International Journal of Computer Integrated Manufacturing Vol 23, No 2, February 2010, 101–112 Agent-based workflow management for RFID-enabled real-time reconfigurable manufacturing YingFeng Zhanga,b, George Q Huanga*, Ting Qua and Oscar Hoa a Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong; bThe State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, China (Received 22 April 2009; final version received 27 October 2009) Recent developments in wireless technologies have created opportunities for developing reconfigurable wireless manufacturing systems with real-time traceability, visibility and interoperability in shop-floor planning, execution and control This paper proposes to use agent-based workflow management as a mechanism to facilitate interactions among RFID-enabled reconfigurable manufacturing resources A production process is modelled as a workflow network Its nodes correspond to the work (process), and its edges to flows of control and data Nodes are represented as agents and edges as messages As a sandwich layer, agents wrap manufacturing services around a work-cell and their operational logics/intelligence for cost-effectively collecting and processing real-time manufacturing data, forming so-called work-cell gateways A reference framework for a shop-floor gateway is proposed based on the three key components: Workflow management, manufacturing services universal description, discovery and integration (namely MS-UDDI) and work-cell agents Work-cell agents are packaged, registered and published at MS-UDDI as web services which are easily reused and reconfigured in the workflow for a specific production process Finally, a prototype system is presented to demonstrate how the proposed method is used to define and execute a real-time reconfigurable manufacturing project Keywords: workflow management; multiple agent systems; reconfigurable manufacturing; real-time wireless manufacturing; RFID/auto ID Introduction With the increasing competition in the global marketplace, manufacturing enterprises have to strive to become responsive to business changes which have further impacts upon production goals and performance at the shop-floor level Many business problems manufacturing enterprises are facing now are caused by lack of timely, accurate, and consistent shop-floor manufacturing data The infrastructure and tools need to be designed and developed for reconfiguring a manufacturing process to visualise, monitor and control its real-time execution according to various production orders Therefore, it is essential for manufacturers to upgrade their capabilities with advanced manufacturing technologies (AMT), in terms of both software and hardware technologies Recent developments in wireless sensors, communication and information network technologies (e.g radio frequency identification – RFID or Auto-ID, Bluetooth, Wi-Fi, GSM, and infrared) have nurtured the emergence of reconfigurable wireless manufacturing (WM) (Huang et al 2009) as next-generation manufacturing systems (NGMS) The concept of RMS (reconfigurable manufacturing systems) was introduced in the mid-nineties by Koren et al (1999) as a cost-effective response to *Corresponding author Email: gqhuang@hku.hk ISSN 0951-192X print/ISSN 1362-3052 online Ó 2010 Taylor & Francis DOI: 10.1080/09511920903440354 http://www.informaworld.com market demands for responsiveness and customisation It was pointed out that RMS was designed at the outset for rapid change in structure, as well as in hardware and software components, in order to quickly adjust production capacity and functionality within a part family in response to sudden changes in market or in regulatory requirements The ultimate goal of RMS is to utilise a systems approach in the design of manufacturing process that allows simultaneous reconfiguration of (1) the entire system, (2) the machine hardware and (3) the control software Radunovic (1999) proposed an innovative RMS paradigm to dissolve the hard borders between hardware and software and join the potentials of both Zhao et al (2000) considered a RMS as a manufacturing system in which a variety of products required by customers are classified into families, each of which is a set of similar products, and which correspond to one configuration of the RMS Mehrabi (2000) proposes five key characteristics for RMSs They are modularity, integrity, convertibility, diagnosability and customisation Yigit and Usloy (2002) describe a modular structure to accommodate new and unpredictable changes in the product design and processing needs through easily upgrading hardware and software 102 Y Zhang et al rather than the replacements of manufacturing system elements such as machines Despite of significant progress achieved in the above researches in utilising RMS, a breakthrough