Introduction to the algebra of separators with application to path planning

Contractor algebra is a numerical tool based on interval analysis which makes it possible to solve many nonlinear problems arising in robotics, such as identification, path planning or robust control. This paper presents the new notion of separators which is a pair of complementary contractors and presents the corresponding algebra. Using the separator algebra inside a paver will allow us to get an inner and an outer approximation of the solution set in a much simpler way than using any other interval approach. A path planning problem will then be considered in order to illustrate the principle of the approach.