Problem: Find the unobstructed reachable space and maximize it. Solutions to this problem are implemented in rapid manufacturing, self-driving cars, UAV obstacle avoidance, and legged robotics.
Solution: Maximize the obstacle-free space using Quadratic and Semi Definite Programming based on the maximal volume ellipsoid inscribed in a polyhedron. Algorithm based on the paper Computing Large Convex Regions of Obstacle-Free Space through Semidefinite Programming by Robin Deits and Russ Tedrake.
The algorithm was developed using MATLAB and CVX as a final project in the Convex Optimization course.
Yves Daoud 