Exploring the Heliogyro’s Orbital Control Capabilities for Solar Sail Halo Orbits

Abstract

Solar sailing is an elegant form of space propulsion that reflects solar photons off a large membrane to produce thrust. Different sail configurations exist, including a traditional fixed polygonal flat (FPF) sail and a heliogyro, which divides the membrane into a number of long, slender blades. The magnitude and direction of the resulting thrust depends on the sail's attitude with respect to the Sun (cone angle). At each cone angle, an FPF sail can only generate force constrained to a particular magnitude and direction, while the heliogyro can arbitrarily reduce the thrust magnitude through the additional control of pitching the blades. This gives the heliogyro more force control authority, which is exploited in this paper for orbital control of solar sail, Sun-Earth, sub-L1 halo orbits through a linear-quadratic regulator feedback controller. Two test cases are considered, quantifying either the maximum error in the injection state or the maximum delay in solar sail deployment due to

Solving the heliogyro’s inverse problem

“…Note that the moment generated by the collective profile is not affected by a non-zero value for the angle  and will always produce a moment along the 1 d -and 2 daxes only. As concluded in previous works [6,9], the results in Figure 3 and Figure 4 show that a heliogyro can fill up a force bubble volume around the Sun-sail line through appropriate choices for the pitch profile, while a traditional flat sail can only generate forces that are constrained to the surface of that bubble. The authors previously demonstrated this unique capability of the heliogyro to provide superior orbital control capabilities compared to a flat sail configuration when correcting for injection errors or solar sail deployment delays upon injection into solar sail Sun-Earth sub-L1 halo orbits [6,9].…”

“…This paper shows that, in many cases, the initial guess can be quite poor (i.e., far from the solution), on the order of tens of degrees, providing a robust approach for solving the inverse problem. Finally, after ` 3 applying the developed method to randomly selected forces and/or moments, the approach is applied to track a reference trajectory that has previously been developed to correct for injection errors into a solar sail Sun-Earth sub-L1 halo orbit [6,9].…”

“…Under these assumptions, the incoming solar photons are specularly reflected and the solar radiation pressure force and acceleration act perpendicular to the heliogyro blade. To define the forces and moments generated by the heliogyro, a set of reference frames is involved (see Figure 1), with their transformations detailed in the Appendix of References [6,9]. This paper expresses the SRP force produced by the heliogyro in the Sun coordinate system  , , S s l p and the SRP moment in the despun coordinate…”

“…Reference [4] and many following works (e.g. References [5,[7][8][9]) define three different pitch profiles, which can be used independently or in combination: the collective profile ('Co'), ½-period cyclic profile (half-p, 'HP'), and the 1period cyclic profile (cyclic, 'Cy'). The collective profile pitches the blades at a constant value, equal for all blades, while the heliogyro rotates, whereas the half-p and cyclic profiles pitch the blades sinusoidally with revolution.…”

Loosely-displaced geostationary orbits with hybrid sail propulsion

“…By partially offsetting or complementing the effects of gravity, NKOs show evident advantages in that new orbits can be designed. The design [4][5][6][7][8][9][10], optimization [4][5][6][7][8][9][10], stability and control [11][12][13] of NKOs have been researched extensively; proposed applications range from pole-sitters [3,4], lunar far-side communication and lunar south-pole coverage [5][6][7], Mars, Mercury and Venus remote sensing [7,8], further Mars exploration [9], to near-Earth asteroids rendezvous [10]. The concept of using an NKO to displace the GEO has already been proposed [1] and the existence of light-levitated GEOs for solar sailing has already been shown by Baig and McInnes [14].…”