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@@ -10,7 +10,69 @@ Python codes for robotics algorithm.
* [What is this?](#what-is-this)
* [Requirements](#requirements)
* [How to use](#how-to-use)
* [Documentation](#documentation)
* [Localization](#localization)
* [Extended Kalman Filter localization](#extended-kalman-filter-localization)
* [Unscented Kalman Filter localization](#unscented-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)
* [k-means object clustering](#k-means-object-clustering)
* [Object shape recognition using circle fitting](#object-shape-recognition-using-circle-fitting)
* [SLAM](#slam)
* [Iterative Closest Point (ICP) Matching](#iterative-closest-point-icp-matching)
* [EKF SLAM](#ekf-slam)
* [FastSLAM 1.0](#fastslam-10)
* [FastSLAM 2.0](#fastslam-20)
* [Graph based SLAM](#graph-based-slam)
* [Path Planning](#path-planning)
* [Dynamic Window Approach](#dynamic-window-approach)
* [Grid based search](#grid-based-search)
* [Dijkstra algorithm](#dijkstra-algorithm)
* [A* algorithm](#a-algorithm)
* [Potential Field algorithm](#potential-field-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)
* [Probabilistic Road-Map (PRM) planning](#probabilistic-road-map-prm-planning)
* [Voronoi Road-Map planning](#voronoi-road-map-planning)
* [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)
* [Informed RRT*](#informed-rrt)
* [Batch Informed RRT*](#batch-informed-rrt)
* [Closed Loop RRT*](#closed-loop-rrt)
* [LQR-RRT*](#lqr-rrt)
* [Cubic spline planning](#cubic-spline-planning)
* [B-Spline planning](#b-spline-planning)
* [Eta^3 Spline path planning](#eta3-spline-path-planning)
* [Bezier path planning](#bezier-path-planning)
* [Quintic polynomials planning](#quintic-polynomials-planning)
* [Dubins path planning](#dubins-path-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)
* [Pure pursuit tracking](#pure-pursuit-tracking)
* [Stanley control](#stanley-control)
* [Rear wheel feedback control](#rear-wheel-feedback-control)
* [Linear–quadratic regulator (LQR) steering control](#linearquadratic-regulator-lqr-steering-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)
* [Arm Navigation](#arm-navigation)
* [Two joint arm to point control](#two-joint-arm-to-point-control)
* [N joint arm to point control](#n-joint-arm-to-point-control)
* [Aerial Navigation](#aerial-navigation)
* [drone 3d trajectory following](#drone-3d-trajectory-following)
* [License](#license)
* [Contribution](#contribution)
* [Support](#support)
@@ -32,18 +94,20 @@ 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))
# Documentation
Documentation is available online: [https://pythonrobotics.readthedocs.io/](https://pythonrobotics.readthedocs.io/)
# Requirements
- Python 3.6.x
- numpy
- scipy
- matplotlib
- pandas
- [cvxpy](http://www.cvxpy.org/en/latest/)
- [cvxpy](http://www.cvxpy.org/en/latest/)
# How to use
@@ -53,10 +117,661 @@ Documentation is available online: [https://pythonrobotics.readthedocs.io/](http
3. Execute python script in each directory.
4. Add star to this repo if you like it :smiley:.
4. Add star to this repo if you like it :smiley:.
# Localization
## Extended Kalman Filter localization
<img src="https://github.com/AtsushiSakai/PythonRobotics/raw/master/Localization/extended_kalman_filter/animation.gif" width="640">
This is a sensor fusion localization with Extended Kalman Filter(EKF).
The blue line is true trajectory, the black line is dead reckoning trajectory,
the green point is positioning observation (ex. GPS), and the red line is estimated trajectory with EKF.
The red ellipse is estimated covariance ellipse with EKF.
Ref:
- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
## Unscented Kalman Filter localization
![2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/Localization/unscented_kalman_filter/animation.gif)
This is a sensor fusion localization with Unscented Kalman Filter(UKF).
The lines and points are same meaning of the EKF simulation.
Ref:
- [Discriminatively Trained Unscented Kalman Filter for Mobile Robot Localization](https://www.researchgate.net/publication/267963417_Discriminatively_Trained_Unscented_Kalman_Filter_for_Mobile_Robot_Localization)
# License
## Particle filter localization
![2](https://github.com/AtsushiSakai/PythonRobotics/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 estimated trajectory with PF.
It is assumed that the robot can measure a distance from landmarks (RFID).
This measurements are used for PF localization.
Ref:
- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
## Histogram filter localization
![3](https://github.com/AtsushiSakai/PythonRobotics/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/PythonRobotics/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/PythonRobotics/raw/master/Mapping/raycasting_grid_map/animation.gif)
## k-means object clustering
This is a 2D object clustering with k-means algorithm.
