Automation in Construction 15 (2006) 398 – 414 www.elsevier.com/locate/autcon

Planning and visualization for automated robotic crane erection processes in construction ShihChung Kang *,a, Eduardo Miranda b,1 b

a Stanford University, 556H Bldg 550 (CIFE), Stanford CA 94305, USA Stanford University, Room 293, Terman Engineering Center, Stanford, CA 94305, USA

Abstract This paper summarizes ongoing research aimed at developing knowledge, methods and tools required to implement automated robotic crane erection processes for the construction industry. In the proposed approach, construction cranes are treated as multi-degree-of-freedom robots and modeled in a virtual environment. Virtual cranes are provided with motion-planning algorithms that enable them to find collisionfree and time-efficient paths for each piece that needs to be erected. Inverse kinematics are then used to determine the crane motions required to move elements in previously computed paths. By using an effective method to coordinate the tasks and motions of multiple cranes, the system is also extended to construction projects that require simultaneous use of closely-spaced cranes. The virtual crane model provides realistic visualizations of erection processes and detailed erection schedules. D 2006 Published by Elsevier B.V. Keywords: Erection processes; Robotic construction; Virtual construction; Cranes; Motion planning; Erection schedule

1. Introduction and motivation Cranes are one of the most heavily used and shared resources in construction sites. Only in the U.S., there are approximately 125,000 cranes operating in the construction industry. These cranes are involved in many different tasks. For example, during the construction of steel or precast reinforced concrete buildings, cranes are not only used for erecting structural members but are also used for lifting precast fac¸ade elements, curtain wall systems and many other materials and nonstructural components. Since so many construction activities heavily rely on cranes for moving structural elements and nonstructural components, an efficient crane operation can have a significantly positive influence on the overall schedule, cost and safety of a construction project. This is particularly true for high-rise * Corresponding author. National Taiwan University, Room 314 Civil Engineering Building, Taipei 10617, Taiwan. Tel.: +886 2 33664346; fax: +886 2 33664346. E-mail addresses: [email protected] (SC. Kang), [email protected] (E. Miranda). 1 Fax: +1 650 723 4450; Fax: +1 650 723 7514. 0926-5805/$ - see front matter D 2006 Published by Elsevier B.V. doi:10.1016/j.autcon.2005.06.008

construction where cranes play a particularly critical role in the overall construction schedule. An important concern in the construction industry is the rapid increases in erection costs that have occurred in recent years relative to other construction costs. In the case of steel structures, Carter et al. [1] reported that from 1983 to 1998, erection labor costs, expressed as a percentage of the total cost of steel structures, increased from 19% to 27%, which represents a 42% increase in 15 years. In contrast, the percentage of the total cost corresponding to material costs has dropped from 41% to 26% representing a 36% reduction in the same period of time (see Fig. 1), indicating that erection costs now represent a higher percentage of the total cost than costs associated with structural materials in steel structures. Hence, optimizing crane usage in order to speed up erection processes can result not only on shorter overall construction schedules but also in smaller costs. Another very important concern related to construction cranes is safety. According to the statistics from the Occupational Safety Health Administration (OSHA) [2], 137 crane operators died in the U.S. as a result of crane accidents from 1992 to 2001. Craneaccidents.com [3], a

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414 Material

% of total cost

activities and performing collision detection. These methods were integrated to a computer system, iCrane, which can automatically generate feasible and efficient paths for a crane, and visualize its erection activities in a virtual environment. This paper will introduce the techniques and algorithms used in iCrane and demonstrate its use in facilitating construction projects.

Shop Labor

45

Erection Labor

40

Other cost

399

35 30 25 20

2. Previous research

15 10 5 0 1983

1988

1993

1998

year

Fig. 1. Price structure of steel construction in the U.S. (modified from Carter et al. [2]).

well-known website dedicated to tracking and documenting crane accidents worldwide, received 516 crane accident reports and 277 fatalities reports from 2000 to 2002. In many cases, these accidents could have been prevented. For example, Braam reported that 39% of crane-related accidents were related to cranes colliding with power lines [4]. Crane accidents not only result in injuries and loss of life but also result in increases to workers compensation insurance premiums, legal costs associated with law suits and construction delays. Computers may assist in preventing many kinds of crane accidents. The objective of this paper is to present the results of a research project aimed at developing knowledge, methods and tools required to implement fully automated robotic crane erection processes in the construction industry. Shortterm objectives of this research are the development of computer systems to provide detailed simulation and visualization of crane operations to optimize crane usage while at the same time providing detailed erection schedules and improving site logistics and safety. Long-term objectives are the development of systems that allow autonomous robotic cranes that ‘‘know’’ where to pick up and place elements in a fully optimized sequence, transport them in safe and time-optimized paths and interact efficiently and safely with other robotic cranes simultaneously operating on the construction site. These systems would consist of robotic cranes linked to computers, 4D models (3D geometry model plus time) [5] and sensors that would provide a faster, more economical and safer erection. In short, current empirical methods of producing the erection plans and manual methods of operating the cranes are insufficient to meet the requirement of modern constructions. Construction projects are becoming more complex and larger in scale, so current state-of-practice approach can cause inefficient and unsafe problems in actual construction sites. Our research developed computer-aided methods for generating erection paths, coordinating crane

Cranes and automation technologies are two important fundamentals in this research, which aimed at automating the crane erection processes. Previous investigators have researched these two topics for years. This section summarizes previous research results and explains how to expand and integrate the previous efforts to achieve the goal of our research. 2.1. Crane-related research An important amount of research related to construction cranes has been published. Previous investigators have conducted research in the following areas: (1) crane selection, e.g., [6– 8]; (2) optimum placement of tower cranes and supply location for erection materials, e.g., [9– 11]; (3) estimation of erection scheduled, e.g., [6,12 – 14]; (4) the usage and coordination of multiple cranes, e.g., [15 –17]; (5) simulation and visualization of crane operations, e.g., [18 –24]. Previous crane-related research has been recently summarized by Tam et al. [10] and Lin and Hass [15]. Several investigations have developed methods to estimate the erection times [6– 14]. These methods are important to simulate construction processes and to evaluate construction plans. In particular, several researchers have developed methods to determine the time for transporting each structural element from the material supply location to the location it supposes to be in a structure (final destination). The total construction time can then be calculated by accumulating the erection time for all structural elements involved in the project. These models can be used for different research purposes. The researchers varied the location of the crane, the position of the supply material or the number of cranes used in a project, and relied on the mathematical models to estimate the erection time to find optimum cranes, optimum position of fixed cranes (e.g., tower cranes) and optimum position of supply points. Some numerical methods, such as genetic algorithm [10] or fuzzy logic [13], have been used to assist the problemsolving process. Since the procedure to estimate erection times of individual elements crane models are usually used thousands times, their estimations for each erection activity need to be very accurate in order to reflect the reality in actual construction sites. Any small mistake in the mathematical model can accumulate to produce large errors after thousands erection cycles.

