ذدà،±ل>‏ے :<‏ےےے9eےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےى¥ءM ّ؟ل,bjbjâ=â= 2`€W€Wy'ےےےےےےlوووو666J>>>8v<²,JP'Lêêêêêززز·&¹&¹&¹&¹&¹&¹&$œ( ¼*üف&-6ز°"زززف&.ووêêئ '...ز0و8ê6ê·&.ز·&.ئ.ôژk%h6ƒ&êق`QuEuإJô>,س%ƒ&4 '0P'م% ¸+.¸+ƒ&.JJووووظ9th International Research/Expert Conference ”Trends in the Development of Machinery and Associated Technology” TMT 2005, Antalya, Turkey, 26-30 September, 2005 WEB ENABLED TOOLS FOR SOLVING PARALLEL IMPLEMENTATION OF ROBOT CONTROL ALGORITHMS Prof. Davor Zorc Ph.D., Prof. Mladen Crnekovic Ph.D. and doc. Zoran Kunica Ph.D. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb Ivana Lu ia 5, Zagreb Croatia ABSTRACT Development of web accessible tools for parallel implementation of robot control algorithms is described. Optimal parallel implementation is known to be a problem hard to solve. Our approach introduces heuristic algorithms that give good sub optimal results for process allocation. To make those algorithms available over the Internet, we use software platform based on PHP technology. Keywords: parallel processing, scheduling, robotics, web technology, Internet. 1. INTRODUCTION Implementation of robot's dynamics, kinematics and path planning algorithms require computers with high processing power. Stability and speed of movement, as well as speed of interaction with unknown environment depend on available processing power. Implementation of some of those algorithms on multiple-processor system may be economically justified, if the required processor is more expensive than several slower processors with equivalent power, or if the processor with enough processing power is not available at all. Recent state of processor technology shows that processor clock speed will not increase as fast as it used to do in the past. This is because of technological problems and heat dissipation. So, major processor producers are shifting their emphasis on building two core and multiple core processors [1]. This means that the whole software industry will gradually shift towards parallel processing technology – a technique first used on supercomputers. There are simple solutions of implementing parallel processing when there are several jobs that are basically independent. But in this paper an implementation of a single job with interdependent parts (processes) is investigated. Most control procedures, for example robot control procedures, are of such a kind. Broadly speaking, to implement the control procedure on the multiple-processor system several problems should be solved: symbol 183 \f "Symbol" \s 10 \h a partition of the job (a control procedure) into computational processes symbol 183 \f "Symbol" \s 10 \h an optimal allocation of processes on local memory of the particular processor symbol 183 \f "Symbol" \s 10 \h the determination of schedule of process execution to complete the job in minimum time symbol 183 \f "Symbol" \s 10 \h there must be some kind of operating system with synchronization and communication primitives, which will enable data exchange between processes. This paper deals with partitioning, allocation and scheduling procedures applied on 6 rotary joints robot's kinematics formulation. 2. FORMULATION AND PARTITION OF 6R - KINEMATICS Here robot inner coordinates qi are calculated from known global coordinates [2, 3]. Formulation is given by the following equations: q1= arctg (py /px) (1) s1= sin(q1) c1= cos(q1) q234 = arctg [az / (c1ax + s1ay)] s234=sin(q234) c234= cos(q234) p'x = c1px + s1py - c234L4 p'y = pz - s234L4 c3 = (p'x 2+ p'y2 - L32 - L22) / 2L2L3 s3 = ± symbol 214 \f "Symbol" (1 - c32) q3 = arctg (s3 / c3) s2 = [(c3L3 + L2)p'y - s3L3p'x] / [(c3L3 + L2)2 + S32L32] c2 = [(c3L3 + L2)p'x + s3L3p'y] / [(c3L3 + L2)2 + S32L32] q2 = arctg (s2 / c2) q4 = q234 - q3 - q2 s5 = c234 (c1ax + s1ay) + s234az c5 = s1ax - c1ay q5 = arctg (s5 / c5) s6 = -c5 [c234 (c1ox + s1oy) + s234oz] + s5 (s1ox - c1oy) c6 = -s234 (c1ox + s1oy) + c234oz q6 = arctg (s6 / c6) For the purpose of parallel processing to be more efficient, we investigate alternative ways to do this calculation. For instance, to obtain shorter sequential ordering of processes it is preferable to modify the above formulation, and to calculate s1, c1 and s234, c234 according to the following equations: s1 = py / symbol 214 \f "Symbol" (px2 + py2) (2) c1 = px / symbol 214 \f "Symbol" (px2 + py2) s234 = az / symbol 214 \f "Symbol" {[(pxax + pyay)2 + az2 (px2 + py2)] / (px2 + py2) } c234 = 1 / symbol 214 \f "Symbol" { 1 + [az2 (px + py)2] / (pxax + pyay)2 } This way those equations may be calculated at any time, so they are not restricted to be calculated after calculating corresponding internal angles (as in formulation (1)). This formulation is partitioned into 30 computational processes. Partitioning strategy and details of this particular example are given in [3]. Once the partition is done, one may construct a process diagram (figure 1). In this graph, the nodes represent