(201203)a fast path planning method for single and dual crane erections

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A fast path planning method for single and dual crane erections

Yu-Cheng Chang, Wei-Han Hung, Shih-Chung Kang

Department of Civil Engineering, National Taiwan University, Taiwan

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

Article history:

Accepted 27 November 2011

Available online 2 January 2012

Keywords:

Crane

Erection

Dual crane

Path planning

Robotic

This research aims to develop a method for planning the erection path automatically and efciently. The pro-

posed method is comprised of two steps. The rst step is to convert the scene of the crane erection into a con-

guration space, in which the crane's load capacity and the obstacles in the environment have been included.

The second step is to

nd a collision-free path in the con

guration space by using the probabilistic road map(PRM) method. Three tests were conducted to validate the action, crane placproposed method in this re-

search. The results show that the proposed method is efcient, and can generate effective erection paths

for operating in near real-time scenarios. The method is appropriate for both single and dual crane erection,

and can help engineers plan more easily, and verify erection-planning decisions such as crane seleement, and

logistcs.

2011 Elsevier B.V. All rights reserved.

1. Introduction

In addition to the usual single crane erection, dual-crane coopera-

tive erection has become more common in modern construction pro-

jects in recent years. Particularly, in industrial construction, it is often

necessary to transport large facilities; this requires cranes with a ca-pacity of 5001000 t. Although available large cranes can move

weights of up to 1300 t, their operation may be restricted by the lim-

ited space on site, while the construction costs will increase if a larger

and more expensive crane is rented. A useful, often used alternative is

to utilize two less expensive cranes to perform a cooperative crane

erection[10,17]. However, in the cooperative dual crane erection pro-

cess, the two cranes need to work together to maintain the equilibri-

um of heavy loads. The complexity of cooperative dual crane erection

is far higher than that of single crane operation, and this can lead to

high risk situations during construction [26]. If a feasible and safer

erection path can be pre-planned for cooperative dual crane erection,

then such high risk situations can be reduced to a minimum; further

justifying the importance of erection path planning.

Erection path planning is a complex topic, and there are three major

difculties involved.Firstly, theload of thecraneshould be withinits lift-

ing capacity during the erection process; the upper limit of the capacity

varies with the angle of the boom, which makes planning more difcult.

Secondly, collisions among the crane, the lifting object, and any obstacle

should be avoided. This makes the planning difcult when there are nu-

merous obstacles on site, and the volume of the lifting object is large.

Thirdly, thecable of thecrane must be kept vertical plumbed duringa co-

operative dual crane erection in order to avoid increased tension from

when the cable is inclined, as increased tension would increase the

load on the crane.

Erection path planning in the past was limited by computational

efciency, and was applied only to path planning for moving in a sim-

ple environment [19]or motion planning with low degrees of free-

dom [15]. However, due to the rapid development in computingtechnology, computational performance has improved, and path

planning, which was not possible in the past is becoming feasible

now. Path planning includes planning for motions of high degrees of

freedom[12], instantaneous avoidance of obstacles[13], and cooper-

ative dual crane erection[22].

Due to advances in the path planning method, many studies have

focused on erection path planning. Computers are used to create 3D

models of construction sites and cranes; check collision in a virtual

construction site; and estimate the lifting capacity of the crane.

Thus, a feasible collision free erection path can be planned[25,2,11].

The method proposed in Refs. [11] and [25] effectively planned the

erection path, but it can only be used for single crane operations.

Wang et al. [31] proposed a sampling-based method for real-time

motion planning of cranes in order to improve construction safety.

Zhang et al. [28] utilized the Ant Colony algorithm to nd a

collision-free-path for a mobile crane with consideration for both ef-

ciency and safety. These studies have demonstrated the potential

and value of utilizing path-planning technique for single crane erec-

tion. The method mentioned in Ref. [2] is applicable to cooperative

dual crane erection planning. It is computationally the most effective

method at present for cooperative dual crane erection planning, but it

still takes between 3 and 12 min to calculate each plan.

Therefore, this research aims at developing a near real-time and

automated method for erection path planning. The method can be ap-

plied for both single crane and cooperative dual crane erection oper-

ations, and can be used to nd the most suitable erection path in the

Automation in Construction 22 (2012) 468480

Corresponding author.

E-mail address:[email protected](S.-C. Kang).

0926-5805/$ see front matter 2011 Elsevier B.V. All rights reserved.

doi:10.1016/j.autcon.2011.11.006

Contents lists available at SciVerse 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 e v i e r . c o m / l o c a t e / a u t c o n
http://dx.doi.org/10.1016/j.autcon.2011.11.006http://dx.doi.org/10.1016/j.autcon.2011.11.006http://dx.doi.org/10.1016/j.autcon.2011.11.006mailto:[email protected]://dx.doi.org/10.1016/j.autcon.2011.11.006http://www.sciencedirect.com/science/journal/09265805http://www.sciencedirect.com/science/journal/09265805http://dx.doi.org/10.1016/j.autcon.2011.11.006mailto:[email protected]://dx.doi.org/10.1016/j.autcon.2011.11.006


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given environment. This method allows crane operators to complete

the job with higher efciency, thereby increasing the value of auto-

mation in the erection path planning process.

2. Method for path planning

In the study of path panning, the most commonly used methods

are Potential Field, Cell Decomposition, Genetic Algorithm, VisibilityGraph, and Probabilistic Roadmap.

In the Potential Field method[9], a force eld is constructed around

the workspace of the robot, and its planned path to be planned. Attrac-

tive and repulsive forces exist in this force eld.The nal position of the

load is the center of the attractive forces, and the obstacles in space are

the center of the repulsive forces. By using this method, the robot can

move to the targeted position. Although it is easy to nd the path

using this method and it is also applicable to paths with narrow spaces,

a disadvantage is that this method can fall into a local-optimum solu-

tion. Applications of the Potential Field method include path planning

of multiple robots [27], danger avoidance of robots [13], and path plan-

ning for high-speed vehicles[6].

