A Modified Twin Arithmetic to Characterize Uncertain Sets

Speaker:
Luc Jaulin (ENSTA Bretagne, Brest, France)

Abstract:
Given an interval [a,b]. When the bounds a and b are not known exactly, then the interval becomes uncertain. When this uncertainty is represented by an interval for the bounds (i.e., a in [a] and b in [b]), then the corresponding set of intervals is called a 'twin'. More precisely, a twin [[x]] is the set of all intervals [x]=[a,b] such that a in [a] and b in [b].

A 'thick set' [[X]] with bounds A and B is a set of all subsets X of R^n such that A is a subset of X which is a subset of B. Thick sets occur naturally in several applications such as in robotics when we want to characterize the zone that has been explored by a robot when the trajectory of the robot is uncertain (for instance represented by a tube). Whereas a twin can be interpreted as an uncertain set of R, a thick set can thus be understood as an uncertain set of R^n.

In this talk, I will show that a modified twin arithmetic will allow us to characterize efficiently thick sets. Some applications related to robotics exploration will be given.