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

1) Restrictive Inflation is designed to ensure the managibility of the generated convex polytope. Based on its characteristic of few variables but rich constraints, an efficient and numerically stable solver is designed. 2) A novel method that formulates the MVIE problem into SOCP formulation is proposed, which avoids directly confronting the positive definite constraints and improves the computational efficiency. 3) Especially for 2-D MVIE, a linear-time exact algorithm is introduced for the first time, filling a gap that existed for several decades and further enabling ultra-fast computational performance. 4) Building upon the above methods, a reliable convex polytope generation algorithm FIRI is proposed. Extensive experiments verify its superior comprehensive performance in terms of quality, efficiency, and managibility. High-performance implementation of FIRI will be open-sourced for the reference of the community.