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https://github.com/AtsushiSakai/PythonRobotics

Python sample codes for robotics algorithms.
https://github.com/AtsushiSakai/PythonRobotics

algorithm animation autonomous-driving autonomous-navigation autonomous-vehicles control cvxpy ekf hacktoberfest localization mapping path-planning python robot robotics slam

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Python sample codes for robotics algorithms.

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README 

        
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# PythonRobotics

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Python codes for robotics algorithm.



# Table of Contents

   * [What is this?](#what-is-this)

   * [Requirements](#requirements)

   * [Documentation](#documentation)

   * [How to use](#how-to-use)

   * [Localization](#localization)

      * [Extended Kalman Filter localization](#extended-kalman-filter-localization)

      * [Particle filter localization](#particle-filter-localization)

      * [Histogram filter localization](#histogram-filter-localization)

   * [Mapping](#mapping)

      * [Gaussian grid map](#gaussian-grid-map)

      * [Ray casting grid map](#ray-casting-grid-map)

      * [Lidar to grid map](#lidar-to-grid-map)

      * [k-means object clustering](#k-means-object-clustering)

      * [Rectangle fitting](#rectangle-fitting)

   * [SLAM](#slam)

      * [Iterative Closest Point (ICP) Matching](#iterative-closest-point-icp-matching)

      * [FastSLAM 1.0](#fastslam-10)

   * [Path Planning](#path-planning)

      * [Dynamic Window Approach](#dynamic-window-approach)

      * [Grid based search](#grid-based-search)

         * [Dijkstra algorithm](#dijkstra-algorithm)

         * [A* algorithm](#a-algorithm)

         * [D* algorithm](#d-algorithm)

         * [D* Lite algorithm](#d-lite-algorithm)

         * [Potential Field algorithm](#potential-field-algorithm)

         * [Grid based coverage path planning](#grid-based-coverage-path-planning)

      * [State Lattice Planning](#state-lattice-planning)

         * [Biased polar sampling](#biased-polar-sampling)

         * [Lane sampling](#lane-sampling)

      * [Probabilistic Road-Map (PRM) planning](#probabilistic-road-map-prm-planning)

      * [Rapidly-Exploring Random Trees (RRT)](#rapidly-exploring-random-trees-rrt)

         * [RRT*](#rrt)

         * [RRT* with reeds-shepp path](#rrt-with-reeds-shepp-path)

         * [LQR-RRT*](#lqr-rrt)

      * [Quintic polynomials planning](#quintic-polynomials-planning)

      * [Reeds Shepp planning](#reeds-shepp-planning)

      * [LQR based path planning](#lqr-based-path-planning)

      * [Optimal Trajectory in a Frenet Frame](#optimal-trajectory-in-a-frenet-frame)

   * [Path Tracking](#path-tracking)

      * [move to a pose control](#move-to-a-pose-control)

      * [Stanley control](#stanley-control)

      * [Rear wheel feedback control](#rear-wheel-feedback-control)

      * [Linear–quadratic regulator (LQR) speed and steering control](#linearquadratic-regulator-lqr-speed-and-steering-control)

      * [Model predictive speed and steering control](#model-predictive-speed-and-steering-control)

      * [Nonlinear Model predictive control with C-GMRES](#nonlinear-model-predictive-control-with-c-gmres)

   * [Arm Navigation](#arm-navigation)

      * [N joint arm to point control](#n-joint-arm-to-point-control)

      * [Arm navigation with obstacle avoidance](#arm-navigation-with-obstacle-avoidance)

   * [Aerial Navigation](#aerial-navigation)

      * [drone 3d trajectory following](#drone-3d-trajectory-following)

      * [rocket powered landing](#rocket-powered-landing)

   * [Bipedal](#bipedal)

      * [bipedal planner with inverted pendulum](#bipedal-planner-with-inverted-pendulum)

   * [License](#license)

   * [Use-case](#use-case)

   * [Contribution](#contribution)

   * [Citing](#citing)

   * [Support](#support)

   * [Sponsors](#sponsors)

      * [JetBrains](#JetBrains)

      * [1Password](#1password)

   * [Authors](#authors)



# What is this?



This is a Python code collection of robotics algorithms.