![2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/Mapping/kmeans_clustering/animation.gif)
## Object shape recognition using circle fitting
This is an object shape recognition using circle fitting.
![2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/Mapping/circle_fitting/animation.gif)
The blue circle is the true object shape.
The red crosses are observations from a ranging sensor.
The red circle is the estimated object shape using circle fitting.
# 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 to points.
![3](https://github.com/AtsushiSakai/PythonRobotics/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)
## EKF SLAM
This is an Extended Kalman Filter based SLAM example.
The blue line is ground truth, the black line is dead reckoning, the red line is the estimated trajectory with EKF SLAM.
The green crosses are estimated landmarks.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/SLAM/EKFSLAM/animation.gif)
Ref:
- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
## 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/PythonRobotics/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)
## FastSLAM 2.0
This is a feature based SLAM example using FastSLAM 2.0.
The animation has the same meanings as one of FastSLAM 1.0.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/SLAM/FastSLAM2/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)
## Graph based SLAM
This is a graph based SLAM example.
The blue line is ground truth.
The black line is dead reckoning.
The red line is the estimated trajectory with Graph based SLAM.
The black stars are landmarks for graph edge generation.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/SLAM/GraphBasedSLAM/animation.gif)
Ref:
- [A Tutorial on Graph-Based SLAM](http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf)
# 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/PythonRobotics/raw/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/raw/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/raw/master/PathPlanning/AStar/animation.gif)
In the animation, cyan points are searched nodes.
Its heuristic is 2D Euclid distance.
### Potential Field algorithm
This is a 2D grid based path planning with Potential Field algorithm.
![PotentialField](https://github.com/AtsushiSakai/PythonRobotics/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)
## Model Predictive Trajectory Generator
This is a path optimization sample on model predictive trajectory generator.
This algorithm is used for state lattice planner.
### Path optimization sample
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/kn05animation.gif)
### Lookup table generation sample
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/lookuptable.png?raw=True)
Ref:
- [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.
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)
### Uniform polar sampling
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/StateLatticePlanner/UniformPolarSampling.gif)
### Biased polar sampling
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/StateLatticePlanner/BiasedPolarSampling.gif)
### Lane sampling
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/StateLatticePlanner/LaneSampling.gif)
## Probabilistic Road-Map (PRM) planning
![PRM](https://github.com/AtsushiSakai/PythonRobotics/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)
　　
## Voronoi Road-Map planning
![VRM](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/VoronoiRoadMap/animation.gif)
This Voronoi road-map planner uses Dijkstra method for graph search.
In the animation, blue points are Voronoi points,
Cyan crosses mean searched points with Dijkstra method,
The red line is the final path of Vornoi Road-Map.
Ref:
- [Robotic Motion Planning](https://www.cs.cmu.edu/~motionplanning/lecture/Chap5-RoadMap-Methods_howie.pdf)
## Rapidly-Exploring Random Trees (RRT)
### Basic RRT
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/RRT/animation.gif)
This is a simple path planning code with Rapidly-Exploring Random Trees (RRT)
Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.
### RRT\*
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/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 dubins path
![PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/RRTDubins/animation.gif)
Path planning for a car robot with RRT and dubins path planner.
### RRT\* with dubins path
![AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/RRTStarDubins/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/raw/master/PathPlanning/RRTStarReedsShepp/animation.gif))
Path planning for a car robot with RRT\* and reeds sheep path planner.
### Informed RRT\*
![irrt](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/InformedRRTStar/animation.gif))
This is a path planning code with Informed RRT\*.
The cyan ellipse is the heuristic sampling domain of Informed RRT\*.
Ref:
- [Informed RRT\*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic](https://arxiv.org/pdf/1404.2334.pdf)
### Batch Informed RRT\*
![irrt](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BatchInformedRRTStar/animation.gif))
This is a path planning code with Batch Informed RRT\*.
Ref:
- [Batch Informed Trees \(BIT\*\): Sampling\-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs](https://arxiv.org/abs/1405.5848)
### Closed Loop RRT\*
A vehicle model based path planning with closed loop RRT\*.
![CLRRT](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/ClosedLoopRRTStar/animation.gif)
In this code, pure-pursuit algorithm is used for steering control,
PID is used for speed control.
Ref:
- [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)
### LQR-RRT\*
This is a path planning simulation with LQR-RRT\*.
A double integrator motion model is used for LQR local planner.
![LQRRRT](https://github.com/AtsushiSakai/PythonRobotics/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)
## Cubic spline planning
A sample code for cubic path planning.
