We are interested in making space assets sustainable by conducting research to support and enable routine on-orbit refueling and servicing missions. One aspect of our research involves trajectory optimization, that is designing optimal low-thrust trajectories that allow a servicing/refueling vehicle to reach its target with minimum propellent usage. Another aspect involves estimation and controller design, in particular approaching the target without contaminating delicate onboard sensors. Yet another aspect involves trajectory propagation using high-fidelity force models. The tools and techniques we are developing are applicable to a multitude of servicing and refueling scenarios, from Earth orbiting vehicles, to cis-Lunar space, to space telescope refueling at Sun-Earth Lagrange point L2, to interplanetary missions.

Trajectory Optimization

Our work involves low-thrust trajectory optimization to support interplanetary space mission design, as well as missions in the vicinity of a central body that requires a high-fidelity spherical harmonic gravity model for accurate orbit propagation (e.g. Earth, Moon, and other planets). We make use of an indirect approach, that seeks to satisfy Pontryagin's maximum principle by applying necessary conditions for optimality. Indirect methods result in a two-point boundary problem that must be solved for the initial costates. These are typically sensitive to an initial guess, however, with appropriate smoothing and continuation of the thruster on/off switches and eclipse entry/exit conditions, improved convergence is achievable. We make use of multiple-shooting methods where appropriate and apply heuristic optimization to find globally optimal solutions. Current applications of our work include fuel-optimal low-thrust missions to support space telescope refueling at Sun-Earth L2, as well as low-thrust transfers in cislunar space.

Figure 1: Low-thrust transfer from GTO to NRHO in the Earth centered inertial frame (left) and Earth centered rotating frame (right).

Animation 1: Low thrust transfer from GEO to Sun-Earth L2.

Animation 2: Low thrust transfer from GTO to GEO.

Animation 3: Low thrust Earth-Mars cycler.

High-Fidelity Models and Picard-Chebyshev Propagation

Accurate mission design and planning requires the use of high-fidelity models. High fidelity gravity models such as EGM2008 (others PDS Geosciences,) can add significant computational burden to simulations. Orbit propagation techniques that can incorporate such information in an efficient manner are essential tools to reduce computational cost. A continuing area of research in our group involves the Adaptive-Picard-Chebyshev (APC) propagator, along with a variable fidelity force model and radial gravitational adaptation, to accelerate computation without loss of accuracy. For Earth, Moon and Mars orbiting mission designs, our models typically include a high degree and order spherical harmonic gravity model, solar radiation pressure, third body effects using the JPL planetary ephemeris, eclipse models for missions using solar electric propulsion, and atmospheric drag models where applicable.

Figure 2: Accuracy and efficiency comparison of three numerical integrators for propagating a LEO and Molniya orbit considering a high-fidelity spherical harmonic gravity force model.

Spacecraft Estimation and Control

On-orbit servicing or refueling events require high-precision proximity operations. Our research involves relative estimation of the target with respect to the approaching service vehicle, as well as simulating optimal approach paths that prevent thruster plume contamination of delicate onboard sensors (e.g. cameras, telescope mirrors).

Figure 3: Schematic showing the cargo and client (telescope) vehicles along with three servicing agents each transporting modular components to and from the client.