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Research Papers

Unmanned Aerial Vehicle Circumnavigation Using Noisy Range-Based Measurements Without Global Positioning System Information

[+] Author and Article Information
Araz Hashemi

Department of Mathematics,
Wayne State University,
Detroit, MI 48202
e-mail: araz.hashemi@gmail.com

Yongcan Cao, David W. Casbeer

Control Science Center of Excellence,
Air Force Research Laboratory,
Wright-Patterson AFB, OH 45433

George Yin

Professor
Department of Mathematics,
Wayne State University,
Detroit, MI 48202

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 29, 2014; final manuscript received June 24, 2014; published online October 21, 2014. Assoc. Editor: Dejan Milutinovic. The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Dyn. Sys., Meas., Control 137(3), 031003 (Oct 21, 2014) (10 pages) Paper No: DS-14-1045; doi: 10.1115/1.4027979 History: Received January 29, 2014; Revised June 24, 2014

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.

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References

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. [CrossRef]
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. [CrossRef]
Tang, Z., and Ozguner, U., 2005, “Motion Planning for Multitarget Surveillance With Mobile Sensor Agents,” IEEE Trans. Rob., 21(5), pp. 898–908. [CrossRef]
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. [CrossRef]
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). [CrossRef]
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. [CrossRef]
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 Control [CrossRef], held jointly with the 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, Dec. 15–18, pp. 8537–8542.
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. [CrossRef]
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.
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.
Øksendal, B., 2003, Stochastic Differential Equations: An Introduction With Applications, Springer-Verlag, Berling, Heidelberg.
Khasminskii, R., 2011, Stochastic Stability of Differential Equations, Springer-Verlag, Berling, Heidelberg.
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.
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. [CrossRef]

Figures

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Fig. 1

We design a control which aims at the tangent of the orbit of radius rs, but will “stabilize” at the orbit of radius rd. Here, γ = sin-1(rs/r).

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Fig. 2

A sample trajectory under uo with small gain: k = 0.2, rd = 10, rs = 8.67, V = 1, and additive white measurement noise σ = 0.5

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Fig. 3

A sample trajectory under uo, with large gain: k = 1 corresponding to rs = 9.95. When measurement error nudges the UAV past the rs threshold, it cuts across the circle.

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Fig. 4

Phase portrait of Eq. (3) using u = uo + ui with k = 2.118, V = 1, rs = 1.9345, and rd = 2

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Fig. 5

A sample trajectory under u using noisy measurements with initial point outside the desired orbit

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Fig. 6

Sample trajectory under u using noisy measurements with initial point inside the desired orbit

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Fig. 7

The recurrent set Uk,ɛ

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Fig. 8

Trajectory with measurement error, k = 0.1

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Fig. 9

Trajectory with measurement error, k = 1

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Fig. 10

Average value of error (r-rd)2 for different values of k

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Fig. 11

Average value of r·2 for different values of k

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Fig. 12

Trajectory with measurement error and wind, k = 0.1

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Fig. 13

Trajectory with measurement error and wind, k = 1

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Fig. 14

Average value of error (r-rd)2 with wind

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Fig. 15

Average value of r·2 with wind

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Fig. 16

Deterministic trajectory with exact r, estimated r·

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Fig. 17

Deterministic control applied with exact r, estimated r·

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Fig. 18

Trajectory with exact r, noisy r· (σrr = 0.5), time step h = 0.1 s

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Fig. 19

Trajectory with noisy r (σr = 0.1), estimated r·, time step h = 0.5 s

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Fig. 20

Error with exact r, noisy r· (σrr = 0.5), time step h = 0.1 s

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Fig. 21

Error with noisy r (σr = 0.1), estimated r·, time step h = 0.5 s

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Fig. 22

Control with exact r, noisy r· (σrr = 0.5), time step h = 0.1 s

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Fig. 23

Control with noisy r (σr = 0.1), estimated r·, time step h = 0.5 s

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