無限回微分可能な集合間符号付き距離h-NESDFとロボティクス応用
h-NESDF: An Infinitely Differentiable Signed Distance Between Two Sets with Robotic Applications
2つの集合間の距離を滑らかにするパラメータhを導入し、h→0で通常の符号付き距離に収束する無限回微分可能な距離関数h-NESDFを提案。GPU並列化可能で、動作計画での有効性をシミュレーションで示した。
著者: Vinicius Mariano Gonçalves, Pedro Antonio de Souza Campos Rodrigues
分類: cs.RO
原文アブストラクト
Computing distances between sets is important in many robotic applications, such as motion planning and control. In many applications, derivatives of the distance are needed as well. It is well known that the Euclidean distance is not always differentiable, which create issues to algorithms that need a derivative. In this paper, we introduce NESDF, the Normal Euclidean Signed Distance Function between two general (with mild regularity assumptions but possibly non-convex) sets. This metric is still not differentiable, but it allows us to introduce a generalization, $h$-NESDF, which has a smoothing parameter $h$ such that the metric is infinitely differentiable for all $h>0$ and that reduces to the NESDF when $h$ goes to $0$. The metric is amenable to GPU parallelization, and thus can be computed efficiently. We show extensive simulation results to evaluate its viability in motion planning.