### Reimplementing GCS (Shortest Paths in Graphs of Convex Sets)

In a previous blog post , I discussed my experiences reimplementing Iterative Regional Inflation by Semidefinite programming (IRIS) , which is an algorithm for finding large convex regions of collision free space (C-Free). In this blog post, I'll be discussing my experiences reimplementing shortest paths in Graphs of Convex Sets (GCS) , an algorithm for motion planning when the configuration space is described as the union of convex sets. Disclaimer: the intent is not to build a codebase for future use, since the Drake toolbox has mature implementations of both IRIS and GCS . Disclaimer: if you have not read the previous blog post , you should do so before reading this one. In this blogpost, I'll give a brief overview of the GCS paper, and then discuss my experiences reimplementing it. Before reading this blog post, you should read my previous blog post about reimplementing IRIS, as it provides some background and context which I will not repeat in this post. I have also ma