AUTOMATIC CONSTRUCTION PROCESS OF PREFABRICATED BUILDINGS ON GEOMETRIC REASONING Wenfa Hu1 ABSTRACT Construction process is very important in construction management, development of AI and IT technology provides feasibility of automatic construction. This paper presents a model of geometric reasoning to automatic construction process planning of prefabricated buildings. Based on the principle of construction by disassembly, a prefabricated building can be decomposed into components. Components are disassembled from the building and the sequence of disassembly of components are derived from the connection graph and disassembling directions of the building. On the reverse of the disassembly process, construction process is gotten in the end. INTRODUCTION With development of science and technology, information technology and information management is becoming more important than ever. Computer-based technology, such as CAD, CAM, AEC, CAPP and so on, is used to improve quality of products, to accelerate draft design and lower cost of products. Automatic manufacture was presented early in the industrial revolution, now manufacturing automation is popular in improving manufacturing productivity. Construction industry is different from manufacturing because construction usually need site working, and a large mount of labors in site. Automatic construction process can help contractors and owners to understand construction project well and make correct decisions in construction, now many people become to concentrate on it. A modern view of the automation field can be summarized as follows: At the center are computer models of products, such as components of a building; processes, such as a sequence of construction activities; and resources, such as tools or robots. Around this center are the activities that create and use the computer models. Automatic planning of construction process is an important premise of construction automation, but it is difficult to find out a suitable geologic or physical reasoning method for automatic construction process planning, most of practical construction process planning is decided manually. Planner is more important in choosing construction process and is more at will, and a feasible construction process usually needs several trying and adjusting. Construction of a prefabricated building is something like the assembly of products. The assembly and disassembly is a reversible process in manufacturing and also in constructing. Every disassembly is the reverse of assembly. Through disassembly of a product, the 1 Associate Professor, Department of Construction Management and Real Estate, Tongji University, Shanghai 200092, China; PH (+8621) 6598 2955; email: wenfahu@mail.tongji.edu.cn disassembling process can be easily planned. Counter to disassembling process, the assembling process can be derived. This method is efficient in resolving and reasoning assembly processes. This paper presents a method for the automatic determination of a construction sequence from a connection graph representing a prefabricated building through the extraction of components. The extraction of components is based upon the recursive extraction of components by a simultaneous verification of disassemblability. Components which are tightly connected together geometrically and physically, but loosely connected to the rest of the assembly, are selected as a preferred super-component. This process of extracting components not only makes it possible to reduce the problem space by early pruning of infeasible construction sequences, but also explicitly defines temporal and spatial parallelism in construction. COMPONENT MODEL Computer model should be established before construction process can be planned. Building components are basic units of a building, and a building is comprised of and assembled with certain components according to certain rules. The assembly of building components is depended not only on geometric properties of components, but also on assembly relationship of components. So computer model of construction in prefabricated building should consist of solid information, relationship of components and spatial restriction information. COMPONENT FRAMES OF A BUILDING Each component in a prefabricated building is described by geometry, features, and physical properties. DESCRIPTION OF GEOMETRIC SHAPE The geometric shape of a component is described by the set union of the predefined set of geometric primitives such as cuboid, cylinder, and plane. For instance, a typical prefabricated building structure can be decomposed into different components, such as foundations, columns, beams, roofs, slabs, walls and so on, shown in Fig.1. Building Structure Foundations Columns Walls Beams Slabs Roofs Stairs Figure 1: A decomposition sample of prefabricated building structure The prefabricated components are used not only to describe the shape and volume of an object but also to represent the features of component mating and component identification. 3D models are included in the geometric components. The volume of each object is defined by dimensional parameters. DESCRIPTION OF A FEATURE A feature is a geometric configuration formed on surface, edge, or vertex of a component. Each feature frame consists of 1) the entry label. 