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
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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
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N
Q
S
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K
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P
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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
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J
E
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N’
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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.
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A
N’
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N’
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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.
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