Learning Global Properties of Nonredundant Kinematic Mappings

The kinematic mapping x = f(&thetas;) is generally many to one. For nonredundant manipulators, this means that there are a finite number of configurations (joint angles) that will place the end-effector at a target location in the workspace. These correspond to postures of the manipulator, and each configuration lies on a specific solution branch. It is shown that for certain classes of revolute joint regional manipulators (those with no joint limits and having almost everywhere a constant number of inverse solutions in the workspace), the input-output data can be analyzed by clustering methods in order to determine the number and location of the solution branches. As a practical consequence, the inverse kinematic mapping can be directly approximated by applying neural network or other learning-based methods to each branch separately.