MLTS-point-mass

Minimum lap time of a point mass with a G-G-V constraint, solved as an OCP with CasADi and IPOPT.

Installation

pip install MLTS-point-mass

The examples (tracks, vehicles, scripts) are in the repository:

git clone https://github.com/GiacomoCorradini/MLTS-point-mass.git
cd MLTS-point-mass
pip install -e ".[examples]"

Usage

python examples/run_mlts.py examples/tracks/Catalunya.txt   # --ggv, --vehicle, --step, --save sol.csv
python examples/plot_ggv.py
python examples/plot_mesh.py

import json
from mlts_point_mass import MLTS, read_track
from mlts_point_mass.define_mesh import build_dense_start_end_mesh

track = "examples/tracks/Catalunya.txt"
vehicle = json.load(open("examples/vehicle_1/vehicle.json"))
ggv = json.load(open("examples/vehicle_1/ggv_envelope.json"))

mlts = MLTS(track, vehicle, ggv)
sol = mlts.solution(x0=[0, 0, 30, 0, 0])  # initial guess [n, Xi, V, ax, ay]

# Mesh: uniform step in m (default 1), or nodes built with mlts_point_mass.define_mesh
s = read_track(track)["abscissa"]
nodes, _ = build_dense_start_end_mesh(s, coarse_step=5.0, dense_step=1.0)
sol = mlts.solution(
    x0=[0, 0, 30, 0, 0],
    mesh=nodes,
    weights={"w__ax": 1e-4},  # cost weights: w__T (lap time), w__ax, w__ay (control rate)
)

sol (dict, arrays sampled on the mesh along s):

Inputs

• track: path of the track file (tab separated, # comments) or DataFrame with columns abscissa, curvature, dir_mid_line, x_mid_line, y_mid_line, width_no_kerbs_L, width_no_kerbs_R; optional elevation, slope (positive uphill), banking (positive: right side up), default 0.
• vehicle (dict): W_total width [m], v_max [m/s]; optional v_min (5.0), tau_ax, tau_ay (0.03 s).
• ggv, either:
  • CSV / DataFrame with columns V, ax, ay: boundary samples at each speed (symmetric in ay);
  • FWBW dict: tables ax_max(ay, V), ax_min(ay, V), ay_max(V), see ggv_envelope.json.
• ggv_scales: grip scaling [mu], [mu_ax, mu_ay] or [mu_ax_max, mu_ax_min, mu_ay].

The GGV constraint is (rho / r)^2 <= 1, with rho the distance of (ax, ay) from the diagram centre and r that of the boundary in the same direction.