A minimum-time (lap-time optimal) trajectory planner for Formula Student Driverless, developed for AMZ Racing in the 2025–2026 season. The four-wheel vehicle model was formulated by Tanmay Ganguli. Fast-LTO is offline: it was used in testing, and in the second lap of autocross at FSG 2026, and later for skidpad, where it contributed to the fastest FSG driverless skidpad to date at 4.78 s.
Most driverless pipelines use decoupled planning: a minimum-curvature path, then a forwards–backwards pass that assigns the highest feasible speed at each point from identified lateral and longitudinal limits. That is attractive because both stages are convex (and cheap), and because it is a close enough proxy for the true objective, which is minimum time.
We invested in a planner that solves that objective directly for disciplines where a global map exists and computational efficiency is not critical — that is, skidpad and the second lap of autocross. With some simplifications, minimum-time planning can also be pushed close to real time.
On the same vehicle model we use in our MPC, the minimum-time reference outperformed the decoupled one, especially when the controller was still not well tuned. Besides, Fast-LTO was a useful research tool: lap-time sensitivity sweeps over model and config parameters helped decide where to spend engineering effort. The figure below is one such sweep on skidpad (one-at-a-time, ±15% per parameter).
Pipeline stages, space-domain formulation, and event semantics live in
src/fast_lto/README.md.
Python 3.10+ and a CasADi build that ships IPOPT (the usual pip wheel does).
git clone https://github.com/rafaelborges5/Fast-LTO.git
cd Fast-LTO
python -m venv .venv
source .venv/bin/activate # Windows: .venv\Scripts\activate
pip install -e .That registers the fast-lto console script.
| Extra | Install | For |
|---|---|---|
| Dev | pip install -e ".[dev]" |
tests, lint, type checks |
| Research | pip install -e ".[research]" |
Plotly viewers under research/ |
From a source checkout, data defaults to the repo root. After a plain wheel
install, set FAST_LTO_DATA or run from a directory that should own data/
and ocp_plots/.
Pick an event config and run the pipeline:
fast-lto --config configs/trackdrive.yaml --track-id fscz_2025
fast-lto --config configs/autox.yaml --track-id fsg_autox_2026
fast-lto --config configs/skidpad.yamlCLI flags override the YAML. Useful patterns:
# Smoke check
fast-lto --config configs/trackdrive.yaml --track-id ellipse \
--track-type ellipse --model point_mass --ds 3.0 --no-plot
# Actual full solve
fast-lto --config configs/trackdrive.yaml --track-id fscz_2025 \
--model four_wheel --ds 0.5
# Re-solve from an existing discretised track
fast-lto --config configs/trackdrive.yaml --track-id fscz_2025 \
--start-from ocp --integrator rk4Input track. A cone CSV at data/tracks/{track_id}.csv with columns
side,cone_id,x,y (L / R / M). Full format and assumptions:
data/tracks/README.md.
Output trajectory. A controller-reference CSV under
data/output_trajectories/, one row per node, matching the car's
ControllerReferenceTrajectory message. Column list and packing live in
src/fast_lto/export/trajectory.py
(CSV_COLUMNS); the contract is locked by tests/export/test_trajectory_csv.py.
configs/vehicle.yaml describes the car once. Each event file
(trackdrive.yaml, autox.yaml, skidpad.yaml) extends it and only names
what differs. Run one with fast-lto --config configs/autox.yaml.
Four knobs change the answer materially: model_name, ds_m,
boundary_margin, and reg_u / reg_u_l2. Details:
configs/README.md.
Intermediate and final files land under the data root:
| Artifact | Location |
|---|---|
| Track CSV | data/tracks/{track_id}.csv — format in data/tracks/README.md |
| Discretised track | data/discretized/{track_id}.json |
| Track with widths | data/discretized/{track_id}_with_widths.json |
| Solution | data/solutions/{track_id}_{model}_{integrator}_{mode}.json |
| Trajectory CSV | data/output_trajectories/{track_id}_..._{stamp}.csv — columns in export/trajectory.py |
| Plots | ocp_plots/{stamp}/ |
Data root: $FAST_LTO_DATA if set, else the source checkout, else the working
directory. See fast_lto.paths.
| Package architecture | src/fast_lto/README.md |
| Vehicle models | src/fast_lto/vehicle_models/README.md |
| OCP formulation | src/fast_lto/optimization/README.md |
| Configs | configs/README.md |
| Track CSV format | data/tracks/README.md |
| Trajectory CSV columns | src/fast_lto/export/trajectory.py |
| Research scripts | research/README.md |
| Frenet frame | examples/frenet_frame.py |
pip install -e ".[dev]"
# Local. CI also runs the slow golden solves, which are what alert you to a
# breaking change in the physics.
pytest -m "not slow"
ruff check .
black --check .
isort --check-only .
mypy srcDependency management is standard venv + pyproject.toml (optionally via
uv). Formatting is black / isort; lint is ruff; types are mypy.
MIT. See LICENSE.