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A physics-based simulation approach for cooperative erection activities

Hung-Lin Chi Shih-Chung Kang

Dept of Civil Engineering National Taiwan University Taipei City 10617 Taiwan

a b s t r a c ta r t i c l e i n f o

Article history

Accepted 1 March 2010

Keywords

Cooperative erection activities

Rigid body dynamics

Forward kinematics

Construction crane

Physics-based simulation

Erection planning

Virtual reality

Robotics

Cooperative erection activities are critical to projects which involve the erection of heavy loads or the

installation of special equipment Detailed simulation on computer prior to construction can identify

constructability problems and subsequently avoided during actual erections This paper describes an

integrated approach for simulating the detailed motions of cranes This research develops a physics-basedmodel that follows the principle of closed-form forward kinematics and constraint-based dynamics to

present the dual-crane mechanism mathematically mdash a non-trivial task This model can be used to analyze

the inputs from the users (ie virtual crane operators) and simultaneously compute the cables sway and

reaction of collisions We also implemented the model on computer and developed a simulation system

Erection Director to render realistic cooperative erection activities A demonstration of simulating two-crane

lift has been built and three performance tests including a small building (840 elements) a medium building

(1937 elements) and a large building (2682 elements) validate the feasibility of the proposed approach The

test results indicate that Erection Director can support real-time and physics-based visualization of

cooperative erections

copy 2010 Elsevier BV All rights reserved

1 Introduction

Cooperative erection activities are very common in modern

construction projects especially for plant constructions in which a

typical yet critical task is the installation of the major equipment The

installation process usually involves the erection of extremely heavy

equipment Even though a detailed plan is usually developed to level

the erection loads the weight of a single erection can be as high as

1300 t on some larger plant constructions It is ef 1047297cient to complete

such erection tasks using multiple and relatively cheap cranes

cooperatively rather than specifying a single more expensive crane

[12] In most cases two cranes usually a major crane and an assisting

crane work cooperatively to complete such an erection activity

In two-crane cases erection planners need to consider three major

issues to properly arrange and plan cooperative erection activities First

they need to maintain the loads of the cranes within safe working

capacities for the duration of the erection processes However without

the use of an effective computational method it is onerous to analyze

and calculate the loads on each individual crane Most planners simply

rely on their experience or estimate the loads using static mechanics

Dueto a lack of reliable simulationsthe erection plans areusually overly

conservative in order to reduce the possibility of dealing with

unforeseen situations

Avoiding collision is the second issue planners need to consider

carefully Since most of the cooperative erections take place aroundhalf-way into the project the building structures are already partially

built thus the two cranes need to cooperate to transport the

equipment into the building Every part of both the equipment and

the cranes must not collide with any object of or in the partially built

structure This requires the consideration of the 3D geometrical

relationship between the cranes con1047297gurations the rigging object

and the crane cables sway In current practice planners rely on

experience or a simpli1047297ed model that preserves working space to deal

with this problem

Thethirdconsideration is theattitude (ie position andorientation

in space) of the equipment for the entirety of the erection processes

The equipment needs to follow a speci1047297c path or sequence to be

transported safely to the location of installation especially for

processes performed in an environment with many obstacles Two

cranes need to work cooperatively to maintain the equipment on

prede1047297ned paths After reaching the installation location the

equipment needs to be maintained at a certain attitude until

installation commences

To handle such complexities we need to develop a simulation that

can realistically re1047298ect actual erection scenarios This simulation

should not only include the visual presentation of erection processes

but also the related physical informationsuch as force feedback cable

sways and collision behaviors Such a simulation will be workable in

real time and would facilitate erection planners in generating safe

ef 1047297cient and collision-free paths for cooperative erection activities in

the future

Automation in Construction 19 (2010) 750ndash761

Corresponding author

E-mail addresses hlchicaecenet (H-L Chi) sckangntuedutw (S-C Kang)

0926-5805$ ndash see front matter copy 2010 Elsevier BV All rights reserved

doi101016jautcon201003004

Contents lists available at ScienceDirect

Automation in Construction

j o u r n a l h o m e p a g e w w w e l s ev i e r c o m l o c a t e a u t c o n



2 Related work

Many previous studies are aimed at realizing the simulation of

erection activities while considering the safety loading range collision

avoidance and transportation attitude [34] In the 1047297eld of training

simulator development SimLog1 and CMLabs Corporation2 provide

advanced devices for crane operation training These are assistant

tools that help novice crane operators practice their skills using

several different training scenarios each customized to prepareoperators to sit for a particular certi1047297cation examination The

movements of the virtual crane are directed by user manipulation

and the reactions re1047298ect actual physical behaviors

Many construction consulting 1047297rms have developed adds-on or

external modules for existing visualization tools to simulate cooper-

ative erections An engineering consulting corporation Chung-Ting

(CTCI) developedan add-on for the AutoCAD3 system which provides

a visualization interface for erection simulations A product from JGC

Corporation4 also provides a virtual environment with various

viewing interfaces for visualizing the planning movements Both of

these products can automatically generate animations of rigging paths

for erection activities

Some related works can also be found in academia Researchers

usually use automated approaches that integrate modern search

processes [56] or heuristic technologies from the 1047297eld of numerical

kinematics [7] and motion planning [8] to generate the movements of

cooperative virtual cranes automatically Users need to set up the

initial conditions of a construction jobsite and the software deter-

mines the most ef 1047297cient yet safe and collision-free paths for use in

simulating the erection activities

In popular software such as 3D Studio Max [9] and Maya [10]

semi-automation is used to produce animation Users set key frames

so that the frames in-between can be interpolated Such technology is

also feasible for planning the movements of erection processes

These approaches and technologies are capable of simulating

different aspects of erection activities but thereshould be appropriate

ways of integrating these methods to negotiate all of the three major

issues mentioned in Introduction section Therefore due to the

complexity of the combinations of the cranes motions and issues of realism the challenge in the simulation of cooperative erection is to

develop a methodology for generating accurate feasible and

collision-free motion paths that represent the complex interactions

between cooperating cranes and to perform visualizations in real-

time

3 Research goals

This research aims at utilizing physics-based animation methods

which are widely used in game physics and training simulators to

generate detailed cooperative erection activities in a virtual environ-

ment Unlike game environment which focus more on the visual

stimulation instead of precision Our work on the contrary

emphasizes the precision of the simulation By using these methodsand real construction cases it should be more 1047298exible to build up the

simulation scenariosand at themean time to show them at acceptable

frame rate per second The simulation is not just for training purpose

but focuses on the evaluations of erection plans Work-items need to

be simulated as accurately as possible in order to 1047297nd potential

problems before physical operations commence In order to retain

1047298exibility and generality in solving these problems a prototype

system for visualizing the simulations has been developed and

evaluated to perform the simulations

4 Existing methods for generating physics-based simulation

To simulate high-risk erection activities the integration of physics-based simulation methods plays a signi1047297cant role in this research