400

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

Because of the importance of mathematical models to estimate erection time of individual lifts, researchers have kept developing and improving these models. 2.2. Construction automation research An important amount of research has recently been carried out in order to introduce automation in construction industry. Previous research regarding construction automation has mainly focused on the improvement in two directions: the degree of automation and the degree of reality. The research regarding degree of automation aimed at improving the construction equipment or planning processes by using computational methods to reduce the repetitive manual procedures. The research on degree of reality, on the other hand, has taken the advantage of the improvement in computer graphics and on autonomous robots to move abstract models toward the virtual world and the real world. Fig. 2 schematically illustrates some previous research projects in these directions by plotting them into a coordinate system which uses the degree of automation as the horizontal axis and degree of reality as the vertical axis. The degree of automation can be sub-categorized into three levels, which are manual, integrated (partially manual/ partially automatic) and fully automatic levels. The construction cranes belong to the manual level because they are controlled by operators for each motion to complete a given task. Shimizu’s SMART system and the Obayashi’s Big Canopy [25] are examples of the integrated level, which integrate part of the construction knowledge into the

machines to assist operators in completing the jobs more efficiently. The fully automated robotic crane, the long-term goal of our research, is on the level of full automation. A robotic crane is equipped with motion-planning intelligence and has the ability to erect a building automatically. In terms of the degree of reality, the construction technology and research can be separated into three groups: abstract models, virtual reality and the real world. Conventional two-dimensional CAD models used in current construction practice, for example, can be considered abstract models. Since two-dimensional models are presented only on two-dimensional media, such as papers or computer screens, they have inherent shortcomings in terms of their ability to represent dynamic objects and information from the world. Therefore, engineers use abstract symbols or special drawing methods to enrich the 2D models to convey more information. However, these abstract methods impede those people without special training from understanding the meaning of the models, and sometimes even cause communication difficulties between those with different levels of expertise. 4D models [26,27] and animation models present the construction processes in a virtual environment generated by computer graphics. VITASCOPE [28] developed a more detailed and operational-leveled animation to simulate construction processes. These virtual reality models can significantly improve the quality of communication between project members of different backgrounds. The iCrane model is developed in a virtual world but eventually will link to a robotic crane to provide a faster, more economical and safer erection.

Degree of Reality Real world

Construction Crane

SMART SMARTsysystem st e m

Fully automated robotic crane

Big Canopy Ro RoboCrane b o Cr an e

Virtual reality

Animation modeling

VITASC VITASCOPE OPE ALPS

4D model 3Dmo model 3D del

Abstract models

iCrane System MOLOG phphysical ys ica l b abased se d cran crane e

2Dmo model 2D del Mat Mathematical h e m a t ical cran cranee model m od e l

Manual

Integrated (Partially Automatic)

Automatic

Degree of Automation

Fig. 2. The research categorized by the degree of automation and reality.

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

To achieve fully automatic level, motion planning (a.k.a. path planning) [29] is a key element to provide manual cranes’ automated capabilities. Many methods have been developed, primarily in robotics. The main goal of motionplanning methods is to find continuous, collision-free paths by giving a robot initial and target positions. With some modifications, it is an ideal tool to be applied in cranes as an automated planner. Some recent research has applied motion planning to crane usage. The MOtion for LOGics (MOLOG) project [30] developed motion-planning tools inside the usual CAD system, which facilitated the complex and trivial crane operation for the maintenance of a nuclear power plant. Ali et al. [31] and Sivakumar et al. [17] used a motion-planning algorithm to assist a cooperative lifting plan. Although this research only focused on some specific problems in construction, it demonstrated the potential of motion-planning algorithms. Once a reliable motion-planning algorithm for a tower crane is developed, an automatic scheduling system can be developed. Future engineers may use the computer software to schedule the project with both geometrical reasoning and time accuracy. Some previous research has focused on visualizing the crane operations. Lipman and Reed [32] have developed 3D crane models in a virtual environment. The crane model developed from the research can be ‘‘manipulated’’ to complete some construction tasks in a virtual environment. Chui [33] demonstrated the process of operating a tower crane to install curtain walls in a virtual world. Kang and Miranda [18] developed a physical-based model of a tower crane that can simulate the cable dynamics by solving the equations of motion during a crane lifting operation. In industry, Bechtel developed the Automated Lift Planning System (ALPS) [34] to assist in heavy-lifting operations. Although ALPS provided some simulation and visualization capabilities of erection paths before construction, the system still needed users to plan the crane motions manually. To achieve the goal of full automatic robotic construction, we need to further improve the degree of automation in construction sites. The most important research problem is to introduce artificial intelligence to the cranes or other equipment so that they are capable to plan the moving trajectories and motions to complete their tasks safely and efficiently. By adding ‘‘intelligence’’ to construction cranes, we can integrate virtual reality technology to simulate complete erection processes automatically before and during construction. If further integrating with the robotic cranes or other construction equipment, we can eventually achieve the goal of fully automatic robotic erection.

3. Motion planning of a single crane Current efficiency of crane utilization can be significantly improved by optimizing the moving path and crane operation. Today, the cranes are manipulated by the operators mainly depending on their experiences or even

401

by their intuition. This empirical manipulation can be inefficient and often cause some unsafe movement. Since crane operators cannot always find optimal motions for manipulating a crane particularly optimum simultaneous movement of three of four degree of freedoms, the crane may waste time due to follow the inefficient paths. Although the waste of time due to the inefficient operation in an erection cycle (e.g., for erecting one component) may be small, it can grow to a significant amount of time when hundreds or thousands of erection cycles involved in a project are considered. Hence, it is important to develop a reliable method that can help crane operators optimize crane usages by using computer analysis to find the optimum erection sequence and optimal path for each piece that needs to be lifted. However, due to the complexity of construction projects, current manual methods make it difficult to produce precise and detailed erection schedules. Therefore, automatic methods, which facilitate us to visualize and simulate detailed erection activities in the computer, are needed, so they motivate the research. Developing a detailed erection plan requires a great amount of geometrical analysis, consideration of the crane operation and identification of the most efficient and safest path for each element that needs to be erected and identification of the best erection sequence for all elements in the projects. These problems can be facilitated by the techniques in motion planning and computer graphics, two of the most rapidly-developing areas of computer science in recent years. Because there are large amount of techniques developed in these fields, it is very important to select appropriate techniques and develop ways on how to adapt these techniques for our purpose, improving crane operation. Motion planning is one of the most important techniques to automate the erection activities in a construction. The motion-planning problem is to find the operational path of a construction crane in a given three-dimensional environment from an initial configuration to a target configuration. The paths do not only require collision-avoidance between the crane and all obstacles in the given environment but also consider the capacity of the crane and the ability of operators in construction practice. The following sections describe the crane model that was developed in this research and describe the motion-planning methods and algorithms. 3.1. Crane model and its configure space In this research, a construction crane was treated as a robot and Denavit – Hartenberg notation [35] was employed to model a tower crane. The Denavit – Hartenberg notation is a commonly used method for describing a robot kinematically. This method essentially regards any kind of robot as a set of rigid bodies connected in a chain by joints. For each joint, we compute a transformation matrix based on the geometrical relationship of the link (joint) between the neighboring rigid bodies. Once the transformation matrix

402

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

Θ1

Prismatic Joint

d2

Revolving Joint

d3

{B}

Θ4

{H} Fig. 3. Schematic robotic representation of a construction crane.

