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Robot Path and Motion Planning
Published in Jitendra R. Raol, Ajith K. Gopal, Mobile Intelligent Autonomous Systems, 2016
An environment is approximated by a grid, each cell of which will be represented by a vertex in the graph [1]. The cell’s neighbours will have appropriate edges within the graph. If a neighbourhood of each cell is too small, the algorithm will have a limited range of motion. If the neighbourhood of each cell is too large, the algorithm will take too long for processing all the neighbours for each cell. The three common neighbourhoods are: (i) the von Neumann neighbourhood that includes only those cells which are directly North, South, East and West of a given cell, (ii) the Moore neighbourhood in addition to (i) above also includes the diagonal neighbours and (iii) the extended Moore neighbourhood includes the Moore neighbourhood and their own Moore neighbours too. The centre of a chosen neighbourhood is the cell from which this neighbourhood is constructed. The radius r of a neighbourhood is appropriately defined so that the number of rows/columns in a neighbourhood is equal to 2r + 1. The robot might move along the edge of an obstacle until it reaches the obstacle’s corner. If the outer corner of the robot’s neighbourhood is unoccupied, it will attempt to move through the obstacle. This is solved by forming a hierarchy where the neighbours closer to the centre of the neighbourhood determine if the outer neighbours are free.
Cellular Automata
Published in Young W. Kwon, Multiphysics and Multiscale Modeling, 2015
These cells do not have to be colored, but they are assigned to one of a finite number of states at any given time step. These states may be represented by colors or may be represented by integer numbers (0, 1, 2, …). Furthermore, a finite number of alphabets will do. Usually, the number of states is small, but in principle any finite number is acceptable. The way that the neighboring cells are defined may be different. One can only use the four cells on the east, west, north, and south (von Neumann neighborhood), but another can use eight cells, such as east, west, north, south, northeast, southeast, southwest, and northwest (Moore neighborhood). One can even use a hexagonal lattice instead of a square lattice. These are for the two-dimensional (2-D) cases. The concept can be extended to three-dimensional (3-D) problems. For example, the equivalents to von Neumann neighbors in 3-D are east, west, north, south, front, and back.
Evacuation simulation and layout optimization of cruise ship based on cellular automata
Published in International Journal of Computers and Applications, 2020
In the cellular automata, rules are defined in local space, which means the state of a cell next step is determined by the states of itself and its neighbors’. Therefore, for a given cell, it’s important to make it clear which cell belongs to its neighbors. As shown in Figure 1, several common types of neighborhood are illustrated. The yellow cell is the central cell, and green ones are neighboring cells. In the Von Neumann neighborhood, a pedestrian has four alternatives to choose as his target position at each time step. In other words, a pedestrian can wait there or move in one of the four directions. In the Moore neighborhood or extended Moore neighborhood, a pedestrian has eight optional positions. In the extended Moore neighborhood, the number of neighbors for a given cell is ((2r + 1)d − 1), where d is the number of dimensions and r is the radius of the neighborhood. The Moore neighborhood is used to set up the pedestrian evacuation model in this paper.
Localized algorithms for redundant readers elimination in RFID networks
Published in International Journal of Parallel, Emergent and Distributed Systems, 2019
Nafiul Rashid, Salimur Choudhury, Kai Salomaa
A cellular automaton consists of a collection of cells on a grid whose states evolve at discrete time steps according to rules based on the states of the neighboring cells. We can define a 2-dimensional cellular automaton as a quadruple, (C,S,, N) where C is the cellular grid, S is the set of states of the cells, is the transition rule of the automaton and N is the neighborhood of a cell. At time t, each cell of C is assigned a state of S. The state of a cell , at time , is determined via the transition function depending on the current state of c and the states of cells in the neighborhood of c at time t. If all the adjacent cells (maximum 8) of a cell are considered as the neighbors, then this is called a Moore Neighborhood. In a cellular automaton, all the cells synchronously verify the states of their neighbors and change their states accordingly. More details on cellular automaton can be found in [19]. In Figure 2, radius 1 and radius 2 neighborhoods are shown for a cell c. In a radius 1 neighborhood, one cell can have a maximum 8 neighbors (C,E,W, S,N,NW,NE,SW,SE). On the other hand, in a radius 2 neighborhood, one cell can have 24 neighbors. In Figure 2, the radius 2 neighborhood of the cell c consists of all cells that are within the radius 1 and the cells which are marked by 2.