基于完全笛卡尔坐标O(N)次正向动力学研究  

A Fast Algorithm for the Solution of Forward Dynamics Described by Fully Cartesian Coordinates

作　　者：孙宏丽[1] 吴洪涛[1] 缪群华[1] 程世利[1] 赵大旭[1] 

机构地区：[1]南京航空航天大学机电学院,南京210016

出　　处：《机械科学与技术》2010年第3期364-368,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：国防科工委"十一五"某预研基金项目;国家自然科学基金项目(50375071)资助

摘　　要：采用刚体等效质点力学模型,提出一种基于完全笛卡尔坐标快速求解链式机械臂惯量矩阵逆的新方法。选取系统独立变量坐标和完全笛卡尔坐标描述约束方程中不变化的变量作为广义扩展坐标,通过完全笛卡尔坐标与广义扩展坐标变量间的速度映射关系,得到广义扩展坐标表达下质量矩阵的表达形式。该质量矩阵及其逆矩阵的计算演变为对等效质点分别计算求和的过程,实现了机械臂正向动力学的O(n)次的高效率计算。通过与传统的罗伯森-维滕堡方法进行精度和计算效率的比较,验证了本研究内容的准确性和高效性。A new algorithm based on the fully Cartesian coordinates is proposed to calculate inertia matrix inversion of serial manipulators described by equivalent particle mechanical model. New expanded coordinates are formed by adding unchanged variables from constraint equations described by fully Cartesian coordinates to the independent variables array, and a new mass matrix can be obtained through mapping the relationship between fully Cartesian coordinates and the expanded coordinate variables to retain information about the dynamics constraint equations. We decompose the mass-matrix and inverse of the mass-matrix for serial manipulators corresponding to constraint variables and unconstraint variables which are banding-limited, and sparse matrix can be calculated concerning each equivalent particle, and we can obtain the efficiency for calculating the mass matrix inversion. The spatial manipulators with revolute joints are used to illustrate the procedure, and the results are compared with Roberson- Wittenburg method to verify the accuracy and O（n） complexity of the algorithm.

关 键 词：机械臂 O(n) 正向动力学 完全笛卡尔坐标 

分 类 号：TP241.2[自动化与计算机技术—检测技术与自动化装置]