time parameterization

Interpolation:

• segment interpolation: straight-line segment and transition segment
• polynomial curves
• cubic curves: Hermite cubic splines, Bezier curve, B-spline, nonuniform rational B-spline
• cubic spline: 三次样条曲线
• quintic spline: 五次样条曲线
• Reeds-Shepp 曲线
• Dubins 曲线

trajectory processing in moveit:

• class documentation
• github

which contains three executable trajectory processing methods:

• IterativeParabolicTimeParameterization:
  • ref github issue
• IterativeSplineParameterization
  • ref github issue
• TimeOptimalTrajectoryGeneration
  • website
  • TOPP

轨迹规划-离散时间序列

• 三次多项式插值

点到点轨迹规划——三次曲线，五次曲线，梯形曲线，S曲线 ur末端画圆 三次样条插值介绍

插值

• SE3
• SO3

slerp for quaterion

$$Slerp(p_0 ,p_1,;t)=\frac{sin[(1-t)\theta]}{sin\theta}p_0+\frac{sin[t\cdot\theta]}{sin\theta}p_1$$ $$Linear(p_0 ,p_1,;t)=(1-t)p_0+t\cdot q_1$$

TOPP

• TOPP
• TOPPRA

轨迹规划-样条插补-古月