1 / 34

The Flower Constellations An Overview of the Theory, Design Process, and Applications

The Flower Constellations An Overview of the Theory, Design Process, and Applications. Matthew Wilkins Daniele Mortari Christian Bruccoleri Aerospace Engineering Dept. Texas A&M University. Overview. A Brief History Fundamental Concepts of the Theory Design Challenges and Solutions

evan
Download Presentation

The Flower Constellations An Overview of the Theory, Design Process, and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Flower ConstellationsAn Overview of the Theory, Design Process, and Applications Matthew Wilkins Daniele Mortari Christian Bruccoleri Aerospace Engineering Dept. Texas A&M University

  2. Overview • A Brief History • Fundamental Concepts of the Theory • Design Challenges and Solutions • Examples • An Inverse Design Technique • Potential Applications • A Discussion on Perturbations • Conclusions and Future Work The Flower Constellations

  3. It all began with the Clover Constellation! Sistema Quadrifoglio, by Luigi Broglio (1967) John Junkins (right) meets Luigi Broglio in Italy in 2000. The Flower Constellations

  4. Some similar constellation concepts based upon repeating ground tracks • JOCOS • LOOPUS • COBRA The Flower Constellations

  5. JOCOS Constellation (1/2) • Juggler Orbit COnStellation (JOCOS) constellation is so named because it “juggles” 3 + 3 satellites simultaneously with three up and three down at any given time • Goal of JOCOS constellation design is to maximize Earth coverage • 8 hr, circular, inclined, repeating orbits • Inclination of 75 degrees chosen (apogee location irrelevant) • 6 satellites are placed with nodes evenly arrayed and mean anomalies chosen to place 3 satellites in the northern hemisphere and 3 in the southern hemisphere • 1 extra satellite is required to fill in coverage gaps at high latitudes during cross-over The Flower Constellations

  6. JOCOS Constellation (2/2) The Flower Constellations

  7. LOOPUS Constellation (1/2) • LOOPUS (quasi-geostationary Loops in Orbit Occupied Permanently by Unstationary Satellites) • Constructed from circular or HEO orbits • Focuses on solutions where loops are formed in the ground track. • The satellites are arrayed such that two satellites will reach the intersection of the loop (one entering and one leaving) almost simultaneously where a communications hand-over is performed. • For the non-circular orbits, the orbital inclination is chosen to be the critical inclination • The goal of the LOOPUS constellation is to maximize Earth coverage The Flower Constellations

  8. LOOPUS Constellation (2/2) The Flower Constellations

  9. COBRA Constellation (1/2) • The COBRA Teardrop concept involves two MIOs where the argument of perigee is neither 90 degrees nor 270 degrees • By choosing other values for the argument of perigee, a “lean” is created in the ground track • By combining two repeat ground track orbits, one with a right “lean” and the other with a left “lean”, a “teardrop” intersection is created • As in the LOOPUS concept, the intersection points are used to hand over the communications responsibilities between satellites in the constellation The Flower Constellations

  10. COBRA Constellation (2/2) The Flower Constellations

  11. Current Applications • To date, most of the recent applications of multi-stationary inclined orbits (MIOs) have been focused on telecommunications • MIOs are usually comprised of highly elliptic orbits (HEOs) and provide excellent coverage properties • The HEO provide a much larger grazing angle w.r.t. the horizon for higher latitude regions such as countries in northern Europe • The quasi-stationary properties provide an alternative to GEO satellites The Flower Constellations

  12. But Then Came the Flower Constellations… The Flower Constellations

  13. The Flower Constellations Depends on 8 parameters: Np Nd NsFn Fdw hpand i • Compatible Orbits • Phasing rule [M=f()] • Symmetric, Restricted, • and Non-Symmetric • Phasing Schemes The Flower Constellations

  14. FC Theory in Brief (1/4) For a repeating space track relative to an arbitrary rotating reference frame, the period of repetition can be written in two different ways. One is the number of orbit revolutions it takes the satellite to complete the space track. The second is the number of revolutions that the rotating reference frame makes in the same time period. Here, the period of repetition is written w.r.t. an Earth Centered Earth Fixed frame. The Flower Constellations

