In this seminar I present a method for solving fuel-optimal low-thrust orbit transfers using an indirect optimization approach and the Picard-Chebyshev numerical integrator. The indirect optimization method leads to a two-point boundary value problem with a bang-bang control structure. A hyperbolic tangent smoothing law is used on the thrust magnitude to reduce the sharpness of the control switches in early iterations and promote convergence. Two examples
are presented to demonstrate this method. The first is a transfer between two Earth orbiting satellites, where the Earth’s nonlinear high-fidelity spherical harmonic gravity model is included in the simulation. Including the high-fidelity gravity model is computationally expensive, however, the Picard Chebyshev integrator is well suited to solving such computationally
expensive problems. The fixed-point convergence nature of the algorithm allows local force approximations to be made that significantly accelerate the computation. The second example is
an optimal low-thrust orbit transfer from an Earth orbit to a Lyapunov orbit around the Sun-Earth second Lagrange point (SEL2). An application of this type of transfer would to send a spacecraft
on a refueling/servicing mission to the multi-billion-dollar space telescopes, such as the James Webb Space Telescope, that will operate at SEL2. This problem is posed and solved using circular
restricted three-body dynamics. In this dynamical system, invariant manifolds exist that can be utilized to reduce fuel consumption. I present an example solution that allows the refueling/servicing spacecraft to travel for free along the manifold for a significant fraction of the trip.
