Implementing HuPf Algorithm for the Inverse Kinematics of General 6R/P Manipulators

Abstract

We reformulate and extend the HuPf algorithm (see [7]), which was originally designed for a general 6R manipulator (i.e. 6 jointed open serial chain/robot with only rotational joints), to solve the inverse kinematic (IK) problem of 6R/P manipulators (6-jointed open serial robot with joints that are either rotational or prismatic/translational). For the algorithm we identify the kinematic images of 3R/P chains with a quasi-projective variety in $\mathbb {P}^7$ via dual quaternions. More specifically, these kinematic images are projections of the intersection of a Segre variety with a linear 3-space to an open subset of $\mathbb {P}^7$ (identified with the special Euclidean group $\mathrm {SE}(3)$). We show an easy and efficient algorithm to obtain the linear varieties associated to 3R/P subchains of a 6R/P manipulator. We provide examples showing the linear spaces for different 3R/P chains (a full list of them is available in an upcoming paper). Accompanying the extended HuPf algorithm we provide numerical examples showing real IK solutions to some 6R/P manipulators.

J. Capco—Supported and funded by the Austrian Science Fund (FWF): Project P28349-N32 and W1214-N14 Project DK9.

S. M. Manongsong—Supported by the Office of the Chancellor of the University of the Philippines Diliman, through the Office of the Vice Chancellor for Research and Development, for funding support through the Outright Research Grant.