Physics-based simulation methods utilize various theoretical laws of

physics and a variety of mathematics combined they describe a

mathematical model of the real world

Existing methods for generating physics-based simulations can be

generally divided into two categories kinematic and dynamic to

ful1047297ll theneedsof thekinematic anddynamic simulation respectively

Table 1 presents the classi1047297cation of physics-based simulation

methods According to the modeling directions is the two categories

can be further divided into four groups forward kinematics (FK)

inverse kinematics (IK) forward dynamics (FD) and inverse dynamics

(ID)

Kinematics is the study of an objects motion without considering

its mass or the forces acting on it By describing the properties of

geometry and the relations of coordinates the movements of an

object can be formulated in a virtual environment Differing from the

principle of kinematics dynamics takes mass and forces into

consideration and generates more realistic and accurate behaviors

during simulation

Forward modeling means that the position and orientation of

every part of the articulated-object can be manipulated and is known

by the modeler When the next time-step of the animation is

generated there exists only one solution to achieve the resulting

motion from calculation and accumulation of the status of each part of

the object In contrast inverse modeling means that the resultant

position and orientation are known However there is more than one

solution (or sometimes no solution) for each articulated part of the

object to achieve the goal motion

The methods of the inverse kinematics and dynamics group of Table 1 are heuristic and usually used to 1047297nd the feasible paths or

movements by assigning the objective position and orientation They

can be useful in generating animation for automatic construction

planning Kamat and Martinez [7] used the cyclic coordinate descent

method to automatically simulate the operations of articulated

construction equipment

In the forward kinematics and dynamics group of Table 1 key frame

animation is a semi-automatic method where users 1047297rst set up the key

positions and orientations(frames) The softwares built-in function for

key-frame animation then automatically interpolates the continuous

movements between each frame Theparticle systemmethod [12] used

to simulate the movement of points of mass is the base theorem for

deriving rigid body dynamics This means that it does not completely

ful1047297ll the use of rigid body simulation The 1047297nite element method [13]can be used to analyze 1047297ne movements such as vibrations and

1 Simlog Mobile Crane Personal Simulator Retrieved June 25 2007 from http

wwwsimlogcompersonal-cranehtml2 CMLabs Vortex Training Simulators Retrieved April 2 2007 from httpwww

vortexsimcom3 Autodesk AutoCAD Retrieved June 25 2007 from httpusaautodeskcomadsk

servletindexsiteID=123112ampid=27042784 JGC 4D CAD System Retrieved June 25 2007 from httpwwwjgccojpen

03srvs07const02e_const4d_cadhtml

Table 1

The classi1047297cation of physics-based simulation methods (Modi1047297ed from [11])

Forward

kinematics (FK)

Inverse

kinematics (IK)

Forward

dynamics (FD)

Inverse

dynamics (ID)

Closed-form

solutions

Cyclic coordinate

descent

Constraint-based

simulation

Recursive newton

euler method

Key-frame animation

(interpolation)

Jacobian method Particle systems Optimization

problems

Finite element

method

751H-L Chi S-C Kang Automation in Construction 19 (2010) 750ndash761



deformations of cranes However a set of simplifying assumptions is

required to be applied on the conditions and deformations on rigid

equipment are relatively small

Unlike automatic animation this research is focused on operational-

level simulation and controllable manipulations In other words it

targets the situation where the crane operator manipulates the virtual

crane without knowing the exact reaction of the crane when the action

is executed For example the operator can control a gear to rotate

the boom of the crane but the user would not know to where the

hookof the crane will swing For these reasons the remainingmethods

closed-form solutions and constraint-based simulations are appropri-

ate approaches to numerically modeling a crane They will be called

closed-form forward kinematics and constraint-based rigid body

dynamics and are explained in the following sections

5 Single crane modeling

A two-step methodology as will be described is required to develop a cooperative erection simulation The 1047297rst step is single crane modeling

This describes a numerical modeling method using the principle of closed-form forward kinematics and constraint-based rigid body dynamics

The second step is to derive the modeling method for a cooperative dual-crane scenario

The principle of closed-form forward kinematics and constraint-based rigid body dynamics are individually used to model different parts of

the crane Fig 1 shows the architecture of the numerical single crane model

The manipulation model which includes the track cabin and the boom of the crane is modeled using closed-form forward kinematics

Closed-form forward kinematics can modelthe articulated crane piece by piece according to the transformation matrices described between each

rigid part of the crane This transformation information is able to identify the status of every point on the manipulation model during crane

operations By using this method it is easy to simulate the behaviors of the track cabin boom every rigid components of crane and the

connections between these rigid bodies However dynamic properties such as operational vibrations and loading deformations are not

considered in this model Compared with the cable and suspended portion of the crane the dynamic properties are insigni1047297cant and can be

ignored on the rigid parts of a crane Therefore this rigid part also called the manipulation model uses the principle of closed-form forward

kinematics to generate a model for effective simulation

The suspension model which includes the cable and the hook of the crane is produced using constraint-based rigid body dynamics which is

the most widely used principle in the 1047297eld of game physics and caters for physical reactions by modeling every kind of constraint implied in the

real world such as the limitation of the joint the contact point friction and damping These constraints are used to construct the connections

between each part of the suspension model and to generate physical behaviors including cable sway and object collision during simulation

The process of numerically modeling the crane can be completed by combining the manipulation model with the suspension model By

calculating the position and orientation of the top of the boom using the manipulation model we can change the state of the joint attached at the

top of the boom and generate a chain reaction on the suspension model The new status of the top of the boom can be treated as an external force

applied at the top of the cable Therefore the physical swinging behavior of the suspension system can be shown when the user operates this

crane model virtually

The details of these two models are described individually in following sections

51 Manipulation model

The purpose of using closed-form forward kinematics in this research is to describe the motions of the rigid part of the crane mdash manipulation

model mdash in a mathematical form The rigid part of the crane can be treated as a stationary robot that is composed of a series of rigid bodies By

describing all spatial information between these rigid bodies a controllable model in a virtual environment can be developed The spatial

information between these rigid bodiescan be represented by a 4times 4 matrixwhichdescribes the position and orientation of speci1047297c connections