The Cell Decomposition method[4]divides the space into several

subspaces, and nds the boundary conditions among the subspaces to

obtain a connectivity map. The method then looks for subspaces and

decides the order in which it will proceed from the starting point to

the goal. Themachine then follows this order to changefrom one sub-

space to the next in order to arrive safely at the destination. For the

solution of non-polygonal obstacles and 3D space problems, Morse

Decomposition was proposed [1]. Another method is Visibility-

Based Decomposition[8]; it is designed especially for solving the pur-

suitevasion problem.

The Genetic Algorithm method[7,21]is mainly based on Darwin's

theory of evolution; based on the law of nature i.e. the principle of

the survival of the ttest. The method considers the path of the gene

and uses the biological procedure of evolution to obtain a solution for

an optimal path. The algorithm comprises three steps: reproduction,

crossover, and mutation. The good genes can be retained by reproduc-

tion, which is followed by crossover and probabilistic mutation. Thesethree steps are repeated until the termination condition is satised.

Thedisadvantages of this method include the large volume of computa-

tion required, the fact that the termination condition may be satised

before an optimal solution is found. However, it is easier to apply the

Genetic Algorithm method to solve other optimization problems than

for path planning. Examples of such problems are circuit design [29],

control system design[16], and time-history design.

The Visibility Graph method[24,18]considers the vertex of the

obstacle as a path node, and considers all possible paths between

the starting and end point. In other words, it considers all possible

paths that do not go through the obstacles, and connects the starting

point, the nodes, and the end point to nd the shortest path. To avoid

the problem of having too many nodes, once an obstacle is not on the

path with the shortest length, it is excluded from consideration. How-ever, a drawback of this method is that it is hard to decide whether to

use the vertex of that obstacle as a node if the path with shortest

length was not calculated. In addition, this method cannot work

with smooth obstacles.

Probabilistic Roadmap Methods (PRM) [12,5] are a widely used set

of methods for robotic action design and path design. The main ap-

proach is to sample within the space in order to make a node, and

to connect all nodes without obstacles in between in order to create

the path; thus producing a roadmap. Then, from the roadmap, we

must nd all possible paths from the starting point to the end point,

and the shortest path is then selected as the path for the robot. If

such a path does not exist, more nodes are sampled until a path can

be identied. PRM has been proven to be relatively complete [14],

as long as the probability ofnding a path between the starting and

end point is not nil. If the computational time is not limited, PRM

can certainly be used to nd a feasible path.

The PRM method is based on probability, where the basic process

is to repeatedly guess the collision-free points and try to link them

into a collision-free path. The computation time for PRM depends

on the number of path nodes. The fewer nodes there are, the shorter

is the computation time. However, the probability ofnd a feasible

path is also lower, and vice-versa, having more nodes leads to longer

computation time and a higher probability of

nding a feasible path.The PRM method is suitable for erection path planning. Erection

path planning is different from the maze problem of robotics, which

involves guring out where the corner is and how to navigate

through narrow paths. In construction practice, we usually maximize

the working space for cranes. This means PRM can compute (or

guess) a collision-free path in a very short amount of time, and only

a few nodes are sufcient to plan an erection path. For a more compli-

cated erection operation, more nodes can be used to nd a feasible

path. Furthermore, regarding efciency, a crane operator may be

more interested in obtaining a feasible path quickly rather an optimal

path slowly. This is consistent with the main concept of the PRM

method. Therefore, this research makes use of the PRM method for

erection path planning, making it possible to nd a feasible erection

path in near real-time automatically.

3. Erection path planning for single crane erection

In this sectionwe will introduce howa CongurationSpace (C-Space)

is builtfor thesingle crane erection procedure, andnding a collision free

path from the C-space as the erection path for single crane operations.

3.1. Assumptions

The method for erection path planning presented in this research

is valid only under the following assumptions:

1. For the calculation of path planning, all the obstacles are assumed

to be static during the erection operation, except for the crane and

the lifting object.2. There is no change in the location where the crane is set up during

the erection operation. In almost all erection operations, the crane

is set up at a xed location and the crane cannot move during the

erection operation.

3. The sway of the lifting object during the erection process is

accounted for using a larger boundary for the lifting object

model. We can measure the possible sway range and set an outer

boundary. Then we use the boundary to computer the collision-

free path. This avoids virtually all possible collisions due to the

sway. Crane operators are asked to minimize the cable sway to re-

duce risks. They usually stop moving the lifting object when it is

swinging until the object becomes static. However, the problem

of whether the dimensions of the lifting object model are enough

is beyond the scope of this research.

3.2. Procedure of erection path planning

For the erection path planning method presented here, theow is

divided into three parts as shown in Fig. 1. Before planning an erec-

tion path, the user must provide information about the selected

crane including its lifting capacity and initial location. A C-space is

then constructed for the selected crane, and path planning is then

conducted in the C-space. Finally, operation planning is performed

for the hoisting, and a collision free and feasible erection path is

planned. If a feasible erection path cannot be found, users then can al-

ternate the crane with other cranesthat have better capacity or adjust

the initial location of the selected crane until they can nd a feasible

erection path.

469Y.-C. Chang et al. / Automation in Construction 22 (2012) 468480


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3.3. Building the C-space for single crane

We consider the crane's base-swing angle and its boom-luffangle as coordinates in order to construct a 2D C-space for thecrane. Construction of the C-space comprises three steps: rst, the

range of the space has to be dened; then the C-obstacle region is de-

ned; andnally, we record the limits of hoist height and the heights

of obstacles for all collision free congurations in the space.

To dene the region of C-space, we need to rstnd the extent of

possible changes in the boom-luff angle. According to crane's tableof loading capabilities and considering the weight Wof the lifting ob-

ject, the maximum rotation anglemax(W) and the minimum rota-tion angle min(W) can be identied; and thus the range of the C-space coordinates can be determined. For safety considerations, the

load in the boom hold not exceedS%of the upper safety limit during

the erection operation, the weight of the object is considered as W/S,

and the table of loading capabilities should be used tond max(W/S)andmin(W/S). in the planning process.

