Multiple Rapidly-exploring Random Tree (RRT)

Multiple RRT implementation for mobile robot path planning or C-space manipulator motion planning

% See Usage section in RrtPlanner.m file. This is a basic example of usage:

treesMax = 28; %How many multiple trees (must be at least 2, 1 for source and 1 for destination

seedsPerAxis = 3; %Number of seeds allowed on each axis (discretely placed seeds which idealy helps the RRT expansion)

wallCount = 5; %Number of mock walls to be placed in the environment

rrt = RrtPlanner(treesMax,seedsPerAxis,wallCount)
rrt.SetStart([0 -0.9 0]);
rrt.SetGoal([0 +0.9 0]);
rrt.Run()
plot3(rrt.smoothedPath(:,1),rrt.smoothedPath(:,2),rrt.smoothedPath(:,3),'k*');
delete(rrt);

obstacleFilename = 'obstacles.txt';
seedsPerAxis = 7;
treesMax = seedsPerAxis^3*3+2;
rrt = RrtPlanner(treesMax,seedsPerAxis,obstacleFilename);
rrt.drawingSkipsPerDrawing = 30;
rrt = RrtPlanner(treesMax,seedsPerAxis,obstacleFilename);
rrt.Run()
plot3(rrt.path(:,1),rrt.path(:,2),rrt.path(:,3),'k*');

% To generate an obstacle: create them by specifying rectangular planes as a set of 4 points around the bounds of a rectangle
A-------- B
| |
| |
| |
D---------C

% If this is flat on the z plane at 0.5 then the file would look something like this (with the x,y,z of A, B, C, D on separate lines)
0 0 0.5
1 0 0.5
1 1 0.5
0 1 0.5

A YouTube video of a simple case of this planner can be found here:
http://youtu.be/LodUn86QAfg

About RRTs:
RRTs first published in [1] are randomised planners especially adept at solving difficult,high-dimensional path planning problems. However, environments with low-connectivity due to the presence of obstacles can severely affect convergence. Multiple RRTs have been proposed as a means of addressing this issue, however, this approach can adversely affect computational efficiency.

This paper [2] published by the authors of this Matlab code is the implementation of multiple Rapidly-exploring Random Tree (RRT) algorithm work. This paper introduces a new and simple method which takes advantage of the benefits of multiple trees, whilst ensuring the computational burden of maintaining them is minimised. Results indicate that multiple RRTs are able to reduce the logarithmic complexity of the search, most notably in environments with high obstacle densities.

[1] LaValle, S. M., ‘Rapidly-Exploring Random Trees: A New Tool for Path Planning’, TR 98-11, Computer Science Department, Iowa State University, Oct. 1998.
[2] Matthew Clifton, Gavin Paul, Ngai Kwok, Dikai Liu, Da-Long Wang, "Evaluating Performance of Multiple RRTs", IEEE conference on Mechatronic and Embedded Systems and Application, 2008