Through the de1047297nition of a rigid objectin a three-dimensional space we transfer the manipulation model of the crane into the schematics of a

manipulator A manipulator identi1047297es each connection and describes the relative motion between neighboring pieces In the case of Fig 1 the

type of joint used between every part of the manipulation model is always a hinge For example the joint between the track and cabin or the

cabin and boom are hinges and have 1047297nite rotation along a speci1047297c plane between the neighboring rigid objects As for rotation between the

track and cabin this is along the xndash y plane in an ideal situation

In the manipulation model of the crane shown in Fig 2(a) the top of the boom can be temporarily treated as a free end (without connecting

the suspension model in this discussion) There are three rotation hinges and the contact plane between the ground and the track is also

considered as a hinge This is because if the movable base is excluded the track is allowed to rotate along the contact plane changing the

Fig 1 The architecture of the numerical single crane model

752 H-L Chi S-C Kang Automation in Construction 19 (2010) 750ndash761



orientation of the entire crane Therefore the rotation angles θ1 θ2 andθ3 denote the working range of these joints while X 0 Y 0 and Z 0 represent

the moveable position where the manipulation model is located A schematic representation is shown in Fig 2(b)

After constructing the schematics of the manipulator we have to 1047297nd out the relationship between neighboring rigid objects and integrate the

transformation matrix to represent them Here we employ the DenavitndashHartenberg notation [14] DndashH notation can be used to describe any type of

articulated manipulator by following a general procedure This general procedure may not only be applied to the simple con1047297guration described inthis paper but also to more complex mechanisms for further use In addition DndashH notation presents the relationship between joint movement by a

4times4 matrix This mathematical presentation can aid software developers when designing and implementing the system The notation de1047297nes a

coordinatesystem attached to each joint that is used to describe the displacement of each object relative to its neighbors in a general form Following

the rules of the notation four parameters aiminus1 di α iminus1 and θi are used to describe the relationship between two coordination systems in a general

form By identifying these four parameters the transformation matrix between coordinate system iminus1 and i can be derived We can transfer

coordinate system i t o iminus1 by translating two directions aiminus1 and di and rotatingα iminus1 andθi along aiminus1 and axis iminus1 Similarly this is a general

way to describe any other type of connection The general form of a transformation matrix can be presented as follows

iminus1T i = frac12

cos θi minus sin θi 0 a iminus1

sin θi cos α iminus1 cos θi cos α iminus1 minus sin α iminus1 minus sin α iminus1d i

sin θi sin α iminus1 cos θi sin α iminus1 cos α iminus1 cos α iminus1d i

0 0 0 1

eth1THORN

where iminus1T i maps thecoordinate systemi relative to thecoordinate systemiminus1Notice that it is a 4times 4 homogenous matrixand thefollowing

derivations are all used this kind of representation

Fig 3 illustrates the geometrical relationship using the schematic of the manipulator that we derived earlier The1047297ve coordinatesystems xi yi

and z i (where i represents a number from 0 to 4) are each simpli1047297ed to i and attached to the manipulator We now have every property

represented by four parameters aiminus1 d i α iminus1 and θi between each neighboring coordinate system The coordinate system 0 is the global

reference and is 1047297xedin virtual spaceComparedwith the coordinate system1 which is attached to the contact plane between thetrackand the

ground there are positional offsets ( X 0 Y 0 Z 0) and a directional difference (θ1) between the coordinate systems 0 and 1 Similarly we have

transformation information between each neighboring coordinate system

By assigning these parameters to the general form of the transformation matrixin Eq (1) we can formulate four matrices 0T 1 1T 2 2T 3 and 3T 4to describe all the relationships By multiplying the developed matrices that describe all the relationships between each rigid body of the

manipulation model we can generate motions numerically by identifying the position and orientation of each rigid body when the statuses of

some are changed after a simulation time-step This is the main reason behind using closed-form forward kinematics to model the construction

crane For example the relationship between the top of the boom (coordinate system 4) with respect to the origin (coordinate system 0) can

be represented by multiplying together all the transformation matrices 0T 1 1T 2 2T 3 and 3T 4 as follows

0T 4 =

0T

11 T

22 T

33 T 4 =

c θ1 + θ2eth THORNc θ3 minuss θ1 + θ2eth THORN minusc θ1 + θ2eth THORNsθ3 c θ1 + θ2eth THORN a 2minussθ3d4eth THORN + s θ1 + θ2eth THORNd3 + X 0s θ1 + θ2eth THORNc θ3 c θ1 + θ2eth THORN minuss θ1 + θ2eth THORNsθ3 s θ1 + θ2eth THORN a2minussθ3d4eth THORNminusc θ1 + θ2eth THORNd3 + Y 0

sθ3 0 c θ3 c θ3d4 + d1 + Z 00 0 0 1

2664

3775 eth2THORN

where 0T 4 denotes the transformation matrix between coordinate system 0 and4 Thesymbol c denotes the cosinefunction and s denotes the

sine function

If the crane moves forward and the location is changed by the crane operator the new position and orientation of the top of the boom can be

identi1047297ed by the equation described below

0

P =

0

T

4

4 P eth3THORN

Fig 2 The manipulation model of a single mobile crane (a) illustration (b) schematic representation




where 0P represents the homogenous vector describing the location of the top of the boom with respect to coordinate system 0 Likewise 4P

represents the homogenous location vector of the top of the boom with respect to coordinate system 4 This location vectors form can be seen

as below

P = x y z 1frac12 T eth4THORN

After multiplying the transformation matrices we can 1047297nd the value of the vector in the same coordinate system

Similarly any other vector described in this chain relationship system can be identi1047297ed using the forward kinematics method As the

1047298exibility of the rigid part of the crane is relatively small compared to the suspension model we can use this method for ef 1047297cient rendering

without having to follow the principles of dynamics

52 Suspension model

This section introduces the principle of constraint-based rigid body dynamics and describes how to formulate the motions of the suspension

model using this principle It is mainly used for simulating the physical motions of articulated objects The articulated objects can be treated as

systems with speci1047297c types of constraints among connected joints and contact planes These constraints represent the limitations of motion and

place restrictions that cause the virtual objects to act as they would in the real physical world For example the constraints can be formed as the

movement range of joints contact points which exhibit spring-like or stiff reactions and even the behaviors of motors