After the C-space is dened, we investigate the collision problem be-

tween the crane, thelifted object, and the obstaclesfor all congurations

[,] to establish a C-obstacle region. We propose the cObstacleCheckmethod to check whether the conguration is a C-obstacle. This method

determines whether there is a collisionbetween thecrane andthe obsta-cle when base-swing is and boom-luff angle is . If there is a collision,then the conguration [,] is withinthe C-obstacle region. If there is nocollision, then proceed to the getHoistHeightRange method for calcula-

tion, which separately examines the collisions between the lifting object

and the crane, and between the lifting object and obstacles. From this,

wend the range of hoist heighthminandhmax. When the hoist height

increases (with incrementh) and reaches a state where thelifting ob-ject and the boom are not in contact with each other, the hoist height is

hmin. When the hoist height increases (byh) and reaches a state wherethe lifting object collides with any one of the three (Building, oor, or

the body of the crane), the hoist height at the time is hmax, as shown

inFig. 2. Ifhminhmax, it indicates that the obstacle is too high and the

lifting object cannot pass through, or that the luff angle is too large

and the lifting object is too close to the crane. In this case, the congu-ration [,] is within the C-obstacle region. Whenhminbhmax, the con-guration [,] is a collision free conguration. The cObstacleCheckand getHoistHeightRange algorithm are shown in Tables 1 and 2,

respectively.

After dening the C-obstacle region, the values for hoist height re-

gionhmin,hmax, and the heightshobof obstacles are recorded. This in-

formation is subsequently used for the planning of the erection path.

After completing the above steps, a 2D C-space can be constructed

for the crane, as shown inFig. 3.

3.4. Path planning for single crane

In this study, we perform path planning by using the PRM method

of path planning. First, we randomly sample a sufcient amount of

nodes in C-space, and then connect all possible nodes to form differ-

ent paths. Finally, we select the optimal path from all possible paths

connecting the starting point to the end point, which forms the erec-

tion path for the crane.

To calculate the optimal path from found paths, we use the varia-

tion in angle of the crane base-swing, the variation in angle of the

crane boom-luff, and variation in length of the hoist height as the

basis for evaluation, and for developing a Pcost function to calculate

the costs for the erection path In, as shown in Eq.(1). The reason

we do not use the length of the path for evaluation is that the position

of the lifting object is the end-point result of the three degrees of free-

dom (base-swing angle, boom-luff angle, and the hoist height). The

shortest path (e.g. a straight path in the 3-dimension space) is usually

more difcult to follow for the crane operators because they have to

simultaneously control these three degrees of freedom with changing

velocities. For a human being, it is easier, safer, and more stable to

control only one or two degrees of freedom with the same velocity.

Therefore, we use the variation of these three degrees of freedom

for the cost measurement.Fig. 4shows an example of cost estimation

by the variation of base-swing angle and boom-luff angle.

In order to have the same evaluation criterion for angle (base-

swing angle and boom-luff angle) and length (hoist height), the de-

veloped cost function uses the time of operation to reach the vibra-tion as shown in Eq. (2), where t represents the total time of

operation needed for the total variation of base-swing angle ,trep-resents the total time of operation needed for the total variation of

boom-luff angle, andthrepresents the total time of operation neededfor the variation of hoist height Hob _ max. The reason we use Hob _ max in-

stead ofi= 1n1|hi| will be discussed in the next section. Therefore,

Eq.(2)can be transformed into Eq.(3), whereis the angular speedof the base-swing,is the angular speed of the boom-luff, and Vhisthe speed of hoisting. Then we can use Eq.(3)as the cost function to

Fig. 1.Flow chart for crane path planning.

Fig. 2.The range of hoist height within hminandhmax.

470 Y.-C. Chang et al. / Automation in Construction 22 (2012) 468480


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measure the path. The larger the calculated result of the Pcostfunction,

the longer it will take to execute the path, and the harder it will be tooperate the crane. The path with the smallest calculated result of the

Pcostfunction is the optimal path.

However in practice, sometimes we may multiply the time cost of

each degree-of-freedom by a weight coefcient (W,W, andWh) be-

fore summing together as shown in Eq.(4). These coefcients can sig-

nicantly inuence the erection path chosen. For example if we lower

the weight of the crane base-swing angle, the method tends to nd a

solution that needs fewer operations on the other parts. The erection

path found then is easier and faster to execute for crane operators.

However, it may increase the working area of the crane and therefore

raise the risk when lifting, making it unsuitable for a narrow working

space. Conversely, if we lower the weight of hoist height variation,

the erection path may tend to cross the obstacle from the top. Howev-

er the retract/release action of the cable costs more time and make

the erection more inefcient. Therefore the cost function can be de-

ned as Eq.(1), where theWrepresents1, theWrepresents

1, andWh representsa Vh

1.

Pcost In W

n1

i1 jij W

n1

i1 jij WhHobmax 1

Pcost In ttth 2

Pcost In 1

n1i1 jij

1

n1i1 jij Vh

1Hobmax 3

Pcost In 1

n1i1 jij

1

n1i1 jij

Vh1

Hobmax 4

In Erection path represented by connecting n node congura-

tions where the 1-st node is the starting conguration and

the n-th node is the end conguration;

i Variation in angle of the crane base-swing angle duringthe path section connecting the i-th node to the (i +1)-th

node in degrees;

i Variation in angle of the crane boom-luff angleduring thepath section connecting the i-th node to the (i + 1)-th node

in degrees;

n Number of nodes for the path;

Hob _ max The highest obstacle among congurations along the path; in

meters (m). Fig. 5 shows an example of a path with four

nodes, and whereHob _ maxis the maximum value of the Hobinthe Fig. 5. Since the2D C-spacemethod in this investigation

does not include a parameter for the hoist height, we use the

maximum height of obstacle that the lifting object needs to

move past as a rough estimate for the change in hoist height.

