Optimization of Tool Posture in Multi Axis Machining by Mathematical Programming

运动物体避碰姿态优化是控制五轴机床、机器人等生产资源的重要问题之一。一般来说，旋转矩阵是由三角函数或非线性函数组成的，它改变了物体在适当方向上的姿态。本文采用混合整数规划方法，在旋转矩阵中提出了一组新的等效约束来规划目标的最优姿态。

The posture optimization of a moving object for collision avoidance is one of important issues to control production resources such as 5 axis machine tools, robots and so on. In generally, a rotating matrix, which changes the posture of the object in an appropriate direction, consists of trigonometric functions, or no-linear functions. In this paper, a new set of equivalent constraints in the rotating matrix is proposed to plan the optimum posture of the object by mixed integer programming.