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An overview on distance and pseudo distance functions and their applications

机译：距离和伪距离函数及其应用概述

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摘要

The fast and accurate collision detection and distance calculation between geometric models is fundamental in robotics, manufacturing and computer-simulated environments. This paper surveys the state of the art in the theory and algorithms of distance and pseudo distance functions between convex sets. An overview on the existing results, including fast algorithms for distance calculation, definitions and properties of various pseudo distance functions (the J-function, the growth distance, and the pseudo minimum translational distance), is presented. The distance and pseudo distance functions are versatile in a wide range of areas. Their applications in robot motion planning, grasp analysis/synthesis, form error evaluation, and engineering optimization is demonstrated.
机译：几何模型之间快速，准确的碰撞检测和距离计算是机器人技术，制造和计算机模拟环境的基础。本文研究了凸集之间的距离和伪距离函数的理论和算法的最新发展。介绍了现有结果的概述，包括用于距离计算的快速算法，各种伪距离函数（J函数，增长距离和伪最小平移距离）的定义和性质。距离和伪距离功能在广泛的领域中都是通用的。演示了它们在机器人运动计划，抓紧分析/综合，形状误差评估和工程优化中的应用。

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