基于最小作用原理的轨迹多维空间动态控制

Based on the Minimum Action Principle Track Multi-dimensional Space Dynamic Control

根据最小作用量原理,探讨运动方法实现几何轨迹的内在原理,解决数控加工轨迹的几何精度和动态精度控制问题。根据最小作用量原理,计算传统的轨迹控制方法的作用量,表明插补方法就是严重违反自然法则。采用泛函分析方法分析路径与运动的映射关系,建立运动状态矢量空间,同时度量轨道几何函数及其导数,控制状态矢量误差,监控曲率或高价导数的变化,让速度和微小位移都沿着给定的方向。分析时间和空间的相对性,提出用参考时间控制工艺进程。提出根据几何函数转化的运动方程控制运动的轨迹实现方法。经过试验和仿真,证明该方法作用量最小,能实现几何与运动的综合控制,减少计算次数,提高轨迹精度,增加路径规划对环境的适应能力,是机床轨迹控制的好方法。

Based on the principle of action, movement method of geometric track internal principle is discussed, in order to solve the geometry precision of numerical control and dynamic accuracy control problem of CNC processing track. According to the principle of action, the action of traditional path control method is calculated. It shows that interpolation method is a serious violation of the laws of nature. Functional analysis method is used to analyze the path and the mapping relationship of movement and to establish the motion vector space, measuring orbit geometry function and its derivative, controlling state vector error, monitoring curvature or high prices of derivative changes at the same time. The speed and small displacement are all along the given way. Analyzing of time and space of relativity, the use of a reference time is proposed to control technology process. It presents a new method for trajectory control, which uses motion law taking the place of position parameters to control, And uses self defined time to substitute real time to control proceeding. It is proved that it is a good way to control geometry and motion comprehensively, to reduce computation times and to increase the ability of environmental adaptation for path planning.