The guidance of a solar sail spacecraft along a minimum-time path from an Earth orbit to a region near the Sun-Earth L_2 libration point is investigated. Possible missions to this point include a spacecraft "listening" for possible extra-terrestrial electromagnetic signals and a science payload to study the geomagnetic tail. A key advantage of the solar sail is that it requires no fuel. The control variables are the sail angles relative to the Sun-Earth line. The thrust is very small, on the order of 1 mm/s^2, and its magnitude and direction are highly coupled. Despite this limited controllability, the "free" thrust can be used for a wide variety of terminal conditions including halo orbits. If the Moon's mass is lumped with the Earth, there are quasi-equilibrium points near L_2. However, they are unstable so that some form of station keeping is required, and the sail can provide this without any fuel usage. In the two-dimensional case, regulating about a nominal orbit is shown to require less control and result in smaller amplitude error response than regulating about a quasi-equilibrium point. In the three-dimensional halo orbit case, station keeping using periodically varying gains is demonstrated. To compute the minimum-time path, the trajectory is divided into two segments: the spiral segment and the transition segment. The spiral segment is computed using a control law that maximizes the rate of energy increase at each time. The transition segment is computed as the solution of the time-optimal control problem from the endpoint of the spiral to the terminal point. It is shown that the path resulting from this approximate strategy is very close to the exact optimal path. For the guidance problem, the approximate strategy in the spiral segment already gives a nonlinear full-state feedback law. However, for large perturbations, follower guidance using an auxiliary propulsion is used for part of the spiral. In the transition segment, neighboring extremal feedback guidance using the solar sail, with feedforward control only near the terminal point, is used to correct perturbations in the initial conditions.
- Pub Date:
- Engineering: Aerospace, Physics: Astronomy and Astrophysics