MIT's biconvex motion planner guarantees smooth minimum-time trajectories around obstacles

A new paper from MIT CSAIL presents a biconvex optimization framework for minimum-time robot trajectory planning around convex obstacles. The method, developed by Peter Werner, Tobia Marcucci, and Daniela Rus, jointly convexifies the minimum-time objective and all derivative constraints via a change of variables, then handles collision avoidance with time-varying separating planes. The resulting biconvex program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory—a strategy that lets the solution jump between obstacles and escape local minima. The algorithm is anytime, meaning it can return a valid trajectory if stopped early, and it is guaranteed to converge from a simple collision-free polygonal curve.

In experiments on drone navigation and dual-arm bin unloading, the approach produced high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a broader class of problems and showing substantially more robustness to poor initialization. Because it supports derivative constraints to arbitrary order, the planner can enforce smoothness on velocity, acceleration, jerk, and beyond, which is critical for physically feasible robot motion. The paper is 18 pages with 9 figures and 4 tables, has been submitted to IEEE Transactions on Robotics, and includes an associated project page and code release.