for each link has been calculated, a global transformation matrix, also called direct kinematics of manipulators, can be obtained by multiplying all of the transformation matrices. This research employs the crane model developed in by the authors previously [36]. The research basically treats a tower crane as a four-degree-of-freedom (4DOF) robot. Each degree of freedom represents each movable joint in the crane. The four-degree-of-freedom can be represented by four variables, denoted by h 1, d 2, d 3 and h 4. As shown in a robotic schematic representation of a tower crane in Fig. 3, h 1 represents the rotation of the jib, d 2 represents trolley radial movement, d 3 represents the lowering or rising of the hook and h 4 represented the rotation of the hook. Applying the Denavit Hartenberg notation, the direct kinematics of manipulator are obtained as follows. T ðh1 ;d2 ;d3 ;h4 Þ 2 c1 c4 þ s 1 s 4 6 s 1 c4  c1 s 4 ¼6 4 0 0

s 1 c4  c1 s 4  c1 c4  s 1 s 4 0 0

3 0  d1 s 1 0 d 2 c1 7 7 1 d3 5 0 1

ð1Þ

where c 1 in the equation is represented cos(hsub 1), c 2 is represented cos(hsub 2), s 1 is represented sin(hsub 1) and s 2 is represented sin(hsub 2). The matrix found in Eq. (1) permits the computation of the orientation and position of the hook of a crane. The left and upper three-by-three sub-matrix elements correspond to the three space vectors, which are used to determined the orientation of the hook, and the fourth column, which represents the position of the hook. Knowing the crane’s movement in each joint, i.e., h 1, d 2, d 3 and h 4, we can use Eq. (1) to obtain the hook’s location and orientation. Conversely, if we have the hook’s location first, we can inverse the process to find the crane’s movement in each degree of freedom. This method is called inverse kinematics of manipulator.

In this research, the main purpose of developing direct and inverse kinematics of manipulators was to transfer the crane model between Cartesian space (real world space) and configure space (C-space). In C-space, we are able to describe the crane geometry in space using the minimal set of parameters. For example, the position in space (the attitude) of a tower crane in Cartesian space can be described by only four variables, h 1, d 2, d 3 and h 4. Because C-space is constructed by the four space factors, a set of the four variables is a point in C-space. A motion of a tower crane can be described by a series of these four variables, which can form a continuous line in C-space. In C-space, an area in which the crane is not allowed to move, due to the collision with obstacles or the crane itself (self-collision), is called C-obstacle (Fig. 4). After the direct and inverse kinematics of manipulators are derived, we can transfer the crane model and obstacles from the Cartesian space to a Cspace. The problem of finding a collision-free erection path on a complex construction site can be simplified by finding a path that does not go into C-obstacle regions in the Cspace. Because this method does not need to deal with the full geometry and kinematics information of the whole crane in the Cartesian space, the computation and complexity of the path-planning problem is significantly reduced. 3.2. Path-planning and motion-planning methods Path-planning and motion-planning methods have been developed in computer science and robotics in the last 30 years [37]. Previous methods have mainly focused on the topics related to computer games and robots. Recently, because of the significant improvement in computation power, some research has started using path-planning methods for medicine and engineering purposes. To the best of our knowledge, little research has been done to develop path-planning methods specifically for cranes. A major challenge in finding the erection paths for a crane is to consider both geometrical obstacles and operation problems. Unlike many other applications in which the obstacles remain constant in time, in this application, every piece that is erected becomes an obstacle for the erection of the following pieces. This research separates the problem into

Pgoal

C-space

C-obstacle

Pinial

collision-free points

collision-free path Fig. 4. Motion planning in C-space.

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

two parts. The first part focused only on finding a collisionfree path efficiently, and the second part focuses on refining and optimizing the path for better crane operations. Inherent to the nature of path-planning methods, the methods that have a higher success rate in finding a collision-free path generally have a higher computation cost than those with a lower success rate. For this reason, we have developed and implemented three different pathplanning methods, QuickLink, QuickGuess and RandomGuess, to handle different path-planning problems to minimize the computation cost. The algorithms can be found in Fig. 5. QuickLink is the most inexpensive algorithm but has the lowest success rate in finding a collision-free path among the three methods. The basic idea of QuickLink is to build up two trees starting from both an initial point and end point by adding random points above those two points. QuickLink then attempts to link the end points in the two trees from the bottom up. If the connection between the points is found to be collision-free, a collision-free path is returned by linking the trees passing the connection. RandomGuess is the most expensive method among the three path-finding methods but offers the greatest possibility of finding a collision-free path if there is any. This method keeps ‘‘guessing1,’’ i.e., sampling, random points in Cspace until finding a path. If the guessed points can be linked to the initial tree without any collision, we can add

Algorithm QuickLink (Tinit, Tend): try to link two trees, Tinit, Tend, from the root. If find any node in the tree can see the other node in the other tree, then link two trees. 1 FOR EACH node nodeInit in Tinit 2 FOR EACH node nodeEnd 3 IF (seeEachOther(nodeInit, nodeEnd) 4 THEN link Tinit and Tend by passing nodeInit and nodeEnd 5 END FOR 6 END FOR Algorithm QuickGuess (Tinit, Tend): try to link two trees, Tinit, Tend, by adding some point which can see both trees. 1 Get random point pt 2 Find the lowest node nodeInit from Tinit which pt can see 3 Find the lowest node nodeEnd form Tend which pt can see 4 IF (both nodeInit and nodeEnd can be found) 5 THEN link Tinit and Tend by passing nodeInit, pt, and nodeEnd Algorithm RandomGuess (Tinit, Tend): keep adding new nodes to both trees and try to link two trees. 1 REPEAT 2

ptInit

3 4 5 6 7 8 9 10

ptEnd random point IF ptInit can be seen from the Tinit THEN add ptInit to Tinit IF ptEnd can be seen from the Tend THEN add ptEnd to Tend IF Tinit or Tend changes THEN QuickLink (Tinit, Tend) UNTIL two trees have been linked

random point

Fig. 5. Path-finding algorithms.

403

the point to the initial tree. Similarly, the end tree is grown by using the same process. If one or both of the trees are changed, the RandomGuess method will call the QuickLink function to examine whether the two trees can be linked without any collisions. This process is repeated until a path is found. Because the method needs to blindly guess random points in C-space and perform collision-detecting tests, the method can be extremely expensive in some cases. However, if there is at least one collision-free path in the given configuration, in theory, RandomGuess will eventually find the path after a sufficient amount of attempts. QuickGuess compromises the computation and completion by quickly guessing a random point in C-space. This method is essentially a middle point between the two trees. If the guessed point can reach both the initial tree and the end tree without collision, then we can connect the two trees by passing the guessed random point to obtain a collisionfree path. Adding more middle points can improve the success rate of path finding. This research implements QuickGuess method by using both single and double middle points. The QuickGuess method with a single middle point is shown in Fig. 5. The GeneratePath function, which integrates the tree path-planning methods, is implemented in the iCrane system. The function GeneratePath sequentially used QuickLink, QuickGuess and RandomGuess methods for finding paths. Since the function uses the path-planning methods, going from the one with less computation cost to the more costly one, the efficiency of the function can be maximized. We tested GeneratePath function on a 12-story building with 2105 structural elements and found that 62% of the paths were found by QuickLink, 35% were found by QuickGuess, and 3% were found by RandomGuess. In addition, we also estimated computation effort (computational time) by counting the number of times that the collision-detecting function was called in each of the three path-finding methods. QuickGuess was approximately ten times more computationally expensive than QuickLink and RandomGuess was ten to one hundred times more expensive than QuickGuess. The results showed that the GeneratePath function, which integrates QuickLink, QuickGuess and RandomGuess, can successfully adopt different methods and effectively find collision-free paths within reasonable computation times. 3.3. Path refining methods The purpose of path-refining methods is to optimize a given path and make this path more realistic and easier to follow, either by robotic cranes or by crane operators. The aforementioned path-planning methods may generate collision-free paths, which may involve redundant movements or awkward crane motions. After testing and fine-tuning various alternatives, we developed and implemented an effective path-refining method to eliminate these problems. The path-refining method is composed of three steps: the

