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 a new notion of separators which is a pair of complementary contractors and presents the corresponding algebra. Using 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.