Observer design for monocular visual inertial SLAM
-
Geoff Fink
Geoff Fink received his B. Sc. in Computer Engineering in 2007 from the University of Alberta and M. Sc. in Robotics Engineering in 2011 from the University of Guadalajara. Since September 2012 he has been a Ph. D. student at the University of Alberta.His current research interests include nonlinear control, unmanned aerial vehicles, and visual servoing.
, Mirko Franke
Mirko Franke received his Dipl.-Ing. degree in Electrical Engineering from the Technische Universität Dresden in 2014. Since February 2015 he is research assistent at the Institute of Control Theory at Technische Universität Dresden.His fields of activity include nonlinear control, observer design and algorithmic differentiation.
Alan F. Lynch obtained his B. A. Sc. at the University of Toronto in Engineering Science (Electrical Option) in 1991, M. A. Sc. in Electrical Engineering from University of British Columbia in 1994, and Ph.D in Electrical and Computer Engineering from the University of Toronto in 1999. Since 2001 he has been a faculty member at the Department of Electrical & Computer Engineering, University of Alberta and currently holds the rank of Full Professor. His interests include nonlinear control and its application to electrical and electromechanical systems including power converters, unmanned systems, and self-bearing motors.
Klaus Röbenack received his Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from the Technische Universität Dresden in 1993 and 1999, respectively. Moreover, he received the Dipl.-Math. degree in 2002 and the postdoctoral qualification (habilitation) in 2005. Prof. Röbenack is head of the Institute of Control Theory at Technische Universität Dresden since 2009. His research interests include nonlinear control, observer design, descriptor systems and scientific computing.
Abstract
This paper examines the state estimation problem for unmanned aerial vehicles when commonly used positioning systems such as the global positioning system or indoor motion capture systems are unavailable. The proposed method uses inertial sensor measurements along with scaled position measurements from an onboard computer vision system which implements visual simultaneous localization and mapping. A state transformation puts the system into a linear time-varying form which simplifies observability analysis and allows for an observer design with sufficient conditions for convergence. The proposed design is validated by simulation.
Zusammenfassung
Dieser Beitrag untersucht das Problem der Zustandsschätzung für unbemannte Fluggeräte, wenn Referenzsysteme wie das globale Positionsbestimmungssystem oder Multikamera basierte Systeme zur Bewegungserfassung nicht verfügbar sind. Der vorgestellte Ansatz nutzt Messwerte eines Inertialsensors in Verbindung mit einem auf visueller simultaner Lokalisierung und Kartierung basierenden internen Computer Vision System. Mittels Zustandstransformation wird das System in eine lineare zeitvariante Form überführt, welche die Beobachtbarkeitsanalyse vereinfacht und einen Beobachterentwurf mit hinreichenden Konvergenzbedingungen erlaubt. Der Entwurf wird mittels Simulation verifiziert.
About the authors
Geoff Fink received his B. Sc. in Computer Engineering in 2007 from the University of Alberta and M. Sc. in Robotics Engineering in 2011 from the University of Guadalajara. Since September 2012 he has been a Ph. D. student at the University of Alberta.His current research interests include nonlinear control, unmanned aerial vehicles, and visual servoing.
Mirko Franke received his Dipl.-Ing. degree in Electrical Engineering from the Technische Universität Dresden in 2014. Since February 2015 he is research assistent at the Institute of Control Theory at Technische Universität Dresden.His fields of activity include nonlinear control, observer design and algorithmic differentiation.
Alan F. Lynch obtained his B. A. Sc. at the University of Toronto in Engineering Science (Electrical Option) in 1991, M. A. Sc. in Electrical Engineering from University of British Columbia in 1994, and Ph.D in Electrical and Computer Engineering from the University of Toronto in 1999. Since 2001 he has been a faculty member at the Department of Electrical & Computer Engineering, University of Alberta and currently holds the rank of Full Professor. His interests include nonlinear control and its application to electrical and electromechanical systems including power converters, unmanned systems, and self-bearing motors.
Klaus Röbenack received his Dipl.-Ing. and Dr.-Ing. degrees in electrical engineering from the Technische Universität Dresden in 1993 and 1999, respectively. Moreover, he received the Dipl.-Math. degree in 2002 and the postdoctoral qualification (habilitation) in 2005. Prof. Röbenack is head of the Institute of Control Theory at Technische Universität Dresden since 2009. His research interests include nonlinear control, observer design, descriptor systems and scientific computing.