processes, and the arcs represent data exchange. The diagram is created by observing data flow between processes. Arcs between processes impose partial ordering in time: a process must not be allowed to start execution before all of his predecessors are executed (but may be started any time later). Violation of those precedence constraints would result in false calculation. This kind of graph is unidirectional and non cyclic. Partition strategy in general has the goal to produce many independent data flows, i.e. to make processes that are more or less data independent. Special attention should be given to long sequential chains of processes. Effort should be made to break such chains into smaller parts. Of course we must exploit the natural parallelism of a given formulation. EMBED SmartDraw.2 Figure 1. Process diagram for 6R- Kinematics 3. ALLOCATION AND SCHEDULING OF 6R - KINEMATICS Allocation algorithm will decide which processes will be executed by which processor. A number of different allocation algorithms are discussed in [3, 4, 5, 6]. For the sample results that follow, allocation based on process levels was used [4]. This heuristic algorithm insures good sub-optimal allocation and schedule and it is executed in a fraction of the second on a personal computer. Other algorithms are also tried on the same problem [3]. General scheduling problem is known to belong in the class of so called NP-complete computational problems. As a consequence it is very computationally intense and needs very long time to get optimal schedule. Allocation algorithm is executed in system design phase, so it does not add significant overhead to target computer that actually controls the robot. After the allocation is set, process execution schedule is also determined, so for each computational process a starting moment is given. At this stage parallel execution time may be estimated together with speedup factor. Speedup is the measure of improvement in execution time of parallel computer over single processor system. In our case it is calculated for job allocation on 2-6 processors (figure 2). The main problem of this implementation is long sequential ordering of processes in this formulation, which limits possible speedup. EMBED Excel.Chart.8 \s Figure 2. Speedup factor vs. number of processors 4. WEB ENABLED TOOLS FOR PARALLEL IMPLEMENTATION Almost any computer language may be used to develop allocation and scheduling algorithms. With a group of students, we are currently developing (porting) those algorithms to the PHP scripting language [8] and Javascript. As it is well known, PHP program source code is executed on a server machine and the results of calculation are available through Internet browser. This makes those programs available to a wide range of users working on a wide range of computing platforms. In our project, the first program that is ported to PHP is process level calculation [3, 4]. This is the first necessary step to calculate when using level based allocation algorithms. The other algorithms will be posted later on our web site [7]. 5. CONCLUSION Parallel processing may be a cost effective approach for implementation of complicated control procedures. Speedups that may be obtained depend on several factors: inherent parallelism of control formulation, partitioning strategy and effectiveness of allocation/scheduling procedure. We have taken this relatively simple 6R- Kinematics formulation as an example, to show the possibility of effective implementation on systems with 2-4 processors. This result may be well suitable for new generation of two core processors. Some of our software tools for allocation and scheduling are now available on the Internet, which could make the transition to parallel processing a bit easier. It is our plan to post more tools to the Internet in the future. 6. REFERENCES (1( Intel dual core technology, 15.06.2005., HYPERLINK "http://www.intel.com/personal/desktop/dualcore/" http://www.intel.com/personal/desktop/dualcore/ (2( Paul R.P.: Robot Manipulators: Mathematics, Programming and Control, MIT Press, Cambridge, Mass. USA, 1981. (3( Zorc D.: Decomposition of mechanical manipulator's control algorithms for execution on multiple processor systems, Doctor's thesis, FER - Faculty of Electrical engineering and Computing, Zagreb, Croatia, 1990. (4( Coffman E.G., jr.: Computer and Job- Shop Scheduling Theory, John Wiley & Sons, New York, 1976. (5( Davor Zorc, Mladen Crnekovic, Zoran Kunica: Local Search Algorithm for Scheduling of Robot Dynamics Calculation on a Parallel Computer, 7-th International Research/Expert Conference “Trends in the Development of Machinery and Associated Technology” – TMT 2003, Barcelona, Spain, 15-16 September, 2003. (6( Watanabe T. et al.: Improvement in the Computing Time of Robot Manipulators Using a Multi-microprocessor, Transactions of the ASME, Vol. 108, September 1986. 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