Inverse kinematic solutions of 6-D.O.F. biopolymer segments

Abstract

SUMMARYWe present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

Numerically stable solution to the 6R problem of Inverse Kinematics

“…"" "" pointed out in [11]. Following the method in [12], Kim and Chirikjian [11] introduce a Jacobian-based method to handle this issue, presumably due to failure of the basic method.…”

The optimized algorithm based on machine learning for inverse kinematics of two painting robots with non-spherical wrist

“…Right and left matrices, elements (3,4), (3,3), (3,2) were correspondingly equal, obtaining the following equations.…”

“…[3] proposed the pseudo-inverse Jacobian matrix method, which will lead to great joint velocity in singular configuration. Elimination method and Jacobian inverse iterations method were combined in [4] to obtain the full set of inverse kinematic solutions. In [5,6], a damping least squares method (DLS), also known as Levenberg-Marquardt stabilization method, was proposed, and the damping factor was selected based on the minimum singular value.…”

An iterative algorithm for inverse displacement analysis of Hyper-redundant elephant’s trunk robot

“…Chirikjian and Burdick [22, 23] proposed a modal approach based on the hyper-redundant manipulator’s overall geometrical characteristics, which abstracted the backbone curve into a continuous, smooth spatial curve, and used the curve fitting to obtain the inverse kinematics solutions. Kim and Chirikjian [24] put forward two solutions for the inverse kinematics of a six DOFs robot based on biopolymer segments. One is the extended elimination method [25], which can act on the biopolymer segment directly, the other is a heuristic algorithm based on the Lie group theory.…”