基于4阶Bézier曲线的路径平滑方法研究  

Research on Path Smoothing Method Based on the Fourth-order Bézier Curve

作　　者：杨鹏飞 赵坤[1] 武林伟[1] 刘培波 YANG Peng-fei;ZHAO Kun;WU Lin-wei;LIU Pei-bo(The 27^(th)Research Institute of China Electronics Technology Group Corporation,Zhengzhou 450047,China)

机构地区：[1]中国电子科技集团公司第二十七研究所,河南郑州450047

出　　处：《中国电子科学研究院学报》2024年第5期448-454,共7页Journal of China Academy of Electronics and Information Technology

摘　　要：路径平滑技术旨在采用以曲代直的方法解决路径规划中存在的尖角问题,实现路径的平滑化,以满足外形设计和运动规划等工程应用需求。文中在深入探讨了Bézier曲线在路径平滑领域的应用优势及其在路径拟合中产生的较大偏差后,提出了一种基于内外比例因子的4阶Bézier曲线路径平滑新方法。通过严谨的理论分析,证明了该方法能够有效控制平滑误差,在不考虑路径节点坐标的情况下,误差上限为4.25,从而实现对原始路径的高精度平滑近似。在无人机路径平滑的仿真实验中,该方法耗时0.0061 s,证明了其在平滑处理速度方面的优越性。综合理论分析与实验结果,该方法不仅在平滑效果上表现出色,而且在处理速度上也具有明显优势。同时由于仅涉及内外比例因子两个自由参数,因此,操作简单,易于实现,具有较强的适用性和灵活性。Path smoothing technology aims to address the issue of sharp corners in path planning by utilizing curved paths instead of straight ones,in order to achieve smooth paths that meet the requirements of engineering applications such as contour design and motion planning.After discussing the advantages of Bezier curves in path smoothing and their significant deviation in path fitting,a new method of fourth-order Bezier curve path smoothing based on internal and external scale factor is proposed in this paper.Through rigorous theoretical analysis,it is demonstrated that this method can effectively control the smoothing error.Without considering the coordinates of the path nodes,the upper limit of the error is 4.25,thus achieving high-precision smoothing approximation of the original path.In simulation experiments for UAV path smoothing,this method has an average time cost of only 0.0061 seconds,exhibiting its superiority in processing speed.Based on theoretical analysis and experimental results,this method not only performs well in terms of smoothing effect but also exhibits clear advantages in processing speed.Additionally,with only two free parameters involved-internal and external scaling factors-it offers simplicity in operation,ease of implementation,and greater applicability and flexibility.

关 键 词：路径平滑 4阶Bézier曲线 内外比例因子 平滑误差 无人机 

分 类 号：TP23[自动化与计算机技术—检测技术与自动化装置]