绝对连续参数曲线的逼近算法
Proximity Queries for Absolutely Continuous Parametric Curves
摘要：
在自主机器人（如自动驾驶汽车）的运动规划问题中，机器人必须确保其规划的路径不靠近环境中的障碍物。然而，评估接近度的问题通常是非凸的，并且作为运动规划算法的显著计算瓶颈。在本文中，我们提出的方法，为一般类的绝对连续的参数曲线计算：（i）最小分离距离，（ii）公差验证，和（iii）碰撞检测。我们的方法有效地计算边界上的障碍物接近边界的曲线在一个凸区域。这个界限是基于曲线弧长的上限，该弧长可以用封闭形式表示，用于一类有用的参数曲线，包括具有三角或多项式基的曲线。我们证明了我们的方法的计算效率和准确性，通过数值模拟几个邻近问题。
英文摘要：
In motion planning problems for autonomous robots, such as self-driving cars, the robot must ensure that its planned path is not in close proximity to obstacles in the environment. However, the problem of evaluating the proximity is generally non-convex and serves as a significant computational bottleneck for motion planning algorithms. In this paper, we present methods for a general class of absolutely continuous parametric curves to compute: (i) the minimum separating distance, (ii) tolerance verification, and (iii) collision detection. Our methods efficiently compute bounds on obstacle proximity by bounding the curve in a convex region. This bound is based on an upper bound on the curve arc length that can be expressed in closed form for a useful class of parametric curves including curves with trigonometric or polynomial bases. We demonstrate the computational efficiency and accuracy of our approach through numerical simulations of several proximity problems.
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