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Journal of Dynamic Systems, Measurement, and Control | Volume 140 | Issue 1 | research-article
Research Papers

The Right Invariant Nonlinear Complementary Filter for Low Cost Attitude and Heading Estimation of Platforms

[+] 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 September 17, 2016; final manuscript received July 8, 2017; published online September 8, 2017. Assoc. Editor: Suman Chakravorty.

J. Dyn. Sys., Meas., Control 140(1), 011011 (Sep 08, 2017) (10 pages) Paper No: DS-16-1447; doi: 10.1115/1.4037331 History: Received September 17, 2016; Revised July 08, 2017
Article
References
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This paper presents a novel filter with low computational demand to address the problem of orientation estimation of a robotic platform. This is conventionally addressed by extended Kalman filtering (EKF) of measurements from a sensor suit which mainly includes accelerometers, gyroscopes, and a digital compass. Low cost robotic platforms demand simpler and computationally more efficient methods to address this filtering problem. Hence, nonlinear observers with constant gains have emerged to assume this role. The nonlinear complementary filter (NCF) is a popular choice in this domain which does not require covariance matrix propagation and associated computational overhead in its filtering algorithm. However, the gain tuning procedure of the complementary filter is not optimal, where it is often hand picked by trial and error. This process is counter intuitive to system noise based tuning capability offered by a stochastic filter like the Kalman filter. This paper proposes the right invariant formulation of the complementary filter, which preserves Kalman like system noise based gain tuning capability for the filter. The resulting filter exhibits efficient operation in elementary embedded hardware, intuitive system noise based gain tuning capability and accurate attitude estimation. The performance of the filter is validated using numerical simulations and by experimentally implementing the filter on an ARDrone 2.0 micro aerial vehicle (MAV) platform.
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References

1
Lefferts, E. , Markley, F. L. , and Shuster, M. D. , 1982, “ Kalman Filtering for Spacecraft Attitude Estimation,” J. Guid. Control Dyn., 5(5), pp. 417–429. [CrossRef]
2
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De Silva, O. , Mann, G. K. I. , and Gosine, R. G. , 2014, “ Pairwise Observable Relative Localization in Ground Aerial Multi-Robot Networks,” European Control Conference (ECC), Strasbourg, France, June 24–27, pp. 324–329.
4
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Blackman, S. , and Popoli, R. , 1999, Design and Analysis of Modern Tracking Systems, Artech House, Norwood, MA.
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Farrell, J. , 2008, Aided Navigation: GPS With High Rate Sensors, McGraw-Hill, New York.
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Mahony, R. , Hamel, T. , and Pflimlin, J.-M. , 2008, “ Nonlinear Complementary Filters on the Special Orthogonal Group,” IEEE Trans. Autom. Control, 53(5), pp. 1203–1218. [CrossRef]
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Hamel, T. , and Mahony, R. , 2006, “ Attitude Estimation on SO[3] Based on Direct Inertial Measurements,” IEEE International Conference on Robotics and Automation (ICRA), Orlando, FL, May 15–19, pp. 2170–2175.
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Markley, F. L. , 2003, “ Attitude Error Representations for Kalman Filtering,” J. Guid. Control. Dyn., 26(2), pp. 311–317. [CrossRef]
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Hervier, T. , Bonnabel, S. , and Goulette, F. , 2012, “ Accurate 3D Maps From Depth Images and Motion Sensors Via Nonlinear Kalman Filtering,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura, Portugal, Oct. 7–12, pp. 5291–5297.
12
Bonnabel, S. , 2012, “ Symmetries in Observer Design: Review of Some Recent Results and Applications to EKF-Based SLAM,” Robot Motion and Control, Springer, London, pp. 3–15. [CrossRef]
13
De Silva, O. , Mann, G. K. I. , and Gosine, R. G. , 2014, “ Relative Localization With Symmetry Preserving Observers,” Canadian Conference on Electrical and Computer Engineering (CCECE), Toronto, ON, Canada, May 4–7, pp. 1–6.
14
Barczyk, M. , Member, S. , and Lynch, A. F. , 2013, “ Invariant Observer Design for a Helicopter UAV Aided Inertial Navigation System,” IEEE Trans. Control Syst. Technol., 21(3), pp. 791–806. [CrossRef]
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16
Martin, P. , and Salaün, E. , 2010, “ Design and Implementation of a Low-Cost Observer-Based Attitude and Heading Reference System,” Control Eng. Pract., 18(7), pp. 712–722. [CrossRef]
17
Bonnable, S. , Martin, P. , and Salaün, E. , 2009, “ Invariant Extended Kalman Filter: Theory and Application to a Velocity-Aided Attitude Estimation Problem,” IEEE Conference on Decision and Control (CDC), Shanghai, China, Dec. 15–18, pp. 1297–1304.
18
Arnold, W. , and Laub, A. , 1984, “ Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations,” Proc. IEEE, 72(12), pp. 1746–1754. [CrossRef]
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Suksakulchai, S. , Thongchai, S. , Wilkes, D. , and Kawamura, K. , 2000, “ Mobile Robot Localization Using an Electronic Compass for Corridor Environment,” IEEE International Conference on Systems, Man, and Cybernetics (ICSMC), Nashville, TN, Oct. 8–11, pp. 3354–3359.
20
Markley, F. L. , 1988, “ Attitude Determination Using Vector Observations and the Singular Value Decomposition,” J. Astronaut. Sci., 36(3), pp. 245–258.

