by the Space Systems Product Development Class, Department of Aeronautics and Astronautics, MIT, under the direction of Professor David Miller. We at the Lockheed Martin Advanced Technology center have been working with the MIT group under contract (ATC Project KQ8) to support this effort. In particular, we were tasked with examining control options for satellite formations, studying the feasibility of magnetic control in general, and producing simulations of particular magnetic control scenarios. This report details our efforts in these areas. The reasons for looking at this type of technology, its possible applications, its advantages and drawbacks, are presented in MIT’s Preliminary Design Review of May 7, 2002, entitled Electro Magnetic Formation Flight of Rotating Clustered Entities. This document also discusses generic requirements for a possible Electro Magnetic Formation Flight (EMFF) implementation and presents a plan for further study. Of more immediate interest to us, for the purposes of this report, are the technical results that are presented. These include trade studies between different dipole configurations, the design of a magnetic control system, analytical results obtained on sample two- and three-satellite constellations, and a simple hardware validation demonstration. All this provided an excellent starting point for our own investigations into the subjects. APPROACH We decided to use our own tools (AUTOLEV and ANIMAKE) to reproduce MIT’s results to date on formation dynamics and then to continue from there. There were two reasons for choosing this approach: the first was frankly didactic; we felt it was the quickest way for us to catch up to MIT’s level of expertise in the field and start making our own contributions. The second was a desire, shared by MIT, to independently validate their results to date and to incorporate them in a dynamic simulation that would visually and compellingly demonstrate the efficacy of the technology. From the beginning we also considered ways to expand on MIT’s work; therefore, in consultation with them, we defined new simulation scenarios and considered ways to generalize their results. These are presented below. Our principal analysis tool is a symbolic dynamics program distributed by OnLine Dynamics, Inc., and developed jointly by David Schaechter and David Levinson of Lockheed Martin, Professor Emeritus Thomas R. Kane of Stanford University, and Paul Mitiguy, currently of MSC.Software, Inc. AUTOLEV permits a user to formulate exact, literal equations of motion for any system of interconnected rigid bodies and particles, and creates ready-to-compile-link-and-run Fortran or C simulation programs incorporating the equations. In the words of Professor Kane, “AUTOLEV makes it possible to teach, learn, and practice mechanics in an exceptionally effective way because, in addition to saving the user a great deal of time and effort, it furnishes excellent means for communicating mechanics ideas with clarity and precision.” 1ANIMAKE, a companion program to AUTOLEV, was developed by Ting Hong Chung and Thomas R. Kane of Kane Dynamics, Inc. It permits one to employ directly the numerical output produced by AUTOLEV-generated Fortran and C motion simulation programs to create animations of the motions under consideration. The problems we studied are as follows: 1. Steady Planar Rotation of Two Solenoids 2. Steady Planar Rotation of Three Solenoids 3. Three-Dimensional Motions of Two Solenoids 4. Spinup of Two Solenoids from Rest 5. Expansion and Contraction of Formations A magnetically-controlled satellite is represented herein by a solenoid of given size and number of turns of wire, through which a variable electric current can be impressed. Control is effected by varying the current through the solenoid wire. In some cases, reaction wheels are mounted on the pitch and yaw axes for attitude control. The quantities in which we are interested, as functions of the currents, mass properties, magnet parameters, and initial conditions, are the intersatellite distances and the attitude of the formation as a whole as well as that of the individual satellites. For two satellites it is sufficient to control the current in only one of them to achieve the desired behavior (as can be inferred from symmetry considerations); for three satellites this cannot always be done, as we will show below. We make the following assumptions in calculating the satellite motions: 1. the satellites are far away from any disturbing body (no gravity, no atmosphere, etc.) 2. all systems are assumed to be “ideal” (ideal current sources, for instance.) 3. system aspects which have no bearing on our analyses are neglected (ohmic heating, if any; solar panel effects, etc.) 4. each satellite is in the far magnetic field of the others, so that a far-field mathematical approximation can be used 5. the satellites are identical as to size and mass properties 6. roundoff error in the simulation algorithm can be used as a surrogate for random system noise. The expression for the far electromagnetic field B of a solenoid at a point P in space can be written B = [µ 4π 3()] (− m / p + 3m ⋅ pp /p5 )0 where p is the position vector from P to the center of the solenoid, p