International Journal of COMPUTER INTEGRATED MANUFACTURING EDITOR-IN-CHIEF Stephen T Newman Department of Mechanical Engineering University of Bath, Bath BA2 7AY, UK e-mail: IJCIMeditor@bath.ac.uk EDITOR: ASIA (PACIFIC) EDITOR: NORTH AMERICA George Q Huang Paul Kenneth Wright Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China e-mail: gqhuang@hkucc.hku.hk Department of Mechanical Engineering University of California, 5133 Etcheverry Hall Berkeley, CA 94720-1740, USA e-mail: pwright@robocop.berkeley.edu EDITOR: NORTH AMERICA Paul G Ranky MANAGING EDITOR and BOOK REVIEWS EDITOR Aydin Nassehi Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK e-mail: ijcim@bath.ac.uk Founding Editor: David Hughes Department of Industrial and Manufacturing Engineering New Jersey Institute of Technology University Heights, Newark NJ 07102, USA e-mail: ranky@njit.edu EDITOR: EUROPE Franc¸ois Vernadat IT & Telecommunications Division European Court of Auditors 12, Rue Alcide de Gasperi 1615 Luxembourg e-mail: Francois.Vernadat@eca.europa.eu CONSULTING EDITOR CONSULTING EDITOR George Chryssolouris David J Williams* Laboratory for Manufacturing Systems, Department of Mechanical Engineering and Aeronautics, University of Patras, Patras 26110, Greece e-mail: gchrys@hol.gr Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leics LE11 3TU, UK e-mail: IJCIM@lboro.ac.uk *CIRP Representative INTERNATIONAL EDITORIAL BOARD C R Boe¨r ICIMSI Istituto CIM della Svizzera Italiano, Switzerland J Browne National University of Ireland, Galway F T S Chan The Hong Kong Polytechnic University, China B.-K Choi KAIST, South Korea I Choi Pohang University of Science and Technology, South Korea H A ElMaraghy University of Windsor, Ontario, Canada Y Fan Tsinghua University, China P Ferreira University of Illinois at Urbana-Champaign, USA Y Furukawa Tokyo Metropolitan University, Japan N N Z Gindy University of Nottingham, UK A Gunasekaran University of Massachusetts, USA K Hitomi Kyoto University, Japan S Hobbs Delcam Plc, Birmingham, UK S.-L Hwang National Tsing Hua University, Taiwan M Jeng National Taiwan Ocean University, Taiwan A Jones National Institute of Standards & Technology, USA S Joshi Pennsylvania State University, USA F Jovane Politecnico di Milano, Italy H Katayama Waseda University, Japan K Kosanke CIMOSA, Germany A Kusiak University of Iowa, USA A Molina ITESM Monterrey, Mexico L B Newnes University of Bath, UK S Y Nof Purdue University, USA P O’Grady University of Iowa, USA P Pokorny Technical University of Liberec, Czech Republic P Rogers University of Calgary, Canada I Sabuncuoglu Bilkent University, Turkey M K Tiwari Indian Institute of Technology, Kharagpur, India R Uzsoy Purdue University, USA H Van Brussel Katholieke Universiteit TE Leuven, Belgium H Van Dyke Parunak ERIM Center for Electronic Commerce, USA J Vancza MTA Sztaki, Hungary R Veeramani University of Wisconsin-Madison, USA L Wang University of Sko¨vde, Sweden H.-J Warnecke Fraunhofer-IPA, Germany R H Weston Loughborough University, UK X Xu University of Auckland, New Zealand International Journal of Computer Integrated Manufacturing Vol 23, No 12, December 2010, 1059–1070 Towards expressive ontology-based approaches to manufacturing knowledge representation and sharing Nitishal Chungooraa*, Osiris Canciglieri Jr.b and R.I.M Younga a Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, UK; bLaboratory of Automation and Systems (LAS), Pontifical Catholic University of Parana´ (PUCPR), Rua Imaculada Conceic¸a˜o, 1155 Prado Velho, Curitiba, PR, Brazil, CEP 80215-030 (Received 25 April 2010; final version received 24 August 2010) The present capability that ontological approaches offer to formally represent and share manufacturing knowledge is dependent on the choice of ontological formalism Currently, there exists a spectrum of these formalisms, which is being subjectively exploited across multiple domains in design and manufacture Hence, there is an important prerequisite to achieve an understanding of which family of formalism strictly enables the expressive capture of semantics to progress towards meaningful information and viable knowledge sharing This article analyses the relative strengths and weaknesses in employing a ‘lightweight’ ontology versus a ‘heavyweight’ version of the ontology to represent and share knowledge between multiple domains in injection moulding design and manufacture A pertinent direction, from an ontology perspective, is then exposed as a prescription for the improved capture and dissemination of formal semantics, to support multi-domain knowledge sharing Keywords: design and manufacture; lightweight ontology; heavyweight ontology; semantics; knowledge sharing; injection moulding Introduction Ontological approaches are nowadays increasingly being applied to support the formal capture and sharing of the meaning and intent (i.e semantics) of design and manufacture concepts For a particular domain, the representation of the required semantics is held in an ontology and the knowledge base (KB) deployed from the ontology is used to populate knowledge which should consistently derive from the semantic structures within the ontology Represented knowledge in a KB provides useful support for key engineering decisions, for example the ways in which a designer’s intent in the design domain could affect the selection of manufacturing processes in the manufacturing domain Thus, expressive manufacturing knowledge refers to populated knowledge in a KB, based on the unambiguous definition of semantics structures, which carry enriched formal meaning Unfortunately at present, the seamless exchange of design and manufacture semantics for knowledge sharing is still not achievable as a result of domain models that not carry sufficiently expressive semantics This is because there are currently several ontological formalisms, of varying expressiveness (Ray 2004) and system interaction capabilities, which not all necessarily address the knowledge capture and *Corresponding author Email: n.chungoora@lboro.ac.uk ISSN 0951-192X print/ISSN 1362-3052 online Ó 2010 Taylor & Francis DOI: 10.1080/0951192X.2010.518976 http://www.informaworld.com sharing needs in product design and manufacture Consequently, there exists an ongoing requirement to refine the understanding of the level of logical expressiveness capable of semantically structuring the meaning of product lifecycle concepts (Young et al 2009, Chungoora 2010) This article investigates the capture and intrasystem sharing of ontology-based knowledge using the basis of two broad categories of ontological formalisms, notably ‘lightweight’ and ‘heavyweight’ approaches (Go´mez-Pe´rez et al 2004), further explained in the next section By understanding the implications of each approach applied to concepts in injection moulding design and manufacture, the article contributes to a clarification of (1) the ways of expressively capturing domain semantics and (2) the mechanisms for sharing semantics across intra-system domains to support engineering decisions A case study has been devised to expose the relative strengths and weaknesses between a lightweight ontological model and a version of the model formalised using a heavyweight formalism It has been shown that the existence of an axiom layer in the heavyweight model is paramount to capturing rigorous semantics and for prompting the potential for knowledge sharing Moreover, certain characteristics 1060 N Chungoora et al of the lightweight model have proved to be pertinent to aiding intra-system knowledge sharing Following this case study, a suitable ontological direction is then identified, as a benchmark for design and manufacture domains that intend to exploit expressive semantics alongside knowledge inference support Lightweight and heavyweight ontological approaches 2.1 A categorisation