光电工程
光電工程
광전공정
OPTO-ELECTRONIC ENGINEERING
2014年
12期
1-6
,共6页
机械臂%路径规划%最短路径%Euler方程
機械臂%路徑規劃%最短路徑%Euler方程
궤계비%로경규화%최단로경%Euler방정
manipulator%path planning%the shortest-path%Euler equations
为求解机械臂最短路径问题，导出了机械臂末端路径长度的表示式，并将最短路径问题归结为一个泛函极值问题。为简化求解过程，将泛函极值问题转化成另一个同解的泛函极值问题，并利用变分法求出了表示后一问题解的微分方程组。利用上三角矩阵逆矩阵的表示式，将该微分方程组转化成了标准状态方程组，与微分几何方法相比，避免了逆矩阵计算，使转化过程更加简单。利用Matlab进行仿真，求出了3R机械臂最短路径所对应的三个关节角度的位移函数。
為求解機械臂最短路徑問題，導齣瞭機械臂末耑路徑長度的錶示式，併將最短路徑問題歸結為一箇汎函極值問題。為簡化求解過程，將汎函極值問題轉化成另一箇同解的汎函極值問題，併利用變分法求齣瞭錶示後一問題解的微分方程組。利用上三角矩陣逆矩陣的錶示式，將該微分方程組轉化成瞭標準狀態方程組，與微分幾何方法相比，避免瞭逆矩陣計算，使轉化過程更加簡單。利用Matlab進行倣真，求齣瞭3R機械臂最短路徑所對應的三箇關節角度的位移函數。
위구해궤계비최단로경문제，도출료궤계비말단로경장도적표시식，병장최단로경문제귀결위일개범함겁치문제。위간화구해과정，장범함겁치문제전화성령일개동해적범함겁치문제，병이용변분법구출료표시후일문제해적미분방정조。이용상삼각구진역구진적표시식，장해미분방정조전화성료표준상태방정조，여미분궤하방법상비，피면료역구진계산，사전화과정경가간단。이용Matlab진행방진，구출료3R궤계비최단로경소대응적삼개관절각도적위이함수。
In order to search out the shortest path of the 3R manipulator, a path length expression of manipulator’s end-effectors is given first, and then the problem is modeled as a functional extreme problem. For the purpose of simplifying the solving process, the functional extreme problem is translated into a new one with the same solution, and the solution of the latter expressed by a system of differential equations is derived by using variational method. By means of the inverse matrix expression of the upper triangular matrix, the system of differential equations is translated into a new one consisted of normal state equations. The method can avoid complex inverse matrix computing, and make the computation of the transition process simpler when compared with differential geometry method. By using Matlab simulation method, 3 joint angle functions corresponding to the shortest path of the 3R manipulator’s end-effectors is obtained.
