Invited talk: Motion Planning around Obstacles with Convex Optimization by Tobia Marcucci, MIT

From quadrotors delivering packages in urban areas to robot arms moving in confined warehouses, motion planning around obstacles is a core challenge in modern robotics. Planners based on numerical optimization can design trajectories in high-dimensional spaces while taking into account the robot dynamics. However, in the presence of obstacles, these optimizations become nonconvex and very hard to solve, even just locally. Thus, when facing cluttered environments, roboticists typically fall back to sampling-based planners that do not scale equally well to high dimensions and that struggle with continuous differential constraints. In this talk I will present a new framework that enables convex optimization to efficiently and reliably plan optimal trajectories around obstacles. Specifically, I will focus on collision-free motion planning with cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Using optimization techniques that we recently developed for finding shortest paths in graphs of convex sets, we design a practical convex relaxation of the planning problem. This relaxation is typically very tight, to the point that a cheap post-processing of its solution is almost always sufficient to identify a globally-optimal collision-free trajectory. Through numerical and hardware experiments, I will demonstrate that our planner can outperform widely-used sampling-based algorithms and can reliably design trajectories in high-dimensional cluttered environments.