Haskell Spaceflight Workshop
In celebration of the 50th Anniversary year of the Apollo 11 moon landing, we present a spaceflight-themed exploration of numerical methods in Haskell!
This workshop focuses on both the joys and pain-points of intentionally using Haskell's abstraction capabilities for numerical work. We consider what approaches are available to make the time-domain simulation of dynamical systems safer. To do this, we solve practical problems by combining
linear, and several other libraries. The results are not always ergonomic (warning: may contain some horrible type errors), but we feel they help to demonstrate what is currently possible and motivate further development. Unlike many more theoretical presentations of this topic, our focus in this workshop is very much on solving real problems, selected from the published spaceflight literature.
Participants will use abstractions from the
vector-spaces library, applied to numerical integration of ordinary differential equations (ODEs) and simple optimization algorithms. They will see how algorithms written using these abstractions are more generic, even allowing types with statically-checked units to be used with them.
On the spaceflight side, participants will implement some basic spacecraft manoeuvres, and we include some pre-baked simulations that interact with participants' code. Among the scenarios examined is a simulation of the lunar ascent phase of the Apollo missions, including a faithful transcription into Haskell of the actual guidance algorithm used during the lunar ascent (our Haskell version has statically-checked units!).
We encourage all forms of participation; from people who want to follow the prescribed set of problems, to those who may want to re-implement our examples in other languages, or just deep-dive into the spaceflight theory. All the problems have fallback solutions that can be examined or called directly.
Outline/Structure of the Workshop
Participants will be presented with a series of problems in a Haskell project.
The more complicated scenarios covered in the workshop are "pre-baked", with most of the setup provided to call participants' implementations of various things as appropriate. They are based either on broad descriptions in the published academic spaceflight literature or on specific research papers. Miscellaneous functionality such as plotting results is generally already set up.
Chronological list of topics / scenarios (this is an outline, NOT the workshop instructions):
- Integration of ODEs. Solving the initial value problem using Euler's method and RK4, implemented with both concrete types and affine spaces. Introduction to derivatives as linear maps, with the motivation of enabling type-safe units.
- Use the participant's RK4 implementation for the lunar ascent simulation.
- Implement triggers in ODE driver using bisection.
- Investigate rocket staging and mass budget. Simple setup of ODEs; comparison with closed-form results.
- Orbital mechanics:
- Simulated Hohmann transfers.
- Rendezvous manoeuvres with multiple transfers.
- Optimization methods. Implement gradient descent.
- Optimizing "pitchover" angle for a gravity-turn trajectory in a vacuum flight.
- Optimizing multiple objectives for an atmospheric flight.
- Introduction to practical examples of affine spaces, vector spaces, derivatives as linear maps, and the interactions of these with other numeric types, such as when type-checked units are introduced.
- Appreciation of the benefits of writing more generic numerical algorithms, abstracted over more than just a single scalar type (ie.
Num ais only the beginning of useful abstraction).
- Appreciation of cost-benefit, and some of the more difficult, thorny points that arise: some difficulties in making libraries work together, necessary orphans, the horrible type errors that can appear when you have a unit type wrapping a vector type wrapping some underlying scalar, dependent-type-checking failures, etc. (NB: we have made sure that these are all "solved problems" in the
workshop, but we mention them as appropriate.)
- Introduction to time-domain simulation of dynamical systems.
Everyone interested in numerical methods or spaceflight!
Prerequisites for Attendees
Bring a MacOS or Linux machine (or an appropriate VM). Ideally check out the workshop git repository ahead of time to download the dependencies.