Abstract-This paper proposes an interval based method for the validation of reliable and robust navigation rules for mobile robots. The main idea is to show that for all feasible perturbations, there exists a safe subset of the state space such that the system cannot escape. The methodology is illustrated on the line following problem of a sailboat and then validated on an actual experiment where an actual sailboat robot, named Vaimos, sails autonomously from Brest to Douarnenez (more than 100 km).

This paper proposes a new method for guaranteed integration of state equations. Within this framework, the variables of interest are trajectories submitted to both arithmetic and differential equations. The approach consists in formalizing a problem thanks to a constraint network and then apply these constraints to sets of trajectories. The contribution of the paper is to provide a reliable framework to enclose the solutions of these differential equations. Its use is shown to be simple, more general and more competitive than existing approaches dealing with guaranteed integration, especially when applied to mobile robotics. The flexibility of the developed framework allows to deal with non-linear differential equations or even differential inclusions built from datasets, while considering observations of the states of interest. An illustration of this method is given over several examples with mobile robots.