Angular speed of base-swing, in (degrees/s). Angular speed of boom-luff, in (degrees/s).Vh Speed of hoisting, in (meter/s).

Theweight of thecrane base-swing angle changein the costestimation for the path.

The weight of the crane boom-luff angle change in the costestimation for the path.

The weight of the hoist height change in the cost estimationfor the path.

W The factor of the crane base-swing change in the cost esti-

mation for the path.

W The factor of the crane boom-luff change in the cost estima-

tion for the path.

Wh The factor of hoist height change in the cost estimation for

the path.

Table 1

Algorithm ofcObstacleCheck.

AlgorithmcObstacleCheck(,): determine theconguration(,) is C-obstacle or not: base-swing angle.: boom-luff angle.

IF obstacle collided withboom(,) or base() THEN

theconguration(,) is C-obstacle

ELSE

getHoistHeightRange(,)

IFhminhmaxTHEN

theconguration(,) is C-obstacleELSE theconguration(,) is not C-obstacle

Table 2

Algorithm ofgetHoistHeightRange.

AlgorithmgetHoistHeightRange(,): nd hoist height range hminandhmax: base-swing angle.: boom-luff angle.

h: hoist height

h: hoist height increase in each interaction

hmin: minimal hoist height for (,)

hmax: maximal hoist height for (,)

LETh =0

REPEAT:IFhminnot found THEN

IFobject(,) does not collided with boom(,) THENhmin =h

ELSE

h =h +h

ELSE

IFobject(,) collided with obstacle, ground, or base() THEN

hmax =h

ELSE

h =h +h

UNTILhmaxfound

RETURN hminand hmax

Fig. 3.Layout of a crane's 2D C-space.

Fig. 4.Cost estimation of a feasible path.



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3.5. Hoisting planning for single crane

Since the 2D crane C-space in this investigation does not include

hoist height as a coordinate in space, the obtained path does not con-

tain information regarding the hoisting operation. Thus, we need to

perform hoisting planning on the path obtained in Section 3.4.Initially, we may take the maximum hoist height hmax of all cong-

urations along the path as the hoisting parameter. However, this

leads to unnecessary hoist operation during the erection operation,

as can be seen from the solid black line inFig. 6. To avoid this situa-

tion, an additional optimization process is required on the hoisting

parameter, starting from the initial conguration and before the

cable elongation reaches the minimum value ofhmax. If the present

hoist height is greater than hmax, then we reduce the elongation to

hmax; and if the hoist height is less than hmax, then the hoist height re-

mains unchanged. After the hoist height has become the smallest

value ofhmax, the hoist height is not adjusted until the goal is reached

and the lifting object is set down. The resulting hoisting parameter

after optimization is shown inFig. 6in gray.

Even though unnecessary change in hoist height can be avoidedeffectively after adjusting the hoisting parameters, it is possible for

the load and boom to collide with each other because the hoist height

will no longer be adjusted after the hoist height has reached the min-

imum hmax along the path, and the boom-luff angle may keep increas-

ing. Therefore, we need to inspect the hoisting parameter after the

hoist height has reached its minimum value. If the hoist height is

less than hmin in the current congurations, then the hoist height

should be increased to hmin, and the adjusted hoist height for the

path is shown as a dashed line in Fig. 6. After the adjustment, the

path conguration and the hoisting parameter form the optimal erec-

tion path.

3.6. Features of the proposed erection path planning

In the existing research on erection path planning [26], the opera-

tion of crane is expressed by a 3D C-space under the condition that

the crane does not move during the erection operation. The coordinates

of C-space are the crane base-swing angle , the boom-luff, and thehoist height h. All crane operations are expressed in the C-space by

[,,h].

In this research, we have found that it is not necessary to considerthe hoist height as one of the coordinates in the C-space. This is be-

cause in the erection operation, we change the hoist height to lift

the load higher in order to avoid collisions between the load and

the ground or obstacles. In fact, we only need to know the extent of

hoist height reduction during the erection operation to enable the

load to clear the obstacles. After the load is lifted during the erection

operation, the load must be raised to a height above the obstacles in

the planned path to ensure that the load does not collide with either

the ground or the obstacles. Therefore, in this investigation, we have

found the minimum hoist height hmin, the maximum hoist height

hmax, and the height of obstacleHobcorresponding to each congura-

tion in the C-space, we have also simplied the 3D crane C-space to a

2D conguration space [,]. This method signicantly reduces thecomputational time and complexity of path planning, and thus we

are able to achieve a faster erection path planning procedure.

4. Erection path planning for dual cooperative crane

This study extends the aforementioned method for single crane

erection path planning to a method for a dual, cooperative crane.

The path planning ow chart is still the same as in Fig. 1, except

that in order to model the dual crane system, two 2D C-spaces are

used. A method was developed to connect the two C-spaces con-

structed for each crane, and nd all possible path nodes so that erec-

tion path planning can be conducted for dual cooperative cranes.

4.1. Building the C-space for dual cranes

In order to describe the dual crane system, we built the individualC-space for each of the two cranes, and address them as two cranes,

crane A and crane B. The C-space for crane A is CAand that for crane

B isCB.

Werst dene the coordinate ranges for CAand CB. The weight of

the object isW. For the object, since the dual crane cooperative oper-

ation is evenly divided between the two cranes, the weight ofW/2 is

separately substituted into the weight tables of crane A and crane B to

nd crane booms largest luff angle max(W) and its smallest luff anglemin(W). CongurationCArepresents a possible connection point be-tween crane A and the object, and CongurationCBrepresents a pos-

sible connection point between crane B and the object.

