The kinematic Hessian and higher derivatives

Author

Hourtash, Arjang

Author_Institution

Simplify Robotics Inc., Houston, TX, USA

fYear

2005

fDate

27-30 June 2005

Firstpage

169

Lastpage

174

Abstract

A number of problems in manipulator analysis and control call for the second derivative of the joint-to workspace kinematic mapping of serial or branched manipulators. A derivation of all derivatives of the kinematic mapping is presented, including the second derivative namely the Hessian tensor. A fast formulation for its computation is derived which is based on components of the Jacobian matrix. The resulting formulae are verified symbolically with differentiation, and showcased numerically in Taylor series approximations and in a singularity escapability analysis for the example of the International Space Station´s Canadarm2, a.k.a. the Space Station Remote Manipulator System (SSRMS).

Keywords

Hessian matrices; Jacobian matrices; manipulator kinematics; series (mathematics); tensors; Hessian tensor; Jacobian matrix; Space Station Remote Manipulator System; Taylor series approximations; branched manipulator; kinematic Hessian derivatives; manipulator analysis; serial manipulator; singularity escapability analysis; workspace kinematic mapping; Acceleration; International Space Station; Jacobian matrices; Manipulator dynamics; Motion control; Robot kinematics; Space stations; Taylor series; Tensile stress; Torque control; escapability; kinematic derivatives; rate control; selfmotion; singularity;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Intelligence in Robotics and Automation, 2005. CIRA 2005. Proceedings. 2005 IEEE International Symposium on

Print_ISBN

0-7803-9355-4

Type

conf

DOI

10.1109/CIRA.2005.1554272

Filename

1554272