Faster Algorithms for Growing Collision-Free Convex Polytopes in Robot Configuration Space

TL;DR

This paper introduces two new algorithms, IRIS-NP2 and IRIS-ZO, that significantly improve the speed and scalability of constructing convex collision-free regions in robot configuration space, facilitating advanced motion planning.

Contribution

The paper presents novel algorithms that enhance the efficiency and scalability of convex region construction in configuration space, building upon and improving IRIS-NP with sampling-based acceleration and parallel optimization.

Findings

IRIS-ZO achieves an order-of-magnitude speedup over IRIS-NP.

IRIS-NP2 constructs larger polytopes with fewer hyperplanes.

Both algorithms outperform IRIS-NP in complex environments.

Abstract

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