This work develops and analyzes a control algorithm for an unmanned aerial vehicle (UAV) to circumnavigate an unknown target at a fixed radius when the UAV is unable to determine its location and heading. Using a relationship between range-rate and bearing angle (from the target), we formulate a control algorithm that uses the range-rate as a proxy for the bearing angle and adjusts the heading of the UAV accordingly. We consider the addition of measurement errors and model the system with a stochastic differential equation to carry out the analysis. A recurrence result is proven, establishing that the UAV will reach a neighborhood of the desired orbit in finite time, and a mollified control is presented to eliminate a portion of the recurrent set about the origin. Simulation studies are presented to support the analysis and compare the performance against other algorithms for the circumnavigation task.

References

References
1.
Kearns
,
A.
,
Shepard
,
D.
,
Bhatti
,
J.
, and
Humphreys
,
T.
,
2014
, “
Unmanned Aircraft Capture and Control via GPS Spoofing
,”
J. Field Rob.
,
31
(4), pp.
617
636
. 10.1002/rob.21513
2.
Sahinoglu
,
Z.
, and
Genzici
,
S.
,
2006
, “
Ranging in the IEEE 802.15.4a Standard
,”
IEEE
Wireless and Microwave Technology Conference, WAMICON 06, IEEE Annual, Clearwater Beach, FL, Dec. 4–5
.10.1109/WAMICON.2006.351897
3.
Tang
,
Z.
, and
Ozguner
,
U.
,
2005
, “
Motion Planning for Multitarget Surveillance With Mobile Sensor Agents
,”
IEEE Trans. Rob.
,
21
(
5
), pp.
898
908
.10.1109/TRO.2005.847567
4.
Summers
,
T.
,
Akella
,
M.
, and
Mears
,
M.
,
2009
, “
Coordinated Standoff Tracking of Moving Targets: Control Laws and Information Architectures
,”
J. Guid., Control, Dyn.
,
32
(
1
), pp.
56
69
.10.2514/1.37212
5.
Deghat
,
M.
,
Shames
,
I.
,
Anderson
,
B.
, and
Yu
,
C.
,
2014
, “
Localization and Circumnavigation of a Slowly Moving Target Using Bearing Measurements
,”
IEEE Trans. Autom. Control
(accepted). 10.1109/TAC.2014.2299011
6.
Shames
,
I.
,
Dasgupta
,
S.
,
Fidan
,
B.
, and
Anderson
,
B.
,
2012
, “
Circumnavigation Using Distance Measurements Under Slow Drift
,”
IEEE Trans. Autom. Control
,
57
(
4
), pp.
889
903
.10.1109/TAC.2011.2173417
7.
Matveev
,
A.
,
Teimoori
,
H.
, and
Savkin
,
A.
,
2009
, “
The Problem of Target Following Based on Range-Only Measurements for Car-Like Robots
,”
IEEE
Conference on Decision and Control10.1109/CDC.2009.5400217, held jointly with the 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, Dec. 15–18, pp.
8537
8542
.
8.
Cao
,
Y.
,
Muse
,
J.
,
Casbeer
,
D.
, and
Kingston
,
D.
,
2013
, “
Circumnavigation of an Unknown Target Using UAVs With Range and Range-Rate Measurements
,”
IEEE
52nd Annual Conference on Decision and Control, Firenze, Dec. 10–13, pp. 3617–3622
. 10.1109/CDC.2013.6760439
9.
Hashemi
,
A.
,
Cao
,
Y.
,
Casbeer
,
D.
, and
Yin
,
G.
,
2014
, “
UAV Circumnavigation of an Unknown Target Without Location Information Using Noisy Range-Based Measurements
,”
Proceedings of the IEEE American Control Conference
, Portland, OR, June 2014, pp. 4587–4592.
10.
Cao
,
Y.
,
2014
, “
UAV Circumnavigation of an Unknown Target Using Range Measurements and Estimated Range Rate
,”
Proceedings of the IEEE American Control Conference, Portland, OR
, June 2014, pp. 4581–4586.
11.
Øksendal
,
B.
,
2003
,
Stochastic Differential Equations: An Introduction With Applications
,
Springer-Verlag
, Berling, Heidelberg.
12.
Khasminskii
,
R.
,
2011
,
Stochastic Stability of Differential Equations
,
Springer-Verlag
, Berling, Heidelberg.
13.
Multinovic
,
D.
,
Casbeer
,
D.
,
Cao
,
Y.
, and
Kingston
,
D.
,
2014
, “
Coordinate Frame Free Dubins Vehicle Circumnavigation
,”
Proceedings of the IEEE American Control Conference, Portland, OR
, June 2014, pp. 891–896.
14.
Mateos-Núnẽz
,
D.
, and
Cortés
,
J.
,
2013
, “
Stability of Stochastic Differential Equations With Additive Persistent Noise
,”
American Control Conference
, Washington, DC, June 17–19, pp. 5427–5432.10.1109/ACC.2013.6580686
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