is yet to come in reality One critical hurdle is the lack of a RMS infrastructure imminently required for manufacturing enterprises to achieve real-time and seamless dual-way connectivity and interoperability between application systems at enterprise, shop-floor, work-cell and device levels The following questions are open for investigation: (1) How rapidly and flexibly to define reconfigurable manufacturing resources (which tasks/ processes should be allocated to which workcells) according to the real-time manufacturing data when production orders are changed, and to monitor the real-time manufacturing progress during the execution stage? (2) How to wrap applications and services around work-cells and their flexible manufacturing objects so that they can be easily reused and reconfigured for different customer orders that require different production processes? (3) How to capture the real-time manufacturing data by installing Auto-ID devices as manufacturing services into manufacturing devices? This research adopts and develops three important concepts in order to address the above questions in building up an RMS infrastructure They are workflow management, multiple agent system, and automatic identification and data capturing technologies Workflow management (Elmagarmid and Du 1998) is a wellknown technology supporting the reengineering of business and information processes, involving two main stages: definition and execution The concept can be readily extended to define and execute manufacturing processes to implement reconfigurable manufacturing Agent technologies provide necessary autonomy, flexibility and reconfigurability (Sikora and Shaw 1998, Macchiaroli and Riemma 2002) in reconfigurable manufacturing Agents are used in this research to wrap the work-cell applications related to manufacturing objects such that they can be easily reused and reconfigured in a manufacturing process defined as a workflow system Auto-ID technologies, such as RFID, can be used to capture the real-time manufacturing data by deploying RFID devices (Readers and Tags) to manufacturing resources (Huang et al 2007) This RFID-enabled real-time RMS provides a new paradigm for production systems which accommodates higher flexibility in terms of product volumes and types This paper discusses the challenges of integrating the above three concepts into a coherent infrastructure framework for implementing real-time RMS The rest of the paper is organised as follows Section reviews the literature of workflow management, agent-based manufacturing and automatic data capturing for wireless manufacturing Section outlines a systematic overview of the real-time reconfigurable manufacturing infrastructure A referenced framework of shopfloor gateway is proposed in Section Section presents the concept of agent-based workflow management and its key enabling technologies A case for shop-floor assembly line is designed and demonstrated in Section Conclusions are drawn in Section Literature review Three streams of literature are relevant to this research They are workflow management, agent-based manufacturing applications and automatic data capturing for real-time manufacturing 2.1 Workflow management Workflow management is a diverse and rich technology and is now being applied over an ever increasing number of industries Hollingsworth (1994) defines that a workflow process is a coordinated (parallel and/ or serial) set of process activities that are connected in order to achieve a common business goal According to Schal (1996), the workflow management system is used to define, manage, and perform ‘workflows’ through the execution of software, whose order of execution is driven by a computer representation of the workflow logic Workflow technology is increasingly used to manage complex processes in e-commerce (van der Aalst 1999, Lazcano et al 2000) and virtual enterprises (Casati et al 1995, Liu and Pu 1998) In manufacturing systems, Huang et al (2000) proposes a distributed workflow management model to develop distributed manufacturing execution system Lau et al (2000) present a methodology for the design and development of a flexible workflow supply chain (FWSC) system for achieving flexibility to cope with unexpected changes Chiu et al (2001) use an integrated, event-driven approach for execution, coordination, and exception handling in workflow management system Montaldo (2004) applies workflow management system to enhance business performance for small-medium enterprise Tan and Fan (2007) adopt a novel dynamic workflow model fragmentation algorithm to execute the distributed processes 2.2 Agent-based manufacturing Agent technology is a branch of artificial intelligence (AI) and has been widely accepted and developed in International Journal of Computer Integrated Manufacturing