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首页> 外文期刊>IEEE Transactions on Robotics >Accurate and Efficient Approximation of Clothoids Using Bézier Curves for Path Planning
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Accurate and Efficient Approximation of Clothoids Using Bézier Curves for Path Planning

机译：使用贝塞尔曲线进行路径规划的精确有效的类齿波近似

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摘要

An accurate and efficient clothoid approximation approach is presented in this paper using Bézier curves based on the minimization of curvature profile difference. Compared with existing methods, the proposed approach is able to guarantee higher order geometric continuity with smaller approximation error in terms of position, orientation, and curvature. The approximation scheme takes place in three stages. First, a subset of clothoids with specific winding angle constraints referred to as elementary clothoids is approximated using quintic Bézier curves. Then, a basic clothoid defined in the first quadrant is formulated, which is composed of a series of transformed elementary clothoids. An adaptive sampling stra-tegy is applied to ensure that the resulting Bézier segments are computed within a specified accuracy and all the required information can be obtained offline and stored in a lookup table. Finally, a general clothoid with arbitrary parameters can be conveniently approximated based on the lookup table through appropriate geometric transformations. A comparison with the recent circular interpolation and rational Bézier curve based approximation shows that the proposed approach is able to achieve equivalent or greater computational efficiency in most scenarios.
机译：本文基于最小化曲率轮廓差的Bézier曲线，提出了一种准确有效的回旋曲线逼近方法。与现有方法相比，所提出的方法能够保证高阶几何连续性，并且在位置，方向和曲率方面具有较小的近似误差。近似方案分为三个阶段。首先，使用五次贝塞尔曲线对具有特定绕角约束的回旋子集（称为基本回旋）进行近似。然后，公式化了在第一象限中定义的基本回旋曲线，它由一系列变换后的基本回旋曲线组成。应用自适应抽样策略以确保在指定的精度范围内计算所得的贝塞尔曲线段，并且可以脱机获取所有所需信息并将其存储在查找表中。最后，可以通过适当的几何变换，基于查找表方便地近似具有任意参数的一般回旋曲线。与最近的圆弧插值法和基于有理贝塞尔曲线的近似方法的比较表明，所提出的方法在大多数情况下能够实现等效或更高的计算效率。

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  • 来源
    《IEEE Transactions on Robotics》 |2017年第5期|1242-1247|共6页
  • 作者

    Yong Chen; Yiyu Cai; Jianmin Zheng; Daniel Thalmann;

  • 作者单位

    Institute for Media Innovation, and School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore;

    Institute for Media Innovation, and School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore;

    Institute for Media Innovation, and School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore;

    Institute for Media Innovation, and School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore;

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  • 正文语种 eng
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  • 关键词

    Iron; Optimization; Mobile robots; Windings; Fresnel reflection; Shape;

    机译：铁;优化;移动机器人;绕组;菲涅耳反射;形状;

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