based on expressiveness The requirements and preferences adopted by different communities have led to the development and utilisation of various ontological formalisms Ontological formalisms are essentially formal languages that support the construction of ontology-based models and the encoding of the subject matter within these models Some commonly occurring formalisms are illustrated in Figure 1, featuring the Unified Modelling Language (UML 2009), frame-based languages (Wang et al 2006) and description logic-based languages (Baader et al 2007) among others To distinguish families of ontological formalisms, the ontology community has introduced a categorisation based on the expressiveness of the subject matter contained within ontologies, and enabled via the use of ontological formalisms This categorisation involves the notions of ‘lightweight’ and ‘heavyweight’ ontological approaches, which primarily differ in the degree of formality and granularity with which they can represent the same knowledge (Go´mez-Pe´rez et al 2004, Casely-Hayford 2005) Lightweight models predominantly consist of a taxonomy of concepts, with simple relationships established among these concepts and very basic constraints over the meaning of the ontological terms On the other hand, heavyweight models, in addition to Figure Examples of lightweight and heavyweight ontological approaches having the lightweight structures, are accompanied by a rich set of formal axioms that constrain the interpretation of ontological terms In Figure 1, UML and Frames used on its own are examples of lightweight ontological approaches (A), while DL and frames with a first-order logic constraint language are examples of heavyweight ontological approaches (B) In the field of manufacturing engineering research, both lightweight and heavyweight methods have been used for the formalisation of domain models (ISO 18629 2005, Patil et al 2005, Kim et al 2006, Lin and Harding 2007) It is clear, from the extent of the exploited lightweight and heavyweight ontological approaches, that there is currently no discernable consensus on a preferred ontological direction This is largely because of the ongoing need to establish the suitability of these approaches to meet the semantic and knowledge sharing requirements of design and manufacture Hence, the aim of assessing the benefits and limitations of both approaches becomes a key step towards identifying the essential elements to progress towards expressive ontology-based approaches 2.2 Multi-domain knowledge representation and sharing using lightweight and heavyweight approaches The methodology to achieve the previously mentioned aim is identified in Figure Emphasis is placed on multi-domain knowledge representation and intrasystem knowledge sharing in the context of injection moulding The methodology involves considering a simple consumer product concept, namely a rotational container (C), as shown in Figure Using both lightweight UML and heavyweight Frames with a firstorder logic constraint language, the product representation is first to be captured in the mouldability domain (D), by using the semantic structures supported in both methods Then, populated knowledge from the mouldability domain is to be shared with the mould design domain (E) for obtaining a representation of the mould product model knowledge Following this stage, the mould product model knowledge from the mould design domain is to be shared with the mouldmanufacturing domain (F) to capture the manufacturing representation knowledge for the mould The sharing process between domains is to be achieved by using the adequate translation/mapping mechanisms accommodated in both ontology-based approaches A number of reasons justify the selection of UML and Frames with a first-order logic constraint language, as the preferred lightweight and heavyweight ontological formalisms respectively In the first place, a range of lightweight information models has exploited UML for multi-viewpoint modelling applied to design International Journal of Computer Integrated Manufacturing Figure Methodology for multi-domain knowledge representation and sharing realisation stages (Tam et al 2000, Kugathasan and McMahon 2001, Canciglieri and Young 2009) Thus, by performing an assessment of UML against the exposed methodology, it becomes possible to provide an appreciation of one extensively used lightweight formalism Frames with a first-order logic constraint language as heavyweight formalism presents characteristics that overlap with a range of other heavyweight formalisms This explains its suitability for this investigation For example the formalism bears several structural similarities to description logic-based languages, which have witnessed unprecedented relevance in product design ontologies (AIM@SHAPE 2004, Lukibanov 2005) Furthermore, the chosen heavyweight formalism holds key commonalities with the common logic interchange format (ISO/IEC 24707 2007), which has been used to encode the process specification language (PSL) ontology (ISO 18629 2005) 3.1 1061 Case study Overview of case study Figure identifies the case study scenario for the analysis of the selected lightweight and heavyweight ontological approaches, to support multi-domain knowledge representation and sharing This scenario provides a more detailed view on the use of the methodology portrayed in Figure Based on Figure 3, the study concentrates on the analysis of a UML multidomain injection moulding model against a similar model formalised in Frames with a first-order logic constraint language A detailed understanding behind the UML development of the multiple viewpoint domains can be found in an earlier manuscript (Canciglieri and Young 2003) For implementation purposes, the Knowledge Engineering Methodology, prescribed by Noy and McGuinness (2001), has been adopted during ontology development An appropriate UML tool has been utilised to formalise the lightweight UML model Furthermore, the formalism Frames with the Prote´ge´ Axiom Language (PAL), as first-order logic constraint language, has been used in the Prote´ge´ Frames 3.4 ontology editor (Prote´ge´ 2009) for representing the heavyweight model An important facet of the case study is related to the formal representation of the semantics of multidomain injection moulding and the corresponding populated knowledge This involves the following: the explicit representation of the mouldability, mould design and mould manufacturing domain semantics 1062 Figure N Chungoora et al Case study scenario representing knowledge that is either common across domains or needs to be translated/mapped to a different domain capturing logical pre-conditions that exist in one domain that can drive the translation/mapping of the appropriate knowledge manufacturing domain represents the semantics of the rotational core insert from a machining viewpoint, for example in terms of the types of machining features that the rotational core insert holds in the manufacturing domain (K) The representation of the rotational product in the mouldability domain is partly comprised of internal and external profiles (G) that pertain to primary and transition features that form the wall of the product The dimensional knowledge captured in these profiles is to be shared with the mould design domain (H) It is to be noted that emphasis is laid on the semantics of the internal profile of the rotational product, which are then used to drive the rotational core insert representation knowledge (I) in the mould design domain In this case, the mould design domain has been referred to as the ‘rotational core design domain’ to clarify that the intended representation is for the rotational core component of the mould The knowledge shared from the mouldability domain to the rotational core design domain, is then used to