# 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.

### D* algorithm¶

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

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

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### 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.

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## 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¶

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## 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.

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- Optimal rough terrain trajectory generation for wheeled mobile robots
- State Space Sampling of Feasible Motions for High-Performance Mobile Robot Navigation in Complex Environments

### Uniform polar sampling¶

### Biased polar sampling¶

### Lane sampling¶

## Probabilistic Road-Map (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.

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## Voronoi Road-Map planning¶

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.

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## Rapidly-Exploring Random Trees (RRT)¶

### Basic RRT¶

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*¶

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.

### 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 reeds-sheep 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*.

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### Closed Loop RRT*¶

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.

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### LQR-RRT*¶

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

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

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## 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.

## B-Spline planning¶

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.

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## 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:

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## Quintic polynomials planning¶

Motion planning with quintic polynomials.

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

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## 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.

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