机械臂运动路径设计问题  

A Design on the Moving Trcuk of Mechanism-arm

作　　者：胡淼[1] 雷思磊[1] 商晓燕[1] 

机构地区：[1]解放军理工大学通信工程学院,南京210007

出　　处：《数学的实践与认识》2008年第14期94-102,共9页Mathematics in Practice and Theory

摘　　要：针对机械臂运动的逆问题,提出了无障碍空间的牛顿迭代算法.并对牛顿迭代法进行了改进,建立了有障碍空间中避碰问题的一般模型,并对问题进行了求解.对于求出的机械臂指尖的姿态,先采用最大步长调整,再对剩余部分采用一次微调的方法生成指令序列,使生成的序列尽可能的短.针对具体问题1,给出了达到目标点的一个指令序列,步数为89步,精度为0.179mm;对于问题2,离散化裂纹,应用大步长调整的牛顿迭代法,给出了一个运动序列,实现了避碰焊接,各点的平均精度达到0.188mm,并对最低点附近在1mm误差范围内不可达到的区域进行了讨论,用解析和仿真的方法证明和验证了最低点不可达;对于问题3,改进了避碰问题的一般模型和算法,用试探法实现了四个焊接点的无碰焊接,并对圆台内表面在1mm误差范围内不可焊接的区域进行了分析.This passage put forward Newton-lterative-Arithmetic to solve the inverse problem of the mechanism-arm kinematics in the free space. After improving the Newton-lterative- Arithmetic, the general model is founded to keep away from the barrier in the space. Toward the pose of the mechanism-arm, This passage adopt the maximum interval to adjust the pose, then, inching the residual to get the instruction list, at the same time, make the list as short as possible. For problem （1）, this passage present a instruction list which make the mechanism-arm get to the object point, the number is 89, the precision is 0. 1779mm. For problem （2）, after discrete the crack, adopt Newton-lterative-Arithmetic and the longer interval to adjust, a instruction list is gained, and avoid the collision, the precision is 0. 188mm. This passage else discuss the area which the mechanism-arm cannot reach in the given precision, and prove the lowest point cannot be reached. For problem （3）, improve the general model and arithmetic, and joint the four points without collision. At last, we analyse the area which cannot be reached the inside surface in the lmm precision.

关 键 词：牛顿迭代法 盲点 试探法 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置] TP241[自动化与计算机技术—控制科学与工程]