An algorithm for solving the inverse kinematics of a 6R serial manipulator using dual quaternions and Grassmannians

摘要

Inverse kinematics (IK) of a 6R serial manipulator (6Rsm) is formulated in the homogeneous projective space of dual quaternions (DQ). This leads to a robust algorithm because the 8-space of DQ together with Grassmannian extension ensures that only valid solutions, which satisfy all of the constraint equations, are admitted. Numerical examples, based on two real 6Rsm architectures, are presented to illustrate the efficacy of the new algorithm. Its fiber (solutions) and critical locus (singularities) are described.