Features:



1. Easy to read for understanding each algorithm's basic idea.



2. Widely used and practical algorithms are selected.



3. Minimum dependency.



See this paper for more details:



- [\[1808\.10703\] PythonRobotics: a Python code collection of robotics algorithms](https://arxiv.org/abs/1808.10703) ([BibTeX](https://github.com/AtsushiSakai/PythonRoboticsPaper/blob/master/python_robotics.bib))



# Requirements



For running each sample code:



- [Python 3.11.x](https://www.python.org/)

 

- [NumPy](https://numpy.org/)

 

- [SciPy](https://scipy.org/)

 

- [Matplotlib](https://matplotlib.org/)

 

- [cvxpy](https://www.cvxpy.org/) 



For development:

  

- [pytest](https://pytest.org/) (for unit tests)

  

- [pytest-xdist](https://pypi.org/project/pytest-xdist/) (for parallel unit tests)

  

- [mypy](http://mypy-lang.org/) (for type check)

  

- [sphinx](https://www.sphinx-doc.org/) (for document generation)

  

- [pycodestyle](https://pypi.org/project/pycodestyle/) (for code style check)



# Documentation



This README only shows some examples of this project. 



If you are interested in other examples or mathematical backgrounds of each algorithm, 



You can check the full documentation online: [Welcome to PythonRobotics’s documentation\! — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/index.html)



All animation gifs are stored here: [AtsushiSakai/PythonRoboticsGifs: Animation gifs of PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs)



# How to use



1. Clone this repo.



   ```terminal

   git clone https://github.com/AtsushiSakai/PythonRobotics.git

   ```



2. Install the required libraries.



- using conda :



  ```terminal

  conda env create -f requirements/environment.yml

  ```

 

- using pip :



  ```terminal

  pip install -r requirements/requirements.txt

  ```



3. Execute python script in each directory.



4. Add star to this repo if you like it :smiley:. 



# Localization



## Extended Kalman Filter localization



EKF pic



Ref:



- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html)



## Particle filter localization



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/particle_filter/animation.gif)



This is a sensor fusion localization with Particle Filter(PF).



The blue line is true trajectory, the black line is dead reckoning trajectory,



and the red line is an estimated trajectory with PF.



It is assumed that the robot can measure a distance from landmarks (RFID).



These measurements are used for PF localization.



Ref:



- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)



## Histogram filter localization



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/histogram_filter/animation.gif)



This is a 2D localization example with Histogram filter.



The red cross is true position, black points are RFID positions.



The blue grid shows a position probability of histogram filter.  



In this simulation, x,y are unknown, yaw is known.



The filter integrates speed input and range observations from RFID for localization.



Initial position is not needed.



Ref:



- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)



# Mapping



## Gaussian grid map



This is a 2D Gaussian grid mapping example.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/gaussian_grid_map/animation.gif)



## Ray casting grid map



This is a 2D ray casting grid mapping example.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/raycasting_grid_map/animation.gif)



## Lidar to grid map



This example shows how to convert a 2D range measurement to a grid map.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/lidar_to_grid_map/animation.gif)



## k-means object clustering



This is a 2D object clustering with k-means algorithm.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/kmeans_clustering/animation.gif)



## Rectangle fitting



This is a 2D rectangle fitting for vehicle detection.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/rectangle_fitting/animation.gif)



# SLAM



Simultaneous Localization and Mapping(SLAM) examples



## Iterative Closest Point (ICP) Matching



This is a 2D ICP matching example with singular value decomposition.



It can calculate a rotation matrix, and a translation vector between points and points.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/iterative_closest_point/animation.gif)



Ref:



- [Introduction to Mobile Robotics: Iterative Closest Point Algorithm](https://cs.gmu.edu/~kosecka/cs685/cs685-icp.pdf)



## FastSLAM 1.0



This is a feature based SLAM example using FastSLAM 1.0.



The blue line is ground truth, the black line is dead reckoning, the red line is the estimated trajectory with FastSLAM.



The red points are particles of FastSLAM.



Black points are landmarks, blue crosses are estimated landmark positions by FastSLAM.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM1/animation.gif)



Ref:



- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)



- [SLAM simulations by Tim Bailey](http://www-personal.acfr.usyd.edu.au/tbailey/software/slam_simulations.htm)



# Path Planning



## Dynamic Window Approach



This is a 2D navigation sample code with Dynamic Window Approach.



- [The Dynamic Window Approach to Collision Avoidance](https://www.ri.cmu.edu/pub_files/pub1/fox_dieter_1997_1/fox_dieter_1997_1.pdf)



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DynamicWindowApproach/animation.gif)



## Grid based search



### Dijkstra algorithm



This is a 2D grid based the shortest path planning with Dijkstra's algorithm.



![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Dijkstra/animation.gif)



In the animation, cyan points are searched nodes.



### A\* algorithm



This is a 2D grid based the shortest path planning with A star algorithm.



