BSplines properties with Interval Analysis for Constraint Satisfaction Problem: Application in robotics.

Rawan Kalawoun (1) , Sebastien Lengagne (1) , François Bouchon (2) , Youcef Mezouar (1)

1 IP - Institut Pascal
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

Interval Analysis is a mathematical tool that could be used to solve Constraint Satisfaction Problem. It guarantees solutions, and deals with uncertainties. However, Interval Analysis suffers from an overestimation of the solutions, i.e. the pessimism. In this paper, we initiate a new method to reduce the pessimism based on the convex hull properties of BSplines and the Kronecker product. To assess our method, we compute the feasible workspace of a 2D manipulator taking into account joint limits, stability and reachability constraints: a classical Constraint Satisfaction Problem in robotics.

Mots clés: Interval analysis; Pessimism; BSplines; Kronecker product; Constraint Satisfaction Problem; Robot; Feasible workspace

Domaines: Automatique / Robotique

Rawan Kalawoun, Sebastien Lengagne, François Bouchon, Youcef Mezouar. BSplines properties with Interval Analysis for Constraint Satisfaction Problem: Application in robotics.. 15th International Conference on Intelligent Autonomous Systems IAS-15, Jun 2018, Baden-Baden, Germany. pp.490-453, ⟨10.1007/978-3-030-01370-7_39⟩. ⟨hal-01913931⟩