Han Solo's Kessel Run is a shortest path problem. The Voyager 2 grand tour is a traveling salesman problem with gravity assists. In this project, you will discover that the mathematics underlying iconic science fiction is the same mathematics NASA uses to design real spacecraft missions — and you will build the software to solve it.
How do you plan an optimal mission tour through a solar system when every transfer cost depends on when you depart, which gravity assists you exploit, and which observations must be completed before others are permitted? How does the same mathematics that solves the Millennium Falcon's navigation through the Maw also determine whether NASA's Ice Giant flagship mission should visit Uranus's moons in a clockwise or counterclockwise sequence?
This project develops, tests, and extends two open-source mission planning benchmarks built on a common mathematical framework — the augmented Graph of Convex Sets (GCS) — which combines convex optimization, graph theory, and formal logic to simultaneously find the optimal visit order and the optimal continuous trajectory, with certified near-optimality guarantees.
The GCS framework unifies combinatorial planning (which targets to visit, in what order) with continuous trajectory optimization (the exact path between them) into a single convex program. This means the solution is not just good — it comes with a certificate of how close it is to optimal. This is rare in mission planning, and it is one of the reasons this benchmark is publishable research, not just software.
An interstellar trajectory benchmark in which an autonomous probe surveys the habitable zones of real stellar systems drawn from the ESA Gaia catalog, while navigating astronomical obstacles and satisfying rich mission specifications motivated by science fiction.
Data: ESA Gaia DR3 stellar catalog
A companion solar system benchmark in which a spacecraft visits planets, moons, and asteroids using real JPL ephemeris data, satisfying specifications drawn from funded NASA and ESA mission concepts: Europa Clipper, Voyager, BepiColombo, and the Ice Giant flagship.
Data: JPL ephemeris DE440, JPL Horizons
Each science fiction narrative identifies a mission constraint whose formal structure maps precisely onto the temporal logic specification library. The same mathematics then applies directly to real NASA missions.
A strict ordering constraint on which stellar systems must be surveyed before others — a sequence planning problem with precedence logic.
The Millennium Falcon's shortest-path boast through the Maw of black holes. Why it is a shortest-path problem — and why it is not a speed record.
Mission constraints that mirror the film's conditional planet visitation logic — formal temporal specifications on observation order.
Contingent communication relay constraints: certain systems can only be contacted after others have been surveyed and cleared.
Multi-flyby tour of Jupiter's moons with radiation dose constraints — the same planning problem that drove Europa Clipper's design.
Jupiter, Saturn, Uranus, Neptune — the planetary alignment that occurs once every 176 years, optimized as a gravity-assist trajectory.
NASA's highest-priority large mission: a tour of Uranus's moons with science return constraints from the 2023 Planetary Science Decadal Survey.
The GSP and SSP are under active development toward journal publication. Early cohorts run the first systematic experiments. Later cohorts push toward harder open problems.
Audit the codebase, establish team workflows, run existing GSP experiments (star count sweep, habitable zone radius sweep, obstacle density sweep), and produce a results summary. Survey the science fiction narratives and NASA mission analogs. Identify gaps for Semester 2.
Complete the GSP experimental study including specification complexity scaling. Implement the geometric SSP using JPL DE440 data via Skyfield. Run SSP-1 (inner planets survey) and SSP-2 (asteroid belt tour). Develop publication-quality visualizations of both benchmarks.
Implement the astrodynamic SSP with Lambert arc cost precomputation via PyKEP. Run SSP-3 (Jovian system tour) and SSP-4 (Ice Giant flagship). Develop pruning heuristics for larger instances. Explore one team-chosen extension: multi-spacecraft coordination, non-Euclidean GCS, or conformal prediction integration.
Consolidate results for the GSP and SSP journal papers. Develop comprehensive onboarding documentation and a public-facing demo. Present at a departmental event, research showcase, or conference. Identify open problems for the next cycle.
Interstellar probe trajectory through the Gaia stellar catalog, colored by mission specification constraints.
Optimal spacecraft trajectory through the Jovian system, with Lambert arc transfers and flyby constraints.
Associate Professor, Mechanical Engineering. Research in distributed control, trajectory optimization, and autonomous systems.
PhD candidate, Summers Lab. Research focus on trajectory optimization and the Graph of Convex Sets framework.
PhD candidates, Summers Lab. Support across algorithm development, codebase maintenance, and student mentorship.
Undergraduate and graduate student team members will be listed here as the first cohort is formed — Fall 2026.
Plan a mission through the Dark Forest. Route the Millennium Falcon through the Maw. Send a probe to Europa before the radiation kills it. You will build mission planning software for spacecraft and robots, grounded in real mathematics — convex optimization, graph theory, temporal logic — and tested on both science fiction scenarios and real NASA mission concepts.
You will join a living, longitudinal research team spanning all class years, contribute to publishable research, and leave knowing how to solve problems that most engineers never encounter until graduate school.
Students enroll through the ECS RIDE program for course credit. Effort scales with credit hours.
No prior robotics or space experience required. Curiosity about how complex systems are optimized is everything.
The project has meaningful roles at every preparation level:
Any level — visualization, benchmark data preparation, running experiments, documentation.
Intermediate — codebase extensions, new scenario design, specification variations, scaling experiments.
Advanced — algorithm development, heuristic design, gravity-assist convexification, scientific writing and publication.
Launching Fall 2026. Reach out to express interest.
Express Interest