Abstract
We compute all translations resulting in the union of two finite, convex sets being again convex. Convexity will be established by conditions on the outside of the convex hull. Computations are of low degree polynomial bounds on the worst case number of steps. This results in a set estimator for a mobile robot's translation value.
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Alt, H., Mehlhorn, K., Wagener, H., and Welzl, E.: 1988, Congruence, similarity, and symmetries of geometric objects, Discrete Computational Geometry 3, 237–256.
Bern, M., Dobkin, D., Eppstein, D., and Grossman, R.: 1994, Visibility with a moving point of view, Algorithmica 11, 360–378.
Crowley, J. L.: 1985, Navigation for an intelligent mobile robot, IEEE Journal of Robotics and Automation 1, 31–41.
Feng, L., Borenstein, J., and Everett, H. R.: 1994, Where am I?, Technical report, Dept. of Mechanical Engineering, University of Michigan, Ann Arbor.
Guibas, L. J., Motwani, R., and Raghavan, P.: 1995, The robot localization problem, Technical report, Dept. of Computer Science, Stanford University, Stanford.
Huttenlocher, D. P., Klanderman, G. A., and Rucklidge, W. J.: 1993, Comparing images using the Hausdorff distance, IEEE Journal on Pattern Analysis and Machine Intelligence 15, 850–863.
Kämpke, T.: 1997, Point set matchings in Euclidean space, (in press).
Latombe, J.-C.: 1991,Robot Motion Planning, 2nd ed., Kluwer, Norwell.
Lu, F. and Milios, E.: 1997, Robot pose estimation in unknown environments by matching 2D range scans, Journal of Intelligent and Robotic Systems 18, 249–275.
Prassler, E.: 1997, Distance signatures: distributed spatial relations, in: R. C. Bolles et al. (eds), Modelling and Planning for Sensor-Based Intelligent Robot Systems, World Scientific Publishing, to appear.
Preparata, F. P. and Shamos, M. I.: 1988, Computational Geometry, 2nd ed., Springer, New York.
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Kämpke, T. Convex Translation Estimation. Journal of Intelligent and Robotic Systems 21, 287–300 (1998). https://doi.org/10.1023/A:1007981819788
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DOI: https://doi.org/10.1023/A:1007981819788