Application and Analysis of Bounded-Impulse Trajectory Models with Analytic Gradients

In the companion paper, analytic methods were presented for computing the Jacobian entries for two-sided direct shooting trajectory models that utilize the bounded-impulse approximation. In this paper we discuss practical implementation considerations. Efficient computation of the mathematical components required to compute the partials is discussed and a guiding numerical example is provided for validation purposes. A solar electric power model suitable for preliminary mission design is presented, including a method for handling thruster cut-off events that result in non-smooth derivatives. The challenges associated with incorporating the SPICE ephemeris system into an optimization framework are discussed and an alternative is presented that results in smooth time partials. Application problems illustrate the benefits of employing analytic Jacobian calculations vs. using the method of finite differences. The importance of accurately modeling hardware and operational constraints at the preliminary design stage, and the benefits of using an analytic Jacobian in a solver that combines the monotonic basin hopping heuristic method with a local gradient search are also explored

Analytic Gradient Computation for Bounded-Impulse Trajectory Models Using Two-Sided Shooting

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. This work outlines analytic methods for computing the problem Jacobian for two different bounded-impulse spacecraft trajectory models solved using two-sided shooting. The specific two-body Keplerian propagation method used by both of these models is described. Methods for incorporating realistic operational constraints and hardware models at the preliminary stage of a trajectory design effort are also demonstrated and the analytic methods derived are tested for accuracy using automatic differentiation. A companion paper will solve several relevant problems that show the utility of employing analytic derivatives, i.e. compared to using derivatives found using finite differences

Neptune Odyssey: A Flagship Concept for the Exploration of the Neptune–Triton System

The Neptune Odyssey mission concept is a Flagship-class orbiter and atmospheric probe to the Neptune-Triton system. This bold mission of exploration would orbit an ice-giant planet to study the planet, its rings, small satellites, space environment, and the planet-sized moon Triton. Triton is a captured dwarf planet from the Kuiper Belt, twin of Pluto, and likely ocean world. Odyssey addresses Neptune system-level science, with equal priorities placed on Neptune, its rings, moons, space environment, and Triton. Between Uranus and Neptune, the latter is unique in providing simultaneous access to both an ice giant and a Kuiper Belt dwarf planet. The spacecraft - in a class equivalent to the NASA/ESA/ASI Cassini spacecraft - would launch by 2031 on a Space Launch System or equivalent launch vehicle and utilize a Jupiter gravity assist for a 12 yr cruise to Neptune and a 4 yr prime orbital mission; alternatively a launch after 2031 would have a 16 yr direct-to-Neptune cruise phase. Our solution provides annual launch opportunities and allows for an easy upgrade to the shorter (12 yr) cruise. Odyssey would orbit Neptune retrograde (prograde with respect to Triton), using the moon's gravity to shape the orbital tour and allow coverage of Triton, Neptune, and the space environment. The atmospheric entry probe would descend in ~37 minutes to the 10 bar pressure level in Neptune's atmosphere just before Odyssey's orbit-insertion engine burn. Odyssey's mission would end by conducting a Cassini-like "Grand Finale,"passing inside the rings and ultimately taking a final great plunge into Neptune's atmosphere

Low-thrust trajectory design and optimization of lunar south pole coverage missions

A framework for designing and optimizing low-thrust trajectories for lunar south pole coverage missions is developed. Such missions may involve three, two, or even one satellite to maintain continuous communications between a lunar ground station and the Earth. Special emphasis is dedicated to single satellite communication links, which involve the design and discovery of novel pole-sitter orbits. Pole-sitters are possible, given the availability of an efficient low-thrust force in the model. Low-thrust acceleration can be delivered in various forms; solar sails and electric propulsion engines are obvious examples. Low-thrust propulsion may also be employed to construct transfer trajectories to the coverage orbits of interest as well as end-of-life transfers. Additionally, a low-thrust thruster allows a spacecraft to shift between lunar coverage orbits. In this scenario, an optimal control-based approach is applicable for rapidly computing trajectories, however, in general, the many complexities involved in generating the trajectories are best solved with a direct transcription approach using collocation and mesh refinement. This general process is robust and allows for the inclusion of an unknown control history, path constraints, and the simultaneous optimization of multiple phases while exploiting matrix sparsity for maximum computational efficiency. Even incorporating higher-fidelity dynamical effects, the pole-sitter solutions can be sustained as a long-duration option, using a solar sail, or as a temporary option in excess of one year on a small 500 kg spacecraft, using a solar electric propulsion engine comparable to existing technology

Double Asteroid Redirection Test Mission: Heliocentric Phase Trajectory Analysis

Double Asteroid Redirection Test will be the first mission to demonstrate and characterize the concept of a kinetic impactor for planetary defense, by impacting the smaller member of a binary asteroid system Didymos. The results of this mission will have implications for planetary defense, near-Earth object science, and resource utilization. This research focuses on the heliocentric transfer phase of the mission. The heliocentric trajectory is evaluated using various objective functions, including a search for the latest possible Earth escape date, the shortest time of flight, and the maximum impact energy. Also included in the search is the potential to use Earth gravitational assists, which proves not to offer any useful advantages. A new way to assess the trajectorys margin for missed thrust is used, which quantifies the ability of the spacecraft to recover its mission following unplanned nonthrusting events, such as safe mode. The baseline trajectory is shown to be capable of recovering from missed-thrust events lasting 14 days using only 1% of its propellant as margin. Finally, contingency trajectories that attempt to impact Didymos at a subsequent perihelion are considered