Fast Iterative Region Inflation for Computing Large 2-D/3-D Convex Regions of Obstacle-Free Space

Abstract

Convex polytopes have compact representations and exhibit convexity, which makes them suitable for abstracting obstacle-free spaces from various environments. Existing generation methods struggle with balancing high-quality output and efficiency. Moreover, another crucial requirement for convex polytopes to accurately contain certain seed point sets, such as a robot or a front-end path, is proposed in various tasks, which we refer to as manageability. In this article, we propose fast iterative regional inflation (FIRI) to generate high-quality convex polytope while ensuring efficiency and manageability simultaneously. FIRI consists of two iteratively executed submodules: restrictive inflation (RsI) and maximum volume inscribed ellipsoid (MVIE) computation. By explicitly incorporating constraints that include the seed point set, RsI guarantees manageability. Meanwhile, iterative MVIE optimization ensures high-quality result through monotonic volume bound improvement. In terms of efficiency, we design methods tailored to the low-dimensional and multiconstrained nature of both modules, resulting in orders of magnitude improvement compared to generic solvers. Notably, in 2-D MVIE, we present the first linear complexity analytical algorithm for maximum area inscribed ellipse, further enhancing the performance in 2-D cases. Extensive benchmarks conducted against state-of-the-art methods validate the superior performance of FIRI in terms of quality, manageability, and efficiency. Furthermore, various real-world applications showcase the generality and practicality of FIRI. The high-performance code of FIRI will be open-sourced.