2) the mating type, 3) the representation of mating geometry, and 4) the coordinate of the mating with respect to the component frame. DESCRIPTION OF A COMPONENT FRAME CONNECTION GRAPH I D M H C B G L S R Q The purpose of a component frame is to describe the properties associated with a component, including 1) the component geometry, 2) the mating features, and 3) the physical properties of a component such as weight. The component geometry includes 1) the component coordinate P O describing the position and orientation of the component frame with respect to the assembly frame and 2) the computer model of a component. N A joint is an object which is used to attach two mating components, thereby constraining the motion of both components with respect to each J K other. The information about a joint should be included in the Component Frames. Sometimes there is not an obvious joint between building components because they are connected with E F reinforced concrete. In Fig.2 we describe a simple prefabricated building structure in 2D drawing instead of 3D solid model just for illustration. A A building can be defined by components and its topological relations. As a unified representation Figure 2: Prefabricated building of components and their relations, a Connection Graph is introduced in this paper. A component of a building can be connected with several other components, and only connection relationship between every two components is represented in Connection Graph. In order to depict the topological relationship of all components, an assembled building can be represented as a graph, and the connection relationship can be shown as CG=(V, E), with V representing Vertex aggregation, and E representing connection aggregation. Vertex means the components of a prefabricated building, and means the connection relationships of different components. Connection Graph represents the basic information about construction process planning of a prefabricated building. Connection Graph is so important and fundamental that some definitions should be introduced here: Definition 2.1 A Connection Graph of building components is nondirectional, it will be false if a component is not connected with any other parts in a Connection Graph. Definition 2.2 There is only one Connection Graph that can be derived from a building construction and represent all the connection relationship. Definition 2.3 A connection is said to exist between a pair of components if one component constrains the freedom of motion of the other. The state of a building can be represented by a connection graph. For example, the prefabricated building in Fig.2 can be represented by its connection graph in Fig.3. L G B O J E R A C H N Q S F K D P I M Figure 3: The connection graph for construction of the building In the case of a construction planning system based on the principle of construction by disassembly, the initial state of a building is represented by a connection graph displaying all the required relationships between components. The goal state, wherein all the connections between the components of a prefabricated building have been broken, is represented by a set of disassembled components. The primary objective of disassembly planning is to generate precedence relations among disassembly operations so as to ensure a transformation of the initial state to the goal state. EXTRACTION OF CONNECTION GRAPH Since assembly processes are reversible processes of disassembly, Connection Graph can be simplified by connection relationship of assembled components. A Connection Graph can be transformed into an Extraction Connection Graph (ECG) by merging a group of mutually inseparable nodes (components) into a supernode. A group of inseparable nodes represent those components connected by unbreakable connections due to inaccessible connections, inability to deliver forces required to disconnect parts, or the precedence relations due to functional or physical interdependencies. Definition 3.1 Accessible component. An accessible component is a component that can be manipulated by a hand of cranes or robots in constructing or disassembling directly. So an accessible component should be a component outside of a building at first. The manipulation of construction or disassembly of this component would not interfere with any other components. Definition 3.2 Disassemblability of a component. The disassemblability of a component is decided by the freedom of motion, the accessibility of a component, and the removability of joints. A joint is said to be removable if it is disassemblable by a single translational motion. Definition 3.3 Accessible direction. An accessible direction is a direction from an accessible component to a destination component and there is no any other accessible component between them. For instance, there is an accessible component (or node) Na and there are several no accessible components N1, N2, N3 in Fig. 4. Then Na→N1→N2→N3 is an accessible direction for component N3. Figure 4: Accessible direction Definition 3.4 Immobilized node. An immobilized node is a node having its freedom of motion completely constrained by a supernode. An immobilized node can be detected by moving a supernode in all directions of its freedom of motion and identifying the nodes which interfere with the supernode in all directions. For instance the supernode {N P} makes S an immobilized node in Fig. 3. Definition 3.5 Extraction principle. If the two nodes n1 and n2 are mutually inseparable, they should be merged into a supernode. The Extraction Connection Graph of the prefabricated building is shown in Fig. 5. GEOMETRIC REASONING The construction process planning based on the principle of construction by disassembly involves establishing disassemblability of components. A great deal of geometric reasoning is required to facilitate an automatic deduction of disassemblability. In the subsequent sections, we discuss various concepts in geometric reasoning pertaining to disassemblability