Jacobian motion and its derivatives

作     者：Stadler, W Eberhard, P 

作者机构：San Francisco State Univ Sch Engn San Francisco CA 94132 USA Univ Stuttgart Inst Mech B D-70550 Stuttgart Germany 

出 版 物：《MECHATRONICS》 (机械电子学)

年 卷 期：2001年第11卷第5期

页      面：563-593页

核心收录：

学科分类：0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0802[工学-机械工程] 0811[工学-控制科学与工程] 

主　　题：trajectory planning Jacobian motion numerical methods forward kinematics computational algorithms symbolic algorithms 

摘      要：An innovative, geometrically appealing, derivation of the differential motion of an end-effector and the corresponding Jacobian matrix is presented. The use of the differential. T form of the skew-symmetric matrix W = (A)over dot A(T) and the corresponding differential rotation is central to the development, A being the usual rotation matrix. This allows a novel side-by-side presentation of the vector and matrix form of differential rigid motion based on the forward kinematics of the manipulator. The corresponding treatment of the homogeneous motion includes a detailed discussion of the derivative and differential of homogeneous rigid motion and a clarification of some notational ambiguities and errors in previous treatments of this topic. It is also shown that the results are equivalent to what may be termed classical results, The analytical treatment is followed by a detailed presentation of computational and symbolic methods for the derivation and evaluation of the Jacobian matrix, including the use of recently developed methods of automatic differentiation. The AdeptOne Robot is used as an illustrative example with complete agreement of the theoretical and computational results. (C) 2000 Elsevier Science Ltd. All rights reserved.