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Romain Pepy, Michel Kieffer and Eric Walter

Reliable Robust Path Planning with Application to Mobile Robots

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.

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Rafael Nogueras and Carlos Cotta

Abstract

Multimemetic algorithms (MMAs) are a subclass of memetic algorithms in which memes are explicitly attached to genotypes and evolve alongside them. We analyze the propagation of memes in MMAs with a spatial structure. For this purpose we propose an idealized selecto-Lamarckian model that only features selection and local improvement, and study under which conditions good, high-potential memes can proliferate. We compare population models with panmictic and toroidal grid topologies. We show that the increased takeover time induced by the latter is essential for improving the chances for good memes to express themselves in the population by improving their hosts, hence enhancing their survival rates. Experiments realized with an actual MMA on three different complex pseudo-Boolean functions are consistent with these findings, indicating that memes are more successful in a spatially structured MMA, rather than in a panmictic MMA, and that the performance of the former is significantly better than that of its panmictic counterpart

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J. Sanabria, E. Acosta, M. Salas-Brown and O. Garcia

References [1] Abd El-Monsef M.E., Lashien E.F., Nasef A.A., On I-open sets and I-continuous functions, Kyungpook Math. J., 32(1992), 21-30. [2] Dontchev J., On Hausdorff spaces via topological ideals and I-irresolute functions, In papers on General Topology and Applications, Annals of New York Academy of Sciences, 767(1995), 28-38. [3] Hatir E., Noiri T., On descompositions of continuity via idealization, Acta. Math. Hungar., 96(4)(2002), 341-349. [4] Hayashi E., Topologies defined by local

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A. Durán

). 2 The mathematical model 2.1 On the derivation The two-layer interface problem for internal wave propagation, of interest for the present paper, is idealized in Figure 1 . This consists of two inviscid, homogeneous, incompressible fluids of depths d i , i = 1, 2, with d 2 > d 1 and densities ρ i , i = 1, 2 with ρ 2 > ρ 1 . The upper and lower layers are respectively bounded above and below by a rigid horizontal plane, while the deviation of the interface from a level of rest, denoted by ζ , is supposed to be a graph over the bottom

Open access

Marina Esteban, Enrique Ponce and Francisco Torres

dimensional reduction in the analysis of slow-fast systems, see the Appendix. In [ 10 ] two characteristics of hysteresis are emphasized. First, the non-linearity has a dependence on previous values of the input ( memory effect ). Second, hysteretic systems undergo arbitrary quickly transitions, what is an idealization for real systems. The mathematical analysis of hysteretic systems has emphasized its ability for generating chaotic solutions when the involved dynamics are of focus type. See [ 6 , 7 , 9 ]. Here, we consider instead symmetric hysteretic systems having