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<img src="https://github.com/AtsushiSakai/PythonRobotics/blob/master/icon.png?raw=true" align="right" width="300"/>
# PythonRobotics
[![Build Status](https://travis-ci.org/AtsushiSakai/PythonRobotics.svg?branch=master)](https://travis-ci.org/AtsushiSakai/PythonRobotics)
Python sample codes for robotics algorithm.
# Table of Contents
* [Requirements](#requirements)
* [Path Planning](#path-planning)
* [Grid based search](#grid-based-search)
* [Dijkstra algorithm](#dijkstra-algorithm)
* [A* algorithm](#a-algorithm)
* [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](#uniform-polar-sampling)
* [Biased polar sampling](#biased-polar-sampling)
* [Lane sampling](#lane-sampling)
* [Rapidly-Exploring Random Trees (RRT)](#rapidly-exploring-random-trees-rrt)
* [Basic RRT](#basic-rrt)
* [RRT*](#rrt)
* [RRT with dubins path](#rrt-with-dubins-path)
* [RRT* with dubins path](#rrt-with-dubins-path-1)
* [RRT* with reeds-sheep path](#rrt-with-reeds-sheep-path)
* [Closed Loop RRT*](#closed-loop-rrt)
* [Cubic spline planning](#cubic-spline-planning)
* [Dubins path planning](#dubins-path-planning)
* [Reeds Shepp planning](#reeds-shepp-planning)
* [Mix Integer Optimization based model predictive planning and control](#mix-integer-optimization-based-model-predictive-planning-and-control)
* [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
- Python 3.6.x
- numpy
- scipy
- matplotlib
- [pyReedsShepp](https://github.com/ghliu/pyReedsShepp) (Only for reeds sheep path and RRTStarCar_reeds_sheep)
- [cvxpy](https://cvxgrp.github.io/cvxpy/index.html) (Only for mix integer optimization based model predictive planning and control)
# Path Planning
Path planning algorithm.
## Dynamic Window Approach
This is a 2D navigation sample code with Dynamic Window Approach.
![2](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/DynamicWindowApproach/animation.gif)
## Grid based search
### Dijkstra algorithm
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\* algorithm
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
![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
![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
![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)
## Rapidly-Exploring Random Trees (RRT)
### Basic 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)
### RRT\*
![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 with dubins path
![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.
### RRT\* with dubins path
![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 dubins path planner.
### RRT\* with reeds-sheep path
![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.
### 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)
## Cubic spline planning
A sample code for cubic path planning.
This code generates a curvature continious path based on x-y waypoints with cubic spline.
Heading angle of each point can be also calculated analytically.
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CubicSpline/Figure_1.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CubicSpline/Figure_2.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/CubicSpline/Figure_3.png?raw=True)
## 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)
## Mix Integer Optimization based model predictive planning and control
![2](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/MixIntegerPathPlanning/animation.gif)
A model predictive planning and control code with mixed integer programming.
It is based on this paper.
- [MIXED INTEGER PROGRAMMING FOR MULTI-VEHICLE PATH PLANNING](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.4.2591&rep=rep1&type=pdf)
This code used cvxpy as optimization modeling tool,
- [Welcome to CVXPY 1\.0 — CVXPY 1\.0\.0 documentation](https://cvxgrp.github.io/cvxpy/index.html)
and Gurobi is used as a solver for mix integer optimization problem.
- [Gurobi Optimization \- The State\-of\-the\-Art Mathematical Programming Solver](http://www.gurobi.com/)
# 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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