References
1. B. D. O. Anderson and J. Moore, Time-varying feedback laws for decentralized control, IEEE Trans. Automat. Contr. 26 (1981), 1133–1139.10.1109/TAC.1981.1102770Search in Google Scholar
2. B. D. O. Anderson, R. R. Bitmead, C. R. Johnson Jr., P. V. Kokotovic, R. L. Kosut, I. M. Y. Mareels, L. Praly and B. D. Riedle, Stability of Adaptive Systems: Passivity and Averaging Analysis, MIT Press, Cambridge, MA, USA, 1986.Search in Google Scholar
3. A. Concha, G. Loianna, V. Kumar and J. Civera, Visual-inertial direct SLAM, in: Proc. IEEE Int. Conf. on Robotics and Automation, Stockholm, Sweden, May 2016.10.1109/ICRA.2016.7487266Search in Google Scholar
4. P. Corke, J. Lobo and J. Dias, An introduction to inertial and visual sensing, Int. J. Robot. Res. 26 (2007), 519–535.10.1177/0278364907079279Search in Google Scholar
5. A. J. Davison, I. D. Reid, N. D. Molton and O. Stasse, MonoSLAM: Real-time single camera SLAM, IEEE Trans. Pattern Anal. Mach. Intell. 29 (2007), 1052–1067.10.1109/TPAMI.2007.1049Search in Google Scholar PubMed
6. J. Engel, J. Sturm and D. Cremers, Scale-aware navigation of a low-cost quadrocopter with a monocular camera, Robot. Auton. Syst. 62 (2014), 1646–1656, Special Issue on Visual Control of Mobile Robots.10.1016/j.robot.2014.03.012Search in Google Scholar
7. G. Fink, M. Franke, A. F. Lynch, K. Röbenack and B. Godbolt, Visual inertial SLAM: Application to unmanned aerial vehicles, IFAC-PapersOnLine 50(1) (2017), 1965–1970.10.1016/j.ifacol.2017.08.162Search in Google Scholar
8. G. Fink, M. Franke, A. F. Lynch, K. Röbenack and B. Godbolt, Observer design for visual inertial SLAM scale on a quadrotor UAV, in: Proc. IEEE Int. Conf. on Unmanned Aircraft Systems, pp. 830–839, Miami, FL, Jun. 2017.10.1109/ICUAS.2017.7991497Search in Google Scholar
9. F. Fraundorfer and D. Scaramuzza, Visual odometry: Part II: Matching, robustness, optimization, and applications, IEEE Robot. Autom. Mag. 19 (2012), 78–90.10.1109/MRA.2012.2182810Search in Google Scholar
10. J. Fuentes-Pacheco, J. Ruiz-Ascencio and J. M. Rendón-Mancha, Visual simultaneous localization and mapping: A survey, Artif. Intell. Rev. 43 (2015), 55–81.10.1007/s10462-012-9365-8Search in Google Scholar
11. R. Hermann and A. Krener, Nonlinear controllability and observability, IEEE Trans. Automat. Contr. 22 (1977), 728–740.10.1109/TAC.1977.1101601Search in Google Scholar
12. R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, Trans. ASME, Ser. D, J. Basic Eng. 83 (1961), 95–108.10.1115/1.3658902Search in Google Scholar
13. X. Li, Q. Zhang and H. Su, An adaptive observer for joint estimation of states and parameters in both state and output equations, Int. J. Adapt. Control Signal Process. 25 (2011), 831–842.10.1002/acs.1244Search in Google Scholar
14. A. I. Mourikis and S. I. Roumeliotis, A multi-state constraint Kalman filter for vision-aided inertial navigation, in: Proc. IEEE Int. Conf. on Robotics and Automation, pp. 3565–3572, Rome, Italy, Apr. 2007.10.1109/ROBOT.2007.364024Search in Google Scholar
15. K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice Hall, Englewood Cliffs, NJ, 1989.Search in Google Scholar
16. B. Ni and Q. Zhang, Stability of the Kalman filter for continuous time output error systems, Syst. Control Lett. 94 (2016), 172–180.10.1016/j.sysconle.2016.06.006Search in Google Scholar
17. S. Puntanen and G. P. H. Styan, Historical Introduction: Issai Schur and the Early Development of the Schur Complement, The Schur Complement and Its Applications (F. Zhang, ed.), Springer US, Boston, MA, 2005, pp. 1–16.10.1007/0-387-24273-2_1Search in Google Scholar
18. D. Scaramuzza and F. Fraundorfer, Visual odometry: Part I: The first 30 years and fundamentals, IEEE Robot. Autom. Mag. 18 (2011), 80–92.10.1109/MRA.2011.943233Search in Google Scholar
19. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed., Springer-Verlag, New York, NY, 1998.10.1007/978-1-4612-0577-7Search in Google Scholar
20. S. M. Weiss, Vision Based Navigation for Micro Helicopters, Ph. D. thesis, ETH Zürich, Zürich, Switzerland, 2012.Search in Google Scholar
21. Q. Zhang, Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems, IEEE Trans. Automat. Contr. 47 (2002), 525–529.10.1109/9.989154Search in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Editorial
- Observer design and applications
- Survey
- Invariant observer design for scan matching-aided localization: A tutorial
- Some recent results on the design and implementation of interval observers for uncertain systems
- Methoden
- Generalized dynamic observer design for quasi-LPV systems
- From acceleration-based semi-active vibration reduction control to functional observer design
- Applications
- Observer design for monocular visual inertial SLAM
- Disturbance observer-based visual servoing for multirotor unmanned aerial vehicles
- Applications of observers in medical robotics
Articles in the same Issue
- Frontmatter
- Editorial
- Observer design and applications
- Survey
- Invariant observer design for scan matching-aided localization: A tutorial
- Some recent results on the design and implementation of interval observers for uncertain systems
- Methoden
- Generalized dynamic observer design for quasi-LPV systems
- From acceleration-based semi-active vibration reduction control to functional observer design
- Applications
- Observer design for monocular visual inertial SLAM
- Disturbance observer-based visual servoing for multirotor unmanned aerial vehicles
- Applications of observers in medical robotics