为便于机器人在避障时能高速前进,把整体G²连续的低次避障曲线从参数形式拓展到代数样条形式上。首先,对导向折线段中除去首末线段的其他线段插入中点,以生成一组控制多边形;然后,根据各控制多边形和与之对应的障碍物,得到既能使曲线规避所有障碍物,又能使曲线在整体上保持G²连续的形状因子。低次避障代数样条曲线不仅能够直接得到与给定点之间的位置关系,还具有次数低、连续阶高、计算简单、保形性好和便于控制的优点。曲线在次数为3时更是具有局部可调性,其在设计时的灵活度得以增加。

We extend the construction of a G² continuous curve based on a guiding polyline from the parametric form to the quadric and cubic algebraic spline form to avoid obstacles. First, a series of control polygons are obtained by adding the midpoints of guiding polylines except for the first and last line segments. Then, based on the control polygons and the corres- ponding obstacles, the shape parameter(s)of the whole algebraic spline curve, which avoids every obstacle, can be obtained. The new spline curve not only determines the position relation between the curve and the given point, but also shows its advantages directly, such as low degree, G² continuity, simple calculation, shape-preserving, and adjustment by the control polygon. All shape parameters in the cubic algebraic spline were local, which enhances the flexibility of the geometric design.