manufacturing applications for its autonomy, flexibility, reconfigurability, and scalability (Sikora and Shaw 1998, Macchiaroli and Riemma 2002, Maturana et al 2004) An agent based concurrent design environment (Tan et al 1996, Krothapalli and Deshmukh 1999) has been proposed to integrate design, manufacturing and shop-floor control activities A compromising and dynamic model in an agent-based environment (Sikora and Shaw 1998) has been designed for all agents carrying out their own tasks, sharing information, and solving problems when conflicts occur Some mobile agent-based systems (Shin and Jung 2004) have been applied to the real-time monitoring and information exchange for manufacturing control Jia et al (2004) proposed an architecture where many facilitator agents coordinate the activities of manufacturing resources in a parallel manner Jiao et al (2006) applied the MAS paradigm for collaborative negotiation in a global manufacturing supply chain network Besides, in various kinds of applications such as distributed resource allocation (Bastos et al 2005), online task coordination and monitoring (Lee and Lau 1999, Maturana et al 2004), or supply chain negotiation (Wu 2001), the agent-based approach has played an important role to achieve outstanding performance with agility 2.3 Automatic data capturing for real-time wireless manufacturing Currently, real-time visibility and interoperability have been considered core characteristics of next-generation manufacturing systems (Huang et al 2006) As early as in early 1990s, Udoka (1992) has discussed the roles of Auto ID as a real-time data capture tool in a computer integrated manufacturing (CIM) environment Early RFID manufacturing applications have been briefly quoted in Brewer et al (1999) and further promoted in Li et al (2004) Johnson (2002) presents a RFID application in a car production line The website http:// www.productivitybyrfid.com/ also provides a few links to real-life pilot cases Chappell et al (2003) provides general overview on how Auto ID technology can be applied in manufacturing Pilot projects have recently been implemented and reported (http://www.autoidlabs.com/research archive/) Several relevant whitepapers have been prepared to provide roadmap for developing and adopting Auto ID-based manufacturing technologies (Harrison and McFarlane 2003, Chang et al 2003) More recently, the Cambridge Auto ID Lab has launched an RFID in Manufacturing Special Interest Group (SIG) (http://www.aero-id.org/) Huang et al (2007, 2008) implement RFID technologies to capture the real-time manufacturing data of employees, machines and materials of assembly line 103 Overview of real-time reconfigurable manufacturing The aim of the research reported here is to apply RFID technologies and develop an easy-to-deploy and simpleto-use reconfigurable information infrastructure for manufacturing companies to achieve real-time and seamless dual-way connectivity and interoperability between application systems at enterprise, shop-floor, work-cells and RFID devices Figure shows an overview of the proposed infrastructure This infrastructure is consistent with a normal manufacturing hierarchy That is, a manufacturing factory has one or more shop-floor production lines A production line consists of several work-cells each of which involves a variety of manufacturing objects, such as operators, machines, materials etc Different production lines are often responsible for different production processes According to the manufacturing hierarchy, the proposed RTM infrastructure includes following core components: Shop-floor Gateway (SF-Gateway): SF-Gateway is at the centre of the overall RTM Following Service-Oriented Architecture (SOA), SF-Gateway includes three main components, i.e workflow management, MS-UDDI and work-cell agent These components will be further detailed in the following sections Work-cell Gateway (WC-Gateway): WC-Gateway acts as a server to host and connect all RFIDenabled smart objects of a work-cell A WCGateway has a hardware hub and a suite of software systems The hub physically connects all RFID-enabled smart objects which are represented as software agents in the WC-Gateway operating system All smart objects are used in a ‘universal plug and play (UPnP)’ and interoperable manner RFID-enabled smart objects: Smart objects are those physical manufacturing objects that are made ‘smart’ through equipping them with RFID devices Those with RFID readers are active smart objects Those with RFID tags are passive smart objects Smart objects interact with each other through wired and/or wireless connections, creating what is called an intelligent ambience In addition, smart objects are also equipped with specific operational logics, data memory and processing functions Therefore, smart objects