Good Fibrations: Canonical Parameterization of Fiber Bundles with Self-organizing Maps

A natural parameterization of the redundant degrees of freedom of a robot manipulator is learned from input-output data. A family of direct inverse kinematics functions are constructed by self-organizing maps. As a result, all inverse functions can be computed directly. Optimization of any side function is possible in the low-dimensional space of the natural parameterization, rather than in the full configuration space.