![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/AStar/animation.gif)



In the animation, cyan points are searched nodes.



Its heuristic is 2D Euclid distance.



### D\* algorithm



This is a 2D grid based the shortest path planning with D star algorithm.



![figure at master · nirnayroy/intelligentrobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStar/animation.gif)



The animation shows a robot finding its path avoiding an obstacle using the D* search algorithm.



Ref:



- [D* Algorithm Wikipedia](https://en.wikipedia.org/wiki/D*)



### D\* Lite algorithm



This algorithm finds the shortest path between two points while rerouting when obstacles are discovered. It has been implemented here for a 2D grid.



![D* Lite](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStarLite/animation.gif)



The animation shows a robot finding its path and rerouting to avoid obstacles as they are discovered using the D* Lite search algorithm.



Refs:



- [D* Lite](http://idm-lab.org/bib/abstracts/papers/aaai02b.pd)

- [Improved Fast Replanning for Robot Navigation in Unknown Terrain](http://www.cs.cmu.edu/~maxim/files/dlite_icra02.pdf)



### Potential Field algorithm



This is a 2D grid based path planning with Potential Field algorithm.



![PotentialField](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/PotentialFieldPlanning/animation.gif)



In the animation, the blue heat map shows potential value on each grid.



Ref:



- [Robotic Motion Planning:Potential Functions](https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf)



### Grid based coverage path planning



This is a 2D grid based coverage path planning simulation.



![PotentialField](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/GridBasedSweepCPP/animation.gif)



## 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.



Ref: 



- [Optimal rough terrain trajectory generation for wheeled mobile robots](http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328)



- [State Space Sampling of Feasible Motions for High-Performance Mobile Robot Navigation in Complex Environments](http://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf)



### Biased polar sampling



![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/BiasedPolarSampling.gif)



### Lane sampling



![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/LaneSampling.gif)



## Probabilistic Road-Map (PRM) planning 



![PRM](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ProbabilisticRoadMap/animation.gif)



This PRM planner uses Dijkstra method for graph search.



In the animation, blue points are sampled points,



Cyan crosses means searched points with Dijkstra method,



The red line is the final path of PRM.



Ref:



- [Probabilistic roadmap \- Wikipedia](https://en.wikipedia.org/wiki/Probabilistic_roadmap)



　　



## Rapidly-Exploring Random Trees (RRT)



### RRT\*



![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTstar/animation.gif)



This is a path planning code with RRT\*



Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.



Ref:



- [Incremental Sampling-based Algorithms for Optimal Motion Planning](https://arxiv.org/abs/1005.0416)



- [Sampling-based Algorithms for Optimal Motion Planning](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.419.5503&rep=rep1&type=pdf)



### RRT\* with reeds-shepp path



![Robotics/animation.gif at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarReedsShepp/animation.gif))



Path planning for a car robot with RRT\* and reeds shepp path planner.



### LQR-RRT\*



This is a path planning simulation with LQR-RRT\*.



A double integrator motion model is used for LQR local planner.



![LQR_RRT](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRRRTStar/animation.gif)



Ref:



- [LQR\-RRT\*: Optimal Sampling\-Based Motion Planning with Automatically Derived Extension Heuristics](http://lis.csail.mit.edu/pubs/perez-icra12.pdf)



- [MahanFathi/LQR\-RRTstar: LQR\-RRT\* method is used for random motion planning of a simple pendulum in its phase plot](https://github.com/MahanFathi/LQR-RRTstar)



## Quintic polynomials planning



Motion planning with quintic polynomials.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/QuinticPolynomialsPlanner/animation.gif)



It can calculate a 2D path, velocity, and acceleration profile based on quintic polynomials.



Ref:



- [Local Path Planning And Motion Control For Agv In Positioning](http://ieeexplore.ieee.org/document/637936/)



## Reeds Shepp planning



A sample code with Reeds Shepp path planning.



![RSPlanning](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true)



Ref:



- [15.3.2 Reeds\-Shepp Curves](http://planning.cs.uiuc.edu/node822.html) 



- [optimal paths for a car that goes both forwards and backwards](https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf)



- [ghliu/pyReedsShepp: Implementation of Reeds Shepp curve\.](https://github.com/ghliu/pyReedsShepp)



## LQR based path planning



A sample code using LQR based path planning for double integrator model.



![RSPlanning](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRPlanner/animation.gif?raw=true)



## Optimal Trajectory in a Frenet Frame 



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/animation.gif)



This is optimal trajectory generation in a Frenet Frame.



The cyan line is the target course and black crosses are obstacles.