are able to sense, reason, act/react/ interact in the intelligent ambience community Overview of reconfigurable shop-floor gateway The shop-floor gateway is a high-level key component of the proposed real-time reconfigurable manufacturing infrastructure Figure shows the overall 104 Y Zhang et al Figure RFID-enabled real-time manufacturing infrastructure Figure Overview architecture of reconfigurable shop-floor gateway architecture of the reconfigurable SF-Gateway Following the service-oriented architecture (SOA), workcells, work-cell applications, equipments and smart object in a shop-floor can all be considered as manufacturing services The manufacturing services (agents) are wrapped as a work-cell agent Each agent contains the real-time information and status of the work-cell Work-cell agents can be registered and published at MS-UDDI while SF-Gateway can select, add and deploy these work-cell agents for different production process, enabling a reconfigurable manufacturing (Huang et al., 2008a) Specifically, process planners use configuration facilities to search suitable work-cell agents from MS-UDDI and configure them for a specific production process The configuration result is a workflow among work-cell agents (i.e workcells) which represents a manufacturing process This workflow could be used for the next lifecycle stage – execution During the actual execution, shop-floor managers could monitor and control the status and International Journal of Computer Integrated Manufacturing progress of the manufacturing process through SFGateway tools which communicate with work-cell agents at gateway servers Real-time data are handled centrally at the SF-Gateway repository The proposed reconfigurable SF-Gateway is composed of three major components, namely workflow management, UDDI for manufacturing services (MSUDDI), and work-cell agents 4.1 Workflow management (WM) This WM component is used to (1) define a manufacturing workflow based on a product’s process plan, (2) (re)configure the manufacturing services through using agent-based workflow model and MS-UDDI, and (3) coordinate the involved work-cell agents to execute real-time manufacturing according to the defined workflow Workflow management includes three modules, namely definition module, binding module and execution engine They are described as following Definition module is responsible for defining the workflow according to the specific production processes Bind module automatically records the relationships between the work cell agents and the manufacturing process after work-cell agents are searched and chosen as production process nodes Execution engine not only facilities the execution of work-cell agents according to the defined workflow and logic, but also monitor and control the work-cell agents during the execution process 4.2 Manufacturing services UDDI (MS-UDDI) The function of MS-UDDI is similar to those of standard UDDI (Universal Description, Discovery and Integration), serving as a platform-independent framework for describing and discovering services through Internet MS-UDDI is composed of three main modules, i.e publish and search module, service model and tModel Publish and search module is used to convert work-cell agents into public web services, which can be easily searched to implement flexible and reconfigurable shop-floor manufacturing Service model describes a group of web services which are contained in a businessService structure For each published work-cell agent, there is a set of web services each of which serves for certain specific propose and can be invoked over internet 105 tModel is a data structure representing a service type (a generic representation of a registered service) in UDDI 4.3 Work-cell agent Work-cell agent is responsible for wrapping the workcell applications to process the complex real-time data captured from smart objects The work-cell agent can be used to reflect the real-time manufacturing information and status of a work cell The work-cell agents must be registered and published at MS-UDDI as web services, then found and invoked via MS-UDDI so that the proposed reconfigurable manufacturing can be achieved Along this innovative concept and structure, other users or systems can directly attain the status and real-time information of work cell by visiting or invoking its agents Three models, method model, data model and smart object manager (SOM) model, are involved in this component Method model is used to deal with the huge realtime data captured by RFID devices installed at the work-cell Gateway based on rules and schemas For example, the ‘getMaterials’ method will deal with all the data relevant to materials of this work-cell Gateway and return detailed realtime information such as material item, quantity etc At MS-UDDI, each