Abstract
Interval analysis is a relatively new mathematical tool that allows one to deal with problems that may have to be solved numerically with a computer. Examples of such problems are system solving and global optimization but numerous other problems may be addressed as well. This approach has the following general advantages:
-
it allows to find solutions of a problem only within some finite domain
-
numerical computer round-off errors are taken into account so that the solutions are guaranteed
A further inherent property that is of interest for robotics problems is that this approach allows one to deal with the uncertainties that are unavoidable in robotics. Although the basic principles of interval analysis are easy to understand and to implement, this approach will be efficient only if additional methods are used and if the problem at hand is formulated appropriately. In this paper we will emphasize various robotics problems that have been solved with interval analysis, many of which are currently beyond the reach of other mathematical approaches.
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
Ashokaraj, I., et al.: Sensor based robot localisation and navigation: Using interval analysis and extended kalman filter. In: 5th Asian Control Conference, Melbourne, July 20-23 (2004)
Carreras, C., Walker, I.D.: Interval methods for fault-tree analysis in robotics. IEEE Trans. on Reliability 50(1), 3–11 (2001)
Chablat, D., Wenger, P., Majou, F., Merlet, J.-P.: An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machine. Int. J. of Robotics Research 23(6), 615–624 (2004)
Clerenti, A., et al.: Imprecision and uncertainty quantification for the problem of mobile robot localization. In: Performance Metrics for Intelligent Systems Workshop, Gaithersburg, September 16-18 (2003)
Daney, D., Andreff, N., Chabert, G., Papegay, Y.: Interval method for calibration of parallel robots: a vision-based experimentation. Mechanism and Machine Theory 41(8), 929–944 (2006)
Hansen, E.: Global optimization using interval analysis. Marcel Dekker, New York (2004)
Jansson, C., Rohn, J.: An algorithm for checking regularity of interval matrices. SIAM Journal on Matrix Analysis and Applications 20(3), 756–776 (1999)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, Heidelberg (2001)
Merlet, J.-P.: Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis. Int. J. of Robotics Research 23(3), 221–236 (2004)
Merlet, J.-P.: Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries. Int. J. of Robotics Research 18(9), 902–916 (1999)
Merlet, J.-P., Donelan, P.: On the regularity of the inverse jacobian of parallel robot. In: ARK, Ljubljana, June 26-29, pp. 41–48 (2006)
Moore, R.E.: Methods and Applications of Interval Analysis. SIAM Studies in Applied Mathematics (1979)
Piazzi, A., Visioli, A.: Global minimum-jerk trajectory planning of robot manipulators. Trans. on Industrial Electronics 47(1), 140–149 (2000)
Rao, R., Asaithambi, A., Agrawal, S.K.: Inverse kinematic solution of robot manipulators using interval analysis. J. of Mechanical Design 120(1), 147–150 (1998)
Redon, S., et al.: Fast continuous collision detection for articulated models. In: 9th ACM symposium on Solid modeling and applications, Genoa, pp. 145–156 (2004)
Rouillier, F.: Real roots counting for some robotics problems. In: Merlet, J.-P., Ravani, B. (eds.) Computational Kinematics, pp. 73–82. Kluwer, Dordrecht (1995)
Seignez, E., et al.: Experimental vehicle localization by bounded-error state estimation using interval analysis. In: IEEE/RJS IROS, Edmonton, August 2-6 (2005)
Wu, W., Rao, S.S.: Interval approach for the modeling of tolerances and clearances in mechanism analysis. J. of Mechanical Design 126(4), 581–592 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Merlet, J.P. (2010). Interval Analysis and Robotics. In: Kaneko, M., Nakamura, Y. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14743-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-14743-2_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14742-5
Online ISBN: 978-3-642-14743-2
eBook Packages: EngineeringEngineering (R0)