In this research the joint descriptions of the suspension model are identi1047297ed We use the methodology of formulating the constraints

followed by applying constraint-based rigid body dynamicsThe basic idea for formulating allkindsof constraints is to represent them in a matrix

form First we take the ball-in-socket joint as an example The detailed formulating procedures can be referenced from previous works [15] and

other references [1617] Second we explain how the model of the suspension part of the crane is constructed

The number of degrees of freedom (DOFs) which is the minimum set of parameters needed to describe the motion of a rigid object in the

system is the key part of the constraints formulation A free moving body has six DOFs three parameters x y and z to describe its position and

Fig 3 The geometrical relationship of the manipulation model (a) right side view (b) top view




three parameters ω ψ and κ to describe its orientation If there are two bodies Bi and B j in the system we have twelve DOFs The general form P

for describing these two bodies can be represented as follows

P = xi yi z i ωi ψi κi x j y j z j ω j ψ j κ j

T eth5THORN

A 1047297xed connection between two rigid bodies Bi and B j reduces the number of DOFs of the system to six Similarly if rigid bodies Bi and B j are

connected together by another kind of joint some of the DOFs can be removed the number depending on the type of connection However the

maximum number of DOFs that can be removed is six

Assume that the lth joint is a ball-in-socket joint between the two bodies Bi and B j as represented in Fig 4 With equality in the x y and z

dimensions at the common point we can formulate three equations as follows

Φ x P eth THORN = P i + R iP ianc

minus P j + R jP janc

h i x

= 0 eth6THORN

Φ y P eth THORN = P i + R iP ianc

minus P j + R jP

janc

h i y

= 0 eth7THORN

Φ z P eth THORN = P i + R iP ianc

minus P j + R jP

janc

h i z

= 0 eth8THORN

where P i and P j are the position vectors of Bi and B j respectively Ri and R j are the corresponding rotation matrices of each bodys orientation and

P ianc and P janc are the anchor vectors which represent each bodys center of mass to the connected point By formulating these three constraint

equations three DOFs can be removed from the joint

If we reorganize these formulations the constraint equations can be represented by the following vector form

Φ P eth THORN = Φ x P eth THORN Φ y P eth THORN Φ z P eth THORN T

= 0 eth9THORN

By using the same rules for other types of joints we can 1047297nd the same expression Φ(P ) but with a different row m which represents the

number of constraints or removed DOFs The removed DOFs imply restrictions on the movement capability of the joint

Now we explain how the suspension model of the crane is constructed We built the suspension model of the crane by imitating the relationship of

connections between each piece The cable and hook on the suspension model present dynamic motions and are easily in 1047298uenced by wind force

suspended objects and so on To simulate the natural properties of these components we use ball-in-socket joints andslider joints to represent the DOFs

potentially required on the model Fig 5 illustrates the con1047297guration of joints on the suspension model The ball-in-socket joints attached between the

hook andthe cable or thecable andthetop of boomrepresent therelative movements duringa swinging situationFollowing thesame idea we dividethe

cable into several pieces and consider the ball-in-socket joints as connectors within each part For extension and shortening movements we also attach

slider joints on the cable Thus the 1047298exibility of the cable can be simulated to provide physical suspended actions during an erection simulation

Fig 4 Constraint formulation for a ball-in-socket joint

Fig 5 The connection relationships of the suspension model (a) illustration and joints con1047297guration in static condition (b) illustration and joints con1047297guration in swinging

condition




6 Dual-crane modeling

In this section we present the method for modeling the dual-crane

building cooperative erections Dual-crane cooperation usually involves

high risk and specialized construction events on a jobsite In this

research dual-crane cooperative erection refers to an erection task

performed concurrently by two cranes for a speci1047297c unusual and large-

scaled piece of construction equipment such as a petroleum tank This

kind of erection activity requires the operators to manipulate bothcranes synchronously to keep the rigging object stable during the

erection cycle This requires not only advanced operating skills of a

single crane but also the careful coordination of the two cranes

The numerical crane models of a dual-crane system are derived

from the single crane model as described in the previous section This

is done by connecting the relationship from one crane with the other

by a single suspension model In Fig 6(a) the manipulation models

are used to describe the rigid parts of two cranes in the same way as

with a single crane case However there is only one suspension model

representing the suspended cables hooks spreader-bars and the

erected object This means that thesuspension systemis controlled by

two displacements from each manipulation model Once the position

the top of the boom of one crane is changed the status of the

suspension model would be immediately updated Hence the effects

on the cooperative erection simulation can be composited and any

other kinds of erection scenarios can be easily realized based on this

modeling methodology

In the 1047297eld of erection planning dual-crane cooperative erection is

treated as a key work-item which requires exhaustive planning due to its

uniqueness andexpense In thisresearch we constructed the relationship

of the connections between the two cranes and rigging equipment in

order to simulate the cooperative behaviors In Fig 6(b) ball-in-socket

joints are set between the spreader-bar h and the rigging object r This

connection simulates the ropes of the spreader-bar that are wound

around the protruding part of the rigging object or circled around the

rigging object

In a situation where twoball-in-socket joints arelocated at two sides

of an object and combined with a spreader-bar the joints may work like

hinge joints which only allow single-axial rotation However there can

still be slight twisting motions along the other two axes during

movement Thereforeball-in-socketjointsare appropriate for modeling

this relationship After the joints have been con1047297gured the suspension

model of each crane can be manipulated by the individual craneoperator to generate the physical erection movements