404

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

Algorithm RemoveRedundantNodes (path): remove redundancies in given path 1 WHILE theNode is not the last node of the path 2 Find the farthest node that theNode can see 3 Remove the nodes between theNode and the farthest node 4 theNode.MoveToNextNode 5 END WHILE Algorithm SoftenSharpAngles (path): soften sharp angles. Can be used several times for better results 1 theNode the first node in the path 2 WHILE theNode is not the last second node of the path 3 Pick a random point pt in the line segment from theNode and its next node 4 IF pt can see the node two nodes away from theNode 5 THEN theNode pt 6 theNode.MoveToNextNode 7 END WHILE Algorithm OptimizeCraneRotate (path): remove unnecessary trolley in-and-out motions 1 theNode the first node in the path 2 WHILE theNode is not the last node of the path 3 IF the curve path is collision free 4 THEN replace the line segment from theNode to its next node by a curve 5 theNode.MoveToNextNode 6 END WHILE Fig. 6. Algorithms used for refining paths.

first step is to remove redundant nodes in the path; the second is to soften sharp angles, and the last step is to make the path easier for crane operations. The RemoveRedundantNodes algorithm, as shown in Fig. 6, is an effective method of removing the redundant points within a given path. The basic concept of this method is to examine each of the nodes in the path and identify the farthest node that the examined node can reach directly without collisions. If the farthest reachable node is not the next node in the path, we remove the redundant nodes between the examined node and the farthest node. This process is then applied to all the remaining nodes in the path, and usually, the original path is quickly refined to a shorter and more efficient one. After eliminating redundant nodes, the resulting path is not necessarily an optimal path, especially when the path includes many unnecessary sharp angles. Sharp angles may result in longer and less efficient paths, which waste crane movements during operations. SoftenSharpAngles is an algorithm to eliminate these sharp angles. This algorithm

first picks a random point as a temporary node within a line segment between two nodes and then connects the temporary node and the next node as a temporary new path. If this path is free from collisions, then the temporary node replaces the original node and the temporary path replaces the original path. Similar to the RemoveRedundantNodes algorithm, this process is applied to all the nodes in the path, and thus usually results in a smoother and more efficient path very quickly. In addition, the algorithm can be repeatedly applied to a path for a better result. We found that applying the method three times is generally sufficient to obtain a satisfactory outcome. RemoveRedundantNodes and SoftenSharpAngles can only avoid the redundant nodes and inefficient paths but do not take into account the special nature of crane motions. The main problem of what in Cartesian space appears to be an ‘‘efficient path,’’ in reality, may involve unnecessary crane motions, especially for trolley translation and jib rotations. For example, a straight line is usually a shortest path to move an object in a space. However, to rotate a crane following a straight line may require the trolley to move inward and outward resulting not only in unnecessary motions, but may also result in slower erection times. The algorithm OptimizeCraneRotate developed in this research can effectively improve the path so that it is specifically better suited for crane operations. Fig. 7 presents the path refining procedure. From the left to right figures, we applied the path-refining method by the sequence of RemoveRedundantNodes, SoftenSharpAngles and OptimizeCraneRotate. We found following the sequence has a high likelihood of generating a realistic path with relatively low computation cost. 3.4. Collision-detecting method A particularly important component required to compute collision-free paths is a collision-detecting method. We have developed an effective collision-detecting method, ApproxCheck, to determine whether a crane will have a collision. If any part of a crane collides with any obstacle in a given scenario, the crane is regarded as in a collision status. Otherwise, the crane is collision-free. Collision detecting is the most frequently-used function and usually significantly influences the performance of path-planning methods. Fig. 8 shows the number of times that the collision-detecting function is called by two of three path-planning methods previously described for a structure with 2105 elements to be erected by the crane.

TC

Fig. 7. An example of the path refining process (top view).

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

QuickGuess method

1000000

1000000

900000

900000

Collision Detecting (times)

Collision Detecting (times)

QuickLink method

405

800000 700000 600000 500000 400000 300000 200000

800000 700000 600000 500000 400000 300000 200000 100000

100000

0

0 0

50

100

150

200

Transportation Distance (meters)

0

50

100

150

200

250

Transportation Distance (meters)

Fig. 8. Number of collision-detecting function calls while finding path.

The figure shows that the QuickLink path-planning method calls the collision-detecting function approximately 10,000 to 400,000 times to find a collision-free path; the QuickGuess path-planning methods calls the function 100,000 to 900,000 times. The large numbers reveal the fact that the efficiency of the collision-detecting function significantly influences the efficiency of the path-finding method, as well as the performance of the overall computer system. Current collision-detecting methods [38,39] applied in robotics and computer graphics are generally more complex than necessary to be used for construction purposes and, moreover, relatively difficult to implement efficiently. By introducing reasonable tolerances, we developed a relatively simple and efficient collision-detecting method, ApproxCheck, which can be specifically used in the path-planning problems on construction projects. The method takes full advantage of the features of crane operations and construction elements to increase the efficiency of detecting collisions. In general, crane operators tend to maintain a conservative distance between cranes and obstacles to avoid collisions. With the exception of approaching the target position of the rigging element, operators prefer to move the element along paths in an open space, instead of passing through many obstacles. Therefore, a rough and conservative collision-detecting method is ideal for use in this scenario. While the rigging object is approaching the target position, the crane needs the help of precise collision-detecting methods to move the object correctly. The collision-detecting method also takes advantage for the regular shape of most construction elements. The shapes of most construction elements are typically long cuboids (rectangular boxes), or they at least can be represented as several cuboids. The outermost boundary of a W shape of steel, for example, can be simply represented as a cuboid. Therefore, the system uses cuboids as the outer boundary of objects and develops an algorithm to detect the collisions between cuboids. Using cuboid boundaries instead of complex shapes can significantly reduce the computation cost.