We then use the method given in Section 3.3to separately deter-

mine the regions forCA-obstacle andCB-obstacle. However, unlike the

case of single crane operation, the inspection of object collision is per-formed by the use of the object and a partial crane model at the end of

each connection. Since the purpose of the dual crane C-space is to nd

the connectable congurations for the crane and the object, collision

inspection between the object and obstacles is carried out at the

stage of path planning. After completing the C-obstacle region deter-

mination, we record the cable extension range and heights of obsta-

cles for each conguration.

4.2. Path planning for dual cranes

This research extends the method of single crane path planning

presented in Section 3.4 to dual crane planning. We begin by selecting

one of the two cranes to be thereference crane, and then we randomly

sample the congurations from the C-space to serve as the

Fig. 5.The maximum obstacle height along the erection path.

Fig. 6.Optimization of the cable operations.



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connection point between thereference crane and the load. Next, we

search from the other crane's corresponding connection point, and

use the connection congurations between the two cranes and object

as a set of path nodes. This process continues until an adequate num-

ber of nodes have been obtained and then the nodes are connected to

form the path. Finally, we select the optimal solution from all possible

paths that connect the starting point to the goal as the erection path

for dual cooperative crane operation. The ow chart for dual cooper-

ative crane path planning is shown in Fig. 7.To explain the method of the dual crane path planning proposed in

this research further, we present a simple case of dual cooperative crane

path planning as an example, as shown inFig. 8. First, we enter the road-

map into a path node taken from the connecting point (CA_ s,CB _ s) be-

tween the object and the two cranes at the starting position. Then, we

enter the roadmap into a path node taken from the connecting point

(CA_g,CB_g) between the object and the two cranes at the goal position.

We then advance into the process of path node sampling.

During the path node sampling process, cranes A and B take turns

to serve as the reference node for sampling. When crane A is the ref-

erence node, a sample is arbitrarily taken fromCA(indicated asCA _ n)

that is not within the region of C-obstacle. CA _ nthen act as the con-

nection point between the load and crane A. The next step is to nd

a possible connection point CB _ n, corresponding toCA _ n, which con-

nects crane B and the object. Consider CA _ nas the center of a circle

and use the height of obstacleHobcorresponding toCA _ nas the height

to be lifted. Then, on the XY plane of the workspace with XYZ coordi-

nate system, rotate the object so that it is parallel to the line CACB ,

which connects the centers of rotation of the booms of the two cranes

as shown inFig. 8.If at this time, the object in the XYZ coordinate sys-

tem does not collide with either the obstacle or the cranes and CB _ nandCBare not in the region of C-obstacle, then we use (CA _ n, CB _ n)

as a node and insert it into the roadmap.

However, if the object collides with the obstacle, then subsequent-

ly we takeCA _ nas the center of the circle and rotate the object in the

XY plane both clockwise and counterclockwise until there is no fur-

ther collision. If the rotation angle of the load is 1b 2 or 2b2 and

CB _ nis not C-obstacle, then we use (CA _ n, CB _ n) as a node and insert

it to the roadmap as shown inFig. 9.

The reason for alternatively selecting cranes A and B as the refer-

ence node is to provide a variety of paths. In theory, the more diverse

the sampling points, the higher the possibility ofnding collision-free

paths. Since the PRM method is based on probability where we ran-

domly sample the nodes in the conguration space and try to arrive

at a feasible solution instead of checking all possible solutions and

choose the optimum one. Therefore, alternative selection of the refer-

ence point can increase the randomness without adding to computa-

tional cost. Since this study uses the connection point of the load andthe end of the crane as the center of the circle, the boom is turned in

order to avoid the obstacle so that when a different crane is used as

the reference-sampling node, various nodes will be possible.

When connecting the collision-free path, we connect the nodes

along with the connection point between the object and crane using

straight lines to form the path in the working space with the XYZ co-

ordinate system, as shown inFig. 10. To judge whether the path be-

tween the nodes is a collision-free path, the following three-step

process is needed. First, we nd the height Hobject to lift the object

over the obstacle without collision for the section of erection path be-

tween the two nodes. Secondly, we inspect the connection points be-

tween the object and crane in the trajectory of path to see whether

they will go past the C-obstacle in the spaces between CA and CB. If

Fig. 7.Flow chart for dual cooperative crane path planning.

Fig. 8.Example of cooperative dual crane operation.

2

1

CB_n

CA_n

CB_n

Fig. 9.Node sampling in cooperative dual crane path planning, when an object collides

with an obstacle.



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they do pass the C-obstacle, then this shows that collision will occur

at the loading point of the path so that this section between nodes

will not be a part of the path. Finally, we inspect the amount of

cable extension needed to raise the height to Hobjectand see if the

length exceeds what is permitted. If it exceeds the length limit, it

means that it is not possible to lift the object over the obstacle by

using the path, and therefore the section between these nodes cannot

be a part of the path. If the section between two nodes is judged to be

a collision-free path, then record the height Hobject, which will be usedin the calculation for optimal path and in planning for hoist height.

After completing the collision-free path connection, those paths

that successfully go from the starting point to the end point through

the nodes are designated as allowable erection paths. If no such

path can be found, then further sampling of nodes should be per-

formed and they should be added to the roadmap. The process con-

tinues until a path can be found that connects the starting point to

the end point.

For calculation for the optimal path, we make use of the Pcostfunc-

tion proposed in Section 3.4to calculate the costs for the erection

path. The costs for the paths of crane A and crane B are then separate-

ly estimated by using thePcostfunction in which results are then com-

bined. The larger the resulting value is, the more time it will take to

execute the path and the harder it will be to operate the cranes.