7 Development of erection director

A prototype system Erection Director was developed through this

research to ful1047297ll the research goal of simulating the entire erection

cycle securing the objects moving to the destination releasing the

suspension and repositioning To realize the simulations of these

actions we developed a virtual environment that incorporates the

physical principles that describe every detailed motion and collision

reaction [15] during crane operations This is required for simulating

movements along the erection path and also for lifting and locating

suspended objects

71 Overall work 1047298ow of Erection Director

The overall work1047298ow for applying Erection Director to generate

the simulation of erection activities is illustrated in Fig 7 Once the

timer starts during the simulation the physics engine will calculate

the object attitudes according to joints constraints and user

manipulations The engine also checks collision statuses including

rigging objects existed structures and surrounding facilities in the

virtual environment to provide warning messages and reactions to

potential collisions The manipulation and suspension models we

introduced before are controlled separately according to calculations

by following physics principles and user manipulation The calculated

results and user input will modify the attitude of the suspensionmodel and manipulation model at each time-step and the rendering

processes can then generate movements that simulate real physical

actions

72 System architecture

The overall architecture of Erection Director is illustrated in Fig 8

It has a three-layer structure comprising the interface kernel and

external libraries Each layer is composed of major components (also

called functions) which are represented by blocks in the 1047297gure The

arrows pointing between each layer represent direction of commu-

nication In this architecture the interface layer is responsible for

interactions with users and presenting the simulation results Thekernel layer stores and manages the internal data that is relevant to

scene visualization and collision detection The external libraries layer

includes two open source libraries that are used as application

programming interfaces for providing graphics rendering and physics

calculations The application programming interface (API) is the

interface that the program library provides to support requests for

services made by the computer program It is used as the base engine

of the system

The architecture also provides the1047298exibilityfor a developerto derive

and expand upon the three-layer structure The developer can create

additional functions by constructing vertical connections at each layer

without having to consider horizontal relationships between each

component in the same layer Conceptually the architecture allows

developers to expand the system in an effective way

Fig 6 The connection relationships of a dual-crane model (a) illustration (b) joints

con1047297guration




73 User interface layer

The user interface layer allows users to manipulate the window

layout freely and choose which information is displayed The informa-

tion is divided into four windows each for a different purpose 3D

Rendering Control Panel Erection Information and Recording As

shown in Fig 9 the visualization window of the virtual environment

provided by the 3D rendering window presents construction scenarios

and movements of the crane through each time-step (Fig 9(a)) By

manipulating the Control Panel users can operate the crane model to

observe real-time reactions in the system (Fig 9(b)) At the same time

the detailed status of activities that are generated by the operation

can be seen under Erection Information (Fig 9(c)) for example the

position of the crane the angle of the boom loading capacity and so

on Furthermore the system has the ability to save the object infor-

mation at arbitrary time intervals of the simulation and replay them at

a later stage using the Recording function the functions of which are

shown in Fig 9(d)

74 Kernel layer

In the kernel layer there are two tree structures for managing the

display and collision model The tree structure for scene visualization

contains the data of virtual elements in the scene This data such as

the parameters of the light sources the geometrical properties of

models are necessary for constructing the virtual environment

Furthermore the tree structure used to combine all the elements in

the virtual environment provides hierarchical relationships between

each element This kind of tree structure for scene management is

widely used in the 1047297eld of computer graphics With every time-step

the rendering processor traverses every node on the tree and paints

them to refresh the virtual scene

For ef 1047297cient computation the tree structure for collision detection is

a mechanismthatcan be used to reducethe number of pair comparisons

In the Erection Director every elements including crane components

existed structures and surrounding facilities can be considered as

potential collision object But if the collision evaluations of every pair of

objects are executed it will take too much computation power to

in1047298uence theef 1047297ciencyof thesystem In this researchwe used the Quad

Tree structure [18] where each internal node has up to four children to

build the geometrical relationships between every object in the virtual

environment Firstall theobjects in the virtualenvironment areput into

thetreerootThe virtual environment isthen split into quadrantsand the

objects being covered in each quadrant are recorded into the

corresponding child node Second each quadrant is split and the dateis recorded in the same way repeatedly until there are no objects in the

split block that remain to be recorded The layout of the Quad Tree

structure with respect to the current environment is thus built The

procedures for building the Quad Tree structure can be completed while

preparing the data before the simulation After constructing the Quad

Tree we have reduced the number of groups of pairs which have the

possibility of colliding with each other during each time-step of the

simulation The algorithm which traverses the Quad Tree and identi1047297es

the group to be detected is shown in Fig 10

The algorithm CollisionQuadTree takes two parameters as input

data TreeNode and MovingObj The parameter TreeNode represents

the location in the Quad Tree structure and speci1047297es the node being

traversed in the current stage The parameter MovingObj denotes the

movable object which is usually the hook of the crane in the virtualenvironment The procedure of the algorithm is started by initializing

an empty array Group for recording the potential collision pairs and

identifying whether the volume occupied by MovingObj overlaps

with the space represented by TreeNode If an overlap occurs we

traverse recursively along the children of TreeNode until there are no

leaf nodes left to visit hence recording the objects contained in the

current TreeNode into the Group and returning it By collecting all of

theGroups when the traversing process is1047297nished the smallest group

of potential collision pairs is obtained

By using this approach the time required to detect collisions has

been reduced as most of the pairs unlikely to collide with each other

have been1047297ltered out through the traversing process In an ideal case

the number of pairs can be reduced from N to log 4M The variable N

represents the number of objects in the virtual environment and theFig 8 Three-layer structure of Erection Director

Fig 7 Overall work1047298ow of Erection Director




variable M represents N plus the number of over counting objects

which are located on the border between neighboring spaces Since

the number of over counting objects is constant and relatively small

the M can be treated as an equivalent of N As such this approach

makes collision detection more ef 1047297cient when simulating detailed

erection activities especially in a complex construction site layout

containing numerous obstacles The performance of the system using

this approach is discussed in the Performance Evaluation section

75 External libraries layer

In the external libraries layer we used OpenGL [19] a graphical

language library generally used in the area of computer graphics as

the Rendering Engine to communicate with the graphical hardware

and render the virtual environment OpenGL provides various

functions to draw basic elements such as lines triangles and

polygons for on-screen visualization A detailed model and virtual

environment can be displayed by using these functions to generate

the layout information on the tree structure for scene visualization

The library used to form the Physics Engine is the Open Dynamic

Engine (ODE) [20] The ODE follows the principle of constraint-based

rigid body dynamics and provides object-oriented components for

developing the physics environment in the program The built-in ball-

in-socket joint and slider joint which have de1047297ned constraint

properties are assigned to each node of the suspension model to

present relative motions Similarly the geometrical shape and mass

are also assigned to the nodes for collision detection

After building up all these functions in Erection Director as an

integrated platform for displaying the cooperative erection simula-

tion we implemented the visualization of a dual-crane cooperative

erection by following a practical pattern we observed in a real case

The performance evaluation for the real-time issue is also presented

in the following sections

8 A demonstration of the visualization of cooperative erections

To validate the feasibility of Erection Director we demonstrated a

simulation In order to realistically simulate the cooperative activity a

practical pattern for a dual-crane cooperative erection needs be

followed In the common scenario of dual-crane cooperative erection

the process is usually led by one of the cranes and cooperation only

occurs at the securing step We use the activity of lifting a large-scale

petroleum tank as an example Fig 11 illustrates the common process

of two cranes cooperatively lifting a petroleum tank Firstly the

rigging equipment of both cranes are tied to each side of the tank

separately (Fig 11(a)) The main crane responsible for lifting the tank

Fig 9 Overview of the interface (a) visualization window (b) control panel (c) erection information (d) recording window

