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Proofs of Technical Results Justifying and Illustrating an Algorithm of Navigation for Monitoring Unsteady Environmental Boundaries

A. Matveev,Michael Hoy,K. Ovchinnikov,A. M. Anisimov,Andrey V.Savkin

Published 2015 in arXiv: Optimization and Control

ABSTRACT

We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental scalar field. The field is measured by an on-board sensor in a point-wise fashion at the robot's location. The focus is on unsteady boundaries that evolve over time in an arbitrary fashion, including deformations, i.e., changes of shapes and sizes. We present a sliding mode control method for localizing and tracking such boundaries: the robot is steered to the boundary and circulates in its close proximity afterwards. The proposed control algorithm does not require estimation of the spatial gradient of the field and is non-demanding with respect to both computation and motion. The paper offers the proofs of technical facts required for rigorous justification of non-local convergence of the proposed control law, as well as theoretical illustrations of its performance in specific scenarios.

PUBLICATION RECORD

  • Publication year

    2015

  • Venue

    arXiv: Optimization and Control

  • Publication date

    2015-04-08

  • Fields of study

    Mathematics, Computer Science, Engineering

  • Identifiers
    arXiv 1504.01977
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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