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This paper introduces a biconvex optimization framework for minimum-time motion planning that effectively navigates around convex obstacles while adhering to derivative constraints. By transforming the problem into a biconvex program and employing time-varying separating planes, the method ensures convergence and robustness, even with challenging initial conditions. Experimental results demonstrate that the approach yields high-quality trajectories for drone navigation and dual-arm bin unloading, with computation times on par with leading motion planners.
Achieving reliable, high-quality motion planning around convex obstacles is now feasible even with poor initial conditions, thanks to a novel biconvex optimization approach.
We present a biconvex approach for minimum-time motion planning around convex obstacles that is guaranteed to converge, is anytime, and supports derivative constraints to arbitrary order. We jointly convexify the minimum-time objective and all derivative constraints through a change of variables, and handle collision avoidance via time-varying separating planes, reducing the problem to a biconvex program. This program is solved by alternating between computing maximum-margin separating planes and optimizing the trajectory. By only adding planes for obstacles that the current iterate collides with, the trajectory can jump around obstacles and escape local minima. The method is guaranteed to converge starting from a simple collision-free polygonal curve. In our experiments on drone navigation and dual-arm bin unloading, we find that the proposed method reliably produces high-quality trajectories with computation times comparable to state-of-the-art decomposition-based motion planners, while handling a larger class of problems and being substantially more robust to bad initialization. Project page:https://wernerpe.github.io/bmtp-website/
MIT CSAIL