Abstract
We present “BCAD”, a Bayesian CAD modeller for geometric problem definition and resolution. This modeller provides tools for (i) modelling geometric uncertainties and constraints, and (ii) solving inverse geometric problems while taking into account the propagation of these uncertainties. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements instead of as a simple equality or inequality. To solve geometric problems in this framework, we propose the Monte Carlo Simultaneous Estimation and Maximization (MCSEM) algorithm as a resolution technique able to adapt to problem complexity. Using three examples, we show how to apply our approach using the BCAD system.
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
Alami, R., Simeon, T.: Planning robust motion strategies for mobile robots. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, San Diego, California, vol. 2, pp. 1312–1318 (1994)
Bar-Shalom, Y., Fortmann, T.E.: Tracking and D ata Association. Academic Press, London (1988)
Coué, C., Fraichard, T., Bessière, P., Mazer, E.: Using bayesian programming for multi-sensor multi-target tracking in automotive applications. In: Proceedings of IEEE International Conference on Robotics and Automation, Taipei (TW) September (2003)
Dellaert, F., Fox, D., Burgard, W., Thrun, S.: Monte Carlo localization for mobile robots. In: Proc. of the IEEE Int. Conf. on Robotics and Automation, Detroit, MI May (1999)
Geweke, J.: Monte Carlo simulation and numerical integration. In: Amman, H., Kendrick, D., Rust, J. (eds.) Handbook of Computational Economics, vol. 13, pp. 731–800. Elsevier North-Holland, Amsterdam (1996)
Gondran, M., Minoux, M.: Graphes et Algorithmes, Eyrolle, Paris (1990)
Grefenstette, J.J.: Credit assignment in rule discovery systems based on genetic algorithms. Machine Learning 3, 225–245 (1988)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI (1975)
Jensen, F.: Bayesian N etworks and Decision G raphs. In: Statistics for Engineering and Information Science, Springer, Heidelberg (2001)
Keller, A.: The fast calculation of form factors using low discrepancy point sequence. In: Proc. of the 12th Spring Conf. on Computer Graphics, Bratislava, pp. 195–204 (1996)
Lozano-Pérez, T.: A simple motion-planning algorithm for general robot manipulators. IEEE J. of Robotics and Automation 3(3), 224–238 (1987)
MacKay, D.G.C.: Introduction to monte carlo methods. In: Jordan, M. (ed.) Proc. of an Erice summer school (1996)
Mazer, E., Ahuactzin, J., Bessière, P.: The Ariadne’s Clew algorithm. J. Artif. Intellig. Res (JAIR) 9, 295–316 (1998)
Mekhnacha, K.: Méthodes probabilistes Bayesiennes pour la prise en compte des incertitudes géométriques: application à la CAO-robotique. Thèse de doctorat, Inst. Nat. Polytechnique de Grenoble, Grenoble, France (July 1999)
Mekhnacha, K., Mazer, E., Bessière, P.: A robotic CAD system using a Bayesian framework. In: Proc. of the IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS 2000), Takamatsu, Japan, October 2000, vol. 3, pp. 1597–1604 (2000)
Mekhnacha, K., Mazer, E., Bessière, P.: The design and implementation of a Bayesian CAD modeler for robotic applications. Advanced Robotics, the Int. J. of the Robotics Society of Japan 15(1), 45–70 (2001)
Mekhnacha, K., Ahuactzin, J., Bessière, P., Mazer, E., Smail, L.: A unifying framework for exact and approximate bayesian inference. Research Report RR-5797, INRIA (January 2006)
Moravec, H.P.: Sensor fusion in certainty grids for mobile robots. AI Magazine 9(2), 61–74 (1988)
Neal, R.M.: Probabilistic inference using Markov Chain Monte Carlo methods. Research Report CRG-TR-93-1, Dept. of Computer Science, University of Toronto (1993)
Owen, J.C.: Constraints on simple geometry in two and three dimensions. Int. J. of Computational Geometry and Applications 6(4), 421–434 (1996)
Puget, P.: Vérification-Correction de programme pour la prise en compte des incertitudes en programmation automatique des robots. Thèse de doctorat, Inst. Nat. Polytechnique de Grenoble, Grenoble, France (1989)
Sanderson, A.C.: Assemblability based on maximum likelihood configuration of tolerances. In: Proc. of the IEEE Symposium on Assembly and Task Planning, Marina del Rey, CA (August 1997)
Taylor, R.: A synthesis of manipulator control programs from task-level specifications. Ph.d thesis, Stanford University, Computer Science Department (July 1976)
Yguel, M., Tay, C., Mekhnacha, K., Laugier, C.: Velocity estimation on the bayesian occupancy filter for multi-target tracking. Research Report RR-5836, INRIA (January 2006)
Zhang, Z., Augeras, O.: 3D Dynamic Scene Analysis: A Stereo Based Approach. Springer, Berlin, Heidelberg (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mekhnacha, K., Bessière, P. (2008). BCAD: A Bayesian CAD System for Geometric Problems Specification and Resolution. In: Bessière, P., Laugier, C., Siegwart, R. (eds) Probabilistic Reasoning and Decision Making in Sensory-Motor Systems. Springer Tracts in Advanced Robotics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79007-5_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-79007-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79006-8
Online ISBN: 978-3-540-79007-5
eBook Packages: EngineeringEngineering (R0)