method can be regarded as a service of the registered work-cell agent Data model describes and defines the basic standards of input and output data of work-cell agents The data model adopts XML-based schema that can be easily edited, transformed and extended Smart object manager model aims at managing the behaviors of smart objects installed at a work-cell gateway It is implemented with intelligence logics so as to sense and identify the real-time manufacturing data of single smart agents as well as the communication between multiple smart objects Agent-based workflow management for reconfigurable manufacturing 5.1 Agent-based workflow management model for reconfigurable manufacturing An agent-based workflow management (WFM) model will be firstly defined of its topology of processes and manufacturing resources, i.e indicates the involved manufacturing resource types yet has not been assigned to specific work cells (agents) Then, each node of the workflow will choose its execution agent from MSUDDI based on the actual status of the qualified agents 106 Y Zhang et al Figure shows the agent-based WFM framework, which is used to not only plan and control the flow of production processes and data, but also executes any process (work) node of the workflow from the selected work-cell agent The WFM model is responsible for reusing and reconfiguring the work-cell agents to implement various production orders There are two basic elements in the agent-based WFM model: process and agent A process refers to a portion of a production task and can be assigned to a specific manufacturing resource (work cell) As mentioned in section 3, the work-cell agent wraps the corresponding function of a work-cell, which can execute and finish the process In the SF-Gateway level, the WFM is mainly concerned with the co-ordination of distributed workcell agents As can be seen in Figure 3, process nodes represent production tasks, and the logical nodes represent the trigger conditions Edges represent the logical relationships between production processes, i.e the flows of control and data WFM is built on the concept of agents An agent represents a work package in the workflow All the agents involved in a workflow share the same repository and the repository becomes a common working memory This sharing information ensures the traceability of the decisions at different stages by recording them in a decision tree in terms of the contents of the decisions, the decision-makers, and precedence decisions, etc Agents are only used to define the work or node of a production process workflow Relationships between nodes are separately defined in terms of flows Without flow definitions, agents still not know where inputs Figure Agent-based workflow management model are obtained from and outputs are sent to The separation of flow definition from work definition provides opportunities to reuse agents for different production projects once they are defined for RTM No further changes are necessary when agents are used for other production projects What the project team needs to is to choose the agents according to the different production project and define the flows of control and data between agents to suit specific requirements 5.2 Workflow definition Workflow definition has two work modes One is editing mode which means the process planner defines the agent-based workflow for a specific production project The other is executing mode which means the manager monitors and controls the progress of executing a production workflow Workflow definition in turn involves the ‘work’ definition and the ‘flow’ definition Two types of flow are identified in this WFM They are flow of precedence and flow of data The flow of precedence and logic node between work-cell agents defines their dependencies For example, supposing a simple hypothetical product consists of two components, B and C The component B is an outsourcing and the component C is produced at work-cell Finally, component B and C are assembled to form Product A at work-cell Accordingly, the production of A is decomposed into three production processes which can be depicted by the directional networktopology mode Here, Agent represents a ‘delivery A’ work, Agent represents a ‘producing B’ work and International Journal of Computer Integrated Manufacturing Agent represents an ‘assembling C’ work As shown in Figure 4, Agent can only start its work after Agent and complete their works under the and logical condition Agents and may work simultaneously The flow of data refers to the situation where agents share their property data Some outputs from an agent may be the inputs to other agents Such relationships can be easily defined in a similar way that relationships are defined between data tables in a relational database Flows of data can be