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.

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
.
2.
Roumeliotis
,
S.
, and
Bekey
,
G.
,
2002
, “
Distributed Multirobot Localization
,”
IEEE Trans. Rob. Autom.
,
18
(
5
), pp.
781
795
.
3.
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.
Thrun
,
S.
,
Burgard
,
W.
, and
Fox
,
D.
,
2005
,
Probabilistic Robotics
,
MIT Press
,
Cambridge, MA
.
5.
Blackman
,
S.
, and
Popoli
,
R.
,
1999
,
Design and Analysis of Modern Tracking Systems
,
Artech House
,
Norwood, MA
.
6.
Farrell
,
J.
,
2008
,
Aided Navigation: GPS With High Rate Sensors
,
McGraw-Hill
,
New York
.
7.
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
.
8.
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
.
9.
Markley
,
F. L.
,
2003
, “
Attitude Error Representations for Kalman Filtering
,”
J. Guid. Control. Dyn.
,
26
(
2
), pp.
311
317
.
10.
Bonnabel
,
S.
,
Martin
,
P.
, and
Rouchon
,
P.
,
2008
, “
Symmetry-Preserving Observers
,”
IEEE Trans. Autom. Control
,
53
(
11
), pp.
2514
2526
.
11.
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
.
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
.
15.
Bonnabel
,
S.
,
Martin
,
P.
, and
Rouchon
,
P.
,
2009
, “
Non-Linear Symmetry-Preserving Observers on Lie Groups
,”
IEEE Trans. Autom. Control
,
54
(
7
), pp.
1709
1713
.
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
.
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
.
19.
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
.
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