4.3. Hoisting planning for dual cranes

In the cooperative dual crane operation, due to differences in the

obstacle heights encountered by the connection point between the

crane and the load end of the two cranes, dual crane operation cannot

use the largest hoist heighthmaxas we do for the hoisting parameter

in the case of single crane erection. From the recorded value ofHobjectduring the stage of collision-free path connection, we then obtain the

required height for the object in order to avoid an obstacle, as shown

inFig. 11. Using this height, we can calculate crane A's hoisting pa-

rameterhAand modify it through the method of parameter modica-

tion used inSection 3.5. This will minimize the hoist height change

for crane A and make it fall within the safety limits hminAhAhmaxA

as shown inFig. 12. Finally, based on the corrected parameterhA, wend the hoisting parameter hB of crane B for the same load height,

and then a complete erection path can be found. After we calculate

the hoisting parameter for crane B based on the height of object and

make corrections to the hoisting parameter, we can nd the hoisting

parameterhAof crane A for the same object height, and obtain a dif-

ferent erection path. On comparing hoist height changes in the afore-

mentioned two paths, we found that the path with the smaller hoist

height change is the optimal path for cooperative dual crane opera-

tion as obtained using the planning method of this research.

5. Implementation

We introduce the computer software Erection Plannerin this sec-

tion and its architecture and development environment for erection

path planning. The main function of Erection Planner is to provide a

visualization of a virtual construction site. Using the software, the

user can plan the erection path by providing the starting and end

points for the object to be lifted and by selecting the type of erection

operation. The system will show the planned erection path and the

erection process in the virtual environment.

5.1. The development environment

Erection Planner was developed based on Microsoft's XNA Frame-

work[20]. It renders the virtual construction site by using the graphics

software DirectX. In addition, PhysX developed by NVIDIA is used to de-

tect collisions and to help build the C-space for the crane [23].

The following hardware conguration was used for the tests: CPU

Intel Core2 Duo E7300 2.66 GHz, 3 GB RAM, NVIDIA GeForce8600GT

screen. The operation system used was Windows XP SP3 32 bits.

5.2. The software architecture

Fig. 13 shows the software architectureof the Erection Planner. It in-

cludes ve parts: Erection Project Information Input, C-Space Builder,

Path Planner, Hoisting Planner, and Scene Visualization.

5.2.1. Erection project information input

In order to provide a visualization of a virtual erection scene and

to check for any collisions that occur, we rst use the Autodesk 3ds

Max 2009 3D software [3] to build 3D models for the crane

e3DSMAX, the object, and the obstacles and import them into the

program. In order to work in the XNA Framework, we convert the

model les in the FBX format and import them into the program

which other necessary information for erection path planning, such

Fig. 10.Trajectory for cooperative dual crane operation.

Fig. 11.Taking required height that ensure the object avoids an obstacle as the erection

path.

Fig. 12.Correction method for the cable operation parameter.



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as the load capacity table of the crane, the weight of the object, and

coordinates of starting and end points for the object.

5.2.2. C-space builder

The purpose of this part is to build the C-space. The C-space is built

based on the method for building the C-space presented inSections 3.3

and 4.1, and is built according to the type of erection operation. To imple-

ment the collision detection needed in the C-space building procedure,

we use PhysX to build simple physical models for the crane, the object,and the obstacles. In the PhysX physical action simulation, the base-

swing angle, the boom-luff angle, and the position of object are changed

if any collisions occur.

5.2.3. Path planner

The purpose of this part is to implement the method of path plan-

ning proposed inSections 3.4 and 4.2, and essentially carry out erec-

tion planning to obtain path information including the base-swing

angle and the boom-luff angle.

5.2.4. Hoisting planner

This part plans the hoisting operation for the erection path by the

method of hoisting planning described in Sections 3.5 and 4.3, andsends out the completed erection path information.

5.2.5. Scene visualization

In this part, a virtualerectionsceneis built using XNA, andthe trajec-

tory of the object is shown in the erection scene. Fig. 5.4 shows the

resulting erection path using the current method. The visualization

part can be integrated with other 3D simulation tools for more ad-

vanced and graphically detailed visualization e.g. Maya, 3ds Max and

Blender. Users can retrieve the project information from the Erection

Project Information Input and combine it with the planned output of

the Hoisting Planner (which contains the crane congurations in the

path) and then adapt it to their visualization or simulation tool.

6. Experiment result and discussion

In order to verify the method of erection path planning proposed

in this research, we have conducted a series of erection scene exper-

iments to test if the proposed method can be applied to both single

crane erection operation, and dual cooperative erection operation.

6.1. Experiment 1: Validation test of path planning for single crane

Experiment 1 uses the example of a single crane erection path plan-

ningthat tookplace inan oil renery (CPC Dalin), and its erection scene

is shown in Fig. 14. Thecranewas required to lift a cylindrical oil storage

tank (radius= 4.8 m, length= 30 m) and put it on top of a 37 m high

supporting frame. In the erection scene, the obstacles around the oil

storage tank were an eleven-story high structure (height= 61 m), and

two oil storage tanks already located on the supporting frame(height=42 m). The body of the crane was 20 m long and 12 m wide,

with a boom length of 90 m. It had a base-swing angular velocity of

4/s, a boom-luff angular velocity of 1/s, and a hoist height change

speed of 1 m/s. By using the planning method presented in this re-

search, an erection path was successfully identied. The object did not

collide with the aforementioned obstacles and the supporting frame

at the end point. The path is shown inFig. 15.

6.2. Experiment 2: Validation test of path planning for dual cooperative

cranes

In Experiment 2, we use no.2 of dual cooperative erection opera-

tion from[2] as an example. The erection scene is shown inFig. 16.

The object was a horizontal beam (length= 10 m, width= 1 m,

height=1 m). Each crane was connected to one end of the beam.

There were three obstacles between the starting and end points

(the height of obstacle A was 5 m, the height of obstacle B was

12 m, and the height of obstacle C was 5 m). Collisions with obstacles

had to be avoided when moving the object from one side of the obsta-

cles to the other. The body of the crane had a length of 10 m, and

width of 6 m. The boom length was 45 m, with a base-swing angular

speed of 4/s, boom-luff angular speed of 1/s, and hoist height

change speed of 1 m/s. By using the planning method presented in

this research, an erection path was successfully identied and the ob-

ject did not collide with the aforementioned obstacles. The path is

shown inFig. 17.