compared to messages widely used in multi-agents system (MAS) for communication And the message configuration tool configures where inputs are obtained from and outputs are send E Figure combines some output items of Agents and as the one input item of Agent according to the real requirements Figure Two types flow of work: control flow and data flow Figure Agent-based execution of a workflow model 107 Flows of data, or message passing, are triggered by the flow of precedence and logical condition For example, during the ‘and’ condition, if Agents and have not finished with its work, flows of data associated with Agent will not be processed 5.3 Workflow execution Once a workflow is fully defined, it can be executed as illustrated in Figure During the execution, each node in the workflow will be translated to an agent Each agent will invoke its manufacturing services (e.g workcells, smart objects, etc.) of the real manufacturing environment to enable their intelligent management of the manufacturing process Explorers are provided to operators, managers and supervisors for monitoring 108 Y Zhang et al and controlling the workflow execution lifecycle The users can simply follow the logic and execute relevant production tasks As a high-level user, the shop-floor manager can have a clear overview of the progress of a production project at the SF-Gateway At the WCGateway, on the other hand, the operators of workcells can use this facility to check if the conditions of their tasks are met so that they can start The general procedure of executing a workflow is as follows: The work-cell Agents use Service Oriented Architecture framework to connect to the web server where SF-Gateway is deployed; XML-Based workflow definition file is automatically downloaded to and manually activated at the corresponding Agents; Repository is contacted to retrieve the workflow model defined in advance; The first agent in the workflow is activated The agent is executed according to the procedure discussed in the preceding section Its incoming messages defined as flows of data associated are fired Therefore, this agent knows from where its input data come; After preparing its input data, repository is contacted to save the input/output and other data of the agents; Execution engine notifies all work-cell agents about the changes; The work-cell agent is prompted if the output is accepted or a backtracking is necessary; Upon completion, the control is passed over to subsequent agents; and Figure Overview of the motivating assembly line This process repeats until the last agent in the workflow is completed Case study 6.1 Configuration of a representative assembly line This section demonstrates the usage of the proposed architecture with an example application of an assembly line This proof-of-the-concept test-bed serves the purpose of demonstrating how the proposed real-time reconfigurable WM framework would work in an industrial environment, gaining insights about requirements of WM solutions, and highlighting further issues for research and development of WM solutions The study is based on a simplified motivating scenario shown in Figure The configuration of the assembly line and workcells depends upon the structure of the product (variant) to be assembled The product demonstrated here is composed of five components assembled sequentially across three work-cells, as shown in Figure At the first work-cell, two components, one of which is a critical base module, are put together to form the first level subassembly Two further components are added to the subassembly at the second work-cell The last component is assembled to produce the finished product at the third work-cell where an inspection also takes place to determine if the product is acceptable or rejected All components and subassemblies are moved and maintained in containers or pallets of appropriate sizes and shapes International Journal of Computer Integrated Manufacturing 6.2 Agent publish In order to implement the proposed agent-based workflow management for shop-floor, work-cell agents should be firstly registered and published to MSUDDI Figure illustrates the main steps for publishing a work-cell agent at MS-UDDI, namely Step 1: Login MS-UDDI The manufacturing resource manager is responsible for registering and publishing the work-cell agents of as web services Considering the security, the manufacturing resource manager needs to login the MSUDDI using his account for further operations as seen in Figure 7(a) Step 2: Register Service information of Work-cell Agent The MS-UDDI provides facilities, as shown in Figure 7(b), to describe the service information of the work-cell agent so that users (e.g shop-floor manager) can easily know what services this work-cell can provide The registered information includes