The kinematic Hessian and higher derivatives

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).