Issues in Learning Global Properties of the Robot Kinematic Mapping

The robot kinematic mapping x = f() generally has multiple distinct solution branches fjf() = x d g for a given end{eeector location x d , where each branch can have a nontrivial manifold structure (as in the case of a redundant manipulator). Learning techniques which exploit known topological properties of the mapping are used to determine the number and nature of these branches. Speciically, clustering of input{output data is used to map out the preimage branches. Also, topology preserving networks are used to learn and pa-rameterize 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.