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Tham khảo tài liệu 'innovations in robot mobility and control - srikanta patnaik et al (eds) part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 232 C. Castejón et al. Voronoi diagram referred in this work is the VD generated for sets of points where a generator is defined as a set of points. In this case the region segmentation based on the minimum Euclidean distance computation between a location and a set of points is called Generalized Voronoi Diagram GVD . Definition 5. Generalized Voronoi Diagram Given G - g1 g2gn a collection of n point series in the plane which do not overlap gi c 2 i 1 2 --- n 6.19 g n gj 0 i j 6.20 for every point p e 2 the minimum Euclidean distance from p to another point belonging to the series gi is called dE p gi . dE p gi - min p Pi VPi G gi 6.21 The Voronoi region will be defined as V gi p I p G R dE p gi dE p gj j i 622 and the given sequence V V g1 V g2 -- V gn 6.23 will be the generalized Voronoi diagram generated by G . From now on the GVD term is used when the generators are series of points instead of isolated points. Those series of points will be defined as generator group. The algorithm we present in this work is based on the GVD and is implemented in a sensor based way because it is defined in terms of a metric function dE p gi that measure the Euclidean distance to the closest object gi represented as a set of points supplied by a sensor system. 6 Voronoi-Based Outdoor Traversable Region Modelling 233 6.4.3 TRM Algorithm Supposedly the robot is modelled as a point operating in a subset belonging to the two-dimensional Euclidean space in our particular case although this is true with n-dimension too . The space W which is called Workspace is obstacle populated C1 C2Cn that will be considered as a close set. The set of points where the robot can manoeuvre freely will be called free space and is defined in 5 as FS i n W u Ci i 1 6.24 The workspace W is represented as a two-dimensional binary image B i j where each position i j has assigned a field value 0 or 1 that indicates if a pixel belong to a generator field 0 o not field 1 . For each point belonged to the free
