Guaranteed computation of robot trajectories

- A contractor-based approach is proposed for guaranteed integration of state equations.
- The framework is based on the use of tubes as envelopes of feasible trajectories.
- A dedicated differential contractor is provided to deal with dynamical systems.
- The use of tubes is well suited for multi-differential and non-linear equations.
- An illustration of this approach is given over several mobile robotics examples.

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.