Roby S. Wilson

Halo orbit mission correction maneuvers using optimal control

This paper addresses the computation of the required trajectory correction maneuvers for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the trajectory design space. This approach enables automation of the analysis to perform parametric studies that simply were not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the first trajectory correction maneuver affects the correction @DV. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery Mission being developed for NASA by the Jet Propulsion Laboratory.

Improved Corrections Process for Constrained Trajectory Design in the n-Body Problem

The general objective is the development of efficient techniques for preliminary design of trajectory arcs in nonlinear autonomous dynamic systems in which the desired solution is subject to algebraic interior and/or exterior constraints. For application to then-body problem, trajectoriesmust satisfy specific requirements, e.g., periodicity in terms of the states, interior or boundary constraints, and specified coverage. Thus, a strategy is formulated in a sequence of increasingly complex steps: 1) a trajectory isfirstmodeled as a series of arcs (analytical or numerical) and general trajectory characteristics and timing requirements are established; 2) the specific constraints and associated partials are formulated; 3) a corrections process ensures position and velocity continuity while satisfying the constraints; and finally, 4) the solution is transitioned to a full model employing ephemerides. Though the examples pertain to spacecraft mission design, the methodology is generally applicable to autonomous systems subject to algebraic constraints. For spacecraft mission design applications, an immediate advantage of this approach, particularly for the identification of periodic orbits, is that the startup solution need not exhibit any symmetry to achieve the objectives.

Trajectory Design in the Sun-Earth-Moon System Using Lunar Gravity Assists

Theobjectiveofthisworkisthedevelopmentofefe cienttechniquesforthepreliminarydesignoftrajectoriesthat encounterthemoonandmustsatisfyspecie ctrajectoryrequirements,suchasapogeeplacement,launchconstraints, or end-state targeting. These types of trajectories are highly applicable to mission design in the restricted threeand four-body problems. The general solution approach proceeds in three steps. In the initial analysis, conic arcs and/or other types of trajectory segments are connected at patch points to construct a e rst approximation. Next, multiconic methods are used to incorporate any additional force model effects that may have been neglected in the initial analysis. An optimization procedure is then employed to reduce the effective velocity discontinuities while satisfyinganyconstraints.Finally,anumericaldifferentialcorrectionsprocessresultsinafullycontinuousmultiplelunar-swingby trajectory that satise es the constraints and includes appropriate lunar and solar gravitational models.

Automated Design of Propellant-Optimal, Low-Thrust Trajectories for Trojan Asteroid Tours

The sun–Jupiter Trojan asteroid swarms are targets of interest for robotic spacecraft missions, where low-thrust propulsion systems offer a viable approach for realizing tours of these asteroids. This investigation introduces a novel scheme for the automated creation of prospective tours under the natural dynamics of a multibody regime with thrust supplied by a variable-specific-impulse engine. The procedure approximates tours by combining independently generated fuel-optimal rendezvous arcs between asteroid pairs into a series of trajectory legs. Propellant costs as well as departure and arrival times are estimated from the performance of the individual thrust arcs. Tours of interest are readily constructed in higher-fidelity models, and options for the end-to-end trajectories are easily assessed. In this investigation, scenarios where constant and varying-power sources are available to the low-thrust engine are explored. In general, the automation procedure rapidly generates a large number of potential ...

Optimal Control for Halo Orbit Missions

This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combiningdynamical systems theory with optimal control techniques, we produce a portrait of the complex landscape of the trajectory design space. This approach enables parametric studies not available to mission designers a few years ago, such as how the magnitude of the errors and the timingof the first TCM affect the correction ΔV. The impetus for combiningdynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory.

Design of End-to-End Trojan Asteroid Rendezvous Tours Incorporating Scientific Value

The sun–Jupiter Trojan asteroids are celestial bodies of great scientific interest as well as potential natural assets offering mineral resources for long-term human exploration of the Solar System. Previous investigations have addressed the automated design of tours within the asteroid swarm and the transition of prospective tours to higher-fidelity, end-to-end trajectories. The current development incorporates the route-finding ant colony optimization algorithm into the automated tour-generation procedure. Furthermore, the potential scientific merit of the destination asteroids is incorporated such that encounters with higher-value asteroids are preferentially incorporated during sequence creation.