Abstract
Summary. Using concepts from switched adaptive control theory plus a special parameterization of the class of 2×2 nonsingular matrices, a tractable and provably correct solution is given to the three landmark station keeping problem in the plane in which range measurements are the only sensed signals upon which station keeping is to be based. The performance of the overall system degrades gracefully in the face of increasing measurement and miss-alignment errors, provided the measurement errors are not too large.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Armesto and J. Tornero. SLAM based on Kalman filter for multi-rate fusion of laser and encoder measurements. In Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 1860–1865, 2004.
M. Cao and A.S. Morse. Mainaining an autonomous agent’s position in a moving formation with range-only measurements. In Proc. of the 2007 European Control Conference, 2007. to be presented.
M. Cao and A.S. Morse. Station-keeping in the plane with range-only measurements. In Proc. of the 2007 Amer. Contr. Conf., 2007. to be presented.
S. H. Dandach, B. Fidan, S. Dasgupta, and B.D.O. Anderson. Adaptive source localization by mobile agents. In Proc. of the 45rd IEEE Conf. on Decision and Contr., pages 2045–2050, 2006.
S. H. Dandach, B. Fidan, S. Dasgupta, and B.D.O. Anderson. A continuous time linear adaptive source localization algorithm robust to persistent drift. Systems & Control Letters, 2007. To appear.
M. W. Dissanayake, P. Newman, H. F. Durrant-Whyte, S. Clark, and M. Csorba. An experimental and thoretical investigation into simultaneous localisation and map building. Experimental Robotics, IV:265–274, 2000.
H.J.S. Feder, J.J. Leonard, and C.M. Smith. Adaptive mobile robot navigation and mapping. International Journal of Robotics Research, 18:650–668, 1999.
D. Fox, W. Burgard, F. Dellaert, and S. Thrun. Monte Carlo localization: Efficient position estimation for mobile robots. In Proceedings of the National Conference on Artificial Intelligence (AAAI), 1999.
B. Grocholsky, E. Stump, P. Shiroma, and V. Kumar. Control for localization of targets using range-only sensors. In Proceedings of the International Symposium on Experimental Robotics, 2006.
J.P. Hespanha and A.S. Morse. Certainty equivalence implies detectability. Systems & Control Letters, pages 1–13, 1999.
J.J. Leonard and H.F. Durrant-Whyte. Simultaneous map building and localization for an autonomous mobile robot. In Proceedings of the 1991 IEEE/RSJ International Workshop on Intelligent Robots and Systems, pages 1442–1447, 1991.
A.S. Morse. A gain matrix decomposition and some of its applications. SCL, 21:1–10, 1993.
A.S. Morse. Cyclic switching and supervisory control. In Proceedings of the 1995 IFAC Symposium on Nonlinear Control Systems Design, pages 499–502, 1995.
A.S. Morse. Analysis of a supervised set-point control system containing a compact continuum of finite dimensional linear controllers. In Proc. of Mathematical Theory of Networks and Systems, 2004.
A.S. Morse. Logically switched dynamical systems. In Nonlinear and Optimal Control Theory, pages 1–84. Springer-Verlag, 2005. To appear.
P. Newman. On the Structure and Solution of the Simultaneous Localisation and Map Building Problem. Ph.D dissertation, University of Sydney, Australian Centre for Field Robotics, 1999.
F.M. Pait and A.S. Morse. A cyclic switching strategy for parameter-adaptive control. IEEE Trans. on Automat. Contr., 39(6):1172–1183, 1994.
A.H. Sayed and A. Tarighat. Network-based wireless location. IEEE Signal Processing Magazine, pages 24–40, July 2005.
R. Smith, M. Self, and P. Cheeseman. Estimating uncertain spatial relationships in robotics. In I. Cox and G. Wilfong, editors, Autonomous Robot Vehicles. Springer-Verlag, 1990.
E. Stump, B. Grocholsky, and V. Kumar. Extensive representaions and algorithms for nonlinear filtering and estimation. In Proceedings of the 7th Annual Workshop on the Algorithmic Foundations of Robotics, 2006.
S. Thrun, D. Fox, and W. Burgard. A probabilistic approach to concurrent mapping and localization for mobile robots. Machine Learning, 31:29–53, 1998.
L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38:49–95, 1996.
S.B. Williams, M.W.. Dissanayake, and H.F. Durrant-Whyte. Towards multi-vehicle simultaneous localisation and mapping. In Proceedings of the 2002 IEEE International Conference on Robotics and Automation, pages 2743–2748, 2002.
D.C.K. Yuen and B.A. MacDonald. An evaluation of the Sequential Monte Carlo technique for simultaneous localisation and map-building. In Proceedings of the 2003 IEEE International Conference on Robotics and Automation, pages 1564–1569, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Cao, M., Morse, A. (2008). Convexification of the Range-Only Station Keeping Problem. In: Astolfi, A., Marconi, L. (eds) Analysis and Design of Nonlinear Control Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74358-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-74358-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74357-6
Online ISBN: 978-3-540-74358-3
eBook Packages: EngineeringEngineering (R0)