In addition to the problems of collision and managing the weight

of object during the erection path planning, the interference and in-

uence of the erection operation on other engineering activitiesshould be also be considered. The result of erection path planning,

shown inFig. 17, required additional planning if there were workers

around the obstacles even though the plan was able to successfully

lift the object over the obstacle without any collision. To avoid inter-

ference with the object, the possibility of parts falling and hurting the

workers on the ground, and for the purpose of engineering safety, a

more time consuming and harder to operate substitute erection

path was required. The strategy was to move the object around the

obstacles. Therefore, we tested the substituting erection paths under

various constrained conditions. First, we hoped to nd an erection

path that did not pass through obstacle B in the middle. The test re-

sults are shown inFigs. 18 and 19(The yellow part shows the starting

Fig. 13.Software architecture of Erection Planner. Fig. 14.Erection scene of Experiment 1.



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position of the object and the red part shows the end position). Two

different paths were found: one went around obstacle B from the

left side, while the other from the right side. Afterwards, we hoped

to nd paths that did not go past any obstacles but passed through

the narrow space between the cranes and obstacles. The results are

shown inFigs. 20 and 21.

6.3. Experiment 3: Efciency test

In Experiment 3, we tested using the same two erection scenes

from Ref. [2]. We imitated the method of building the 3D C-space

and also made use of Genetic Algorithm based method of erection

planning, both reported in Ref.[2], and compared it with the method

presented in this research. In addition, we also compared results

obtained by using the proposed PRM and the planning conducted ei-

ther in both 3D and 2D C-spaces.

6.3.1. Erection Scene 1

Erection Scene 1 used the scene 1 from the dual cooperative crane

erection of[2] as shown inFig. 22. The object was a beam (10 m in

length, and with height and width equal to 1 m), and the two cranes

were connected to either end of the beam. The two cranes were re-

quired to lift the object together from the ground and place it on

the platform on top of an obstacle 6 m high. The body of the crane

was 10 m long, 6 m wide, and the length of the boom was 45 m,

with base-swing angular speed of 4/s, boom-luff angular speed of

1/s, and hoist height change speed of 1 m/s. Fig. 23(a) shows the

path planned using 3D C-space with the Genetic Algorithm.

Fig. 23(b) shows the erection path planned using PRM in the 3D C-

space, andFig. 23(c) shows the erection path planned using PRM in

the 2D C-space.

6.3.2. Erection Scene 2

Erection Scene 2 uses scene 2 from the dual cooperative crane erec-

tion of[2]as an example, and its erection scene was the same as that

inExperiment 2. The site arrangement is shown inFig. 16, please refer

toExperiment 2 for details about the site. Fig. 24(a) shows the path

planned using 3D C-space with the Genetic Algorithm. Fig. 24(b)

shows the erection path planned using PRM in the 3D C-space, and

Fig. 24(c) shows the erection path planned using PRM in the 2D C-space.

6.4. Discussion of experimental results

The path planning result ofExperiment 1for single crane erectionobtained using the proposed method, shown inFig. 15, successfully

avoided the obstacles and found feasible collision-free erection

paths. The computation time for planning was 0.27 s. Thus, it took a

very small amount of time to complete the planning.

The path planning result obtained inExperiment 2for cooperative

dual crane erection using the proposed method, shown inFig. 17, suc-

cessfully avoided the obstacles and found feasible collision-free erec-

tion paths. The computation time for the planning was 0.52 s. Again,

the time taken to complete the planning was very short. In addition

to nding an erection path based on the strategy of lifting the object

high enough to avoid collision with obstacles, a feasible path can

also be found based on the strategy of moving the object around the

obstacle. Thus, feasible paths can be found under different conditions

of constraints, as shown inFigs. 1821.InExperiment 3, we planned the erection path for different site

conditions using different methods of erection path planning. We

used 3D C-space with the Genetic Algorithm, the proposed PRM in

the 3D C-space, and the proposed PRM in the 2D C-space. The results

are shown inFigs. 23 and 24. The above methods successfully found

feasible collision-free erection paths for cooperative dual crane erec-

tion. Tables 3 and 4 compare the results of path planning, where

data was obtained from an average of 100 path-planning operations.

The values compared are the planning time, change in angle of the

base-swing, change in angle of the boom-luff, and the change in the

hoist height. By comparing the results, we nd that the average plan-

ning time using the proposed PRM method in the 2D C-space was

much less than the other two methods. In the comparison of crane

operation parameter, no apparent differences could be found in the

Fig. 15.Erection path of Experiment 1 (The goal position of the object is visualized using translucent yellow color).

Fig. 16.Erection scene of Experiment 2.

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base-swing angle change among the three methods. This is because

during an erection operation, the base-swing angle usually started

from the initial angle and gradually rotated to the nal angle; there

was not much change in angle during the operation. In the compari-

son of boom-luff angle change, the PRM in the 2D C-space managed

the least changes and obtained the easiest operate erection path. 3D

C-space with the Genetic Algorithm could nd the approximated op-

timal result. However, it was harder to use PRM in the 3D C-space to

nd the optimal path compared to PRM in the 2D C-space as it was

difcult to have path nodes evenly distributed in the C-space. The

PRM method in this investigation used probabilistic sampling to ob-

tain path nodes and tried to calculate collision-free paths among all

nodes. If the PRM method is improved, it should be possible to obtain

better results. In addition, a planning method for hoisting operation

has been presented in this study for the 2D C-space, reducing unnec-

essary hoist height changes.

7. Benets and contributions

In this research, a method of automated erection path planning

has been developed. The main contributions of this research are:

1. Development of a method of 2D C-space, which reduces the com-

plexity of planning and reduced the path planning time.

2. Development of a exible method of erection path planning,which

could be applied to both single crane operation and cooperative

double crane operation.