disseminate additional knowledge to the rotational core-manufacturing domain (J) (i.e the mould manufacturing domain) The rotational core- 3.2 Lightweight ontology-based model The lightweight UML model has been previously documented (Canciglieri and Young 2009) and therefore, this section concentrates on the most relevant strengths and weaknesses carried by the lightweight UML approach Figure provides a broad understanding of the implementation of the lightweight ontology-based model In the model, UML class diagrams (L) have been exploited to represent the necessary concepts and, to some extent, the basic semantics of each domain These UML class representations capture domain concepts in the form of classes and arrange these classes according to a taxonomy Relations with cardinality information (M) are used to formulate the key associations that hold between different classes The identification, retrieval and sharing of populated knowledge from the mouldability domain to the rotational core design domain and from the design domain to the manufacturing domain is formalised International Journal of Computer Integrated Manufacturing Figure 1063 Using UML class and activity diagrams in the lightweight model through UML activity diagrams (N) These activity diagrams enable the user to create a set of instructions on how to translate the required attributes and knowledge from one domain to another 3.2.1 Strengths and weaknesses UML class diagrams provide a convenient way to design ontologies, because they support a fairly rich set of graphical constructs This can be a particularly useful means of reusing platformindependent ontologies prior to their implementation in the required ontology applications The representation of multi-domain information structures is dominated by the use of UML class diagrams that involve taxonomies of classes and cardinality relationships between classes, which are fundamental to any ontology From the lightweight model explored, it has been possible to exploit UML class diagrams to capture common information content across domains There are two main ways in which classes are allowed to carry some semantics namely (1) through the specification of traits that the classes possess (i.e attributes), and (2) by specifying binary relations that hold between pairs of classes 1064 N Chungoora et al Classes, attributes and relations in UML hold textual descriptions rather than semantic definitions Consequently, domain concepts can only be meaningfully interpreted if the implied semantics of these concepts are understood by the user UML activity diagrams allow translation/mapping knowledge to be captured and aid, at a system development level, to automatically perform information sharing procedures from one domain to another For example, it is possible to trigger the automatic assertion of attributes and dimensional knowledge from the mouldability domain to the rotational core design domain However, in the experiment, because UML activity diagrams depend on UML class diagrams, this implies that translation procedures are dependent on the terms carried by domain concepts rather than the semantics of these concepts Although a low level of computational interpretation can be captured in UML classes purely associated to variations in class names, it is not fully possible to embed pre-conditional knowledge and intent For example in Figure 4, the class name ‘Rot_Wall_Par_Part_Line’ (O) in the mouldability domain is used to imply a rotational primary feature, which is positioned parallel to a parting line configuration (P) However, the condition for parallelism to a parting line cannot be formally stated in UML 3.3 Heavyweight ontology-based model The heavyweight ontological exploration using Frames with the PAL differs both in the degree of formality and granularity when compared with the lightweight approach Figure depicts the heavyweight Figure Heavyweight ontological structures ontological structures used to model multi-domain semantics and to identify sharable knowledge between domains In the heavyweight model, ontological structures consist of taxonomies of classes, relations and functions, accompanied by a rigorous logic-based axiom layer as shown in Figure (Q) This layer is responsible for supporting the meaning of concepts in computational form The axiom layer is built on top of the basic ontological structures and consists of integrity constraints and mapping rules, which are both written in PAL This constraint language accommodates firstorder semantics, thereby providing considerable flexibility in specifying the conditions for semantic conformance and knowledge sharing Integrity constraints are logical restrictions that help to ensure the semantic integrity within the injection moulding domains identified in Figure 3, while mapping rules are logical conditions that help to identify potential knowledge that could be shared from one domain to the other Figure provides a screen shot of the ‘mouldability domain’ (R) class taxonomy in the class browser, which at first glance is very similar to the class taxonomy from the lightweight UML class model Other abstract classes are present namely ‘rotational core design domain’ (S) and ‘rotational core manufacturing domain’ (T), which contain the information structures for the rotational core insert design and manufacture, respectively The abstract class ‘Common Semantics’ (U) regroups reusable behaviours across domains, such as the notions of ‘point’, ‘axis’, ‘length measure’ and ‘dimensional tolerance’ among others An instance of the class ‘rotational mouldability product’ (V) is shown in the instance browser International Journal of Computer Integrated Manufacturing Captured semantics for one specific instance of ‘rotational mouldability product’, named ‘Product Rotational Container’ (W), can be identified in Figure These semantic structures involve, for example the list of point profiles aggregated under the relations ‘holds_internal_profile’ (X) and ‘holds_external_profile’ (Y) and the list of primary and transition features aggregated under the binary relation ‘holds_feature’ (Z) 3.3.1 Integrity constraints From an ontology formalisation viewpoint, PAL is used for model checking This implies that integrity constraints act as semantic prescriptions to ensure that populated knowledge in the KB conforms to the semantics expressed in the heavyweight model To verify whether asserted knowledge violates or conforms to semantics, integrity constraints can be processed and a number of results are retained in the event that these constraints have been infringed In other words, integrity constraints contribute to the semantic integrity and enrichment of the KB To account for the semantic needs of the heavyweight model, integrity constraints have been written for the multiple domains under consideration Over 30 integrity constraints including both simple and complex ones have been modelled for all three domains The expression listed next gives an example of a simple integrity constraint in the mouldability domain to Figure Capturing the semantics of the mouldability domain 1065 ensure that instances of the class ‘rotational mouldability product’ (see Figure (V)) are only allowed to hold one axis of rotation (defrange ?product :FRAME ‘Rotational Mouldability Product’) (forall ?product (¼ (number-of-slot-values holds_axis ?product) 1)) If, for example an instance of ‘Rotational Mouldability Product’ is asserted as having more than one axis in the KB, then an execution of the PAL constraint would show that this instance is violating the fundamental semantics that a rotational mouldability product must always hold one axis Figure illustrates the result of querying an integrity constraint based on an incorrectly populated knowledge element The instance ‘Product - Rotational Container’ (W) is shown to be violating the integrity constraint at query time as a result of an additional ‘Probe Inconsistent Axis’ (A1) having been assigned The identification of inconsistent knowledge, like the one shown in Figure 7, provides a useful way of prompting the user to rectify the incorrect assertions An example of a more complex integrity constraint in the mouldability domain is shown in Figure The axiom captures the relevant logical pre-conditions to ensure the correct specification of parting line features (see Figure (P)), by using the appropriate formalised statement (B1) In the expression, the accurate 1066 N Chungoora et al Figure Reporting an integrity constraint violation Figure Example of a complex integrity constraint definition of a ‘Parting Line Feature’ (C1) is captured based on the known existence of some defined ‘Primary Feature’ (D1) A similar understanding has been followed for the specification of other simple and complex integrity constraints required for the mould design and mould-manufacturing domains 1131 International Journal of Computer Integrated Manufacturing Table Payoff values and feasible strategy profiles for 8 problem 1st generation 80th generation (NE point) Strategy profile J1 J2 J3, J4 J5 J6 J7 J8 Payoff value Process plan decision sub-game Job scheduling sub-game 46 45 47 43 41 43 47 32 pr1,1 pr2,2 pr3,1 pr4,2 pr5,1 pr6,1 pr7,1 pr8,1 (7,5,6) (1,8,4,4,6,8,4) (3,1,2,6,1,5) (3,2,6,5) (1,2,3,8,4) (1,4,5,3,4,3) (1,8,6,5,3) (2,4,4) Figure 10 Convergence curves of proposed solution algorithm and traditional GA-based one references Therefore, a new mathematical model and effective solution algorithm are inevitably required Overall, the experimental results indicate that the proposed approach is an effective and acceptable approach for the problem for the following reasons: (1) the proposed approach considers all the new characteristics, especially the competition relationship between jobs of process planning and scheduling synthetically in networked manufacturing by adopting game theory, and (2) compared with the traditional GA-based solution algorithm, the proposed solution algorithm obtains better results and higher solving efficiency Figure 10 shows the convergence curves of proposed solution algorithm and the traditional GAbased solution algorithm (Zhou et al 2009) for the proposed 6 problem, which means that the proposed solution algorithm has more efficiency and better probability to obtain the best results Conclusions In this study, we made several contributions to research literature with respect to generating optimal process plans of multiple jobs based on game theory in Strategy profile Payoff value Process plan decision sub-game Job scheduling sub-game 34 38 37 29 40 33 29 25 pr1,2 pr2,2 pr3,3 pr4,2 pr5,1 pr6,3 pr7,2 pr8,1 (1,2,5,7) (1,4,4,7,6,8,4) (3,8,7,4) (5,2,3,8) (1,2,3,4,5) (1,5,6) (6,8,4,4,1) (2,4,6) networked manufacturing environment Foremost, we identified the characteristics of deciding process plans in networked manufacturing environment from those in traditional manufacturing environment More importantly, we defined the conceptual model for generating optimal process plans in networked manufacturing based on its new characteristics that act as the reference for building game solution at next step As another contribution, we formulated a model for deciding optimal process plans for the jobs coming from different customers through adopting game theory This game model was divided into two kinds of sub-games, i.e process plan decision sub-game and job scheduling sub-games, which cooperate with each other to decide optimal process plan for every job Owing to the problem’s complexity and intractability, considering effectiveness and efficiency, we proposed a HAGA-based two-level nested solution algorithm to find the NE point of the game The computational results show that the presented game solution is suitable for requirements of generating optimal process plans for multiple jobs in networked manufacturing environment, and the proposed solution algorithm is capable to obtain optimal results for the test problems The new approach presented in this study makes increasing the efficiency of networked manufacturing systems possible An important further research issue is to extend the proposed approach in order that it may be applied to more practical and networked manufacturing systems The increased use of this approach will most likely pave a new way for improving the developments in future networked manufacturing systems Acknowledgements Gratitude is extended to the National Natural Science Foundation of China (Grant No.: 50605050) and Ministry of Education for New Century Excellent Talent Support Program of 2007 (NCET-07-0681) for the financial supports 1132 G Zhou et al Special thanks also to Mr Xuefeng Tian and Miss Rui Wang for the programming efforts in implementing and demonstrating the presented game solution References Brandimarte, P and Calderini, M., 1995 A hierarchical bicriterion approach to integrated process plan selection and 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scheduling International Journal of Computer Integrated Manufacturing, 20, 80–95 Li, X.Y., et al., 2010 An agent-based approach for integrated process planning and scheduling Expert Systems with Applications, 37, 1256–1264 Moon, C., Kim, J., and Hur, S., 2002 Integrated process planning and scheduling with minimizing total tardiness in multi-plants supply chain Computers and Industrial Engineering, 43, 331–349 Saygin, C and Kilic, S.E., 1999 Integrating flexible process plans with scheduling in flexible manufacturing systems International Journal of Advanced Manufacturing Technology, 15, 268–280 Seredyn´ski, F., 1997 Competitive coevolutionary multiagent systems: the application to mapping and scheduling problems Journal of Parallel and Distributed Computing, 47, 39–57 Seredyn´ski, F., 1998 Distributed scheduling using simple learning machines European Journal of Operational Research, 107, 401–413 Seredyn´ski, F., Koronacki, J., and Janikow, C.Z., 2001 Distributed multiprocessor scheduling with decomposed optimization criterion Future Generation Computer Systems, 17, 387–396 Shafaei, R and Brunn, P., 2000 Workshop scheduling using practical (inaccurate) data Part 3: a framework to integrate job releasing, routing and scheduling functions to create a robust predictive schedule International Journal of Production Research, 38, 85–99 Shao, X.Y., et al., 2009 Integration of process planning and scheduling – A modified genetic algorithm-based approach Computers and Operations Research, 36, 2082– 2096 Zhou, G.H., Jiang, P.Y., and Huang, G.Q., 2009 A gametheory approach for job scheduling in networked manufacturing International Journal of Advanced Manufacturing Technology, 41, 972–985 International Journal of Computer Integrated Manufacturing Vol 23, No 12, December 2010, 1133–1148 Robot workspace estimation and base placement optimisation techniques for the conversion of conventional work cells into autonomous flexible manufacturing systems M.F Alya, A.T Abbasb* and S.M Megahedc a Mechanical Engineering Department, The American University in Cairo, New Cairo, Egypt; bMechanical Engineering Department, Engineering College, King Saud University, Riyadh 11421, P.O Box 800, Saudi Arabia; cMechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza, Egypt (Received 15 March 2009; final version received 27 September 2010) Robot arms are used in modern work cells and flexible manufacturing systems (FMS) in handling work pieces and loading/unloading processes The robot arm links may interfere with the bodies of the system components, which are considered as obstacles in the robot workspace In order that the robot works in safe conditions, study of robot workspace in a free space and in the presence of obstacles