agent ID, description, process capability, access point etc Agent ID is used to identify the each work-cell agent; description indicates the machine type of the work-cell agent, e.g lather, mill, assembly etc.; process capability describes the specific machining characters, i.e which processes can be executed at this work-cell; access point shows the internet address of a work-cell agent to enable users or systems to get access Step 3: Publish Work-cell Agent After the registration of agent information, the manufacturing resource manager can physically publish the work-cell agents to MS-UDDI, as can be seen in Figure 7(c) A published work-cell agent can be found and invoked as web service through internet This register and publish processes are repeated until all the work-cell agents are published to MS-UDDI Figure 6.3 109 Workflow definition After all the work-cell agents have been defined and published at MS-UDDI, it is important to establish the workflow of the shop-floor level The definition of a shop-floor workflow includes four steps as can be seen in Figure The main steps are described as following: Step 1: Get the process planning of the specific product A shop-floor workflow is corresponding to a practical production process Generally, different products have different production processes Therefore, process planning of a product is the input information for defining a shop-floor workflow The detailed process planning of a product ‘A’ is given at the top of Figure 8, including three assembly processes, i.e Assembly ‘C’, ‘B’ and ‘A’ Step 2: Define workflow according to the process planning The workflow facility provides graphic interfaces for shop-floor manager to edit the work and flow according to specific process planning As seen in Figure 8(b), the three production processes of product ‘A’ are described by graphic objects The rectangle denotes the ‘Assembly’ work, and the directed arrow represents the sequence of the processes Step 3: Establish mappings between the processes and agents This step is responsible for establishing mapping relationships between processes and agents, as shown in Figure 8(c) For each process, e.g the process ‘Assembly B’, there are several potential work-cell agents registered at the MS-UDDI The optimal agent can be selected to execute a process based on its capabilities, e.g capability and its real-time status Then, a pop-up dialog is used to define the condition constraints and input/output data At this time, the mapping relationship between the process and agent is established Main steps for publishing work-cell agent at MS-UDDI Pi Piþ1 À Fi < e ð2Þ Pi Piþ1 À Fi =Fi < d ð3Þ or where e and d are the given bounds on feedrate error and feedrate relative error, respectively Interpolation algorithm Define a distance function as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðXðvi þ DvÞ À Xðvi ÞÞ2 þ ðYðvi þ DvÞ À YðvÞÞ2 þ ðZðvi þ DvÞ À ZðvÞÞ2 ð4Þ 170 Q Liu et al The key issue in the real-time interpolation is then equivalent to find the parameter increment DvÃi such that Si ðDvÃi Þ À Fi ¼ (or S2i ðDvÃi Þ À F2i ¼ 0), where viþ1 ¼ vi þ DvÃi Thus, the ending point of the line segment at the ith sampling cycle Piþ1 ¼ (X(viþ1), Y(viþ1), Z(viþ1)) is determined, which is also the initial position at the next sampling cycle In this section, a real-time interpolation algorithm is presented to identify the next point rapidly and accurately The proposed algorithm consists of three computing stages in each sampling cycle, which are the initial estimation, the interval analysis and the root localisation The initial estimation is to calculate parameter increment in terms of the parameter increment at previous sampling cycle first, and a neighbourhood interval containing the target point is determined by substituting the initial increment into proposed formulas, then the target point is iteratively approached by means of bisection or secant method for equation resolutions ð0Þ cycle by substituting the parametric increment Dvi into Equations (8) and (9) ð0Þ pi   ð0Þ ¼ Fi =Si Dvi ð1Þ ð1Þ pi ð0Þ ð0Þ ¼ pi Dvi   ð1Þ ¼ Fi =Si Dvi Dvi ð8Þ ð9Þ ð10Þ ð0Þ where pi is a coefficient that relates to the difference between the desired moving distance and computed one The solution of another endpoint can be acquired by recursively computing the following equations, ðnÞ  nÀ1 ð1Þ ð1Þ ¼ pi Dvi ð11Þ ðnÞ   ðnÞ ¼ Fi =Si Dvi ð12Þ Dvi pi ðnÞ 3.1 Initial estimation It is relatively easy to acquire the parameter increment ð0Þ In the first sampling cycle (i ¼ 1), the increment Dvi should be initialised as follows, F ¼ F1 ð0Þ Dv1 ¼ F1 = qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X0 ðaÞ2 þ Y0 ðaÞ2 þ Z0 ðaÞ2 ð5Þ ð6Þ where F is the initial moving distance In the ith interpolation cycle (i 1), suppose the curvature radius at the point Pi is large enough with respect to the desired moving distance Fi (i.e., the length of line segment Pi Piþ1 ), then the following ð0Þ expression is a good estimation of Dvi , ð0Þ Dvi ¼ DviÀ1 Fi =FiÀ1 ð7Þ where Dvi71 ¼ vi7vi71 and Fi71 are the parameter increment and the desired moving distance in the previous cycle, respectively 3.2 where n ! 