desktop, it must be based on runtime its sensorysystem for recording information necessary to achievethe task. It must work in exploring space and solve theproblem of planning in the presence of uncertainties.The problem is to calculate the trajectory generationbased on data received from the motion planner sizesorder to ensure passage of the robot through theestablished points.Generation of movement can be made directly in thespace coordinates kinematics couplings, oroperational area.Navigation strategy refers to determining how(methods) to move the robot according to the type oftask performed.Modelling space implies establishing navigation mapsin the considered space.Modelling methods known in literature are [1‐5]: uniform grid method; tree method; heterogeneous grid method; convex polygon method; method of crossing points.Evolution of the robot in the workspace imposes thestatement that the space of configurations SC isintrinsically independent of the choice of referencesystems SA and SW.Trajectory planning problem in the presence ofobstacles can be expressed as: given a workspacepopulated with obstacles known through theirborders, and by moving objects, must determine apath without collisions with obstacles in bringingmobile objects in the final initial configuration.The problem can be approached in two ways global orlocal, hence the two types of planning methods: globaland local.Application of global methods require completeknowledge of the working space ”in advance”,modelling proper clearance, research and selection ofall possible paths of a certain trajectoriescorresponding to a minimum cost criterion. Such amethod guarantees the existence or absence of asolution. Also global planning methods can be easilyadapted to the off‐line programming.Applying a local method requires partial knowledge ofthe workspace.Such a method does not guarantee reaching the finalconfiguration, but the advantage of good real‐timeadjustments.In both cases, solving the planning problem involvessolving geometric problems (pure geometry) orcombine geometry with kinematics and/or dynamics.In such situations often are used the results ofalgorithmic geometry.In general the application of planning methods mustmeet certain restrictions such as: the safest way, theshortest path, etc.ANALYSES, DISCUSSIONS, APPROACHES ANDINTERPRETATIONSAnalyzing the best methods in place of the theoreticaland the application can highlight the road mapmethod, exact cell decomposition method and thepotential field method. Of these potential field120ACTA TECHNICA CORVINIENSIS – Bulletin of Engineeringmethod treats the robot represented as a point inconfiguration space, that as a particle under theinfluence of an artificial potential field U whose localvariations reflects ”structure” of the free space.Potential function is defined as the amount of freespace on an attractive potential, which attracts therobot toward the final configuration, and a repulsivepotential, which removes the robot from obstacles.The method was originally developed as an "on line”method to avoid collisions to be applied when there isno model of obstacles, in advance, but they may referto during the execution of movement. In particular,the procedure can lock in a local minimum of potentialfunction.This deficiency can be corrected by calculating thefinite element method applied to study a potentialfield.Starting from the potential field finite elementmethod we propose, as an effective tool for theanalysis of optimum road space of the robot.Thus we suggest that the workspace of a robot to bemodelled as a homogenous body which is dependenton structure geometry of components and obstacles.In this space to work tasks the robot must go throughthe obstacles imposed trajectories which it has toavoid.The road through the obstacles can be chosen so thatto avoid the maximum probability collisions. If weaccept that two neighbouring obstacles behave astwo sources of the same physical stationary field andconsider that the moving of the characteristic point iscarried on the same potential trajectory as that of theresulting field we can select a family of trajectoriescorresponding to a certain field potential in a giveninterval.In the application illustrated in Figure 1 the workingspace was modelled as a homogeneous body withknown thermal characteristics.YZ Xut Set: MSC/NAST t0.0.0.0.0.0.0.0.0.100.100.100.100.100.100.100.Figure 1 Thermal analysis of a working space modelled ashomogeneous body found in a field where the heat sourcehot / cold data are boundaries of obstacles.Obstacles are considered as being „hot" or "cold"areas/sources on the boundary of the consideredworking space as being a homogenous body on whicha thermal field is applied from the hot/cold sources(modelled obstacles).Applying the finite element method analysis facility onthe thermal model workspace the outcome isisothermal surfaces. From these areas we can define100.93.7587.581.2575.68.7562.556.2550.43.7537.531.2525.18.7512.56.250.2012. Fascicule 3 [July–September]
ACTA TECHNICA CORVINIENSIS – Bulletin of Engineeringcurves obtained by modelling which can betrajectories of the characteristic point.Using the family of isothermal surfaces in the averagetemperature (resulting from thermal finite elementanalysis) on this can reside optimum trajectories to bepassed.So configurations libraries can be built‐up for theworking space and trajectories to pass, respectivelylocated on the average temperature isothermalsurface.Illustrated in Figure 1 is a workspace of a robotmodelled as homogeneous body found in a field whereheat sources hot / cold data are borders of theobstacles that need to avoid in his motion.Thermal finite element analysis on the isothermalmodel gives us the results. The treaty was exemplifiedin the plan but can be generalized in three‐dimensionalspace. Most times one of the 3D motion parameterscan be imposed by the kinematics couplings whichcontrols programming. Applications can be treatedand depending on who is involved in the processrobot. The most complex situation is found in weldingrail vehicle structures.CONCLUSIONSA key issue in the field of industrial robots operation(i.e. programming the optimal path of motion) enjoysthe benefits of programs devoted to finite elementanalysis to allow for applying the ”potential fieldmethod” as an analysis of a stationary thermal field.Exemplification was performed using MSC NASTRANprogram.REFERENCES[1.] Garbea D., Analiză cu elemente finite Editura TehnicăBucuresti 1990[2.] Hubner H. K., "Metoda Elementului Finit PentruIngineri" Departamentul de inginerie mecanică,Laboratorul de cercetari Genenral Motors, Wiley‐Interscience, John Wiley&Sons, New York, London,Sydney, Toronto, 1990[3.] Pires, J. N, Loureiro, A., Bölmsjo, G., Welding Robots ‐Technology, System Issues and Application, 1stEdition., 2006, XVIII, 180 p. 88 illus., Hardcover, ISBN:978‐1‐85233‐953‐1[4.] Staicu, S., Liu, X‐J., Wang, J., Inverse dynamics of theHALF parallel manipulator with revolute actuators,Nonlinear Dynamics, Springer, 50, 1‐2, pp. 1‐12, 2007[5.] Staicu,S., Zhang, D., A novel dynamic modellingapproach for parallel mechanisms analysis, Roboticsand Computer‐Integrated Manufacturing, Elsevier, 24,1, pp. 167‐172, 2008ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGISSN: 2067‐3809 [CD‐Rom, online]copyright © UNIVERSITY POLITEHNICA TIMISOARA,FACULTY OF ENGINEERING HUNEDOARA,5, REVOLUTIEI, 331128, HUNEDOARA, ROMANIAhttp://acta.fih.upt.roACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGISSN: 2067‐3809 [CD‐Rom, online]copyright © UNIVERSITY POLITEHNICA TIMISOARA,FACULTY OF ENGINEERING HUNEDOARA,5, REVOLUTIEI, 331128, HUNEDOARA, ROMANIAhttp://acta.fih.upt.ro2012. Fascicule 3 [July–September] 121
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