  15. FC Theory in Brief (2/4) If one includes the J2 perturbation, one can solve for the semi-major axis required to achieve a given Flower Constellation initially defined by Np, Nd, i, w, and hp. The Flower Constellations

  16. FC Theory in Brief (3/4) The phasing is a function of two parameters, the right ascension of the ascending node and the initial mean anomaly. These orbit angles are functions of the number of petals, the number of days to repeat, the semi-major axis, the orbit inclination, the height of perigee, and the argument of perigee in addition to two arbitrary phasing parameters Fn and Fd. These angles must be specified in a very particular way in order for all the satellites in a single Flower Constellation to belong to the same repeating space track. The Flower Constellations

  17. FC Theory in Brief (4/4) • In general, there are three kinds of phasing schemes. • Symmetric about the constellation axis of symmetry • Restricted schemes where the RAAN angle is constrained to lie within a certain range • Non-symmetric schemes where the change in RAAN between any two satellites is arbitrary but the relationship between RAAN and initial mean anomaly is maintained The Flower Constellations

  18. Ok, I understand the relative path… The Flower Constellations

  19. But where does this come from??? The Flower Constellations

  20. A New Phenomena in Phasing Secondary Closed Paths! These secondary closed paths (SCP) occur for specific choices of the Flower Constellation parameters. Even though a large number of satellites is required to completely visualize the SCP, any single satellite will trace out both the relative path AND the SCP. The Flower Constellations

  21. Categories of FCs • Basic Flowers • Planar Patterns (i = 0 deg) • Planes of Satellites • Uniformly Distributed Satellites • Helixes • Figure 8’s • Rings • And more… these categories are so named because they are our interpretation of a mathematical phenomena. As we continue to explore Flower Constellations, more categories of constellation types will be developed. The Flower Constellations

  22. Five Basic Steps to Designing a FC • Specify a rotating reference system for the compatible orbits • Specify the orbit inclination, argument of periapsis, and height of periapsis • Decide upon an overall shape (select Np and Nd) • Decide upon a phasing scheme (select Fn and Fd) • Specify an orientation for the axis of symmetry The Flower Constellations

  23. Design Challenges • An infinity of possibilities! • Optimal selection of FC parameters based upon mission design criteria can be difficult. • Specifying a final shape a priori is desirable but how does one solve for the required FC parameters? The Flower Constellations

  24. Fear not! There are solutions! A Simple Design Example • ESA’s Galileo Constellation • 27 active satellites + 3 spares • 3 orbit planes • Circular orbits, a = 23,616 km, i = 56 deg The Flower Constellations

  25. An Inverse Design Technique Projection of an Arbitrary Shape onto a Flower Constellation Surface The Flower Constellations

  26. Example Flower Constellation Surface The Flower Constellations

  27. Projection from an Arbitrary Point The Flower Constellations

  28. Triangle Formation Example The Flower Constellations

  29. Potential Applications • Earth Observation • Deep Space Observation • Global Navigation Systems • Formation Flying • Many more… The Flower Constellations

  30. Global Navigation Systems The GNFC Two uniformly distributed Flower Constellations provide global coverage with superior geometric and attitude dilution of precision (GDOP and ADOP). -Park, Wilkins, Mortari (AAS 04-297 Maui, HI Feb 2004) The Flower Constellations

  31. Some Comments on Perturbations • Resonance is a major concern • Nd = 1 or when Nd | Np (read Nd divides Np) • Critical inclination required to maintain stationary line of apsides • FCs at arbitrary inclinations “wilt” • Secular drift of node, argument of perigee, and mean anomaly • Node drift causes FCs to “spin” • Mean anomaly drift disrupts phasing The Flower Constellations

  32. Conclusions • A novel theory for constellation design has been developed! • Extensive possible applications. • Readily duplicates currently known constellation concepts. The Flower Constellations

  33. Future Work • Add additional phasing parameters • Investigate genetic algorithms for finding optimal designs • Expand projection technique into 3D constellation design • Realistic mission study including perturbations The Flower Constellations

  34. http://flowerconstellations.tamu.eduThank you! The Flower Constellations

More Related