Fast Iterative Region Inflation for Computing Large 2-D/3-D Convex Regions of Obstacle-Free Space
Qianhao Wang, Zhepei Wang, Mingyang Wang, Jialin Ji, Zhichao Han, Tianyue Wu, Rui Jin, Yuman Gao, Chao Xu, Fei Gao
AI summary
Problem
Existing methods for generating convex polytopes from obstacle-free spaces struggle to balance computational efficiency, large volume output, and the critical requirement of accurately containing specified seed points like robot shapes or paths.
Approach
The algorithm iteratively alternates between a Restrictive Inflation step that guarantees seed containment while excluding obstacles, and a Maximum Volume Inscribed Ellipsoid computation that monotonically expands the polytope's volume lower bound.
Key results
- Restrictive Inflation module guarantees seed containment via specialized low-dimensional QP solver
- Novel SOCP formulation for MVIE eliminates positive-definite constraints and boosts efficiency
- First linear-complexity analytical algorithm for 2-D MVIE enables ultra-fast computation
- Orders-of-magnitude speedup and superior quality/manageability over state-of-the-art methods in benchmarks and real-world robotics tasks
Why it matters
Enables real-time, reliable safe corridor and trajectory generation for robotics applications by overcoming the traditional trade-off between speed, volume quality, and seed containment.
Abstract
Convex polytopes have compact representations and exhibit convexity, which makes them suitable for abstracting obstacle-free spaces from various environments. Existing genera- tion 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 paper, we propose Fast Iterative Regional Inflation (FIRI) to generate high-quality convex poly- tope while ensuring efficiency and manageability simultaneously. FIRI consists of two iteratively executed submodules: Restric- tive 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 multi-constrained 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.