Optimization of the Lucy Interplanetary Trajectory via Two-Point Direct Shooting

Lucy is NASAs next Discovery-class mission and will explore the Trojan asteroids in the Sun-Jupiter L4 and L5 regions. This paper details the design of Lucys interplanetary trajectory using a two-point direct shooting transcription, nonlinear programming, and monotonic basin hopping. These techniques are implemented in the Evolutionary Mission Trajectory Generator (EMTG), a trajectory optimization tool developed at NASA Goddard Space Flight Center. We present applications to the baseline trajectory design, Monte Carlo analysis, and operations

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission

Mars, Phobos, and Deimos Sample Return Enabled by ARRM Alternative Trade Study Spacecraft

The Asteroid Robotic Redirect Mission (ARRM) has been the topic of many mission design studies since 2011. The reference ARRM spacecraft uses a powerful solar electric propulsion (SEP) system and a bag device to capture a small asteroid from an Earth-like orbit and redirect it to a distant retrograde orbit (DRO) around the moon. The ARRM Option B spacecraft uses the same propulsion system and multi-Degree of Freedom (DoF) manipulators device to retrieve a very large sample (thousands of kilograms) from a 100+ meter diameter farther-away Near Earth Asteroid (NEA). This study will demonstrate that the ARRM Option B spacecraft design can also be used to return samples from Mars and its moons - either by acquiring a large rock from the surface of Phobos or Deimos, and/or by rendezvousing with a sample-return spacecraft launched from the surface of Mars

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

Tuning Monotonic Basin Hopping: Improving the Efficiency of Stochastic Search as Applied to Low-Thrust Trajectory Optimization

Trajectory optimization methods using monotonic basin hopping (MBH) have become well developed during the past decade [1, 2, 3, 4, 5, 6]. An essential component of MBH is a controlled random search through the multi-dimensional space of possible solutions. Historically, the randomness has been generated by drawing random variable (RV)s from a uniform probability distribution. Here, we investigate the generating the randomness by drawing the RVs from Cauchy and Pareto distributions, chosen because of their characteristic long tails. We demonstrate that using Cauchy distributions (as first suggested by J. Englander [3, 6]) significantly improves monotonic basin hopping (MBH) performance, and that Pareto distributions provide even greater improvements. Improved performance is defined in terms of efficiency and robustness. Efficiency is finding better solutions in less time. Robustness is efficiency that is undiminished by (a) the boundary conditions and internal constraints of the optimization problem being solved, and (b) by variations in the parameters of the probability distribution. Robustness is important for achieving performance improvements that are not problem specific. In this work we show that the performance improvements are the result of how these long-tailed distributions enable MBH to search the solution space faster and more thoroughly. In developing this explanation, we use the concepts of sub-diffusive, normally-diffusive, and super-diffusive random walks (RWs) originally developed in the field of statistical physics

An Automated Solution of the Low-Thrust Interplanetary Trajectory Problem

Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated, which can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on hypothetical missions to Mercury, the main asteroid belt, and Pluto

System Architecture Optimization Using Hidden Genes Genetic Algorithms with Applications in Space Trajectory Optimization

In this dissertation, the concept of hidden genes genetic algorithms is developed. In system architecture optimization problems, the topology of the solution is unknown and hence, the number of design variables is variable. Hidden genes genetic algorithms are genetic algorithm based methods that are developed to handle such problems by hiding some genes in the chromosomes. The genes in the hidden genes genetic algorithms evolve through selection, mutation, and crossover operations. To determine if a gene is hidden or not, binary tags are assigned to them. The value of the tags determine the status of the genes. Different mechanisms are proposed for the evolution of the tags. Some mechanisms utilize stochastic operations while others are based on deterministic operations. All the proposed mechanisms are tested on mathematical and space trajectory optimization problems. Moreover, Markov chain models of the mechanisms are derived and their convergence is investigated analytically. The results show that the proposed concept are capable to search for the optimal solution by autonomously enabling the algorithms to assign the hidden genes