Python codes for robotics algorithm.

• Requirements
• How to use
• Localization
  • Extended Kalman Filter localization
  • Unscented Kalman Filter localization
  • Particle Filter localization
• Path Planning
  • Dynamic Window Approach
  • Grid based search
    • Dijkstra algorithm
    • A* algorithm
    • Potential Field algorithm
  • Model Predictive Trajectory Generator
    • Path optimization sample
    • Lookup table generation sample
  • State Lattice Planning
    • Uniform polar sampling
    • Biased polar sampling
    • Lane sampling
  • Probabilistic Road-Map (PRM) planning
  • Voronoi Road-Map planning
  • Rapidly-Exploring Random Trees (RRT)
    • Basic RRT
    • RRT*
    • RRT with dubins path
    • RRT* with dubins path
    • RRT* with reeds-sheep path
    • Closed Loop RRT*
  • Cubic spline planning
  • B-Spline planning
  • Bezier path planning
  • Quintic polynomials planning
  • Dubins path planning
  • Reeds Shepp planning
  • Optimal Trajectory in a Frenet Frame
  • Mix Integer Optimization based model predictive planning and control
• Path tracking
  • Pure pursuit tracking
  • Stanley control
  • Rear wheel feedback control
  • Linear–quadratic regulator (LQR) steering control
  • Linear–quadratic regulator (LQR) speed and steering control
  • Model predictive speed and steering control
• License
• Author

• Python 3.6.x

• numpy

• scipy

• matplotlib

• pandas

• cvxpy

1. Install the required libraries.

2. Clone this repo.

3. Execute python script in each directory.

4. Add star to this repo if you like it 😃.

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 gren point is positioning observation (ex. GPS), and the red line is estimated trajectory with EKF.

The red ellipse is estimated covariance ellipse with EKF.

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

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 assumued that the robot can measure a distance from landmarks (RFID).

This measurements are used for PF localization.

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

• The Dynamic Window Approach to Collision Avoidance

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

In the animation, cyan points are searched nodes.

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

In the animation, cyan points are searched nodes.

It's heuristic is 2D Euclid distance.

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:

• Robotic Motion Planning:Potential Functions

This is a path optimization sample on model predictive trajectory generator.

This algorithm is used for state lattice planner.

Ref:

• Optimal rough terrain trajectory generation for wheeled mobile robots

　

This script is a path planning code with state lattice planning.

This code uses the model predictive trajectory generator to solve boundary problem.

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

　　

This Voronoi road-map planner uses Dijkstra method for graph search.

In the animation, blue points are Voronoi points,

Cyan crosses means searched points with Dijkstra method,

The red line is the final path of Vornoi Road-Map.

Ref:

• Robotic Motion Planning

This script 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.

This script 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

• Sampling-based Algorithms for Optimal Motion Planningj

Path planning for a car robot with RRT and dubins path planner.

Path planning for a car robot with RRT* and dubins path planner.

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

A vehicle model based path planning with closed loop RRT*.

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

• Real-time Motion Planning with Applications to Autonomous Urban Driving

• [1601.06326] Sampling-based Algorithms for Optimal Motion Planning Using Closed-loop Prediction

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.

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

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:

• Continuous Curvature Path Generation Based on B ́ezier Curves for Autonomous Vehicles

Motion planning with quintic polynomials.

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

Ref:

• Local Path Planning And Motion Control For Agv In Positioning

A sample code for Dubins path planning.

Ref:

• Dubins path - Wikipedia

A sample code with Reeds Shepp path planning.

Ref:

• 15.3.2 Reeds-Shepp Curves

• optimal paths for a car that goes both forwards and backwards

• ghliu/pyReedsShepp: Implementation of Reeds Shepp curve.

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

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

This code uses cvxpy as an optimization modeling tool,

• Welcome to CVXPY 1.0 — CVXPY 1.0.0 documentation

Gurobi is used as a solver for mix integer optimization problem.

• Gurobi Optimization - The State-of-the-Art Mathematical Programming Solver

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:

• A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles

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

Ref:

• Stanley: The robot that won the DARPA grand challenge

• Automatic Steering Methods for Autonomous Automobile Path Tracking

Path tracking simulation with rear wheel feedback steering control and PID speed control.

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

Path tracking simulation with LQR 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,

• Welcome to CVXPY 1.0 — CVXPY 1.0.0 documentation

MIT

Atsushi Sakai (@Atsushi_twi)