Clarifying the definition of redundancy as used in robotics

Several descriptions of redundancy are presented in the literature, often from widely different perspectives. Therefore, a discussion of these various definitions and the salient points would be appropriate. In particular, any definition and redundancy needs to cover the following issues; the difference between multiple solutions and an infinite number of solutions; degenerate solutions to inverse kinematics; task redundancy; and the distinction between non-redundant, redundant and highly redundant manipulators.