This code generates a curvature continuous 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/raw/master/PathPlanning/CubicSpline/Figure_1.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/CubicSpline/Figure_2.png?raw=True)
![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/CubicSpline/Figure_3.png?raw=True)
## B-Spline planning
![B-Spline](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BSplinePath/Figure_1.png?raw=True)
This is a path planning with B-Spline curse.
If you input waypoints, it generates a smooth path with B-Spline curve.
The final course should be on the first and last waypoints.
Ref:
- [B\-spline \- Wikipedia](https://en.wikipedia.org/wiki/B-spline)
## Eta^3 Spline path planning
![eta3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/Eta3SplinePath/animation.gif?raw=True)
This is a path planning with Eta^3 spline.
Ref:
- [\eta^3-Splines for the Smooth Path Generation of Wheeled Mobile Robots](https://ieeexplore.ieee.org/document/4339545/)
## Bezier path planning
A sample code of Bezier path planning.
It is based on 4 control points Beier path.
![Bezier1](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BezierPath/Figure_1.png?raw=True)
If you change the offset distance from start and end point,
You can get different Beizer course:
![Bezier2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/BezierPath/Figure_2.png?raw=True)
Ref:
- [Continuous Curvature Path Generation Based on Bezier Curves for Autonomous Vehicles](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.294.6438&rep=rep1&type=pdf)
## Quintic polynomials planning
Motion planning with quintic polynomials.
![2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/QuinticPolynomialsPlanner/animation.gif)
It can calculate 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/)
## Dubins path planning
A sample code for Dubins path planning.
![dubins](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathPlanning/DubinsPath/animation.gif?raw=True)
Ref:
- [Dubins path - Wikipedia](https://en.wikipedia.org/wiki/Dubins_path)
## Reeds Shepp planning
A sample code with Reeds Shepp path planning.
![RSPlanning](https://github.com/AtsushiSakai/PythonRobotics/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/PythonRobotics/raw/master/PathPlanning/LQRPlanner/animation.gif?raw=true)
## Optimal Trajectory in a Frenet Frame
![3](https://github.com/AtsushiSakai/PythonRobotics/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 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/PythonRobotics/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)
## Pure pursuit tracking
Path tracking simulation with pure pursuit steering control and PID speed control.
![2](https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathTracking/pure_pursuit/animation.gif)
The red line is a target course, the green cross means the target point for pure pursuit control, the blue line is the tracking.
Ref:
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://arxiv.org/abs/1604.07446)
## Stanley control
Path tracking simulation with Stanley steering control and PID speed control.
![2](https://github.com/AtsushiSakai/PythonRobotics/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/PythonRobotics/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) steering 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/raw/master/PathTracking/lqr_steer_control/animation.gif)
Ref:
- [ApolloAuto/apollo: An open autonomous driving platform](https://github.com/ApolloAuto/apollo)
## Linear–quadratic regulator (LQR) speed and steering control
Path tracking simulation with LQR speed and steering control.
![3](https://github.com/AtsushiSakai/PythonRobotics/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.
<img src="https://github.com/AtsushiSakai/PythonRobotics/raw/master/PathTracking/model_predictive_speed_and_steer_control/animation.gif" width="640">
Ref:
- [notebook](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/model_predictive_speed_and_steer_control/notebook.ipynb)
# Arm Navigation
## Two joint arm to point control
Two joint arm to a point control simulation.
This is a interactive simulation.
You can set the goal position of the end effector with left-click on the ploting area.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/ArmNavigation/two_joint_arm_to_point_control/animation.gif)
## N joint arm to point control
N joint arm to a point control simulation.
This is a interactive simulation.
You can set the goal position of the end effector with left-click on the ploting area.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/ArmNavigation/n_joint_arm_to_point_control/animation.gif)
In this simulation N = 10, however, you can change it.
# Aerial Navigation
## drone 3d trajectory following
This is a 3d trajectory following simulation for a quadrotor.
![3](https://github.com/AtsushiSakai/PythonRobotics/raw/master/AerialNavigation/drone_3d_trajectory_following/animation.gif)
# License
MIT
@@ -80,7 +795,7 @@ E-mail consultant is also available.
　
Your comment using [![Say Thanks!](https://img.shields.io/badge/Say%20Thanks-!-1EAEDB.svg)](https://saythanks.io/to/AtsushiSakai) is also welcome.
Your comment using [![Say Thanks!](https://img.shields.io/badge/Say%20Thanks-!-1EAEDB.svg)](https://saythanks.io/to/AtsushiSakai) is also welcome.
This is a list: [Users comments](https://github.com/AtsushiSakai/PythonRobotics/blob/master/users_comments.md)
@@ -97,3 +812,6 @@ This is a list: [Users comments](https://github.com/AtsushiSakai/PythonRobotics/
- [Antonin RAFFIN](https://github.com/araffin)
- [Alexis Paques](https://github.com/AlexisTM)

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