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

Global Search and Trajectory Optimization in Interplanetary and Cislunar Space

This presentation describes active research and development in interplanetary and cislunar trajectory optimization and global search at NASA Goddard Space Flight Center. Two point and parallel direct shooting transcriptions are described, along with monotonic basin hopping and batch seed sharing. Applications to the Lucy mission are presented, as well as a variety of other interplanetary and cislunar examples

Walking the Filament of Feasibility: Global Optimization of Highly-Constrained, Multi-Modal Interplanetary Trajectories Using a Novel Stochastic Search Technique

Interplanetary trajectory optimization problems are highly complex and are characterized by a large number of decision variables and equality and inequality constraints as well as many locally optimal solutions. Stochastic global search techniques, coupled with a large-scale NLP solver, have been shown to solve such problems but are inadequately robust when the problem constraints become very complex. In this work, we present a novel search algorithm that takes advantage of the fact that equality constraints effectively collapse the solution space to lower dimensionality. This new approach walks the filament'' of feasibility to efficiently find the global optimal solution

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

Multi-Objective Hybrid Optimal Control for Multiple-Flyby Interplanetary Mission Design Using Chemical Propulsion

Preliminary design of high-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys and the bodies at which those flybys are performed. For some missions, such as surveys of small bodies, the mission designer also contributes to target selection. In addition, real-valued decision variables, such as launch epoch, flight times, maneuver and flyby epochs, and flyby altitudes must be chosen. There are often many thousands of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This 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 impulsive mission design problem as a multiobjective hybrid optimal control problem. The method is demonstrated on several real-world problems

NEXT Performance Curve Analysis and Validation

Performance curves of the NEXT thruster are highly important in determining the thruster's ability in performing towards mission-specific goals. New performance curves are proposed and examined here. The Evolutionary Mission Trajectory Generator (EMTG) is used to verify variations in mission solutions based on both available thruster curves and the new curves generated. Furthermore, variations in BOL and EOL curves are also examined. Mission design results shown here validate the use of EMTG and the new performance curves

High-Fidelity Multiple-Flyby Trajectory Optimization Using Multiple-Shooting

Rendering a complex spacecraft trajectory in high fidelity can be an expensive endeavor, both computationally and from a human time/cost standpoint. However, in many cases, a low-fidelity trajectory that reasonably approximates a high-fidelity counterpart is much easier to obtain. Thus, it is important to have an efficient process for converting a trajectory from lower-fidelity model to high fidelity. We present a method for converting low-fidelity trajectories into high fidelity that relies on multiple shooting, nonlinear programming, and numerical integration. The procedure converts any zero-radius sphere-of-influence gravity-assist events to fully integrated flyby events. Several numerical examples are presented that showcase the flexibility of the high-fidelity rendering process across multiple mission types and flight regimes

From Basking Ridge to the Jupiter Trojans

This presentation describes the activities of the Global Trajectory Optimization Lab, a subdivision of the Navigation and Mission Design Branch at NASA GSFC. The students will learn the basics of interplanetary trajectory optimization and then, as an example, the Lucy mission to the Jupiter Trojans will be described from both a science and engineering perspective

Rapid Preliminary Design of Interplanetary Trajectories Using the Evolutionary Mission Trajectory Generator

This set of tutorial slides is an introduction to the Evolutionary Mission Trajectory Generator (EMTG), NASA Goddard Space Flight Center's autonomous tool for preliminary design of interplanetary missions. This slide set covers the basics of creating and post-processing simple interplanetary missions in EMTG using both high-thrust chemical and low-thrust electric propulsion along with a variety of operational constraints

Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning

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. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be 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 multi-objective hybrid optimal control problem. The methods is demonstrated on hypothetical mission to the main asteroid belt and to Deimos