A Comparison of Linear Quadratic and Nonlinear Model Predictive Control applied to Station Keeping of Satellites in Areostationary Mars Orbits

There is an ever-growing need for sustainable and reliable telecommunications between Earth and Mars, especially as future crewed missions come into view. Areostationary Mars Orbits (AMOs) are geostationary-equivalent orbits that would allow for reliable communication back to Earth from the surface of the red planet via satellites consistently overhead. Due to the significant gravitational perturbations around Mars, an efficient station keeping policy is needed to minimize fuel consumption, lengthen mission time, and ensure that the satellite remains in its desired position overhead. A high-fidelity orbital model is developed that includes disturbances from high-order spherical harmonic gravitational terms and the gravitational perturbations due to celestial bodies such as the Sun and the Martian moons Phobos and Deimos. This paper formulates two model predictive control (MPC) station keeping policies-linear-quadratic MPC and nonlinear MPC-and discusses the benefits and limitations of each. These proposed methods of MPC satisfy the station keeping requirements while setting new benchmarks for annual Δv required to maintain the satellite within a prescribed station keeping window. Numerical simulations demonstrate that the nonlinear MPC policy provides a significant reduction in the fuel required for AMO station keeping at specific longitudes compared to a linear-quadratic MPC implementation.