Reliable Robot Localization

4Trajectories Under Evaluation Constraints

4.1. Introduction

4.1.1. Contribution of this work

The main purpose of the second part of this book is to study new tools to appropriately deal with state equations of the form:

[4.1a] [4.1b]

to obtain reliable bounds of sets containing the solutions.

In Chapter 3, we have seen how to achieve this resolution, assuming a precise knowledge on the measurement times t_i ∈ ℝ. We are now able to compute the envelope of feasible state trajectories by using tubes as domains and the contractor programming approach expanded to trajectories and enriched with and 𝒞_eval. We recall that:

• – 𝒞_eval ([z_i], contracts the tube [y](·) at time t_i while keeping the set of trajectories going through [z_i] at this instant;
• – smooths the tube [x](·) in order to conserve trajectories compliant with the set of feasible derivatives enclosed in [v](·).

𝒞_eval and can be used together to propagate an observation over the whole domain of a trajectory.

This chapter deals with uncertain measurement times: now, the t_i are known to belong to some interval [t_i]. In this ...