Geometric and numerical aspects of redundancy

Abstract

If some resources of a robot are redundant with respect to a given objective, they can be used to address other, additional objectives. Since the amount of resources required to realize a given objective can vary, depending on the situation, this gives rise to a limited form of decision making, when assigning resources to different objectives according to the situation. Such decision making emerges in case of conflicts between objectives, and these conflicts appear to be situations of linear dependency and, ultimately, singularity of the solutions. Using an elementary model of a mobile manipulator robot with two degrees of freedom, we show how standard resolution schemes behave unexpectedly and inefficiently in such situations. We propose then as a remedy to introduce carefully tuned artificial conflicts, in the form of a trust region.