We propose two novel algorithms for constructing convex collision-free polytopes in robot configuration space. Finding these polytopes enables the application of stronger motion-planning frameworks such as trajectory optimization with Graphs of Convex Sets [1] and is currently a major roadblock in the adoption of these approaches. In this paper, we build upon IRIS-NP (Iterative Regional Inflation by Semidefinite & Nonlinear Programming) [2] to significantly improve tunability, runtimes, and scaling to complex environments. IRIS-NP uses nonlinear programming paired with uniform random initialization to find configurations on the boundary of the free configuration space. Our key insight is that finding near-by configuration-space obstacles using sampling is inexpensive and greatly accelerates region generation. We propose two algorithms using such samples to either employ nonlinear programming more efficiently (IRIS-NP2 ) or circumvent it altogether using a massively-parallel zero-order optimization strategy (IRIS-ZO). We also propose a termination condition that controls the probability of exceeding a user-specified permissible fraction-in-collision, eliminating a significant source of tuning difficulty in IRIS-NP. We compare performance across eight robot environments, showing that IRIS-ZO achieves an order-of-magnitude speed advantage over IRIS-NP. IRISNP2, also significantly faster than IRIS-NP, builds larger polytopes using fewer hyperplanes, enabling faster downstream computation. Website: https://sites.google.com/view/fastiris

翻译：本文提出两种在机器人构型空间中构建无碰撞凸多面体的新算法。寻找此类多面体对于应用更强大的运动规划框架（如基于凸集图的轨迹优化[1]）至关重要，目前是此类方法推广应用的主要障碍。本文基于IRIS-NP（基于半定规划与非线规划的区域迭代膨胀算法）[2]，显著提升了算法可调性、运行效率及对复杂环境的适应能力。IRIS-NP通过结合非线性规划与均匀随机初始化来寻找自由构型空间边界上的构型。我们的核心发现是：通过采样寻找邻近构型空间障碍物的计算成本较低，并能极大加速区域生成过程。基于此，我们提出两种算法：一种通过采样更高效地运用非线性规划（IRIS-NP2），另一种采用大规模并行零阶优化策略完全规避非线性规划（IRIS-ZO）。同时，我们提出一种终止条件，用于控制超出用户指定允许碰撞比例的概率，从而消除了IRIS-NP中一个重要的参数调节难点。通过在八种机器人环境中进行性能对比，实验表明IRIS-ZO相比IRIS-NP实现了一个数量级的加速；IRIS-NP2同样显著快于IRIS-NP，且能以更少的超平面构建更大的多面体，从而加速下游计算。项目网站：https://sites.google.com/view/fastiris