Advances in Interplanetary Trajectory Optimization with Applications to the Lucy Mission Jacob Englander Navigation and Mission Design Branch, GSFC
Global Trajectory Optimization Lab We are a small group within the Navigation and Mission Design Branch Our task is: Design trajectories for interplanetary missions and potential missions Develop new techniques in trajectory design and optimization Develop new software tools Evolutionary Mission Trajectory Generator (EMTG) NASA Exhaustive Lambert Lattice Search (NELLS) Advise graduate students who we some-day hope to recruit Optimize the trajectory for NASA s Lucy mission to the Jupiter Trojans
A diverse, multi-institution team GSFC Navigation and Mission Design Branch Jacob Englander Kyle Hughes JAXA (visiting researcher) Chikako Suzuki Englander and Associates, LLC Arnold Englander Planetary Resources Jeremy Knittel (emeritus) a.i. solutions Matthew Vavrina Donald Ellison Sean Phillips Catholic University of America Bruno Sarli University of Illinois Professor Bruce Conway Purdue University Alec Mudek
Evolutionary Mission Trajectory Generator (EMTG) Rapid preliminary design tool for interplanetary missions Capable of trading and optimizing both mission and systems parameters Mission parameters include destinations, flyby sequence, flight time Systems parameters include propulsion, power, and launch vehicle choices EMTG performs these trades autonomously and in parallel so that we can map a mission and systems trade space for our customers. EMTG can also be run through a meta-script interface called Python EMTG Automated Trade Study Application, or PEATSA, to perform detailed sensitivity analysis on launch window, missed-thrust, etc.
Mission and Systems Design via Hybrid Optimal Control The interplanetary mission design problem has two types of variables: Discrete variables encoding the mission sequence and choice of spacecraft systems (launch vehicle, power, propulsion) Continuous variables defining the trajectory In Hybrid Optimal Control, the problem is divided into two nested loops. The outer-loop solves the discrete problem and identifies candidate missions. The continuous inner-loop then finds the optimal trajectory for each candidate mission. Outer-loop solutions are sorted to find the non-dominated (Paretooptimal) front between multiple objectives. i.e. delivered mass vs flight time vs solar array output 5
The Outer-Loop Mission and Systems Optimization Problem EMTG s outer-loop finds the non-dominated set of missions, those which are not strictly better or worse than other missions in the set based on all of the analyst s chosen objective functions The outer-loop chooses candidate mission sequences and systems designs and then passes them to the inner-loop for trajectory optimization. EMTG uses a version of the Non-Dominated Sorting Genetic Algorithm II (NSGAII) which can evolve to the final non-dominated trade front despite starting from complete randomness. No a priori knowledge of the solution is required. 6
The Inner-Loop Trajectory Optimization Problem We must formulate and solve the following problem: Minimize f x Subject to: x lb x x ub c x 0 Ax 0 where: x lb, x ub are lower and upper bounds on the decision variables c x is a vector of nonlinear constraints Ax is a vector of linear constraints We use the commercial nonlinear programming solver SNOPT by Stanford Business Software, but it requires an initial guess
Two-Point Shooting Transcription for Trajectory Optimization (high-thrust chemical propulsion) Credit: Donald Ellison
Two-Point Shooting Transcription for Trajectory Optimization (low-thrust electric propulsion) Credit: Donald Ellison
Gravity Assist Maneuver We can use a planet s gravity to change the spacecraft s trajectory in interplanetary space. The spacecraft is on a hyperbolic orbit with respect to the planet. Energy is conserved in the reference frame of the planet: v + = v Energy is conserved in the reference frame of the sun because the spacecraft either takes energy from or gives energy to the planet. The turn angle may not be so tight as to require that we pass through the planet: h = μ planet 1 2 v sin δ 1 r planet 2 δ = acos v v v+ + v Credit: Bruce Conway
Two-Point Shooting Transcription for Trajectory Optimization (multi-phase mission) Body 1 (launch) Phase 1 match-point Body 2 (gravity assist) Phase 2 match-point Body 3 (destination)