of building components or super-components. L G B J E A C H N’ F K D I M Figure 5: Extraction connection graph of the building METHOD OF GEOMETRIC DISASSEMBLABILITY OF COMPONENTS If a component is accessible, it may be disassemblable or may be not, further it should be checked whether the disassembling direction of the component interferes other components. Because the calculation of interfering between different components is very difficult and time-consuming, a simple method of interfering check is introduced. The main idea of this method is smartly cutting down calculation cycles. So the interfering check will become easy if the components are at first checked by several definitions below. Definition 4.1 If there is a super-component, representing several components, equivalent to a supernode, then the several components will inherit the disassemblability of their supercomponent. If M(P,S) represents component P can be disassembled from super-component S, several definitions below can be inferred. Definition 4.2 Sufficient condition of disassemblability of components: If component S is a subset of A, component P can be disassembled from super-component A, and if M(P,A) is true, then M(P,S) is true. M ( P, S ) (?) M ( P, A) Definition 4.3 Necessary condition of disassemblability of components: If component P is constrained to set {CS} in super-component A, and the constraint condition set {CS} also exits in super-component S, then the component P is disassemblale. M ( P, S ) (?) (CSi ) With CSi is the ith restraining condition in component P. When all restraining conditions are removed, disassemblability of M(P,S) can not be decided yet. Definition 4.4 Sufficient and necessary condition of disassemblability of components: If restraining condition set of component P disassembled from A is {CS(P,A)}, and if Pc {CS ( P, S )} exits in super-component S, then component P can not be disassembled from super-component S. M ( P, S ) (?) [ Pc ] [ Pq ] , With Pc {CS ( P, A)} , Pq {CS ( P, A)} DIRECTION OF DISASSEMBLING COMPONENTS If a component is connected with other components in a building, other components may restrain this component in constructing. In a prefabricated building, a component usually is assembled under several restraining conditions simultaneously, so every restraining condition will be considered when a disassembling direction is calculated. Through extracting the mating property of geometric components and determining vector directions of conformation coordination of components, a disassembling direction of components can be decided. If there are several different mating properties in this component, its disassembling direction will be determined by intersection set of all potential disassembling directions. Algorithm 4.1 In the general disassembling direction of a prefabricated building is from top components to bottom components in space, the ground as a component can not be disassembled from the building. For instance, a roof would be disassembled at first, columns, walls, floor panels, and so on in the building can be disassembled then. In fact, the disassembling direction of building components is the gravity direction. Components without any other force restraining can be removed directly. Algorithm 4.2 Determination of disassembling direction of geometric components conformation based on mating properties. If mating property of geometry is line type, disassembling direction is calculated by: (a) Parameter equation of mating geometric components is derived from mating geometric identification ID. (b) To translate parameter equation into line parameter equation. (c) To pick up the endpoints of the line equation. (d) Line vector direction can be derived from the endpoints of the line. (e) To translate the line vector direction and the beginning coordination into orthoaxis. (f) The vector axis Z will be the disassembling direction. Disassembling directions set can be derived from Algorithm 4.1 and Algorithm 4.2, and the beginning direction of disassembling components is the intersection set of all disassembling directions. Algorithm 4.3 To calculate the intersection set of disassembling directions of geometric components. Dir Dir DS i By Algorithm 4.3 the disassembling direction of a component can be decided. PLANNING OF DISASSEMBLY PROCESSES After inputting a topological graph of the prefabricated building, a vertex cutset of connection graph may be derived, and disassemlbability of every component can be obtained. Then the connection graph of assembled building will be decomposed until every subgraph can not be decomposed. All disassemblability of components and super-components is recorded and disassembly process of whole assembly is derived. The disassembly process of the prefabricated building in Fig.2 is shown in Fig. 7. N’ is a super-component representing several components N, O, P, Q, R, S. This super-component is the roof structure, which usually be cast as an integrated building component in a prefabricated building. According to Algorithm 4.1, super-component N’ should be dissembled at first while disassembling direction set of other nodes is null and they are not disassemblable without enough freedom. After super-component N’ is removed, components L, M, J, K, G, I, B and D are all accessible components, by checking their accessible directions and according Algorithm method, components L and M could be disassembled simultaneously. Keep on calculating and checking the disassemblability, a disassembly process of the building appears in Fig. 6. B B G L G E L J E J A N’ H C C H F K M N’ A K F M D I I D Figure 6: Disassembly process of the