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Research Papers

Observability Analysis of Relative Localization Filters Subjected to Platform Velocity Constraints

[+] Author and Article Information
Oscar De Silva

Faculty of Engineering and Applied Science,
Memorial University of Newfoundland,
St. John's, NL A1B 3X5, Canada
e-mail: oscar.desilva@mun.ca

George K. I. Mann

Professor
Faculty of Engineering and Applied Science,
Memorial University of Newfoundland,
St. John's, NL A1B 3X5, Canada
e-mail: gmann@mun.ca

Raymond G. Gosine

Professor
Faculty of Engineering and Applied Science,
Memorial University of Newfoundland,
St. John's, NL A1B 3X5, Canada
e-mail: rgosine@mun.ca

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 21, 2016; final manuscript received November 11, 2016; published online March 14, 2017. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 139(5), 051009 (Mar 14, 2017) (11 pages) Paper No: DS-16-1154; doi: 10.1115/1.4035295 History: Received March 21, 2016; Revised November 11, 2016

This research study performs an observability analysis of the relative localization problem related to multirobotic systems. The study considers different constraints related to the availability of relative position measurements and platform velocity measurements. Constraints related to these measurement sources arise due to several reasons such as, sensing limitations especially in aerial platforms, field of view limitations of sensors, and communication bandwidth limitations that may affect the available measurement rate. Although numerous observability studies are reported for localization of multirobot systems, most of these studies do not investigate the problem under constraints related to platform velocity sensing capabilities, and moreover, these do not investigate the global uniqueness of its results. This paper analyzes observability of the relative localization problem in detail for multiple practical scenarios having limited measurement sources and then extends the study with a global uniqueness analysis of the results. The paper establishes theoretical limitations and design recommendations relevant to relative localization frameworks, which are validated through numerical and experimental evaluations using a multirobot system equipped with relative positioning sensors.

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References

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Figures

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Fig. 1

Frames of reference related to relative localization

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Fig. 2

Comparison between the sampled points and the first-order approximation of noise figures related to a high noise relative positioning sensor and a low noise sensor. The standard deviation of sensor 1: σr=10 cm and σθ=20 deg. The standard deviation of sensor 2: σr=3 cm, and σθ=1 deg.

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Fig. 3

The simulated path

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Fig. 4

Localization results for known input cases (S1), of Mesh and Star configurations

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Fig. 7

The experimental trajectory of robots

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Fig. 8

Localization results for known input cases (S1), of Mesh and Star configurations

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Fig. 9

Localization results for unknown input cases (S2), of Mesh and Star configurations

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Fig. 5

Localization results for unknown input cases (S2), of Mesh and Star configurations

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Fig. 6

Localization results for unknown input cases (S3), of Mesh and Star configurations

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Fig. 10

Localization results for unknown input cases (S3), of Mesh and Star configurations

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Fig. 11

Actual and estimated path for a circular trajectory localization experiment

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Fig. 12

Localization results for known input (S1) and unknown input (S2, S3) with Star configuration (for the circular trajectory)

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