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

• Published in: Computer Algebra in Scientific Computing Vol. 11661; pp. 78 - 90
• Main Authors: Capco, Jose, Manongsong, Saraleen Mae
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Elimination theory; Inverse kinematics; Serial manipulator
• ISBN: 9783030268305; 3030268306
• ISSN: 0302-9743; 1611-3349; 1611-3349
• DOI: 10.1007/978-3-030-26831-2_6

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.