基于单位四元数的多点姿态规划算法研究

Research on Multiple-Point Orientation Planning Algorithm Based on Unit Quaternion

“过三点的姿态规划”这一问题,要求姿态曲线平滑经过指定三点,其常规解决思路是构造四元数样条曲线,然而由于四元数插值函数高度非线性,反求控制顶点十分困难。针对此问题,通过增加辅助点的方式重新构造了三段定轴转动,借助多项式插值函数可以将三段定轴转动联结起来,进而推导了姿态曲线表达式。为了验证姿态曲线的连续性,求解了姿态曲线一阶和二阶导数,确定了姿态导数连续条件。推导过程表明,只要辅助点和多项式函数满足特定条件,姿态曲线就具备二阶光滑特性。最后通过仿真分析验证了姿态规划算法的有效性。

Three fixed axis rotation are constructed by adding another two auxiliary points.The three rotations can be combined into one motion by polynomial functions.The first and second order derivations of the orientation curve are derived to obtain to verify its continuity.The derivation process shows that the orientation curve has a second order smoothness property if the auxiliary points and the polynomial functions satisfy certain conditions.In the end,the applicability of orientation algorithm is verified by simulation test.