Resolution-Exact Planner for Thick Non-Crossing 2-Link Robots

Abstract: We consider the path planning problem for a 2-link robot amidst polygonal obstacles. Our robot is parametrizable by the lengths $\ell_1, \ell_2>0$ of its two links, the thickness $\tau \ge 0$ of the links, and an angle $\kappa$ that constrains the angle between the 2 links to be strictly greater than $\kappa$. The case $\tau>0$ and $\kappa \ge 0$ corresponds to "thick non-crossing" robots. This results in a novel 4DOF configuration space ${\mathbb R}^2\times ({\mathbb T}\setminus\Delta(\kappa))$ where ${\mathbb T}$ is the torus and $\Delta(\kappa)$ the diagonal band of width $\kappa$. We design a resolution-exact planner for this robot using the framework of Soft Subdivision Search (SSS). First, we provide an analysis of the space of forbidden angles, leading to a soft predicate for classifying configuration boxes. We further exploit the T/R splitting technique which was previously introduced for self-crossing thin 2-link robots. Our open-source implementation in Core Library achieves real-time performance for a suite of combinatorially non-trivial obstacle sets. Experimentally, our algorithm is significantly better than any of the state-of-art sampling algorithms we looked at, in timing and in success rate.