Introduction

This package contains the IRIS algorithm for iterative convex regional inflation by semidefinite programming, implemented in MATLAB and Python. It is designed to take an environment containing many (convex) obstacles and a start point, and to compute a large convex obstacle-free region. This region can then be used to define linear constraints for some other objective function which the user might want to optimize over the obstacle-free space. The algorithm is described in:

R. L. H. Deits and R. Tedrake, “Computing large convex regions of obstacle-free space through semidefinite programming,” Submitted to: Workshop on the Algorithmic Fundamentals of Robotics, Aug. 2014. [Online]. Available: http://groups.csail.mit.edu/robotics-center/public_papers/Deits14.pdf

Setup

The primary algorithm is distributed as:

inflate_region.m

You'll need to build a few tools first, and in order to do so, you'll need to make sure that the matlab executable is on your system path. The matlab executable lives in /Applications/MATLAB_R2014b.app/bin/ or similar on OSX and /usr/local/MATLAB/R2014a/bin/ on linux. You can either add that folder to your system PATH variable put a symbolic link to the matlab executable somewhere that is already on your path, like /usr/local/bin.

To build IRIS, just cd into the IRIS folder and run:

make

The MATLAB implementation requires the Mosek toolbox for MATLAB, and the Python implementation currently requires both Mosek and Gurobi. The code is distributed as a MATLAB package, so only the matlab directory (the one that contains the "+iris" folder) needs to be added to your MATLAB path. You should be able to test it by running (in MATLAB):

>>> import iris.test.*;
>>> test_poly_2d;

Pods Compatibility

This software is designed to be compatible with the Pods guidelines: http://sourceforge.net/p/pods/home/Home/. If that means nothing to you, don't worry about it: just make sure the matlab folder is on your MATLAB path and/or the python folder is on your PYTHONPATH. If you are familiar with Pods, then you can also use the wrapper pods provided by the RobotLocomotion group to satisfy the Gurobi and Mosek dependencies (licenses for both must be acquired separately).

• Gurobi: https://github.com/RobotLocomotion/gurobi
• Mosek: https://github.com/RobotLocomotion/mosek

Python Implementation

An experimental Python implementation of the base algorithm is also provided in python/irispy. You can see a demonstration of its operation in irispy_exploration.ipynb (an IPython notebook), which can also be viewed online through nbviewer

Python Requirements

To run the Python implementation, you will need at least:

* numpy
* scipy
* PyPolyhedron: http://cens.ioc.ee/projects/polyhedron/

Examples

Here are some animations of the algorithm running in various environments:

2-dimensional space, 30 obstacles:

2-dimensional space, 50 obstacles:

2-dimensional space, 50 obstacles:

2-dimensional space, 1000 obstacles:

3-dimensional space:

3-dimensional space:

3-dimensional configuration space of a rod-shaped robot translating and yawing:

3-dimensional slice of a 4-dimensional region among 4D obstacles:

Example Application

This is a demonstration of path-planning for a simple UAV model around obstacles. Rather than constraining that the UAV be outside the obstacles, we seed several IRIS regions and require that the UAV be inside one of those regions at each time step. This turns a non-convex problem into a mixed-integer convex problem, which we can solve to its global optimum. You can try this out by running iris.test.test_uav_demo(); or iris.test.test_uav_demo('4d');