Issues in learning global properties of the robot kinematic mapping

The robotic kinematic mapping generally has multiple distinct solution branches for a given end-effector location, where each branch can have a nontrivial manifold structure (as in the case of a redundant manipulator). Learning techniques that exploit known topological properties of the mapping are used to determine the number and nature of these branches. Specifically, clustering of input-output data is used to map out the preimage branches. Topology preserving networks are used to learn and parameterize the topology of these branches for certain known classes of manipulators. As a practical consequence, the inverse kinematic mapping can be approximated for each branch separately