Path Tracking Catalog

25 path-tracking algorithms are (goint to be) implemented with python.

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/1b2b39f6-87fc-4f3d-9b18-4ae32f71b5fd

• Vehicle Models for Simulation
  • [x] Dynamic Bicycle Model
  • [x] Kinematic Bicycle Model
  • [x] Unicycle Model
• Control Algorithms
  • [x] Bang-Bang Control
  • [x] PID Control
  • [x] Pure Pursuit Control
  • [x] Stanley Control
  • [x] Fuzzy Logic Control
  • [ ] Genetic Algorithm
  • [x] Dynamic Window Approach
  • [ ] State Lattice Planner
  • [x] State Feedback Control
  • [x] Linear Quadratic Regulator (infinite horizon)
  • [ ] Linear Quadratic Regulator (finite horizon)
  • [ ] Differential Dynamic Programming (infinite horizon)
  • [ ] Differential Dynamic Programming (finite horizon)
  • [ ] Iterative LQR (infinite horizon)
  • [ ] Iterative LQR (finite horizon)
  • [ ] Linear Model Predictive Control (formulated as Quadratic Programming)
  • [ ] Nonlinear Model Predictive Control (solved by C/GMRES method)
  • [x] Model Predictive Path-Integral Control
  • [ ] Sliding Mode Control
  • [ ] Q-Learning
  • [ ] Multi Layer Perceptron
  • [ ] Linear Quadratic Gaussian
  • [ ] H∞ Control (LMI)
  • [ ] Lyapunov
  • [ ] Adaptive Control

Setup

git clone https://github.com/MizuhoAOKI/path_tracking_catalog.git
cd path_tracking_catalog
poetry install

Vehicle Models for Simulation

Definition of Coordinate Systems

Dynamic Bicycle Model

\begin{align}
&\frac{\mathrm{d}}{\mathrm{d}t}
\begin{bmatrix}
p^G_x \\
p^G_y \\
\phi \\
v^B_x \\
v^B_y \\
\omega \\
\end{bmatrix}
=
\begin{bmatrix}
v^B_x \cos\phi - v^B_y \sin\phi \\
v^B_x \sin\phi + v^B_y \cos\phi \\
\omega \\
{a}\cos\beta - (F_{f}^{\rm{lat}}\sin {{\delta}})/m + v^B_y \omega \\
{a}\sin\beta + F_{r}^{\rm{lat}}/m + F_{f}^{\rm{lat}} \cos{\delta}/m - v^B_x \omega \\
(F_{f}^{\rm{lat}}l_f\cos{\delta} - F_{r}^{\rm{lat}}l_r)/I_z\
\end{bmatrix}, \\ \\
& F_{f}^{\rm{lat}} = - C_f \left( \frac{v^B_y + l_f \omega}{v^B_x} - {\delta} \right), \\ \\
& F_{r}^{\rm{lat}} = - C_r \left( \frac{v^B_y - l_r \omega}{v^B_x} \right), \\ \\
& \beta = \tan^{-1} \left( \frac{v^B_y}{v^B_x} \right) \approx \frac{v^B_y}{v^B_x} \ \ \  (\because v^B_y \ll v^B_x ).
\end{align}

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/d51c3821-9b35-4e91-8235-e63b18f33f03

cd path_tracking_catalog
poetry run jupyter notebook notebooks/dynamic_bicycle_model.ipynb

Kinematic Bicycle Model

\begin{align}
& \frac{\mathrm{d}}{\mathrm{d}t}
\begin{bmatrix}
p^G_x \\
p^G_y \\
\phi \\
V
\end{bmatrix}
=
\begin{bmatrix}
V \cos(\phi + \beta) \\
V \sin(\phi + \beta) \\
(V/l_r)  \sin\beta \\
{a}
\end{bmatrix},\\ \\
& \beta = \tan^{-1} \left( \frac{l_r}{l_f + l_r} \tan({\delta}) \right).
\end{align}

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/b85fe31c-3e4a-47a9-bc54-694cde225bd5

cd path_tracking_catalog
poetry run jupyter notebook notebooks/kinematic_bicycle_model.ipynb

Unicycle Model

\begin{align}
\frac{\mathrm{d}}{\mathrm{d}t}
\begin{bmatrix}
p^G_x \\
p^G_y \\
\phi \\
V
\end{bmatrix}
=
\begin{bmatrix}
V \cos\phi \\
V \sin\phi \\
( V / l ) \tan{\delta} \\
{a}
\end{bmatrix}.
\end{align}

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/8cba0010-6a21-4830-8974-b4b57c166bcf

cd path_tracking_catalog
poetry run jupyter notebook notebooks/unicycle_model.ipynb

Control Algorithms

Bang-Bang Control

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/cc88214e-3914-4126-ac57-3f63d8397094

cd path_tracking_catalog
poetry run jupyter notebook notebooks/bangbang.ipynb

PID Control

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/83e813d9-b611-49da-abe2-45333bfb80d2

cd path_tracking_catalog
poetry run jupyter notebook notebooks/pid.ipynb

Pure-Pursuit Control

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/a23f8437-d695-4848-83fb-a8424f311683

cd path_tracking_catalog
poetry run jupyter notebook notebooks/purepursuit.ipynb

Stanley Control

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/43f3ce4f-8181-45ad-bc08-ac96f3a91e2b

cd path_tracking_catalog
poetry run jupyter notebook notebooks/stanley.ipynb

Fuzzy Logic Control

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/d8f9f256-4b2c-4b9e-8b57-e33f05e59e6f

cd path_tracking_catalog
poetry run jupyter notebook notebooks/fuzzy.ipynb

Dynamic Window Approach

Simple Path Tracking

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/23078e50-46a5-48eb-b89b-4a2111b320f0

cd path_tracking_catalog
poetry run jupyter notebook notebooks/dwa_pathtracking.ipynb

Path Tracking with Obstacle Avoidance

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/7b2a80b7-8d3e-4d37-89f4-23337efcb937

cd path_tracking_catalog
poetry run jupyter notebook notebooks/dwa_obstacle_avoidance.ipynb

State Lattice Planner

State Feedback Control

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/8e48380b-f840-49cc-91e0-07dad356b5be

cd path_tracking_catalog
poetry run jupyter notebook notebooks/state_feedback.ipynb

Linear Quadratic Regulator

https://github.com/MizuhoAOKI/path_tracking/assets/63337525/13d6abbc-2904-422d-acba-17ede074a181

cd path_tracking_catalog
poetry run jupyter notebook notebooks/lqr.ipynb

Model Predictive Control

Model Predictive Path-Integral Control

Simple Path Tracking

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/acfefe3a-a22a-4cbc-a5c8-a83086943684

cd path_tracking_catalog
poetry run jupyter notebook notebooks/mppi_pathtracking.ipynb

Path Tracking with Obstacle Avoidance

https://github.com/MizuhoAOKI/path_tracking_catalog/assets/63337525/fe84eaf6-8795-490d-9ef1-efecc427052e

cd path_tracking_catalog
poetry run jupyter notebook notebooks/mppi_obstacle_avoidance.ipynb

Sliding Mode Control

Q-Learning