should be investigated The inverse problem of having an existing working space occupied with a number of CNC machines to which it is supposed to introduce a robot to serve is an interesting problem This is a very common problem when trying to convert conventional work cells into autonomous systems There are two main questions when studying this kind of problem: what type of robots is suitable to satisfy the existing working space? And where to place the base of this robot to efficiently serve the existing machines? The main objective of this article is trying to answer these two questions A computational algorithm is developed to estimate the robot workspace The optimisation of robot base placement is achieved using genetic algorithms A comparative study of the suitability of different robots for a specified working area is also included Finally, robot movement visualisation within a pre-defined FMS using solid edge modelling is presented to verify the proposed algorithm and simulate the robot path within the work cell Keywords: industrial robots; working space; robot movement visualisation; flexible manufacturing systems; autonomous systems; genetic algorithms Introduction Industrial robots are called robotic arms; they are roughly similar to a human arm It can be modelled as a chain of rigid links interconnected by flexible joints These links correspond to features of human anatomy such as the upper arm and chest, while the joints correspond to the shoulder, elbow and wrist The mathematical modelling of the robot links movements is dependent on their geometry, robot configurations, number of links and type of interconnection between them as well as the components of the robot work cell or the FMS The estimation of the values of robot joints for a specified tool centre point (TCP) position in a given workspace (WS) provides useful information for facility layout and robot movement planning for better performance This needs the estimation of the robot WS, which has four main categories of research First, the analytical determination of the WS of robot arms with simple structures (Tsai and Soni 1981, Gupta and Roth 1982, Tsai and Soni 1983, Williams and Reinholtz 1988, Salerno et al 1995) Second, the numerical estimation of the WS of a robot arm with *Corresponding author Email: atabbas1954@yahoo.com ISSN 0951-192X print/ISSN 1362-3052 online Ó 2010 Taylor & Francis DOI: 10.1080/0951192X.2010.528033 http://www.informaworld.com general structural parameters (Kumar and Patel 1986, Liegeios et al 1986, Riley and Torfason 1994, Wang and Hsieh 1998) also presented in the work of Megahed et al (2001a) Third, the robot WS estimation in the presence of obstacles in its accessible region is found in the work of Wenger (1989) and Megahed et al (2001b) At last, the study and optimisation of robot path planning within work cells (Marchis et al 1994; Curto and Moreno 1995; Kavraki 1995; Huang and Lawrence 1999; Kyatkin and Chirikjian 1999; Flordal et al 2007; Tsai and Song 2009) Many software packages are in use for solid modelling as well for animation of robot arms movements Tsai and Soni (1981) derived a closed form solution for two and three link revolute joint robot arms based on loci curves However, when they developed an algorithm for multi-link revolute joint robots (Tsai and Soni 1983), a numerical technique was used to solve the model equations, which were based on a linear optimisation technique Gupta and Roth (1982) gave a general discussion regarding WS shapes and an intuitive approach for simplifying some special cases 1134 M.F Aly et al of robots where there exist three orthogonal mutually intersecting revolute joints by replacing them with an equivalent spherical joint Liegeois et al (1986) developed an algorithm to automatically determine the volumetric model of the WS based on investigating the different postures of the robot along with the mechanical constraints Kumar and Patel (1986) developed an algorithm to generate the WS for general revolute and/ or prismatic joints based on envelope slicing and internal points removal The resulting WS is mapped to computer graphics Wang and Hsieh (1998) developed a numerical technique for determination of the maximum and minimum reaches of parallel robots by formulating an optimisation problem of the distance between the TCP and a fixed point on the robot base along a chosen direction Commercial robots are often provided with a rough estimation of their work envelope with the extreme boundaries without taking into consideration any obstacle presence Any obstacles will require users’ trial and error to identify the workable area of the robot Providers not offer this type of information because of the endless possibilities of obstacle placement within the robot WS, which will lead to a different WS every time This can lead us to the conclusion that most of the research falls under the following categories: WS determination (Gupta and Roth 1982, Tsai and Soni 1983, Salerno et al 1995, Wang and Hsieh 1998, Chen et al 2007), trajectory planning (Curto and Moreno 1995, Sun and Qu 1998, Kyatkin 1999, Solteiro and Tenreiro 1999) and robot synthesis to satisfy specific purposes (Lenarcic et al 1989, Gosselin and Guillot 1990, Merlet 1996) This article is targeted towards the determination of the optimum robot base placement within a specified work cell Therefore, robot WS determination is of special interest for this research A simple and efficient numerical technique is introduced for an approximate estimation of the WS of all simple open chain robots with any desired number of prismatic and/or revolute joints Joints’ axes may have any orientation relative to each other The estimated WS is used to compute an objective function (OF) for the robot base when placed at a specified location within a work cell Optimisation of the OF is performed using genetic search (Goldberg 1989, Davis 1991) utilising real coded optimised variables A comparison is made between the values of the OF at the optimum base placement for different robots This comparison provides a useful knowledge base for robot selection Finally, a simple FMS example is presented to demonstrate the effectiveness and usefulness of the proposed technique in the visualisation of robot movement A computational algorithm of the robot inverse position analysis to numerically estimate the values of its joints generalised coordinates for specified TCP positions is used in the visualisation of the movements of Puma robot arm within the FMS consisting of three CNC machines Robot position analysis and WS determination The mathematical modelling of industrial robot’s WS is based on their geometry, which differs according to their structures and the type of interconnections between links A convenient method of position analysis of simple open chain robots is by using the homogenous transformation matrices in terms of Denavit-Hartenberg (D-H) parameters (Denavit and Hartenberg 1955) A brief explanation of the D-H parameters is provided 2.1 Denavit-Hartenberg representation To determine the relationship between adjacent links of a robot, Denavit and Hartenberg defined a method of establishing a coordinate system attached to each link This representation result is in the form of a homogenous transformation matrix HTM representing each link’s coordinate system relative to the previous link’s coordinate system Thus, through sequential transformations, the robot TCP coordinate system can be expressed in terms of the robot based coordinate system as function of the D-H parameters The robot joints are numbered from to n starting from the base side based on the condition that the ith joint precedes the ith link The coordinate system Riþ1 ¼ (oiþ1, xiþ1, yiþ1, ziþ1) is attached to the end of link i The position and orientation of Riþ1 with respect to Ri ¼ (oi, xi, yi, zi) attached to the end of link i71 is completely defined by four parameters (yi, ri, ai, ai) known as D-H parameters (Figure 1) The zi-axis is selected to be the axis of joint i, which will have two common normals connected to it: xi between zi71 and Figure D-H parameters 1135 International Journal of Computer Integrated Manufacturing zi, and xiþ1 between zi and ziþ1 The distance measured along the joint axis zi between the common normals xi and xiþ1 is called ri The angle from xi to xiþ1 measured about zi axis is called The shortest distance between the joints’ axes zi and ziþ1 of joints i and i þ 1, respectively, measured along the common normal xiþ1 is called The angle between the joints’ axes zi and ziþ1 measured around xiþ1 is called yi Using these defined parameters, the resulting HTM Ti, i þ between the two successive coordinate systems Ri ¼ (oi, xi, yi, zi) and Ri þ ¼ (oiþ1, xiþ1 ,yiþ1, ziþ1) is given by: and  à Ti;iþ1 4Â4 ci 6s i ¼6 40  à Ti;iþ1 4Â4 ¼ Àcai si cai ci sai si Àsai ci sai cai 0 Ri;iþ1 ðqi Þ 0 ¼ 0 Ri;iþ1 ðqi Þ Pi;iþ1 ðqi Þ ! ð4Þ with [xi yi zi 1]t ¼ Ti,iþ1[xiþ1 yiþ1 ziþ1 1]t where: ci ¼ cos yi; si ¼ sin yi; cai ¼ cos and sai ¼ sin Ri,iþ1(qi) defines the orientation matrix between the coordinate frames Ri and Riþ1, Pi,iþ1(qi) define the position vector of the origin of the same coordinate frames qi is the generalised coordinate of the ith joint given by: xi xiþ1 6y  6y à i7 iþ1 7 ¼ Ti;iþ1 4Â4 zi ziþ1 Ri ¼ (oi, xi, yi, zi) and Riþ1 ¼ (oiþ1, xiþ1, yiþ1, ziþ1) is given by: ci Àsi cai si sai ci 6s i ci cai Àci sai si Ti;iþ1 ¼ 40 sai cai ri qi ¼ s0i yi þ si ri c i s i 7 ri ! Pi;iþ1 ðqi Þ ð1Þ ð2Þ where si ¼ for revolute joints, si ¼ for prismatic joints and si ¼ 17si The HTM between the TCP coordinate system Rnþ1 ¼ (onþ1, xnþ1, ynþ1, znþ1) relative to the base coordinate system R0 ¼ (o0, x0, y0, z0) for a robot is given by: where ci ¼ cos(yi), si ¼ sin(yi), cai ¼ cos (ai) and sai ¼ sin(ai); qi is the generalised coordinates of the ith joint given by: qi ¼ s0i yi þ si ri , where si ¼ for revolute joints and si ¼ for prismatic joints, and s0 ¼ 17si Thus, the HTM between the TCP coordinate system Rnþ1 (onþ1, xnþ1, ynþ1, znþ1) relative to the base coordinate system R0 (on, xn, yn, zn) for a robot is given by: T0;nþ1 ¼ T0;1  T1;2  T2;3  T3;4 Tn;nþ1 ð3Þ with [x0 y0 z0 1]t ¼ T0,nþ1 [xnþ1 ynþ1 znþ1 1]t Thus, there exists a frame (set of axes) for every joint and link in the robot The HTMs are used to obtain the position and orientation of all robot frames with respect to the base The position of the TCP defined by (x, y, z) is function of all the robot generalised coordinates (q1, q2, , qn) It can be represented using the homogenous transformation matrix described in the following section 2.2 Homogeneous transformation matrix Using these defined parameters, the resulting HTM Ti,iþ1 between the two successive coordinate systems: ð5Þ T0;nþ1 ¼ T01 T12 ðq1 ÞT23 ðq2 Þ Tn;nþ1 ðqn Þ ! R0;nþ1 ðqÞ P0;nþ1 ðqÞ ¼ ½ x0 y0 z0 Št ¼ T0;nþ1 ½ xnþ1 q ¼ ½ q1 q2 q3 qn Š t ynþ1 znþ1 Št ð6Þ The position vector of the TCP P0,nþ1 defined by its Cartesian coordinates [x, y, z] is given by:  à ½ x y z Št ¼ P0;nþ1 ðqÞ ð7Þ 2.3 Brief note about genetic algorithm The genetic search is basically grounded on random numbers generation These numbers are used to approximate a required solution of a problem that has no direct formulas to substitute in The ultimate goal of the use of genetic algorithm (GA) is to have a close solution near the exact one that fulfils a specified requirement This requirement is stated as an OF that is to be minimised or maximised using the optimisation technique Based on the required grade of accuracy and run time, some parameters are to be defined: Population size, which represents the number of random numbers generated each time 1136 M.F Aly et al The number of generations used till the end of the optimisation procedure The mutation probability of the good population members and the bad ones A population member is said to be good or bad according to its OF value, which is evaluated for each member Finally, a cross over factor is determined to know the probability of cross over between parents gin before the generation of new members 2.4 Robot WS determination The main objective of this algorithm is to numerically estimate the WS of a general robot in presence of obstacles in its accessible region (Megahed 2001b) Equation (7) is used to determine the robot’s accessible region, which is discretised into finite points according to the required degree of accuracy This process is called the sweeping process of the robot joints from its last joint to the first one (Aly 2001) Another use of Equation (7) is when having a set of locations in the robot WS and it is required to determine the values of its joints generalised coordinates [q] to reach each of such locations This inverse problem is numerically solved using genetic search (Goldberg 1989, Davis 1991) and the developed computation algorithm is described and solved in the next section The estimation of the robot WS starts by the discretisation of the region surrounding the robot Such region is termed the search volume (SV) Thus, the SV is represented by a group of finite points forming a hypothetical grid (Figure 2) Every point in the SV becomes a target point for the robot end effector A target point is judged as belonging to the robot WS if the robot TCP can reach it without having any of its linkages interfere with any of the obstacles Such technique is readily applicable if the inverse kinematic position model (IKPM) (Megahed 1993) is Figure WS points generation known However, the IKPM of general n-joint robots is not available in closed form As an alternative, the IKPM problem is formulated in the form of an optimisation problem The OF of this optimisation problem is to minimise the distance between the TCP and the target point (Figure 3) The constraint on the optimisation problem is that none of the robot linkages is allowed to interfere with any of the obstacles The optimisation problem is solved using real-coded variables genetic search (Goldberg 1989, Davis) The computational algorithm is shown by the flow chart in Figure Inputs to the algorithm are the geometric parameters of the robot, ranges of motion of its joints, obstacle data and the SV limits The algorithm proceeds to discretise the SV into a finite set of points The points are stored in a threedimensional array Initially, all points are marked as inaccessible to the robot The main loop of the algorithm repeats a genetic search for a specified target point trying to find a combination of joint positions that minimise the distance between the robot end effector and the target point (global minimum of the OF) Constraints are included as penalty in the OF At the end of the search if the distance between the end effector and the target point is less than a specified tolerance, the point is marked as belonging to the WS Since genetic search involves lots of random guessing, an additional feature is added to the algorithm During random guessing, if a combination of the robot joints positions place the end effector of the robot within a specified tolerance to any point in the SV (not necessarily the target point), the point is marked as belonging to the WS Points marked as belonging to Figure SV discretisation International Journal of Computer Integrated Manufacturing points in genetic search This additional feature is found to significantly reduce the overall computational effort Base placement optimisation Genetic search utilising real coded variables is used in estimating the optimum placement (position and orientation) of a robot base relative to an existing work cell The optimisation is based on maximising an OF that is evaluated for each of the population 1137 members (Goldberg 1989) The population members contain the values of robot base position (x, y, z) and orientation (y) about z-axis with respect to a fixed reference in the work cell 3.1 Objective function There are many possible alternatives to define an OF for the comparison of different choices of robot base placement However, any OF would be somehow related to a set of locations in the work cell, which are to be served or avoided by the robot Possible choices of OF may include trajectory planning and avoiding obstacles The OF adopted in this work uses a much simpler criterion that needs no additional information other than the WS and work cell geometry The goodness of a base placement is expressed by how well the WS contains the target points (TGP), which are the points that the robot is required to serve Mathematically, the OF is expressed as: ‘‘Maximise the closest distance between WS surface points and the target points.’’ At the optimum placement, the TGP are as far as possible from being not included in the WS and the OF value is the minimum distance between the closest TGP to the WS surface and the WS surface itself 3.2 Optimisation procedure The phases of estimating the optimum placement of the robot base (Figure 5) start by obtaining the set of surface points of the robot WS Then, the robot base is placed at a feasible initial position; within the work cell, from which a suitable search for optimised values (Base position, x, y, z, and orientation (q) about the z- Figure Computational algorithm flow chart Figure Base position optimisation flow chart 1138 M.F Aly et al axis of the work cell) is conducted Finally, genetic search proceeds to estimate the optimum values of the base placement variables Case studies The data of eight industrial robots is used for demonstrating the procedure presented in this article for robot base placement optimisation within a specified working area Verification of the WS estimation technique is also performed Figures 6–13 show the robots used in these case studies and their schematic diagrams The data of these robots are given in Tables and 4.1 Verification of WS estimation technique Three case studies of simple chain robots are provided to demonstrate the effectiveness of the proposed technique The WS of the PRRRRRR Unimate 9000 robot in a free space along with the WS of both the RRRP SCARA robot and the RRRRRR PUMA robot WS in the presence of an obstacle in their accessible region is estimated 4.1.1 Unimate 9000 robot Figure 14 shows the manufacturer and the estimated WS A simple comparison between the two figures illustrates the resemblance in the WS Two sections are taken at A and B as shown to demonstrate the similarity between the manufacturer and the obtained WS In this figure, the Unimate 9000 robot WS as provided by the manufacturer is shown on the left side While, the estimated WS produced by the developed algorithm is shown on the right side Two slicing planes are taken at different Z positions to illustrate the similarity between the two WSs Manufacturers could provide 3D models of WS/SV in free space Hence, the power of the developed algorithm is illustrated here by taking a slicing plane at different Z position to show the resemblance between the two Also, points accessible by the robot are automatically Figure (a) SCARA robot, (b) kinematic diagram of SCARA robot Figure (a) Unimate 2000, (b) kinematic diagram of Unimate 2000 International Journal of Computer Integrated Manufacturing Figure (a) Unimate 9000, (b) kinematic diagram of Unimate 9000 Figure (a) Fanuc S-5, (b) kinematic diagram of Fanuc S-5 Figure 10 (a) Hitachi process robot, (b) kinematic diagram of Hitachi process 1139 1140 M.F Aly et al Figure 11 (a) JOB’OT 12; (b) kinematic diagram of JOB’OT 12 Figure 12 (a) Kuka IR 761/60.1 mounted on PU/810/2000/820.1; (b) kinematic diagram of Kuka Figure 13 (a) PUMA robot, (b) kinematic diagram of PUMA robot identified by the program, which will be capable of judging whether a point is within the robot WS or not even if it seemed to be an external point in the WS view in one of the principle projection planes 4.1.2 SCARA robot The figure and the kinematic diagram of the 4-axes SCARA robot of type RRRP is shown in Figure 6(a) 1141 International Journal of Computer Integrated Manufacturing Table Data of case studies industrial robots No of joints Axis No Joint type Unimate 2000 (Figure 7) Unimate 9000 (Figure 8) Fanuc S-5 (Figure 9) Hitachi process robot (Figure 10) JOB’OT 12 (Figure 11) Kuka IR 761/60.1 (Figure 12) 4 5 6 Robot Id D-H parameters Joint motion range y r a a Min Max – R R P R – P R R R R R R – R R R R R R – R R R R R – P R P P R R – P R R 0.0000 q1 q2 0.0000 q4 1.5708 0.0000 q2 q3 q4 q5 q6 q7 0.0000 q1 q2 q3 q4 q5 q6 0.0000 q1 q2 q3 q4 q5 0.0000 0.0000 q2 1.5708 1.5708 q5 q6 0.0000 0.0000 q2 q3 0.0000 1.2000 0.0000 q3 0.0000 0.0000 q1 1.1000 0.0000 0.0000 1.2500 0.0000 0.1000 0.0000 0.8100 0.0000 0.0000 0.5500 70.0700 0.1000 0.0000 0.6500 0.0000 0.0000 0.0000 0.1000 0.0000 q1 0.7000 q3 q4 0.0000 0.2300 0.5000 q1 0.9900 0.0000 R 0.0000 0.0000 0.0000 0.0000 0.1000 0.0000 0.0000 0.0000 1.0000 0.1000 0.0000 0.0000 0.0000 0.0000 0.2000 0.6000 0.1300 0.0000 0.0000 0.0000 0.0000 0.0000 0.6000 0.8000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 70.5000 1.4500 q4 0.0000 1.5708 1.5708 71.5708 0.0000 71.5708 1.5708 1.5708 0.0000 1.5708 71.5708 1.5708 1.5708 0.0000 1.5708 0.0000 1.5708 71.5708 1.5708 1.5708 0.0000 1.5708 0.0000 0.0000 1.5708 1.5708 71.5708 1.5708 0.0000 1.5708 71.5708 1.5708 1.5708 71.5708 1.5708 71.5708 0.0000 0.0000 R R R q5 q6 q7 1.5500 0.0000 0.6600 0.0000 0.0000 70.3000 1.5708 71.5708 0.0000 – 70.2443 1.1170 0.9650 73.4121 – 0.0000 70.7854 0.3491 70.8727 76.2832 71.9199 74.7124 – 71.0472 0.4363 71.3090 73.3161 72.4435 73.1415 – 71.0472 0.7854 72.3562 0.0000 71.6581 – 0.0000 72.8798 0.0000 1.2000 71.9199 71.9186 – 0.8000 72.7925 72.8798 0.0000 70.9599 73.7525 72.0944 77.6794 – 3.3859 2.0944 2.0260 0.2075 – 4.3000 1.5708 1.5708 0.8727 6.2832 1.9199 7.8540 – 4.1888 2.3562 1.0472 3.3161 2.4435 6.2831 – 4.1888 2.4435 71.1345 3.1416 4.7997 – 4.1000 2.8798 1.2000 2.4000 1.9199 5.0615 – 2.1300 2.7925 70.6109 1.5708 1.8326 6.8941 2.0944 4.5379 Note: All lengths are in metres and all angles are in radians and 6(b), while the D-H parameters, joints’ types and ranges of motion are given in Table Due to the special configuration of the SCARA robot, the top view is usually sufficient for specifying the WS Moreover, the top view of the WS can be drawn manually just like a two-link robot and has an exact solution drawn using drafting software; this is the main reason behind choosing the SCARA robot to perform an algorithm validation (Figure 15) The corresponding output of the proposed algorithm is shown in Figure 16 It is observed that good matching between the exact solution and the estimated one is attained Comparison of figures shows good matching between the exact and estimated results 4.1.3 PUMA robot In order to demonstrate the capabilities of the proposed technique in estimating general n-joint robots, estimation of the WS of a RRRRRR PUMA robot is performed The figure and the kinematic diagram of the PUMA robot are given in Figures 13(a) and 13(b) The D-H parameters, joints’ types and ranges of motion are given in Table The unconstrained WS of the PUMA robot is known to roughly resemble a sphere Figure 17 shows a three-dimensional view of sections in the estimated WS taken at different levels after an obstacle is placed close to the robot base Estimated WS of the PUMA robot with 1142 Table M.F Aly et al Data of case studies of industrial robots for WS with obstacle presence Joint motion range D–H parameters Robot Id No of joints Joint No Joint type y r a a Min Max SCARA (Figure 6) PUMA 760 (Figure 13) 4 – R R R P – R R R R R R 0.0000 q1 q2 q3 0.0000 0.0000 q1 q2 q3 q4 q5 q6 0.0000 