In our research, the collision-detecting method determined the collision status between objects in three levels, rough check, fine check and finest check. Since most of the objects in a construction were cuboids, we approximated all objects by cuboid boundaries. Each cuboid boundary has length L 1, L 2, L 3, where L 1  L 2  L 3. The rough check uses the longest length L 1 to form an external sphere as the outer boundary of each object. Checking the distance between two objects simply involves calculating the distance between the two spheres. The fine check uses the second longest length L 2 to construct spheres to make the outer boundary of an object. Therefore, describing an object typically requires a pile of spheres. The maximum number of spheres, M, is set to be equal to the ratio between longest and second longest length (M = [L 1/L 2]). The finest check uses the shortest length in the cuboid to construct M  N spheres, where M = [L 1/L 2] and N = [L 1/L 2]. Although the algorithm may not return the exact value of the distance between objects, the value is relatively close to the minimum distance between the two objects and always remains conservative (i.e., larger than the actual minimum distance). Previous research has concluded that using this method on a construction site results in errors ranging from 100 cm to 300 cm with a rough check, 15 cm to 50 cm by using fine check, and 5 cm to 15 cm with the finest check [26]. The accuracy of ApproxCheck is sufficient for dealing with most of the collision-detecting problems in construction projects. Another advantage of using ApproxCheck is that it not only detects whether an object collides with obstacles but also finds the distances between the object and obstacles without extra cost. This allows the user to define a minimum distance (margin of safety) between the crane, rigging system, erected piece and structure. Knowing the distances can significantly reduce the cost of determining a collision-free path. Without the distances, we may have to naively perform collision-checking functions for numerous points in a path. It may require thousands of function calls to determine a path and cannot always produce a reliable result. We have developed a function called

406

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

4. Motion planning of multiple cranes

P goal

P initial

e Obstacle Obs sttaca lec l

C- o b

Safety boundary Fig. 9. Collision detecting for a path.

SeeEachOther to determine whether the path between two given points is collision-free or not. SeeEachOther starts detecting collisions from both ends in the C-space of a given crane. If the end point is collision-free, then the function stores the free distance between the end point and the nearest obstacle, denoted by d, and moves the end point toward another end by d. The same process is performed from the other end. If the sum of two free distances is bigger than the distance between two ends, the path is collision-free. If a¨ is less than a predefined small number a˚ , the path is determined as not-collisionfree. Fig. 9 illustrates the procedure. This function minimizes the number of calls of SeeEachOther, so we can greatly reduce the computational effort involved in determining whether a path or a segment of the path is collision-free or not.

Increasing number of multi-crane constructions is an important motivation for the research. Using multiple cranes in construction is becoming common these days because of the trend toward large-scale or fast-track constructions. It can create several working fronts, which can significantly reduce total erection time. Moreover, very large cranes are often much more expensive and less available in certain areas. In many cases, modifying the design to allow the use of several smaller cranes may instead decrease cost and availability problems. In addition, several cranes provide more flexibility for scheduling a project. The downside of using multiple cranes in a construction is that it is very complex to plan and coordinate multiple cranes especially in a narrow construction site in urban areas. As shown in the photos in Fig. 10, when multiple cranes are in operation, crane-operating areas often overlap. In this case, the coordination and planning of the cranes become a very important factor in the success of the project. Spatial conflict is a main concern during a planning process. Construction engineers have to plan the crane activities carefully to minimize the likelihood that several cranes work in the same area during the same time. Crane operators also need to carefully operate their cranes to avoid collisions during construction. Some tower cranes have installed sensors that force the cranes to stop when they are too close to each other, but it is a passive method and may not

Fig. 10. Crane construction sites and planning.

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

be relied on very often. Producing a detailed erection plan in advance to avoid collision, together with collision detection sensors, is a better approach. The motion planning when multiple potentially colliding cranes are simultaneously operating is significantly more complex because we have to find safe and coordinated paths for each crane at all times. Collisions must be avoided between each pair of cranes and obstacles in the given environment. This section first introduces the two common methods, the centralized planning method and the decoupled planning method, broadly used in coordinating the motions of multiple robots, and then explains how these methods were adopted and modified to coordinate the motions of multiple construction cranes. 4.1. Centralized planning

involved in the centralized planning method. This method is a two-phase approach. When applied to construction cranes, the first phase consists of generating a collision-free path for each crane by considering only the obstacles in the environment and ignoring other cranes. In the second phase, called velocity tuning, the relative velocities of the robots along their respective paths are selected to avoid collision among them [40]. Velocity tuning consists of searching a coordination space. Here, we consider two robotic cranes, for example, and let s 1 and s 2 be their respective paths computed in the first phase. By forcing the crane to move along these paths, we reduce the number of degree of freedom of each crane into 1. Hence, the composite configuration space, now called coordinate space, becomes two dimensions. Let each path s i (i = 1, 2) be parameterized by some s i Z [0,1]. The set P = [0, 1]2 represents the coordination space of two cranes (Fig. 11). Each point (s 1, s 2) Z P defines a placement of the cranes at their configurations s 1(s1) and s 2(s2). This point is collision-free if at this placement the two cranes do not collide with each other. A path joining the point (0, 0), where both cranes are at their initial configuration, to (1, 1), where they are at their goal configurations, in the collisionfree subset represents a successful coordination of the cranes along s 1 and s 2. The cranes can tune their velocity to follow the pre-calculated paths, s 1 and s 2, to avoid the conflict between them. Decoupled planning searches lower dimensional spaces more than centralized planning does, significantly reducing the computation cost. However, it is inherently incomplete, even if the core planning algorithm used in the first and second phases are completed. Velocity tuning may fail because the paths generated in the first phase cannot be coordinated without collision between robots, while such coordination would have been possible had other paths be selected. A decoupled planner based on global coordination is less incomplete than one based on pair-wise coordination, since a specific path selected in the path space P i may result into P i + 1 with no collision-free path between (0,. . . 0) to (1,. . . 1). Nevertheless, pair-wise coordination has been more widely used than global coordination. Crane2 Crane2 finished

(1, 1)

Crane1 finished

Centralized planning is a straightforward way of coordinating the activities between several robots. This method considers all the robots as if they form a single multi-boom robot by encoding their degree of freedoms in a single composite configuration space N˜ and searching that space for a collision-free path between the initial and goal configurations. This method turns the coordination problem between robots to the self-collision-detecting problems within the composite single robot. The composite configuration space is C = C 1  C 2  . . .  C p , where p is the number of robots and C i is the configuration space of the ith crane (i Z [1, p]). Thus, the number of the dimension of C is equal to the total number of degree of freedoms of all the robots. If there are three, four-degree-of-freedom cranes, for example, then the composite configuration C-space has 12 dimensions. Let s:s Z [0, 1][s(s) Z F be a path in the free set F of C. The projection s i of s into C i is the path to be followed by the ith robot. For each s Z [0,1], s(s) is the form (s 1(s), s 2(s). . . s p (s)), which describes the configurations of the p robots at a single point along the path s. Hence, a path in F, if one exists, not only describes the individual path to be followed by each robot, but also presents how the robots are to be coordinated. In principle, any general path-planning algorithm can be used to implement centralized planning by applying this algorithm to the composite space C. However, because the method usually requires finding a path in a C-space with a large number of dimensions, it is inefficient in practice given existing computation power. Most centralized planners today are based on incomplete heuristics, such as potential field techniques. Completed centralized planning algorithms have only been proposed for very simple systems, such as the coordination of two discs among polygonal obstacles.

407

4.2. Decoupled planning with velocity tuning The decoupled planning method was developed to facilitate the problem of expensive computation efforts

(0, 0)

Crane1 Fig. 11. Coordinator space of two robotic cranes.

