Reducing pessimism in Interval Analysis using Bsplines Properties: Application to Robotics

Interval Analysis is interesting to solve optimization and constraint satisfaction problems. It makes possible to ensure the lack of the solution or the global optimal solution taking into account some uncertainties. However, it suffers from an over-estimation of the function called pessimism. In this paper, we propose to take part of the BSplines properties and of the Kronecker product to have a less pessimistic evaluation of mathematical functions. We prove that this method reduces the pessimism, hence the number of iterations when solving optimization or constraint satisfaction problems. We assess the effectiveness of our method ∗Submitted: December 12, 2018; Revised: March 12, 2020; Accepted: July 23, 2020. †R. Kalawoun was supported by the French Government through the FUI Program (20th call with the project AEROSTRIP).