3. Development of a near real-time method of erection path plan-

ning. This could be used to quickly alter the path during the erec-

tion operation and plan a new feasible path if, just before or

during operation, it is found that the actual site environment was

differs from the conditions originally planned for.

4. Development of a costs estimation function with the weight coef-

cients for each degree of freedom of crane operation. Planners

can adjust the weight values to generate feasible and suitable erec-

tion paths for different specications and site environments.

The developed method can potentially benet many aspects of

current construction practice. The possible benets of this research

are summarized in the following paragraphs:

Crane selection: Rather thanhavinga qualitative crane selection, the

methods and tools developed in this research can be used to provide

quantitative information about the differences from using the vari-

ous candidate cranes. Similarly, for large or high-rise construction

projects, this research developed tools that provide data to enable

proper evaluation of the compromises and benets of using of mul-

tiple cranes at the site as opposed to using a single crane.

Crane placement: The methods developed in this research enable

computers to simulate the erection processes automatically by

utilizing the planned erection path. They can also be extended to

obtain erection times produced by placing the crane at different

locations and searching for an optimum location within the site

that will minimize erection times.

Logistics for scheduling material deliveries to the site: This study can

be used to improve various aspects of the logistics at construction

sites. In particular, the generation of a precise and detailed erec-

tion plan prior to construction can minimize onsite storage re-

quirements by delivering only the materials that will be erected

soon to the site. For example, structural elements can be delivered

only one day prior to their erection, or for a site where no onsite

temporary storage is available, they can be delivered just a few

hours prior to erection. Furthermore, elements to be lifted by the

crane can be delivered to the site and even placed in the delivery

truck in accordance with the plan for lifting them using the crane.

Planning and visualization of erection virtually prior to actual erection

activities: This research provides tools for planning and visualizing

Fig. 17.Experiment 2 Erection path with no constrained conditions.

Fig. 18.Experiment 2

Substituting path 1 when the path did not go through the middle obstacle.



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Fig. 19.Experiment 2 Substituting path 2 when the path did not go through the middle obstacle.

Fig. 20.Experiment 2 Substituting path 1 when the path did not go through any obstacle.

Fig. 21.Experiment 2 Substituting path 2 when the path did not go through any obstacle.

Fig. 22.Erection scene of Experiment 3

Site arrangement of the example.

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erection processes on the computer before actual construction. This

provides an excellent planning and management tool for superinten-

dents, construction managers, erection crews and crane operators to

allow them to fully understand the planned erections next week,next day, next three days, next hour, etc. Being able to visualize

these erection activities prior to actual construction can help identify

and eliminate many otherwise unforeseen problems ahead of time.

Computer-assisted cranes erections: Methods and tools developed in

this research do notjust provide benets to conventional cranes, they

provide the basis for developing computer-assisted cranes. In the

near future, this research could be used to provide information for

operators in real time to assist them in manipulating construction

cranes more efciently and more safely. For example, a computer-

assisted crane could prevent operators from coming in contact withpower lines or in preventing the crane from colliding with obstacles

or with other cranes. They may integrate the Augmented Reality

and tele-operation to visualize computer-generated collision-free

(safe) and time-optimized paths to be followed by crane operators,

and even auto-pilotcapabilities for portions of the erection cycle

or for entire erection cycles.

Autonomous robotic crane erections: Many of the methods and al-

gorithms developed in this research, together with new sensor

technology, and the development of new types of structural con-

nections, can provide the basis for autonomous robotic cranes.

These robotic cranes could rst be used for construction in dan-

gerous environments (e.g., erection of containment structures in

environments contaminated by hazardous chemicals or radioac-tivity, erection of a bridge during armed conict, etc.), but could

eventually be used in more standard constructions.

8. Conclusion

In this research, we developed a fast path-planning method for

single and dual crane erections. This method replaces the use of

hoist height as a coordinate of the C-space, which can signicantly re-

duce computation time needed during the planning process. The

hoist height is determined after the path-planning processes. This

can ensure minimal changes in the hoist height, fullling the needs

of construction practices. To validate the usability of the proposed

method, we conducted three experiments: (1) path planning for sin-

gle crane, (2) path-planning for dual crane and (3) efciency test. The

Fig. 23.Scene 1 of Experiment 3 Erection path planned: (a) Genetic Algorithm in 3D C-space; (b) by PRM in 3D C-space; and (c) by PRM in 2D C-space.

Fig. 24.Scene 2 of Experiment 3 Erection path planned: (a) Genetic Algorithm in 3D C-space; (b) by PRM in 3D C-space; and (c) by PRM in 2D C-space.

Table 3

Scene 1 of Experiment 3. Efciency comparison for different methods of path planning.

Planning method Problem 1

GA

(3D C-space)

PRM

(3D C-space)

PRM

(2D C-space)

Average planning time (sec) 36.33 11.26 0.51Variat ion of base- swing angle ( de g) 71.47 69.81 67.64

Variat ion of boo m-luf f angle (deg) 12.29 13.15 10.32

Variation of hoist height (m) 31.51 32.77 26.69

Table 4

Scene 2 of Experiment 3. Efciency comparison for different methods of path planning.

Planning method Problem 2

GA

(3D C-space)

PRM

(3D C-space)

PRM

(2D C-space)

Average planning time (sec) 59.42 11.32 0.52

Variation of base-swing angle (deg) 144.96 143.55 142.93

Variati on of boom-luff angle (deg) 24.81 23.22 19.14

Variation of hoist height (m) 106.11 109.78 93.06



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results ofrst two tests show that the proposed method can help nd

a collision-free erection path that satises safety requirements, and

can assist engineers in solving the path-planning problem. From the

third experiment, we found that the proposed method of erection

path planning is time efcient when used to nd a feasible erection

path compared to existing methods. The obtained path by the pro-

posed method is also easier to operate. The method is also exible

in being able to nd suitable erection paths under different condi-

tions, as required on the erection site.

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