408

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

4.3. Incremental decoupled method To coordinate multiple cranes on a construction site, we need to consider more issues than in typical robotics problems. A typical environment to manipulate robots, such as welding robots in vehicle manufacturing, involves relatively less moving obstacles than the one to operate a construction crane. For example, the list of obstacles before and after welding may change very little or can even be ignored. On the contrary, within a construction project, the number of structural elements is increasing as erection progresses. Cranes need to avoid collision with all structural elements that have previously been erected and find a collision-free path for each subsequent element to be erected. Namely, the obstacle list is increasing as construction progresses. To deal with the continuously changing environment, we developed a more specific method for researching and coordinating the activities between cranes. We proposed a method, called incremental decoupled method, to plan motions for multiple cranes. Similarly to the decoupled planning method, the incremental decoupled method has two phases. The first phase is to find the motion of a crane and obtain its individual erection paths without considering other cranes. Then the second phase is to coordinate the activities between cranes. Instead of planning the crane motions for an entire project, this method plans the motions of an individual crane during a certain amount of time and coordinates the motions of cranes during that time period by using velocity tuning as decoupled planning method does. The generalized algorithm of incremental decoupled method for multiple-crane projects (including two or more than two cranes) can be found in Fig. 12. Here, we use a two-crane construction as an example to explain the procedure. Assume two cranes, Crane1 and Crane2, are involved in a project. The first step to plan the project is to conduct the motion planning of Crane1 during a user defined time interval d. This involves providing collision-free paths of all elements to be erected by Crane1 during time interval d? and also considering as obstacles all the elements to be erected by Crane2 during the same time Algorithm IncrementalDecoupledCoordinator (CraneList CList, BuildingList BList): Coordinate the cranes in crane list to erect the buildings in building list. 1t starting time 2δ time increment 3 REPEAT 4 FOR EACH crane Cr in CList 5 obstacleList BList[1](t+δ) + BList[2](t+δ) + ..... BList[i](t)+...BList[n](t+δ) 6 Plan the motion of Cr using obstacleList 7 END FOR 8 Coordinate cranes in CList in coordinate space 9 t t+ δ 10 UNTIL all the buildings in BList is erected

Fig. 12. Incremental decoupled coordination method.

interval d? At this stage, motion planning avoids the cranes from colliding with elements in their final (erected) position but does not consider the possibility of the cranes or the structural elements colliding with each other as they are being erected. This possible collision is then eliminated in the second stage by using velocity tuning in the coordinator space. In this phase, the motion in each crane required to erect pieces during the time interval d is adjusted to avoid possible collisions during this time interval. Phases one and two are then repeated at times id (i = 1, 2, . . . n) until all the elements in the project have been erected. The time interval usually needs to be a short period of time that is equivalent approximately to the average time required to erect three or four elements. Moreover, this time interval does not need to remain constant and, for example, in the case of high-rise construction, d could be increased as the erection progresses, in order to take into account the increase in average time to erect an element as erection of the building progresses.

5. Implementation and results 5.1. Implementation of iCrane We implemented the intelligent crane in a computer system, iCrane, which can automatically generate the operation-leveled simulation of erection processes. iCrane was equipped with algorithms developed in this research, having the capacity of (1) generating erection sequence; (2) finding collision-free erection paths of each structural element; (3) planning the motions of construction crane(s) to follow the calculated erection paths; and (4) coordinating the motions between multiple cranes. The basic workflow of iCrane is illustrated in Fig. 13. Users are allowed to choose an engineering model (SAP2000 format) and import it to iCrane system. The system then converts the engineering model to a construction model and generates a template of erection sequences. Users are given the option to modify automatically generated sequences by using an interactive graphical interface until obtaining a satisfactory result. After the sequence is decided, the iCrane system sequentially calculates the erection path using path-planning algorithms developed in this research. Finally, an animation of construction processes will be generated in a virtual environment. If there is more than one crane, the coordination function will be called to coordinate the activities between cranes. If desired, a traditionally Gantt chart schedule can also be generated. Engineers can revise the engineering model and repeatedly run the virtual construction to achieve the purpose of design-for-manufacturing. Project planners can use the system to test different erection processes to obtain an optimal schedule. Since the animation is real-time generated, users are able to select a preferred view angle and

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

98 81

409

99 82

83

91

92

31

32

CoConstruction nstr uc ti on mode model l

En Engineering gineerin g mo model de l

24 1

De

25 2

3

sig

n-f

or-

ma

Se Sequenced quence d

nu

fac

tur

ing

le

du

che

s ize

tim

Interactive animation

Precise schedule

Op

SiSimulation mu la ti on

ErErection ec ti on path pa th

CoCoordination ordina ti on

virtual construction (iteratively) iCrane Fig. 13. Workflow of iCrane system.

speed to observe the construction in different aspects, to maximize the understanding of a construction project for various purposes. This system can produce precise and detailed planning and scheduling before real construction to eliminate potential risky and inefficient activities. We use OpenGL, a graphical language broadly used in computer graphics, to implement the intelligent crane in a 3D graphical environment. Site layout and the tower cranes are visualized in the virtual world. The system was developed in the Microsoft.Net platform providing a user friendly graphical interface which allows users to control the view angles and play speed of the animation. Users are able to shift the view points between front view, side view, top view, operators’ view and user-defined observation points, or even navigate in space in the virtual environment. Visualization will illustrate the path to be followed by each piece, which can be used to operate robotic cranes or as a training tool for crane operators using conventional cranes. An interactive animation with a precise schedule can be generated by iCrane. In the visualization module, users are able to see and study the erection in the computer before actual erection takes place. For this purpose, users may choose different play speeds, or may pause, rewind or forward the animation to understand the erection processes clearly. Visualization will be able to be done for specific pieces, for groups of pieces, for specific periods of times (e.g., 1 h, one shift, 1 day, 1 week, etc.) or for the whole project duration. The goal of the visualization is to provide a powerful tool to assist crane operators, project superintendents and project managers in making correct decisions before and during the project.

iCrane is also an excellent tool for planning the transportation of the material to be erected from the shop or precast-yard to the construction site, in order to avoid the crane having to wait for the material to arrive to the site or to minimize storage on site. 5.2. Comparison with previous research To evaluate the proposed method, we compare the erection times computed by using iCrane to those computed by using the method developed by Zhang et al. [11,13]. In the evaluation, a 48-m high tower crane with a 50-m working radius was selected to erect a 12-story building containing 2105 structural elements. The material to be erected was assumed to be picked up by the crane remains at the same location during the entire erection and has already been transported to the site when they will be erected. The erection time of each piece was calculated by using iCrane, Zhang’s model and a revised Zhang’s model. The results are plotted in Fig. 14. Zhang’s model considered crane motions in both horizontal and vertical planes. It first calculated the differences in the vertical, angular and radial direction corresponding to the position of the hook, before and after each erection activity, and divided the differences by the average velocity of each degree of freedom to obtain travel time of each degree of freedom. Presenting the procedure by mathematical notation, the previous researchers defined point with coordinates S(X Si , Y Si , Z Si ) as the start point of the ith erection activity, and point with coordinates D(X Di , Y Di , Z Di ) as its destination point (see Fig. 15). The base of the tower located on the

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

Erection Time (Sec)

410 350

iCrane Model

Zhang's Model

Revised Zhang's Model

300 250

200 150

100 50 0 0

500

1000

1500

2000

Sequence No Fig. 14. Erection time of each element estimated by Zhang and iCrane.

point with coordinate Cr(X Cri , Y Cri , Z Cri ). The average travel time in vertical direction T v can be calculated as follows: Tv ¼

