An analytical solution for the inverse kinematics of a redundant 7DoF Manipulator with link offsets

This work addresses the inverse kinematics problem for the 7 Degrees of Freedom Barrett Whole Arm Manipulator with link offsets. The presence of link offsets gives rise to the possibility of the in-elbow & out-elbow poses for a given end-effector pose and is discussed in the paper. A parametric solution for all possible geometric poses is generated for a desired end-effector pose (position and orientation). The set of possible geometric poses are completely defined by three circles in the Cartesian space. A method of computing the joint-variables for any geometric pose is presented. An analytical method of identifying a set of feasible poses for some joint-angle constraints is also addressed.