PythonRobotics
Python codes for robotics algorithm.
Table of Contents
 What is this?
 Requirements
 How to use
 Localization
 Mapping
 SLAM
 Path Planning
 Dynamic Window Approach
 Grid based search
 Model Predictive Trajectory Generator
 State Lattice Planning
 Probabilistic RoadMap (PRM) planning
 Voronoi RoadMap planning
 RapidlyExploring Random Trees (RRT)
 Cubic spline planning
 BSpline planning
 Eta^3 Spline path planning
 Bezier path planning
 Quintic polynomials planning
 Dubins path planning
 Reeds Shepp planning
 LQR based path planning
 Optimal Trajectory in a Frenet Frame
 Path tracking
 License
 Contribution
 Support
 Authors
What is this?
This is a Python code collection of robotics algorithms, especially for autonomous navigation.
Features:

Widely used and practical algorithms are selected.

Minimum dependency.

Easy to read for understanding each algorithm’s basic idea.
Requirements

Python 3.6.x

numpy

scipy

matplotlib

pandas
How to use

Install the required libraries.

Clone this repo.

Execute python script in each directory.

Add star to this repo if you like it :smiley:.
Localization
Extended Kalman Filter localization
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:
Unscented Kalman Filter localization
This is a sensor fusion localization with Unscented Kalman Filter(UKF).
The lines and points are same meaning of the EKF simulation.
Ref:
Particle filter localization
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:
Histogram filter localization
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:
Mapping
Gaussian grid map
This is a 2D Gaussian grid mapping example.
Ray casting grid map
This is a 2D ray casting grid mapping example.
kmeans object clustering
This is a 2D object clustering with kmeans algorithm.
Object shape recognition using circle fitting
This is an object shape recognition using circle fitting.
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.
Ref:
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.
Ref:
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.
Ref:
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.
Ref:
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.
Ref:
Path Planning
Dynamic Window Approach
This is a 2D navigation sample code with Dynamic Window Approach.
Grid based search
Dijkstra algorithm
This is a 2D grid based shortest path planning with Dijkstra’s algorithm.
In the animation, cyan points are searched nodes.
A* algorithm
This is a 2D grid based shortest path planning with A star algorithm.
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.
In the animation, the blue heat map shows potential value on each grid.
Ref:
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
Lookup table generation sample
Ref:
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:
Uniform polar sampling
Biased polar sampling
Lane sampling
Probabilistic RoadMap (PRM) planning
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:
Voronoi RoadMap planning
This Voronoi roadmap 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 RoadMap.
Ref:
RapidlyExploring Random Trees (RRT)
Basic RRT
This is a simple path planning code with RapidlyExploring Random Trees (RRT)
Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.
RRT*
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:
RRT with dubins path
Path planning for a car robot with RRT and dubins path planner.
RRT* with dubins path
Path planning for a car robot with RRT* and dubins path planner.
RRT* with reedssheep path
)
Path planning for a car robot with RRT* and reeds sheep path planner.
Informed RRT*
)
This is a path planning code with Informed RRT*.
The cyan ellipse is the heuristic sampling domain of Informed RRT*.
Ref:
Batch Informed RRT*
)
This is a path planning code with Batch Informed RRT*.
Ref:
Closed Loop RRT*
A vehicle model based path planning with closed loop RRT*.
In this code, purepursuit algorithm is used for steering control,
PID is used for speed control.
Ref:

Motion Planning in Complex Environments using Closedloop Prediction

Realtime Motion Planning with Applications to Autonomous Urban Driving

[1601.06326] Samplingbased Algorithms for Optimal Motion Planning Using Closedloop Prediction
LQRRRT*
This is a path planning simulation with LQRRRT*.
A double integrator motion model is used for LQR local planner.
Ref:
Cubic spline planning
A sample code for cubic path planning.
This code generates a curvature continuous path based on xy waypoints with cubic spline.
Heading angle of each point can be also calculated analytically.
BSpline planning
This is a path planning with BSpline curse.
If you input waypoints, it generates a smooth path with BSpline curve.
The final course should be on the first and last waypoints.
Ref:
Eta^3 Spline path planning
This is a path planning with Eta^3 spline.
Ref:
Bezier path planning
A sample code of Bezier path planning.
It is based on 4 control points Beier path.
If you change the offset distance from start and end point,
You can get different Beizer course:
Ref:
Quintic polynomials planning
Motion planning with quintic polynomials.
It can calculate 2D path, velocity, and acceleration profile based on quintic polynomials.
Ref:
Dubins path planning
A sample code for Dubins path planning.
Ref:
Reeds Shepp planning
A sample code with Reeds Shepp path planning.
Ref:
LQR based path planning
A sample code using LQR based path planning for double integrator model.
Optimal Trajectory in a Frenet Frame
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

Optimal trajectory generation for dynamic street scenarios in a Frenet Frame
Path tracking
Pure pursuit tracking
Path tracking simulation with pure pursuit steering control and PID speed control.
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:
Stanley control
Path tracking simulation with Stanley steering control and PID speed control.
Ref:
Rear wheel feedback control
Path tracking simulation with rear wheel feedback steering control and PID speed control.
Ref:
Linear–quadratic regulator (LQR) steering control
Path tracking simulation with LQR steering control and PID speed control.
Ref:
Linear–quadratic regulator (LQR) speed and steering control
Path tracking simulation with LQR speed and steering control.
Ref:
Model predictive speed and steering control
Path tracking simulation with iterative linear model predictive speed and steering control.
This code uses cvxpy as an optimization modeling tool.
Ref:
License
MIT
Contribution
A small PR like bug fix is welcome.
If your PR is merged multiple times, I will add your account to the author list.
Support
You can support this project financially via Patreon.
You can get email technical supports about the codes if you are being a patron.
PayPal donation is also welcome.