ðZSi  ZDi Þ Vh

ð2Þ

where (Z Si  Z Di ) is the difference of the height between point S and point D and V h is average lifting velocity of the hook. Similarly, the time for trolley radial movement can be calculated as: Tr ¼

jqðDi Þ  qðSi Þj Vr

ð3Þ

where q(S i ) is the horizontal distance between the trolley at the start point S and the intersection of the tower and the boom. Similarly, q(D i ) represents the horizontal distance the trolley in the destination point D and the intersection of the tower and the boom. Vr is the average trolley velocity during the erection. Radial distances q(D i ) and q(S i ) can be found as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð4Þ qðDi Þ ¼ ðXDi  XCri Þ2 þ ðYDi  YCri Þ2 qðSi Þ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðXSi  XCri Þ2 þ ðYSi  YCri Þ2

h Vx

While T v, Tr, T x are reasonable times for avoiding an element from in the vertical, radial and angular directions, the time required to move an element from point S to point D cannot be simply estimated as the sum of these times. This is because these cranes motions do not occur one after the other, but rather crane operators, will be simultaneously moving the inward and outward trolley, rotating the boom and lifting or lowering the hook. In order to approximately account for simultaneous crane motions, Zhang et al. introduced two parameters: a and b. The first parameter, a, represents the degree of coordination of hook movement in radial and tangential directions in the horizontal plan. There are two extreme

iCrane

ð5Þ

The average time for rotational movement, T x, can be obtained by dividing the rotational angle between the start point and destination point h by the average angular velocity of the crane V x as follows: Tx ¼

And the l i is the horizontal distance between the start and destination points which is given by: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ li ¼ ðXDi  XSi Þ2 þ ðYDi  YSi Þ2

Zhang’s

ð6Þ

where h ¼ cos

1

li2  qðDi Þ2  qðSi Þ2 2IqðDi ÞIqðSi Þ

! ð7Þ Fig. 15. Paths generated by Zhang and iCrane model.

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

situations for a: full simultaneous movement occurs when a = 0, and consecutive movement occurs when a = 1. By assigning an appropriate value a, Zhang et al. approximate can calculate the erection time required in the horizontal plane T h as. Th ¼ maxðTr ;Tx Þ þ aminðTr ;Tx Þ

ð9Þ

The parameter b accounts for simultaneous motions in the vertical and horizontal plane. This parameter also has two extreme situations: full simultaneous movement occurs in horizontal and vertical planes when b = 0, and consecutive movement occurs when b = 1. Choosing a b value from 0 to 1 Zhang et al. estimated the erection time considering both the simultaneous horizontal and vertical motions with the following equation. T ¼ maxðTh ;Tv Þ þ bminðTh ;Tv Þ

ð10Þ

Although Zhang’s model considered the simultaneous motions in both horizontal and vertical planes, this model cannot reflect many of the real situations in actual jobsites. In particular, they assume that a and b were the same for all lifts in the project. Furthermore, if there are many obstacles within the region between the starting point and destination point, the operator would be forced to choose farther paths to avoid collisions with the obstacles. This situation happens very often but cannot be simulated by previous models. It is resulted from that the model estimates erection times based on the linear (direct) distances between the initial and destination points together with rough estimates of the degree of simultaneity of horizontal and vertical crane motions (empirical parameter a, b), but it neither considers actual paths nor variations from ideal paths due to obstacles. Zhang et al. [13] and Tam et al. [14] both selected a = 0.25 and b = 1 from the crane operators’ experience. However, because the construction projects are very different from each other, empirical parameters are difficult to estimate a priori, especially in an environment with many obstacles. To improve the accuracy of the crane model, this research provided a new approach to estimate the erection time. In the research, we used computers to calculate the collision-free paths for structural elements needed to be erected and simulate the motions of the crane to follow these pre-defined paths. Since this method did not include any empirical parameters and has taken the geometrical constrains and crane capacity into account, the estimated times are move representative of erection time in actual construction. iCrane used the algorithms developed in the research to find a collision-free and operational-optimal path for erecting each structural element. By using inverse kinematics of the tower crane, iCrane transfers the path to the motions of the crane and obtains the erection time. This method considers both kinematical limits (such as velocity and acceleration) of the crane and geometrical constraints

411

(such as the building under construction and obstacles on the construction site) and estimates the erecting time close to what we observe on actual construction sites. The major difference between iCrane and Zhang’s model is that Zhang’s model considers little about constraints in the environment. This model transfers the coordinators of the initial point and the target point into the movement of each degree of freedom of a crane. The travel time of each degree of freedom can be obtained by dividing the velocity of that degree of freedom. Since the crane’s motions sometimes involves simultaneous movements between the degree of freedoms, Zhang’s model introduces two empirical parameters, a and b, to simulate the situation. a represents the degree of simultaneity of motions between trolley radial motion and the boom rotation, and b reflects the degree of simultaneity of motions between the vertical and horizontal motions. In the experiment, we adopt empirical parameters used in Zhang’s research, a = 0.25 and b = 1. a = 0.25 means 25% simultaneous motion between trolley motion and boom rotation. b = 1 means that the horizontal motion and vertical motion are fully independent and always happening consecutively. Since Zhang’s model does not consider the vertical motions required at the initial and target points, it tends to underestimate the erection time when compared with the times generated by iCrane. Therefore, we add 3 m as the minimum vertical movements, 3 m to both ends of the path and revise Zhang’s model by adding the additional travel times. The results showed that Zhang’s model tends to underestimate erection times while comparing with iCrane method. The erection time per piece estimated by Zhang’s model is on average 26.1% less than that computed by the iCrane model. The standard deviation is 11.9%. The revised Zhang’s model still has an average 13.0% underestimation, compared to the iCrane model. The standard deviation is also 11.9%. Although Zhang’s and revised Zhang’s model underestimate the erection times, we found the three models have similar tendency in terms of travel time in most structural elements. In the analysis, we found that some structural elements lead to large differences in erection time between iCrane and Zhang’s model. Approximately 5% of the structural elements have more than 200% difference; and approximately 38% of the structural elements have at least a 150% difference. We found the large errors come from the unrealistic paths used in Zhang’s model. Zhang’s model oversimplifies the erection path without considering collisions in the erection paths. We also found that the more obstacles between the supply location and target position, the more difference between the estimate from iCrane and Zhang’s model. Fig. 16 illustrates the situation when large error occurs between the models. In this case, since the crane has to avoid the obstacles between the initial and target point, the path generated by iCrane is much longer than by Zhang’s model which computes the erection time

412

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

(XSi, YSi, ZSi)

D ρ(Di )

S

li

(XDi, YDi, ZDi)

θ

ZDi

ρ(Si )

(XCri, YCri)

ZSi

Fig. 16. Crane model (modified from Zhang et al. [12]).

with the distance between the initial and target (final) points (Table 1).