Fig 10 Algorithm for traversing the Quad Tree and targeting of the minimum pair comparisons to perform the collision detection




from horizontal to vertical starts to raise the top of the tank by

hoisting its cable The tail crane responsible for keeping the tank

stable and minimizing swinging follows the movement of the main

crane and raises the bottom of the tank until it is at an appropriate

height away from the ground (Fig 11(b)) The main crane then

continues the lifting action while the tail crane steadily moves closer

to the main crane (Fig 11(c)) The tank then gradually becomes

vertical during this step Finally the connections of the tail crane are

disconnected when the tank is completely vertical (Fig 11(d)) The

main crane then completes the remaining movements of the erection

cycle

By using the con1047297guration mentioned in the dual-crane modeling

sectionthe movementsduring theerectioncan be fully simulated and

the appropriate motions can be created through manipulation of thevirtual crane The developed method is also feasible for mapping the

usual patterns followed by operators to the virtual construction site

These patterns can be induced as the most ef 1047297cient ways of operating

a crane where cables sway and vibrations are minimized These are

relatively safe motions that prevent dangerous situations such as

collisions or reactions of the suspension system to large amounts of

acceleration

When thesesteps are simulatedin ErectionDirectorthe visualization

results in a smooth animation sequence The snapshots shown in Fig 12

aresequential Theseare ordered from left to right to present thedetailed

lifting process of a dual-cranecooperative erectionThe time representa-

tions marked on each image highlight the key moments during erection

and show the time duration between each snapshot These time

durations are not equal as the simulation is generated from manual

manipulations and theoperation of thecraneis not uniform throughout

Therefore we only present the relatively signi1047297cant time steps in this

1047297gure Also the times have been scaled and are not exact values

At the beginning of the sequence binding processes are executed

to tie the suspension cables to the two spreader-bars and the tank(from Time 000 to Time 020) The main crane located on the right

side of the picture starts to lift the tank and the tail crane located on

the other side follows the movement until the appropriate height is

reached (from Time 020 to Time 038) The lifting speed has to be

slow enough to keep the movements synchronized After that the

Fig 11 Illustrations of the lifting process of a dual-crane cooperative erection (a) Tying (b) Lifting cooperatively (c) Gradually erecting the tank (d) Unsecure the connections

from the tail crane

Fig 12 Snapshots of the cooperative lifting of a large-scale petroleum tank using two cranes




main crane continues with the lifting movement while the tail crane

moves forward to make the tank vertical (from Time 038 to Time

104) The rotations due to gravity can be seen from the connections

between the tank and the spreader-bars After the erection process is

complete the objective of the dual-crane cooperative erection has

been attained

9 Performance evaluation

To prove that physics-based motions of dual-crane cooperation can

be simulated and visualized in real-time we created three virtual

scenarios with different levels of rendering complexity for performing

the cooperative erection activity in three different scenarios As shown

in Fig 13 the scenes are the construction site of steel-frame buildings

with different numbers of beam andcolumn objects They arecomposed

of 840 1937 and 2682 elements to be rendered The three scenarios

represent alternative ways for crane manipulators to complete the

cooperative erection tasks We implemented the cooperative erection

activity in these tasks on the Erection Director system and evaluate the

performance by recording the average and lowest value of the frames

per second (FPS) during the simulations The FPS value represents the

capacity of a 3D-graphics system in rendering a virtualscene it denotes

the numberof framesthat can be rendered per second We recorded the

average value observed throughout theentire simulation andthe lowest

value observed during simulation The results table is shown in Table 2

We used a computer with an Intel Pentium M 740 CPU and 1G RAM to

execute these performance tests

The result shows that the simulation of erection activities can be

consideredsmoothand real-time visualization during the entire process

of the construction scenario is feasible Typically an animation is

observed to be continuous when thevalue of the FPS is greater than 30

and delay cannot be observed when the value of the FPS is greater than

60 According to the result in Table 2 the simulations were acceptable

for the human eye when the erection is performed on Scenario 1 and

Scenario 2 The worst case Scenario 3 had an average FPS value of 55

but still greater than the requirement of 30

In current stage of our research we only focus on the usability of the

simulation method but not address its effectiveness We actually invited

many industrial partners to reviewthe work Many of them show positive

feedbacks in our research results And currently the system is integrating

to an engineering consulting company for construction simulation

High-leveled project managers were potential users for our system

One of the project managers commented that the simulations could be

very useful during the bidding process Because the installation of the

equipmentis themajorconcernsin a plant construction theowners will

appreciate a detailed simulation especially with physics feedbacks Site

planners also believe the simulations can be useful They can replace

their current paper-based erection plan usually cumbersome and hard

to review with strong engineering background

In thenear future we planto perform morequantitative evaluations

This including comparison between guided operations based on the

simulations and transitional operation ways will be provided We also

planto improve thesystem (ErectionDirector) to make theresults more

practical

10 Conclusions and future works

The approach and prototype system developed in this research

allows for the generation and visualization of a physics-basedsimulation

Fig 13 The orthographic view of the construction scenes (a) Scenario 1 (b) Scenario 2 and (c) Scenario 3

