Proving the Stability of the Rolling Navigation

Author:

Bourgois Auguste1ORCID,Chaabouni Amine2,Rauh Andreas3ORCID,Jaulin Luc4ORCID

Affiliation:

1. FORSSEA Robotics

2. Ecole Polytechnique

3. Carl von Ossietzky University of Oldenburg

4. ENSTA Bretagne

Abstract

In this paper, we propose to study the stability of a navigation method that allows a robot to move in an unstructured environment without compass by measuring a scalar function ϕ which only depends on the position. The principle is to ask the robot to roll along an isovalue of ϕ . Using an interval method, we prove the stability of our closed loop system in the special case where ϕ is linear.

Publisher

University of Szeged

Subject

Computer Vision and Pattern Recognition,Software,Computer Science (miscellaneous),Electrical and Electronic Engineering,Information Systems and Management,Management Science and Operations Research,Theoretical Computer Science

Reference36 articles.

1. Geometrical Methods in the Theory of Ordinary Differential Equations

2. Viability Kernels and Capture Basins of Sets Under Differential Inclusions

3. Viability Theory

4. Set-Theoretic Methods in Control

5. Bourgois, A. Safe and Collaborative Autonomous Underwater Docking. PhD dissertation, Université de Bretagne Occidentale, Brest, France, 2021.

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