prefabricated building Figure 7: Construction process of the prefabricated building PLANNING OF CONSTRUCTION PROCESS Construction process is the reverse disassembly process of buildings, which is called construction process by disassembly process in this paper. A construction process of the prefabricated building in Fig.2 can be easily derived from the disassembly process. In this paper the restraints in construction planning are transformed into calculating disassemblability of buildings, which may be an easy problem to be resolved. The construction process of the prefabricated building is shown in Fig. 7. If there are more than one assembling processes in a building construction, then the best process can be selected by comparing construction processes activities. In planning of construction processes, the goal may be construction operations of cranes reach minimum and all construction activities do not interfere with other construction activities and conform to any restraints. IMPLEMENTATION We have developed an Automatic Construction Process Planning System which consists of 5 parts: Interactive CAD inputs; Visual Output; Object Model Library; Geometric Reasoning; Resource Library. This system can mainly generate construction processes of prefabricated buildings automatically. Though some detail construction activities can not be recognized correctly from CAD drawings in this system, it really accelerates to plan several construction buildings’ scheduling and is useful to generate construction processes. CONCLUSION This paper presented an automatic construction process planning based on a geometry reasoning method, our main goal was to provide efficient computational support to help construction project managers plan construction process that are easier to construction and service. Though the proposed techniques were used in construction prefabricated buildings, they could also be used to plan construction processes of other construction projects. The principle of automatic process planning is the reversed calculus and extraction of super-component, which provides an efficient way of realizing temporal and spatial problem in construction. At first the disassembly processes are calculated, and then the construction processes are planned based on reversing disassembly processes. This notion of construction by disassembly is one contribution of this paper. Our current research goal is to develop this approach for more complex building construction processes and design a more complex additional constraints set of efficient evaluation methods. On the experimental side, we are integrating the algorithms into a highly interactive construction-assistant system. REFERENCES Arditi, D., and Tokdemir, O. B. (1999). “Comparison of Case-Based Reasoning and Artificial Neural Networks.” J. Computing in Civil Engrg., ASCE, 13(3), 162-169. Boothroyd, G. (1991). Assembly Automation and Product Design. Marcel Dekker, New York. Chan, W.T., and Hu, H., (2002) “Constraint Programming Approach to Precast Production Scheduling.” J. Construction Engineering and Management. ASCE, 128(6), 513-521. Dawood, N. N., and Neale, R. H. (1990), “A survey for the current production planning practices in the precast industry.” Constr. Manage. Econ. J. 8, 365-383. Han, J.H., and Requicha, A.A.G. (1995) “Integration of feature based design and feature recognition.” In. Proc. of the ASME International Conference on Computers in Engineering. Boston, MA, 569-578. Joshi, S., and Chang, T.C. (1988). “Graph-based heuristics for recognition of machined features from a 3-D solid model.” Computer-Aided Design, 20(2), 58-66. Karumanasseri, G., and AbouRizk, S. (2002). “Decision Support System for Scheduling Steel Fabrication Projects.” J. Construction Engineering and Management, ASCE, 128(5), 393-399. Kasravi, K. (1994). “Understanding knowledge-based CAD/CAM.” Comp.-Aided Engrg., 13(10), 72-78. Lee, J.Y., and Kim, W. (1996). “Geometric reasoning for knowledge-based parametric design using graph representation.” Commuter-Aided Design. 26(10) 831-841. Lee, S., and Shin, Y.G. (1990). “Assembly planning based on geometric reasoning.” Comput. & Graphics, 14 (2), 237-250. Leu, S. S., Chen, A. T., and Yang, C. H. (1999). “Fuzzy Optimal Model for ResourceConstrained Construction Scheduling.” J. Computing in Civil Engineering, ASCE, 13(3), 207-216. Lottaz, C., Clement, D. E., Faltings, B. V., and Smith, I. F. C. (1999), “Constraint-based support for collaboration in design and construction.” J. Comput. Civ. Eng., ASCE, 13(1), 23-35. Messner, J. I., Sanvido, V. E., and Ikeda, M. (1994). “Developing an object based planning system for precast concrete building structures.” Proc., 1st Congress on Computing in Civil Engineering, ASCE, Reston, Va., 1426-1429. Nilsson, N.J. (1980). Principles of Artificial Intelligence. Morgan Kaufmann, Los Altos, CA. Qamhiyah, A.Z., Venter, R.D., and Benhabib, B. (1996). “Geometric reasoning for the extraction of form features.” Computer-Aided Design, 28(11), 887-903. Requicha, A.A.G. (1996). “Geometric Reasoning for Intelligent Manufacturing.” Communications of ACM, 39(2), 71-76 Spyridi, A.J., and Requicha, A.A.G. (1994). “Automatic programming of coordinate measuring machines.” Int. Proc. of the IEEE International Conference on Robotics & Automation, San Diego, Calif., 1107-1112. Wilson, R. H. and Latombe, J. C. (1994). “Geometric Reasoning About Mechanic Assembly”. Artificial Intelligence, 71, 371-396. Wolter, J.D., Chakrabarty, S. and Tsao, J. (1992). “Mating constraint languages for assembly sequence planning.” IEEE International Conference on Robotics and Automation, Nice, France, 2367-2374.