Circumnavigation Using Distance Measurements Under Slow Drift

Iman SHAMES; Soura DASGUPTA; Banş FIDAN; Brian D. O ANDERSON

doi:10.1109/TAC.2011.2173417

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Circumnavigation Using Distance Measurements Under Slow Drift

Journal article

Peer reviewed

Circumnavigation Using Distance Measurements Under Slow Drift

Iman SHAMES, Soura DASGUPTA, Banş FIDAN and Brian D. O ANDERSON

IEEE transactions on automatic control, Vol.57(4), pp.889-903

2012

DOI: 10.1109/TAC.2011.2173417

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Abstract

Consider an agent A at an unknown location, undergoing sufficiently slow drift, and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own position in some reference frame. This paper considers this problem, which has applications to surveillance and orbit maintenance. In many of these applications it is difficult for B to directly sense the location of A, e.g. when all that B can sense is the intensity of a signal emitted by A. This intensity does, however provide a measure of the distance. We propose a nonlinear periodic continuous time control law that achieves the objective using this distance measurement. Fundamentally, a) B must exploit its motion to estimate the location of A, and b) use its best instantaneous estimate of where A resides, to move itself to achieve the circumnavigation objective. For a) we use an open loop algorithm formulated by us in an earlier paper. The key challenge tackled in this paper is to design a control law that closes the loop by marrrying the two goals. As long as the initial estimate of the source location is not coincident with the intial position of B, the algorithm is guaranteed to be exponentially convergent when A is stationary. Under the same condition, we establish that when A drifts with a sufficiently small, unknown velocity, B globally achieves its circumnavigation objective, to within a margin proportional to the drift velocity.

Solid Mechanics

Physics

Applied Sciences

Fundamental areas of phenomenology (including applications)

Exact sciences and technology

Computer science; control theory; systems

Spatial dimensions (e.g.: position, lengths, volume, angles, displacements, including nanometer-scale displacements)

Measurements common to several branches of physics and astronomy

Control system synthesis

General

Control theory. Systems

Solid dynamics (ballistics, collision, multibody system, stabilization...)

Metrology, measurements and laboratory procedures

Details

Title: Subtitle: Circumnavigation Using Distance Measurements Under Slow Drift
Creators: Iman SHAMES - ACCESS Linnaeus Centre, Electrical Engineering, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
Soura DASGUPTA - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA 52242, United States
Banş FIDAN - Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Brian D. O ANDERSON - Australian National University and National ICT Australia, Canberra, Australia
Resource Type: Journal article
Publication Details: IEEE transactions on automatic control, Vol.57(4), pp.889-903
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/TAC.2011.2173417
ISSN: 0018-9286
eISSN: 1558-2523
Language: English
Date published: 2012
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984083218302771

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