Point Automaton Research Articles

Simulation of Dendritic Growth in Multicomponent Aluminium Alloys by Point Automata Method

A numerical model is developed to describe the dendritic growth of multicomponent aluminium alloys, based on a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized growth model that takes into account the undercooling temperature, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The dendritic growth model of multicomponent alloy [1,2] is solved by a novel Point Automata (PA) approach [3,4] where the regular cells of the Cellular Automata (CA) method are replaced by the randomly distributed points and neighborhood configuration, similar as appears in meshless methods. The PA method was developed in order to circumvent the mesh anisotropy problem, associated with the classical CA method. The present paper extends our previous developments of Pa method to multicomponent alloys. A comparison of the results, obtained by the PA and CA method is shown for Al-5.3% Zn-2.35% Mg-1.35% Cu-0.5% alloy.

Solution of Dendritic Growth in Steel by the Novel Point Automata Method

The aim of this paper is the simulation of dendritic growth in steel in two dimensions by a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized phase change kinetics model taking into account the undercooling, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat, and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by a novel Point Automata (PA) approach. The PA method was developed [1] in order to circumvent the mesh anisotropy problem, associated with the classical Cellular Automata (CA) method. The PA approach is established on randomly distributed points and neighbourhood configuration, similar as appears in meshless methods. A comparison of the PA and CA methods is shown. It is demonstrated that the results with the new PA method are not sensitive to the crystallographic orientations of the dendrite.

局所センサ情報を用いた未知環境における複数の移動ロボットの運動計画法

When multiple mobile robots are working in the same environment, it is necessary to plan such motions for the robots that they never collide each other. This paper proposes a useful algorithm for planning a collision-free coordination for two mobile robots in an unknown environment on the basis of local information from their sensors. This algorithm conquers the problem of coordination planning by a two-levels strategy. In the case that no collision between two robots is detected, the robots are independently guided by the motion planning algorithm proposed by V. Lumelsky. However, in the case that a potential collision is expected, their motions are coordinated to avoid the collision. To coordinate the robots, a two-dimensional task space (T-space) and a point automaton are introduced. By controlling the motion of the automaton in the T-space, any collision between the robots can be successfully aboided. Convergence of the proposed algorithm is proved, and its usefulness is shown by a simulation.

Incorporating range sensing in the robot navigation function

A model of mobile robot navigation is considered in which the robot is a point automaton operating in an environment with unknown obstacles of arbitrary shapes. The robot's input information includes its own and the target-points coordinates as well as local sensing information such as that from stereo vision or a range finder. These algorithmic issues are addressed: (1) Is it possible to combine sensing and planning functions to produce 'active sensing' guided by the needs of planning? (The answer is yes). (2) Can richer sensing (e.g., stereo vision versus tactile) guarantee better performance, that is, resulting in shorter paths? (The general answer is no). A paradigm for combining range data with motion planning is presented. It turns out that extensive modifications of simpler tactile algorithms are needed to take full advantage of additional sensing capabilities. Two algorithms that guarantee convergence and exhibit different styles of behavior are described, and their performance is demonstrated in simulated examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles

An approach of dynamic path planning (DPP) was introduced elsewhere, and nonheuristic algorithms were described for planning collision-free paths for a point automaton moving in an environment filled with unknown obstacles of arbitrary shape. The DPP approach was further extended to a planar robot arm with revolute joints; in this case, every point of the robot body is subject to collision. Under the accepted model, the robot, using information about its immediate surroundings provided by the sensory feedback, continuously (dynamically) generates its path. Various kinematic configurations of planar arms with revolute and sliding joints are analyzed in this paper from the standpoint of applying the same strategy. It is shown that, depending on the arm kinematics, specific modifications must be introduced in the path planning algorithm to preserve convergence. The approach presents an attractive method for robot motion planning in unstructured environments with uncertainty.