Toward obtaining all possible contacts-growing a polyhedron by its location uncertainty

A large number of robotic tasks require precision and thus the dealing with uncertainties. The effects of various uncertainties often manifest to location (i.e., position and orientation) uncertainties of objects. Thus, an important problem that often arises is how to assess the region that an object may occupy in the presence of uncertainties. This paper addresses the problem by describing how to grow exactly an arbitrary polyhedral object in the three-dimensional Cartesian space by its position and/or orientation uncertainties. Three types of related regions for the object are described: (1) the grown regions, regions possibly occupied by the object due to uncertainties in its position, orientation, or both, (2) the grown shell regions, regions possibly occupied by the boundary (surfaces) of the object due to uncertainties in its position, orientation or both, and (3) the core regions, regions (which could be empty) definitely occupied by the object in spite of uncertainty. The exact representations introduced in this paper can serve as benchmarks against which efficient but approximate algorithms may be evaluated. A particularly important application of the grown shell regions is in obtaining the set of all possible topological contacts among polyhedral objects due to location uncertainties. Such a set can serve as a basis from which more precise contact information can be extracted by additional sensing means, such as vision and force/moment sensing. The approach for this application and its implementation is introduced and discussed