Stochastic Global Search via Monotonic Basing Hopping Credit: Donald Ellison
Time for an example Lucy: Exploring the Diversity of the Jupiter Trojans
Gas giant migration and the Nice model What happened after the planets formed? Gravitational interactions among the giant planets caused them to migrate outward from the sun to their current orbits and, temporarily, drove Uranus and Neptune into eccentric orbits. As the gas giants moved outward, they scattered the remaining planetesimals in the outer solar system. Most of those planetesimals were ejected from the solar system, but some migrated inward Credit: Hal Levison Hal Levison, Lucy PI and author of the Nice model
Jupiter and its Trojans Credit: Astronomical Institute of CAS/Petr Scheirich
Lucy: A Sun/Jupiter L4-L5 Cycler
Lucy Trajectory (from the side)
Lucy s targets span the diversity of the Trojan Swarms 52246 Donaldjohanson is a main-belt object that serves as an engineering dress rehearsal for Lucy s Trojan encounters. 3548 Eurybates is a large, rare C-type and the parent body of the only known collisional family in either Trojan swarm. 15094 Polymele is a small P-type, possibly a fragment from some long-ago collision. 11351 Leucus is a medium-size D-type with a very slow rotation period almost three weeks! It may have a moon 21900 Orus is a large D-type that is typical of much of the Trojan population. 617 Patroclus-Menoetius is an equal mass binary P-type and is unique among the Trojans but resembles outer solar system objects that we can only see in telescopes! The Jupiter Trojans are the only remnants of the early solar system that we can reach and study up close with current technology.
Lucy s Trajectory as an Optimization Problem We want to maximize the mass available for scientific instruments. This is a balance between the initial velocity imparted by the launch vehicle and the maneuvering done by the spacecraft s thrusters. We also have to make sure that any propellant used by the spacecraft fits in the tank and we have to satisfy the trajectory continuity and flyby feasibility constraints that we discussed several slides ago. The final Lucy trajectory is the globally optimal solution to this optimization problem.
Lucy s Trajectory as an Optimization Problem EGA2 2024 Launch 2021 EGA1 2022 Orus 2028 Leucus 2028 Polymele 2027 Eurybates 2027 Donaldjohanson 2025 EGA3 2030 Patroclus-Menoetius 2033 9 phases 108 decision variables 100 constraints Objective: maximize mass delivered to Patroclus-Menoetius
Some other designs
Double Asteroid Redirect Test (DART) DART is a planetary defense demonstrator led by the Johns Hopkins Applied Physics Laboratory. GSFC, specifically Bruno Sarli, is tasked with evaluating the mission s sensitivity to a temporary loss of thrust anywhere in the mission. The trajectory shown here is the current baseline.
Smallsat designs to Venus and Mars
Hybrid Optimal Control trade space and trajectory for a notional mission to Neptune
A tour of the moons of Jupiter Proof-of-concept of an optimal low-fidelity moon tour. Gas giant moon tours are large and complex problems, to our knowledge there exists no software package that can optimize an entire moon tour simultaneously. This is a low-fidelity tour seeded with an initial guess from the NELLS grid search tool. EMTG reduced the total v by 55%. We hope to evolve towards a high-fidelity moon tour optimization capability. This will position GSFC and its partners to compete in a new business area. This particular tour is just a proof of concept from Donald Ellison s dissertation not anyone s mission!
Transfers between science orbits at a small body (electric propulsion)
Conclusion The Global Trajectory Optimization Lab is responsible for trajectory optimization for existing interplanetary missions and for performing early trajectory and systems trades for mission proposals. In the latter role, we think of ourselves as being responsible for finding new interplanetary work for GSFC and our partners. EMTG is a powerful, in-house tool that we use to do much of our analysis. We currently specialize in missions to small bodies and the inner planets, but we are branching out into gas giant moon tour and atmosphere probe missions. The NELLS tool, and version 9 of EMTG, are being specifically developed to enable these new business areas.