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# PythonRobotics
Python sample codes for robotics algorithm.
# Table of Contents
=================
* [PythonRobotics](#pythonrobotics)
* [Requirements](#requirements)
* [Path Planning](#path-planning)
* [Dijkstra grid search](#dijkstra-grid-search)
* [A star grid search](#a-star-grid-search)
* [Model Predictive Trajectory Generator](#model-predictive-trajectory-generator)
* [Path optimization sample:](#path-optimization-sample)
* [Lookup table generation sample:](#lookup-table-generation-sample)
* [State Lattice Planning](#state-lattice-planning)
* [Uniform polar sampling results:](#uniform-polar-sampling-results)
* [Biased polar sampling results:](#biased-polar-sampling-results)
* [Lane sampling results:](#lane-sampling-results)
* [RRT](#rrt)
* [RRTStar](#rrtstar)
* [RRT Car](#rrt-car)
* [RRTStarCar](#rrtstarcar)
* [RRTStarCar_reeds_sheep](#rrtstarcar_reeds_sheep)
* [Dubins path planning](#dubins-path-planning)
* [Reeds Shepp planning](#reeds-shepp-planning)
* [Closed Loop RRT*](#closed-loop-rrt)
* [Path tracking](#path-tracking)
* [Pure pursuit tracking](#pure-pursuit-tracking)
* [Rear wheel feedback control](#rear-wheel-feedback-control)
* [Linear–quadratic regulator (LQR) control](#linearquadratic-regulator-lqr-control)
* [License](#license)
* [Author](#author)
# Requirements
- numpy
- scipy
- matplotlib
- [pyReedsShepp](https://github.com/ghliu/pyReedsShepp) (Only for reeds sheep path and RRTStarCar_reeds_sheep)
# Path Planning
Path planning algorithm.
## Dijkstra grid search
This is a 2D grid based shortest path planning with Dijkstra's algorithm.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/Dijkstra/animation.gif)
In the animation, cyan points are searched nodes.
## A star grid search
This is a 2D grid based shortest path planning with A star algorithm.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/AStar/animation.gif)
In the animation, cyan points are searched nodes.
It's heuristic is 2D Euclid distance.
## Model Predictive Trajectory Generator
This script is a path planning code with model predictive trajectory generator.
### Path optimization sample:
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/ModelPredictiveTrajectoryGenerator/kn05animation.gif)
### Lookup table generation sample:
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/ModelPredictiveTrajectoryGenerator/lookuptable.png?raw=True)
see:
- [Optimal rough terrain trajectory generation for wheeled mobile robots](http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328)
　
## State Lattice Planning
This script is a path planning code with state lattice planning.
This code uses the model predictive trajectory generator to solve boundary problem.
### Uniform polar sampling results:
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_1.png)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_2.png)
### Biased polar sampling results:
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_3.png)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_4.png)
### Lane sampling results:
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_5.png)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/StateLatticePlanner/Figure_6.png)
## RRT
Rapidly Randamized Tree Path planning sample.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/RRT/animation.gif)
This script is a simple path planning code with Rapidly-Exploring Random Trees (RRT)
see (in Japanese) :
[PythonによるRapidly-Exploring Random Trees (RRT)パスプランニングサンプルプログラム - MyEnigma](http://myenigma.hatenablog.com/entry/2016/03/23/092002)
## RRTStar
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/RRTstar/animation.gif)
This script is a path planning code with RRT \*
- [Incremental Sampling-based Algorithms for Optimal Motion Planning](https://arxiv.org/abs/1005.0416)
## RRT Car
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/RRTCar/animation.gif)
Path planning for a car robot with RRT and dubins path planner.
## RRTStarCar
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/RRTStarCar/animation.gif)
Path planning for a car robot with RRT\* and dubings path planner.
## RRTStarCar_reeds_sheep
![Robotics/animation.gif at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/RRTStarCar_reeds_sheep/animation.gif))
Path planning for a car robot with RRT\* and reeds sheep path planner.
## Dubins path planning
A sample code for Dubins path planning.
[Dubins path - Wikipedia](https://en.wikipedia.org/wiki/Dubins_path)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/DubinsPath/figures/figure_1.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/DubinsPath/figures/figure_13.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/DubinsPath/figures/figure_15.png?raw=True)
## Reeds Shepp planning
A sample code with Reeds Shepp path planning.
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/ReedsSheppPath/figure_1-4.png?raw=true)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/ReedsSheppPath/figure_1-5.png?raw=true)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/ReedsSheppPath/figure_1-7.png?raw=true)
## Closed Loop RRT\*
A sample code with closed loop RRT\*.
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CRRRTStar/Figure_1.png?raw=True)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CRRRTStar/Figure_4.png?raw=True)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CRRRTStar/Figure_5.png?raw=True)
see:
- [Motion Planning in Complex Environments
using Closed-loop Prediction](http://acl.mit.edu/papers/KuwataGNC08.pdf)
- [Real-time Motion Planning with Applications to
Autonomous Urban Driving](http://acl.mit.edu/papers/KuwataTCST09.pdf)
- [[1601.06326] Sampling-based Algorithms for Optimal Motion Planning Using Closed-loop Prediction](https://arxiv.org/abs/1601.06326)
# Path tracking
Path tracking algorithm samples.
## Pure pursuit tracking
Path tracking simulation with pure pursuit steering control and PID speed control.
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/pure_pursuit/Figure_1-3.png?raw=True)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/pure_pursuit/2Figure_1-2.png?raw=True)
![PythonRobotics/figure_1-5.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/pure_pursuit/4Figure_1-2.png?raw=True)
## Rear wheel feedback control
Path tracking simulation with rear wheel feedback steering control and PID speed control.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/rear_wheel_feedback/animation.gif)
## Linear–quadratic regulator (LQR) control
Path tracking simulation with LQR steering control and PID speed control.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/lqr/animation.gif)
# License
MIT
# Author
Atsushi Sakai ([@Atsushi_twi](https://twitter.com/Atsushi_twi))
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