2, and Dvi is another endpoint of the interval Noted that the recursive computations of another endpoint continue until Equation (13) is satisfied,    ð1Þ ðnÞ À pi À pi and y from Equation (10) With ðnÞ Equation (14), Dvi increases (with the negligence of O(y), which is substantially small) and finally it arrives at the right side of DvÃi Similar result can be achieved for ð1Þ the case where Dvi lies to the right side of the target ð1Þ point, i.e when pi < and y Hence ð1Þ ðnÞ ð1 À pi Þð1 À pi Þ < will be eventually satisfied for some n irrespective of the value of y Thus, the increment ð1Þ ðnÞ ðnÞ ð1Þ DvÃi will be in the interval ½Dvi ; Dvi Š or ½Dvi ; Dvi Š for some n Interval analysis The following section will describe how to determine the neighbourhood interval containing the target point DvÃi As to the initial estimation mentioned above, it is ð1Þ easy to obtain one of the endpoints Dvi at the ith 3.3 Root resolution When the interval is known, the solution for the target point has been converted into an extracting root of International Journal of Computer Integrated Manufacturing equation In order to illustrate easily, let s1 substitute for the smaller endpoint of the interval while s2 for the larger one, i.e DvÃi ½s1 ; s2 Š To find the root DvÃi of Si(Dv)7Fi ¼ in the interval of [s1, s2] for which (Si(s1)7Fi)(Si(s2)7Fi) 0, various equation solving methods, such as Secant method, Bisection method and Newton method, etc., are implemented to obtain the root DvÃi quickly Take the secant method as an example, which is a root finding algorithm that uses a succession of zeros of secant lines to approach the zero of a function, i.e the root of the corresponding equation, as shown in Figure At the beginning, the intersection of the straight line with the s-axis can be obtained by using the following equations s3 À s2 À gðs2 Þ ¼ s2 À s1 gðs2 Þ À gðs1 Þ Similarly the root of Si(Dv)7Fi ¼ can be resolved from Newton method etc Let the feedrate relative error be di ¼ j1 À Si ðDvÃi Þ=Fi j Giving the maximum iteration number M and the expected feedrate error d, the iterative computations of the root DvÃi with a proper root resolution method proceed until: (1) the number of recursive computations reaches M; (2) or di d; (3) or di cannot be reduced Then the feedrate commands along X, Y, Z axes in the ith cycle are given as below, ð15Þ that is, s3 ¼ s2 À gðs2 Þ s2 À s1 gðs2 Þ À gðs1 Þ ð16Þ If g(s3) 0, the next zero point is obtained from the straight line through two points [s2, g(s2)] and [s3, g(s3)], otherwise [s1, g(s1)] and [s3, g(s3)] In general, the next zero point is iteratively calculated from the two previous points [sk71, g(sk71)] and [sk, g(sk)] as sà ¼ sk À gðsk Þ sk À skÀ1 gðsk Þ À gðskÀ1 Þ ð17Þ With the bisection method, the root is finally estimated as follows for some k: sà ¼ sk þ skÀ1 ð18Þ Dxi ¼ Xðviþ1 Þ À Xðvi Þ ð19Þ Dyi ¼ Yðviþ1 Þ À Yðvi Þ ð20Þ Dzi ¼ Zðviþ1 Þ À Zðvi Þ ð21Þ where viþ1 ¼ vi þ DvÃi , and the end-point of the line Piþ1 ¼ (X(viþ1), Y(viþ1), Z(viþ1)) at the ith cycle is determined, which is also the start point of the next sampling cycle The above computations are performed in each sampling cycle, and the corresponding coordinate increments (feedrate commands) are sent to drive the machine tool Analysis of the chord error Chord error (contour error) is one of the major concerns in real-time curve interpolations, which is subjected to many factors in interpolation (Yong and Narayanaswami 2003, Lee et al 2004, Sun et al 2006), such as the chosen interpolating method, the feedrate and sampling cycle etc It must be confined within a pre-defined range to meet machining requirements With the proposed interpolation algorithm, it is the procedure of line substituting arc for each interpolation cycle The end-points of the line segment Pi Piþ1 are always on the curve, so there is no accumulative error But the chord error, i.e the difference between a curve segment and its replacing line segment, is introduced The chord error is approximated by: Graphical representation of the secant method rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi r2i À Dx2i þ Dy2i þ Dz2i =4 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi % ri À r2i À F2i =4 ei ¼ ri À Figure 171 ð22Þ 172 Q Liu et al where ri ¼ 1/ki, ri and ki are the radius of curvature and curvature at point Pi respectively The curvature (Yeh and Hsu 2002) is given as: ki ¼ " [...]... 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