Global Regularization of Inverse Kinematics for Redundant Manipulators

The inverse kinematics problem for redundant manipulators is ill-posed and nonlinear. There are two fundamentally different issues which result in the need for some form of regularization; the existence of multiple solution branches (global ill-posedness) and the existence of excess degrees of freedom (local ill-posedness). For certain classes of manipulators, learning methods applied to input-output data generated from the forward function can be used to globally regularize the problem by partitioning the domain of the forward mapping into a finite set of regions over which the inverse problem is well-posed. Local regularization can be accomplished by an appropriate parameterization of the redundancy consistently over each region. As a result, the ill-posed problem can be transformed into a finite set of well-posed problems. Each can then be solved separately to construct approximate direct inverse functions.