This paper reviews one method of global kinematic analysis, based on a manifold mapping reformulation of manipulator kinematics, which is suitable for both non-redundant and redundant serial chain manipulators. Two applications of this approach are considered: the relationship between changing pose and singularities for non-redundant manipulators and the homotopy class of redundant manipulator self-motions. The first relationship has important implications for non-redundant manipulator regrasping operations. Variations in redundant manipulator self-motion homotopy can have an important effect on motion and redundancy resolution planning, since they can lead to algorithmic singularities and unexpected loss of manipulator capabilities.
Joel W. Burdick,
"Global Kinematics for Manipulator Planning and Control", Proc. SPIE 1196, Intelligent Control and Adaptive Systems, (1 February 1990); doi: 10.1117/12.969907; https://doi.org/10.1117/12.969907