中国农业机械化科学研究院集团有限公司 主管

北京卓众出版有限公司 主办

基于参数多项式的农机导航局部路径平滑算法研究

Research on local path smoothing algorithm for agricultural machinery navigation based on parametric polynomial

  • 摘要: 离散路径点形式的路径通常存在不够平滑及分布不均匀问题,同时其航向不连续,使得离散点路径不便于直接用于农机路径跟踪。提出一种基于五次参数多项式曲线的局部路径平滑算法。首先根据农机实时坐标确定路径点序列上的目标参考点并通过扩充得到平滑区间。计算序列内各点与起始点之间近似弧长并将其用作多项式曲线初始自变量,通过最小二乘法得到多项式各项参数,进而采用牛顿法迭代优化平滑区间内各节点对应的自变量取值。重复此过程并最终确定出五次多项式曲线表达式。试验选取3段轨迹进行平滑和分析,结果表明,平滑曲线与原始轨迹点之间平均偏差绝对值≤0.0946 cm、最大偏差绝对值≤8.35 cm,说明该算法可以有效地对局部路径进行平滑并且具备良好精度。

     

    Abstract: Paths represented by discrete points are not suitable for agricultural machinery navigation path tracking directly for they are usually not smooth enough and have uneven distribution as well as discontinuous heading angle.A local path smoothing algorithm based on quintic parametric polynomial curve was proposed.Firstly, target reference point on path point list was calculated using real-time coordinates of agricultural machinery and smoothing section was required by expansion.Approximate arc lengths between each point and starting point within sequence were calculated and used as initial independent variables for polynomial curve.Polynomial parameters were calculated by the least squares method, and independent variables corresponding to each path point in smoothing section were optimized iteratively using Newton algorithm.Quintic polynomial curve was generated by repeating iteration process mentioned above.Three path sections were selected for path smoothing test and analysis.Results showed that the maximum absolute average error between smoothed curve and initial trajectory points was ≤0.0946 cm and the maximum absolute extreme error was ≤ 8.35 cm, indicating that algorithm could effectively smooth local discrete path with high precision.

     

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