0.3000 0.0000 0.0000 q4 0.0000 1.0300 0.0000 0.0000 0.6000 0.0000 0.1000 0.0000 0.2500 0.1500 0.0000 0.1000 0.0000 0.0000 0.6500 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 3.1415 0.0000 0.0000 1.5708 0.0000 1.5708 71.5708 1.5708 1.5708 – 71.6755 72.0071 73.9269 0.1500 – 71.2217 70.3491 70.7854 74.6426 71.9199 74.6426 – 1.6755 2.0071 3.9269 0.2500 – 4.3633 3.4907 3.9270 4.6426 1.9199 4.6426 Note: All lengths are in metres and all angles are in radians Figure 14 WS of Unimate 9000: (a) manufacturer WS, (b) estimated WS obstacle present at 0.5, 1, 1.5 and m height are shown in this figure illustrating the obstacle shape and position relative to the robot base Knowing the PUMA robot to have a great accessibility in its working area, we can see that the WS is inferior affected by the obstacle presence in the area surrounding the obstacle Some positions in the robot attainable region were not reached due to robot linkage interference with the obstacle This case study demonstrates the capability of the proposed algorithm in estimating the WS of larger and more complicated robots that have no closed form solution when obstacles are present in their accessible region 4.2 Base placement optimisation: a simple work cell A work cell consisting of three machines (centre lathe, milling machine and drill) arranged as in Figure 18 contains locations that are to be serviced by a robot Seven industrial robots (Table 1) are studied according to the procedure described earlier in this article The International Journal of Computer Integrated Manufacturing genetic search parameters are (Goldberg 1989) as follows: Population size Number of generations Mating probability scaling factor, Cmult Crossover probability Mutation probability of above average fitness members Mutation probability of below average fitness members 50 50 1.6 0.9 0.02 the whole population becomes very close to that of the best member in the population (Goldberg 1989) Convergence check of the genetic search is presented in Table This table shows the convergence of the OF of each robot to ensure that the solution tends to move towards the same value to have an optimised solution The optimum placement of each of the robots with respect to the work cell is shown in Figure 19 0.5 The search results (optimum base placement and corresponding OF value) are given for the six robots that have feasible solutions in Table This table provides the coordinates of each robot within the workplace and its orientation with respect to the reference point identified in the work cell Convergence of genetic search is achieved when the average OF for Figure 15 Top view of exact WS of SCARA robot – with obstacle presence Figure 16 1143 Estimated WS of SCARA robot – obstacle present Solid modelling of PUMA robot within an FMS A simple FMS is used for the evaluation of the visualisation effectiveness using the UNIGRAPHICS software package The FMS consists of an input supply of work pieces, a centre lathe, two milling machines, Puma robot and a workpiece storage for the final product A layout of the FMS given in Figure 20 is presented to illustrate the various steps of solid modelling technique of Puma robot The solid modelling is mainly concerned with four steps: (1) creation of robot structure, (2) served locations identification, (3) determination of robot joints generalised coordinates for the served locations and (4) visualisation of the movements of Puma robot within the FMS using a run from a predefined spreadsheet 5.1 Robot structure creation Puma robot consists of a fixed base and six moving links connected to each other by revolute joints A simple one-dimensional drawing of each link is first drafted, and then extruded in the third dimension to create each link After completion of all robot links, they are all gathered and assembled to obtain the whole robot structure 1144 5.2 M.F Aly et al Served locations identification It is required that the robot links perform a specified sequence of motions to fulfil a certain sequence of jobs predefined by the user The robot job can be defined as a simple handling process as it is requested to translate a work piece from a specific location to another To demonstrate the UNIGRAPHICS NX (UG) simulation capabilities a sequence of robot movements is suggested as follows: The robot picks up a work piece from the stocking place Delivers the work piece to the centre lathe (Figure 21) Translates the work piece to the first milling machine (Figure 22), after the required cutting time by the centre lathe If the first milling machine is already loaded, the robot will translate the work piece from the centre lathe to the second milling machine (Figure 23) After operations completion, the robot will translate the work piece to the storing place The main served locations in the FMS for which the robot is requested to reach are defined by their Cartesian coordinates [x, y, z] in the robot base frame R0 Table shows the output values of the Puma robot joints [q] for each of the served locations’ coordinates on the three CNC machines Note that, however, q6 does not show up in Puma position equations its values are given in Table These values are obtained from the genetic search and can be changed for different runs with the same location coordinates 5.3 Figure 17 Three-dimensional view of estimated PUMA robot WS – obstacle present Puma movement visualisation and animation Table gives the D-H parameters of this robot and the limits of the generalised coordinates [q] of its joints Puma generalised coordinates [q] are calculated using Equation (8) for the served locations and given in Table x ¼ ðððc1  c2  c3 À c1  s2  s3Þ Â c4 þ s1  s4Þ Â s5 À ðÀs3  c1  c2 À c1  c3  s2Þ Â c5Þ Â r6ðs3  c1  c2 þ c1  c3  s2Þ Â r4 þ c1  c2  a2 y ¼ ðððc2  c3  s1 À s2  s2  s3Þ Â c4 À c1  s4Þ Â s5 À ðÀs1  s3  c2 À c3  s1  s2Þ Â c5Þ Â r6 þ ðs1  s3  c2 þ c3  s1  s2Þ Â r4 þ s1  a2  c2 z ¼ ððs2  c3 þ c2  s3Þ Â c4  s5 À ðÀs2  s3 þ c2  C3Þ Â c5Þ Â r6 þ ðs2  s3 À c2  c3Þ Â r4 þ a2  s2 þ r1 Figure 18 Table ð8Þ Work cell layout Genetic search results Best base placement according to genetic search Robot ID x-base y-base z-base y-base Objective function value Unimate 9000 Fanuc S-5 Hitachi Process Robot JOB’OT-12 Kuka IR 761/60.1 Puma 760 4.2823 1.1024 1.1911 0.8799 2.9059 1.1234 0.0006 1.2425 1.2286 1.3828 1.1339 1.1870 70.0083 70.2467 70.1098 70.3579 71.5884 70.4280 0.0000 72.8340 72.6862 1.0285 1.5038 2.4413 0.4400 0.2806 0.0073 0.7000 2.6250 0.2169 Note: All lengths are in metres and all angles are in radians 1145 International Journal of Computer Integrated Manufacturing Table Genetic search convergence check Average population OF Robot ID Unimate 9000 Fanuc S-5 Hitachi process robot JOB’OT-12 Kuka IR 761/60.1 Puma 760 1st generation 50th generation Final OF value Convergence achieved? 0.0026 0.0020 0.0023 0.2265 0.5181 0.0072 0.4400 0.2805 0.0073 0.6987 2.6227 0.2166 0.4400 0.2806 0.0073 0.7000 2.6250 0.2169 Yes Yes Yes Yes Yes Yes Note: All lengths are in metres Table Served locations and corresponding values of robot joints [q] Served location Corresponding values of robot joints [q] Location name x y z q1 q2 q3 Q4 q5 q6 Centre lathe Milling M/c Milling M/c 71.53 0.776 0.102 0.717 0.420 70.61 0.663 0.345 0.345 2.704 0.496 71.22 70.21 70.03 70.11 1.569 0.363 0.066 70.64 0.007 71.56 0.000 0.100 71.45 70.27 0.129 0.471 Note: All lengths are in metres and all angles are in radians Figure 19 Work cell layout with optimum placement of robots A set of values of the robot generalised coordinates [q] corresponding to each desired served location are automatically fed to the UNIGRAPHICS software by an articulation procedure Hence, an interpolation procedure is calculated to capture the robot movements between two different positions The initial [...]... 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