手术机器人高阶多项式插值的轨迹规划

The Trajectory Planning for Surgical Robot Using High-Multinomial Interpolation

为保证运动的平稳性,要求手术机器人关节空间的位移、速度光滑连续,为此提出了基于高阶多项式插值的轨迹规划方法。根据手术要求,在机器人末端的笛卡尔空间中规划出轨迹。选取轨迹上若干个路径点,运用运动学逆解求出关节空间中的若干个型值点。通过对相邻型值点进行高阶多项式插值,得到关节空间连续光滑的位移函数;对位移函数求导可以得到各关节连续光滑的速度函数。利用MATLAB进行仿真,得出每个关节的连续光滑的角度、速度曲线,精度很高。表明该方法完全可行,能够满足机器人平稳性的要求。

For the purpose of ensuring a motion steadiness, the continuity and smoothness of the displacement and velocity in the joint space should be satisfied when the surgical robot is operating. Therefore, a method of trajectory planning based on high-multinomial interpolation is put forward here. The trajectory of the end effector in Cartesian space should be computed according to the requirements of surgeon~ Then it selects a series of discrete points on the trajectory and regards them as path points. By u^ing inverse kinematics, the data of every joint could be obtained. And smooth displacement functions could be established for every joint through interpolating two adjacent data points. The smooth functions of velocity could also be derived by derivation of the displacement. The algorithm has been tested by MATLAB yielding good results that the resulting curves of displacement and velocity are smooth with little error. The method approved to be feasible, can meet the requirements of stationarity.