“…Consequently, computing roadmaps in the Euclidean space has remained a strong area of research. Current motion planning algorithms that compute roadmaps rely on visibility graphs (Jiang et al, 1999; Neus & Maouche, 2005), Voronoi diagrams (Diaz de León & Sossa, 1998; Wilmarth et al, 1999; Foskey et al, 2001; Garber & Lin, 2002; Lee & Choset, 2005; Geraerts & Overmars, 2007), silhouette curves of semialgebraic sets (Canny, 1993), or probabilistic roadmap planners (Kavraki et al, 1996);- potential field methods that introduce artificial attractive/repulsive field in the environment can conceptually handle both static and moving obstacles (Rimon & Koditschek, 1992; Xidias et al, 2007). These methods cannot take into consideration the exact geometry of the obstacles, and therefore they cannot be applied to those problems in which the moving object is moving in close proximity with the obstacles.
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