Consistency techniques for continuous constraints

Abstract

We consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.Our approach is based on approximating regions of feasible solutions by 2 k-trees, a representation commonly used in computer vision and image processing. We give simple and stable algorithms for computing labelings with arbitrary degrees of consistency. The algorithms can process constraints and solution spaces of arbitrary complexity, but with a fixed maximal resolution.Previous work has shown that when constraints are convex and binary, path-consistency is sufficient to ensure global consistency. We show that for continuous domains, this result can be generalized to ternary and in fact arbitrary n-try constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.

Set-membership state estimation with fleeting data

“…Many problems of estimation, control, robotics, and related fields can be represented by continuous constraint satisfaction problems (CSP) [12], [18], [23]. A CSP is composed of a set of variables V = {x 1 , .…”

Interval propagation and search on directed acyclic graphs for numerical constraint solving

“…Those techniques perform reasoning procedures on constraints and explore the search space by intelligently enumerating solutions. In order to solve NCSPs by means of constraint satisfaction, continuous domains have often been converted into discrete domains by using progressive discretization techniques [12,19]. Later on, many mathematical computation techniques for continuous domains have been integrated into the framework of constraint satisfaction in order to solve NCSPs more efficiently.…”

Novel Approaches to Numerical Software with Result Verification

“…Recent works have been interested in advanced propagation techniques [47], relaxations for specific problems [71,44], solver cooperation [29], processing of differential equations [20], quantified formulas [61] or applications [65,18,25,28,31,15]. The combination of box-consistency and hull-consistency has been shown to be efficient in [4].…”