# Path Planning¶

## Dynamic Window Approach¶

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

## Model Predictive Trajectory Generator¶

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

This algorithm is used for state lattice planner.

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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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### Lane sampling¶

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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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.

#### Simulation¶

from IPython.display import Image
Image(filename="Figure_1.png",width=600)


### 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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### Batch Informed RRT*¶

This is a path planning code with Batch 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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## Eta^3 Spline path planning¶

This is a path planning with Eta^3 spline.

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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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## Dubins path planning¶

A sample code for Dubins path planning.

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## Reeds Shepp planning¶

A sample code with Reeds Shepp path planning.

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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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