The red line is the predicted path.



Ref:



- [Optimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frame](https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf)



- [Optimal trajectory generation for dynamic street scenarios in a Frenet Frame](https://www.youtube.com/watch?v=Cj6tAQe7UCY)



# Path Tracking



## move to a pose control



This is a simulation of moving to a pose control



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/move_to_pose/animation.gif)



Ref:



- [P. I. Corke, "Robotics, Vision and Control" \| SpringerLink p102](https://link.springer.com/book/10.1007/978-3-642-20144-8)



## Stanley control



Path tracking simulation with Stanley steering control and PID speed control.



![2](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/stanley_controller/animation.gif)



Ref:



- [Stanley: The robot that won the DARPA grand challenge](http://robots.stanford.edu/papers/thrun.stanley05.pdf)



- [Automatic Steering Methods for Autonomous Automobile Path Tracking](https://www.ri.cmu.edu/pub_files/2009/2/Automatic_Steering_Methods_for_Autonomous_Automobile_Path_Tracking.pdf)



## 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/PythonRoboticsGifs/raw/master/PathTracking/rear_wheel_feedback/animation.gif)



Ref:



- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://arxiv.org/abs/1604.07446)



## Linear–quadratic regulator (LQR) speed and steering control



Path tracking simulation with LQR speed and steering control.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_speed_steer_control/animation.gif)



Ref:



- [Towards fully autonomous driving: Systems and algorithms \- IEEE Conference Publication](http://ieeexplore.ieee.org/document/5940562/)



## Model predictive speed and steering control



Path tracking simulation with iterative linear model predictive speed and steering control.



MPC pic



Ref:



- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html)



- [Real\-time Model Predictive Control \(MPC\), ACADO, Python \| Work\-is\-Playing](http://grauonline.de/wordpress/?page_id=3244)



## Nonlinear Model predictive control with C-GMRES



A motion planning and path tracking simulation with NMPC of C-GMRES 



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/cgmres_nmpc/animation.gif)



Ref:



- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/path_tracking/cgmres_nmpc/cgmres_nmpc.html)



# Arm Navigation



## N joint arm to point control



N joint arm to a point control simulation.



This is an interactive simulation.



You can set the goal position of the end effector with left-click on the plotting area. 



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/n_joint_arm_to_point_control/animation.gif)



In this simulation N = 10, however, you can change it.



## Arm navigation with obstacle avoidance 



Arm navigation with obstacle avoidance simulation.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/arm_obstacle_navigation/animation.gif)



# Aerial Navigation



## drone 3d trajectory following 



This is a 3d trajectory following simulation for a quadrotor.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/AerialNavigation/drone_3d_trajectory_following/animation.gif)



## rocket powered landing



This is a 3d trajectory generation simulation for a rocket powered landing.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/AerialNavigation/rocket_powered_landing/animation.gif)



Ref:



- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/aerial_navigation/rocket_powered_landing/rocket_powered_landing.html)



# Bipedal



## bipedal planner with inverted pendulum



This is a bipedal planner for modifying footsteps for an inverted pendulum.



You can set the footsteps, and the planner will modify those automatically.



![3](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Bipedal/bipedal_planner/animation.gif)



# License 



MIT



# Use-case



If this project helps your robotics project, please let me know with creating an issue.



Your robot's video, which is using PythonRobotics, is very welcome!!



This is a list of user's comment and references:[users\_comments](https://github.com/AtsushiSakai/PythonRobotics/blob/master/users_comments.md)



# Contribution



Any contribution is welcome!! 



Please check this document:[How To Contribute — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/how_to_contribute.html)



# Citing



If you use this project's code for your academic work, we encourage you to cite [our papers](https://arxiv.org/abs/1808.10703) 



If you use this project's code in industry, we'd love to hear from you as well; feel free to reach out to the developers directly.



# Supporting this project



If you or your company would like to support this project, please consider:



- [Sponsor @AtsushiSakai on GitHub Sponsors](https://github.com/sponsors/AtsushiSakai)



- [Become a backer or sponsor on Patreon](https://www.patreon.com/myenigma)



- [One-time donation via PayPal](https://www.paypal.me/myenigmapay/)



If you would like to support us in some other way, please contact with creating an issue.



## Sponsors



### [JetBrains](https://www.jetbrains.com/)



They are providing a free license of their IDEs for this OSS development.   



### [1Password](https://github.com/1Password/1password-teams-open-source)



They are providing a free license of their 1Password team license for this OSS project.   



# Authors



- [Contributors to AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/graphs/contributors)