Table 2

The performance of the Erection Director system

Scenario Number of structural

elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21

The performance has reached the rendering limitation of the system




of cooperative erection activities The combination of the manipulation

and suspension model for modeling a numerical crane model can be

used to derive various construction scenarios to simulate actual

situations The simulations in this research provide detailed information

on the motions of cooperative erection activities by following the

principleof kinematics and dynamics Fromthe performance evaluation

realistic simulations can be performed in real time The prototype

system Erection Director was developed to plan erection scenarios and

provides physical actions in an instructive way and rigging informationto assist users in evaluating feasibility and rationality before actual

construction It will be a clear and simple way for engineers and non-

engineers alike to identify potentially dangerous situations due to

irregular movements or collisions Planners may then generate several

alternative plans or modify existing plans to produce different

simulations A preferred ef 1047297cient solution based on the results of the

simulations can then be implemented

In the future the evaluations for performing the real cooperative

crane operations based on the simulationresults will be promoted And

it will be able to examine the physics-based simulation in practical

perspective Furthermore the boarder applications of the system could

be extended to many purposes For example the simulation methods

can be used to review of erection plan Because precise simulations are

available the designers can ldquoseerdquo the construction progress during

designphase Many unsafecrane movements canbe avoidedduringthe

review process Another example is that the physics-based simulation

can become a good reference in a bidding process Because all the

erection details can simulated the owners can have more con1047297dence to

adopt the proposed solution In addition our work can also be extended

for training purpose by designing appropriate learning lessons and

integrating them into the virtual environmentAlso it canbe assisted by

other equipments such as HMD immersivescreen setups and so on to

improve the training performance

Acknowledgments

This work was supported by the National Science Council of

Taiwan We thank RUENTEX Corporation for providing the construc-

tion information of the practice erection patterns

References

[1] Hornaday W C Haas C T and OConnor J T Computer-aided planning for heavylifts Journal of Construction Engineering and Management 119(3) (1993)pp 498ndash515

[2] Lin K L and Haas C T Multiple heavy lifts optimization Journal of ConstructionEngineering and Management 122(4) (1996) pp 354ndash362

[3] Kamat V R and Martinez J C Visualizing simulated construction operations in3D Journal of Computing in Civil Engineering 15(4) (2001) pp 329ndash337

[4] Kamat V R and Martinez J C Ef 1047297cient Interference Detection in 3D Animationsof Simulated Construction Operations Proceedings of the 2005 International

Conference on Computing in Civil Engineering American Society of Civil EngineersReston Virginia

[5] Sivakumar P L Varghese K and Babu N R Automated path planning of cooperative crane lifts using heuristic search Journal of Computing in CivilEngineering 17(3) (2003) pp 197ndash207

[6] Ali M S Babu N R and Varghese K Collision free path planning of cooperativecrane manipulators using genetic algorithm Journal of Computing in CivilEngineering 19(2) (2005) pp 182ndash193

[7] Kamat V R and Martinez J C Dynamic 3D visualization of articulatedconstruction equipment Journal of Computing in Civil Engineering 19(4)(2005) pp 356ndash368

[8] Kang S C Computer Planning and simulation of construction erection processesusing single or multiple cranes PhD Dissertation Department of Civil andEnvironmental Engineering University of Stanford California 2005

[9] Bicalho A and Feltman S MAXScript and the SDK for 3D Studio MAX Sybex[10] Derakhshani D Introducing Maya 6 3D for Beginners Sybex[11] K Erleben J Sporring K Henriksen H Dohlmann Physics-Based Animation

Charles River Media Boston 2005[12] Reeves W T Particle Systems mdash a Technique for Modeling a Class of Fuzzy

Objects ACM Transactions on Graphics (TOG) 2(2) (1983) pp 91ndash108[13] Ju F and Choo Y S Dynamic Analysis of Tower Cranes Journal of Engineering

Mechanics 131(1) (2005) pp 88ndash96[14] Denavit J and Hartenberg R S A kinematic notation for lower-pair mechanism

based on matrices Journal of Applied Mechanics (1955) pp 215ndash221[15] SC Kang HL Chi E Miranda Three-dimensional Simulation and Visualization of

Crane Assisted Construction Erection Processes Journal of Computing in CivilEngineering 23 (6) (2009) 363ndash371

[16] KG Murty Linear Complementarity Linear and Nonlinear Programming Helderman-Verlag 1988 This book is now available for download from httpioeenginumichedupeoplefacbooksmurtylinear_complementarity_webbook

[17] H Goldstein CP Poole CPJ Poole JL Safko Classical Mechanics3 rd EditionPrentice Hall 2002

[18] Finkel R and Bentley J L QuadTrees A data structure for retrieval on compositekeys Acta Informatica 4(1) (1974) pp 1ndash9

[19] Shreiner D Woo M Davis T and Neider J OpenGL Programming Guide TheOf 1047297cial Guide to Learning OpenGL Version 14 Fourth Edition Addison-WesleyProfessional 2003

[20] R Smith OpenDynamic Engine 2006 Retrieved May 23 2006 from httpodeorg




2 Related work

Many previous studies are aimed at realizing the simulation of

erection activities while considering the safety loading range collision

avoidance and transportation attitude [34] In the 1047297eld of training

simulator development SimLog1 and CMLabs Corporation2 provide

advanced devices for crane operation training These are assistant

tools that help novice crane operators practice their skills using

several different training scenarios each customized to prepareoperators to sit for a particular certi1047297cation examination The

movements of the virtual crane are directed by user manipulation

and the reactions re1047298ect actual physical behaviors

Many construction consulting 1047297rms have developed adds-on or

external modules for existing visualization tools to simulate cooper-

ative erections An engineering consulting corporation Chung-Ting

(CTCI) developedan add-on for the AutoCAD3 system which provides

a visualization interface for erection simulations A product from JGC

Corporation4 also provides a virtual environment with various

viewing interfaces for visualizing the planning movements Both of

these products can automatically generate animations of rigging paths

for erection activities

Some related works can also be found in academia Researchers

usually use automated approaches that integrate modern search

processes [56] or heuristic technologies from the 1047297eld of numerical

kinematics [7] and motion planning [8] to generate the movements of

cooperative virtual cranes automatically Users need to set up the

initial conditions of a construction jobsite and the software deter-

mines the most ef 1047297cient yet safe and collision-free paths for use in

simulating the erection activities

In popular software such as 3D Studio Max [9] and Maya [10]

semi-automation is used to produce animation Users set key frames

so that the frames in-between can be interpolated Such technology is

also feasible for planning the movements of erection processes

These approaches and technologies are capable of simulating

different aspects of erection activities but thereshould be appropriate

ways of integrating these methods to negotiate all of the three major

issues mentioned in Introduction section Therefore due to the

complexity of the combinations of the cranes motions and issues of realism the challenge in the simulation of cooperative erection is to

develop a methodology for generating accurate feasible and

collision-free motion paths that represent the complex interactions

between cooperating cranes and to perform visualizations in real-

time

3 Research goals

This research aims at utilizing physics-based animation methods

which are widely used in game physics and training simulators to

generate detailed cooperative erection activities in a virtual environ-

ment Unlike game environment which focus more on the visual

stimulation instead of precision Our work on the contrary

emphasizes the precision of the simulation By using these methodsand real construction cases it should be more 1047298exible to build up the

simulation scenariosand at themean time to show them at acceptable

frame rate per second The simulation is not just for training purpose

but focuses on the evaluations of erection plans Work-items need to

be simulated as accurately as possible in order to 1047297nd potential

problems before physical operations commence In order to retain

1047298exibility and generality in solving these problems a prototype

system for visualizing the simulations has been developed and

evaluated to perform the simulations

4 Existing methods for generating physics-based simulation

To simulate high-risk erection activities the integration of physics-based simulation methods plays a signi1047297cant role in this research

