Resolution-Exact Planner for Thick Non-Crossing 2-Link Robots
This addresses path planning for a specific class of robots with practical constraints like thickness and non-crossing links, offering improved performance over existing methods.
The paper tackles path planning for thick non-crossing 2-link robots in polygonal obstacles by designing a resolution-exact planner using Soft Subdivision Search, achieving real-time performance and significantly outperforming state-of-the-art sampling algorithms in timing and success rate.
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 $τ\ge 0$ of the links, and an angle $κ$ that constrains the angle between the 2 links to be strictly greater than $κ$. The case $τ>0$ and $κ\ge 0$ corresponds to "thick non-crossing" robots. This results in a novel 4DOF configuration space ${\mathbb R}^2\times ({\mathbb T}\setminusΔ(κ))$ where ${\mathbb T}$ is the torus and $Δ(κ)$ the diagonal band of width $κ$. 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.