Figures

Grahic Jump Location
Fig. 1

The overview of this study and filters designed as part of this work

+The overview of this study and filters designed as part of this work
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The overview of this study and filters designed as part of this work
Grahic Jump Location
Fig. 2

Gain matrix K(t) of (a) the RIEKF*, (b) the LIEKF*, and (c) the RINCF for a smooth trajectory

+Gain matrix K(t) of (a) the RIEKF*, (b) the LIEKF*, and (c) the RINCF for a smooth trajectory
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Gain matrix K(t) of (a) the RIEKF*, (b) the LIEKF*, and (c) the RINCF for a smooth trajectory
Grahic Jump Location
Fig. 3

The simulated trajectory of the platform and the estimation accuracy provided by the RINCF for case 1

+The simulated trajectory of the platform and the estimation accuracy provided by the RINCF for case 1
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The simulated trajectory of the platform and the estimation accuracy provided by the RINCF for case 1
Grahic Jump Location
Fig. 4

Performance of the RINCF for case 1 compared with main attitude estimators reported in this work

+Performance of the RINCF for case 1 compared with main attitude estimators reported in this work
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Performance of the RINCF for case 1 compared with main attitude estimators reported in this work
Grahic Jump Location
Fig. 5

Gain matrix K(t) of the RIEKF* (top) and the RINCF2 (bottom), for a smooth trajectory with maximum angular velocity ωmax=π/3 (left), ωmax=2π/3 (middle), and ωmax=5π/3 (right)

+Gain matrix K(t) of the RIEKF* (top) and the RINCF2 (bottom), for a smooth trajectory with maximum angular velocity ωmax=π/3 (left), ωmax=2π/3 (middle), and ωmax=5π/3 (right)
View Large  |  Save Figure  |  Download Slide (.ppt)
Gain matrix K(t) of the RIEKF* (top) and the RINCF2 (bottom), for a smooth trajectory with maximum angular velocity ωmax=π/3 (left), ωmax=2π/3 (middle), and ωmax=5π/3 (right)
Grahic Jump Location
Fig. 6

Comparative performance of the RINCF for all cases

+Comparative performance of the RINCF for all cases
View Large  |  Save Figure  |  Download Slide (.ppt)
Comparative performance of the RINCF for all cases
Grahic Jump Location
Fig. 7

The experimental validation setup used in the study

+The experimental validation setup used in the study
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The experimental validation setup used in the study
Grahic Jump Location
Fig. 8

(a) Attitude heading estimates of the EKF and (b) attitude heading estimates of the RINCF for experimental data

+(a) Attitude heading estimates of the EKF and (b) attitude heading estimates of the RINCF for experimental data
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(a) Attitude heading estimates of the EKF and (b) attitude heading estimates of the RINCF for experimental data
Grahic Jump Location
Fig. 9

Attitude heading estimates of the filters for experimental data. RINCF performance was validated by implementing the filter on the MAV platform.

+Attitude heading estimates of the filters for experimental data. RINCF performance was validated by implementing the filter on the MAV platform.
View Large  |  Save Figure  |  Download Slide (.ppt)
Attitude heading estimates of the filters for experimental data. RINCF performance was validated by implementing the filter on the MAV platform.

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