Physics-based simulation methods utilize various theoretical laws of

physics and a variety of mathematics combined they describe a

mathematical model of the real world

Existing methods for generating physics-based simulations can be

generally divided into two categories kinematic and dynamic to

ful1047297ll theneedsof thekinematic anddynamic simulation respectively

Table 1 presents the classi1047297cation of physics-based simulation

methods According to the modeling directions is the two categories

can be further divided into four groups forward kinematics (FK)

inverse kinematics (IK) forward dynamics (FD) and inverse dynamics

(ID)

Kinematics is the study of an objects motion without considering

its mass or the forces acting on it By describing the properties of

geometry and the relations of coordinates the movements of an

object can be formulated in a virtual environment Differing from the

principle of kinematics dynamics takes mass and forces into

consideration and generates more realistic and accurate behaviors

during simulation

Forward modeling means that the position and orientation of

every part of the articulated-object can be manipulated and is known

by the modeler When the next time-step of the animation is

generated there exists only one solution to achieve the resulting

motion from calculation and accumulation of the status of each part of

the object In contrast inverse modeling means that the resultant

position and orientation are known However there is more than one

solution (or sometimes no solution) for each articulated part of the

object to achieve the goal motion

The methods of the inverse kinematics and dynamics group of Table 1 are heuristic and usually used to 1047297nd the feasible paths or

movements by assigning the objective position and orientation They

can be useful in generating animation for automatic construction

planning Kamat and Martinez [7] used the cyclic coordinate descent

method to automatically simulate the operations of articulated

construction equipment

In the forward kinematics and dynamics group of Table 1 key frame

animation is a semi-automatic method where users 1047297rst set up the key

positions and orientations(frames) The softwares built-in function for

key-frame animation then automatically interpolates the continuous

movements between each frame Theparticle systemmethod [12] used

to simulate the movement of points of mass is the base theorem for

deriving rigid body dynamics This means that it does not completely

ful1047297ll the use of rigid body simulation The 1047297nite element method [13]can be used to analyze 1047297ne movements such as vibrations and

1 Simlog Mobile Crane Personal Simulator Retrieved June 25 2007 from http

wwwsimlogcompersonal-cranehtml2 CMLabs Vortex Training Simulators Retrieved April 2 2007 from httpwww

vortexsimcom3 Autodesk AutoCAD Retrieved June 25 2007 from httpusaautodeskcomadsk

servletindexsiteID=123112ampid=27042784 JGC 4D CAD System Retrieved June 25 2007 from httpwwwjgccojpen

03srvs07const02e_const4d_cadhtml

Table 1

The classi1047297cation of physics-based simulation methods (Modi1047297ed from [11])

Forward

kinematics (FK)

Inverse

kinematics (IK)

Forward

dynamics (FD)

Inverse

dynamics (ID)

Closed-form

solutions

Cyclic coordinate

descent

Constraint-based

simulation

Recursive newton

euler method

Key-frame animation

(interpolation)

Jacobian method Particle systems Optimization

problems

Finite element

method






































































iminus1T i = frac12




0 0 0 1

eth1THORN














0T 4 =

0T

11 T

22 T

33 T 4 =


sθ3 0 c θ3 c θ3d4 + d1 + Z 00 0 0 1

2664

3775 eth2THORN


sine function



0

P =

0

T

4

4 P eth3THORN







as below






52 Suspension model



















T eth5THORN








h i x

= 0 eth6THORN


minus P j + R jP

janc

h i y

= 0 eth7THORN


minus P j + R jP

janc

h i z

= 0 eth8THORN






= 0 eth9THORN












condition




































rigging object

















suspended objects














actions















of the system








con1047297guration




















shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References


























































































iminus1T i = frac12




0 0 0 1

eth1THORN














0T 4 =

0T

11 T

22 T

33 T 4 =


sθ3 0 c θ3 c θ3d4 + d1 + Z 00 0 0 1

2664

3775 eth2THORN


sine function



0

P =

0

T

4

4 P eth3THORN







as below






52 Suspension model



















T eth5THORN








h i x

= 0 eth6THORN


minus P j + R jP

janc

h i y

= 0 eth7THORN


minus P j + R jP

janc

h i z

= 0 eth8THORN






= 0 eth9THORN












condition




































rigging object

















suspended objects














actions















of the system








con1047297guration




















shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References


























as below






52 Suspension model



















T eth5THORN








h i x

= 0 eth6THORN


minus P j + R jP

janc

h i y

= 0 eth7THORN


minus P j + R jP

janc

h i z

= 0 eth8THORN






= 0 eth9THORN












condition




































rigging object

















suspended objects














actions















of the system








con1047297guration




















shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References



























T eth5THORN








h i x

= 0 eth6THORN


minus P j + R jP

janc

h i y

= 0 eth7THORN


minus P j + R jP

janc

h i z

= 0 eth8THORN






= 0 eth9THORN












condition




































rigging object

















suspended objects














actions















of the system








con1047297guration




















shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References
























































rigging object

















suspended objects














actions















of the system








con1047297guration




















shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References








































shown in Fig 9(d)

74 Kernel layer
















































































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References

















































































cycle









acceleration


















from the tail crane










been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References





























been attained














































practical





Table 2



elements

Number of rendering

triangles

Average

FPS

Lowest

FPS

1 840 33280 64 45

2 1937 73388 64 45

3 2682 103632 55 21




































Acknowledgments




References























































Acknowledgments




References






















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