6. Utilizing iCrane in construction practice iCrane can automatically search the erection paths, plan the crane motions and visualize detailed erection processes before or during construction. While applied iCrane in construction practice, iCrane system can broadly benefit crane operators and construction management to perform their work more efficiently. The system eventually can be used in design phase to facilitate the design processes. Having computational methods, we can input construction criteria and geometrical information related to erection activities in a computer system, ask the system to generate detailed erection planning and visualization. By introducing appropriate motion-planning algorithms, we can use computers to find paths for erecting a structural element, calculate the time required by the crane and superimpose all erection activities as an entire erection plan. It is possible to do the process as many times as necessary to find the most optimal erection plan. After the erection plan is generated, the computer can visualize overall erection activities in different speeds and with different details, which provides more versatile functions to different users than the traditional approach. Furthermore, the computa-

tion methods provide more reliable erection schedules than those purely based on experience from previous projects. The computer-aided planning method can also increase the accuracy and efficiency of project management to support larger, more complex, safer and faster projects in the future. Utilizing iCrane in a construction site can significantly improve the communication between the cranes. On most construction sites, tower crane operators are responsible for controlling most of the progress of erection processes. iCrane can facilitate communication and coordination between crane operators and crews. The operators have to manipulate the machine in continuous working hours, carefully considering both load limit and moving trajectories. At the same time, they need to communicate with the crews on the ground to assure material preparation or welding/bolting progress. The long continuous working hours under high pressure make the job tougher and riskier. The simulation tool provides a great help for crane operators, allowing the operators and crews to ‘‘see’’ the erecting process in advance and have the computer control a robotic crane. The simulation in a virtual world will help improve the communication between the crane operators, onsite crews and construction managers. Many spatial conflicts and unsafe situations will be found and eliminated during the simulation instead of in on an actual jobsite. Hence, we believe introducing iCrane to a construction project will improve the working environment for the crane

Table 1 Comparison between current state of practice and the research current state of practice using iCrane Current state of practice

Using iCrane

Operators

hDepend on operator’s experience hNot always follow the most efficient and safest erection paths hCommunicate with crews by body language or walky-talky

Construction managers

hSchedule by rough estimate hPlan the site layout using previous experience hCoordinate/Solve onsite problems during the construction

Designers

hDesign by structural criteria hConsider structural safety and material economic hConsider little about constructibility

hPlan/Coordinate in advance hImprove communication between crane operator, crews, and construction managers hEliminate unsafe situations in the simulation hAccurate schedule hOptimal site layout hFind/Solve potential problems during a simulation hMay decrease insurance premium because of the safety improvement. hConsider constructibility in design hImprove design quality hBe able to evaluate alternative design

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

operators and help the erection operation become safer and more efficient. The quality of coordinating and scheduling the tasks in construction projects can also be improved by iCrane. Coordination of personnel and resources is the major job for construction managers. One of the most difficult parts in the job is to coordinate all onsite crews with the crane operators. iCrane enables the visualization of the erection process in different viewpoints for different users. The visualization helps the operators and crews on the ground understand what is going on in the jobsite and what will happen next from their own viewpoints. This effective coordinating method will shorten the time for communication and reduce the possibility of misunderstanding between the parties. Furthermore, the simulation system will significantly improve the accuracy of scheduling. An accurate schedule will facilitate the construction manger to control the expense and scheduling of equipment rental, personnel management and material delivery. iCrane can also help integrate construction knowledge in the design phase to increase constructibility of a project. Although the decision-making in design phase is a less expensive and quicker procedure than it in construction phase, its influence is much more significant than in construction phase. In other words, if we are capable to fix construction problems in early design phase and prevent them happening during the construction processes, we can significantly reduce the expense and uncertainty in the project. The design decisions significantly influence entire construction projects. Most structural engineers, however, are trained to design a building based only on the structural analysis of the complete structure, but with little or no consideration of constructibility. The computer system developed in this research enables the simulation and visualization of the erecting process in the early design phase. Engineers can use the tool to evaluate design candidates with enough details. With a little extra cost and time in design phase, they are able to select the best design that benefits the overall project.

7. Conclusions We have developed effective methods to model construction cranes in computers and equipped them with pathplanning, collision-detecting and optimization algorithms. The crane models had the capacity of analyzing the geometrical information from given buildings, cranes and construction environments and for searching the safest and most efficient paths to erect a building. We also developed methods to coordinate multiple cranes in a continuously changing construction environment. The intelligent cranes are implemented and visualized in a computer system, iCrane. By comparing iCrane with the mathematical model developed by previous researchers, we concluded that

413

iCrane can reflect the reality of erection processes and result in a more accurate simulation. Due to the rapid growth of computation power, we can implement the intelligent crane to simulate and visualize the fully robotic construction in nearly real time. iCrane can be executed in most personal computers and enables users to simulate construction processes virtually as many times as necessary before a real construction project begins. This operation-leveled simulation assists structural designers and construction managers to select more efficient and economic sequences with a solid basis. The system can be also used to provide an accurate and detailed schedule for erection processes, which will improve the safety of crane operations and constructibility of entire projects. Although iCrane is currently developed only for the virtual construction, we believe that much of this research will be useful for future design-for-manufacturing and fully automated robotic construction.

References [1] C. Carter, T. Murry, W. Thornton, Cost-effective steel building design, Progress in Structural Engineering and Materials 2 (1) (2000) 16 – 25. [2] Census of Fatal Occupational Injuries, Fatalities by Detail Occupation: Crane and Tower Crane Operators, [online] Available at: , [Accessed October 2004]. [3] Crane Accident Statistics, Accident Reports Received for Year 2001, 2002, 2003., [online] Available at: , [Accessed November 2004]. [4] A.C. Braam, Crane Accidents Evaluating the Risk and Feasibility of Potential Practices to Eliminate/Reduce Future Occurrences, North Carolina Department of Transportation, 2002. [5] K. McKinney, M. Fischer, Generating, evaluating and visualizing construction schedules with 4D-CAD tools, Automation in Construction 7 (6) (1998) 433 – 447. [6] S. Furusaka, C. Gray, A model for the selection of the optimum crane for construction sites, Construction Management & Economics 2 (1984) 157 – 176. [7] C. Gray, J. Little, A systematic approach to the selection of an appropriate crane for a construction site, Construction Management & Economics 3 (1985) 121 – 144. [8] C.W. Farrell, K.C. Hover, Computerized crane selection and placement for the construction site, Proceeding of International Conference on Civil and Structural Engineering Computing, vol. 1, 1989 (Sept.), pp. 91 – 94. [9] C.W. Choi, F.C. Harris, A model for determining optimum crane position, Proceeding of Institution in Civil Engineers, vol. 1, 1991, pp. 627 – 634. [10] C.M. Tam, K.L. Tong, K.W. Chan, Genetic algorithm for optimizing supply location around tower crane, Journal of Construction Engineering and Management 127 (4) (2001) 315 – 321. [11] P. Zhang, F.C. Harris, P.O. Olomilaiye, G.D. Holt, Location optimization for a group of tower cranes, Journal of Construction Engineering and Management 125 (2) (1999) 115 – 122. [12] W.T. Leung, C.M. Tam, Models for assessing hoisting times of tower cranes, Journal of Construction Engineering and Management 125 (6) (1991) 385 – 391. [13] H. Zhang, C.M. Tam, J. Shi, Application of fuzzy logic to simulation for construction operations, Journal of Computing in Civil Engineering 17 (1) (2003) 38 – 45.

414

S.C. Kang, E. Miranda / Automation in Construction 15 (2006) 398 – 414

[14] C.M. Tam, W.T. Leung, D.K. Liu, Nonlinear models for predicting hoisting times of tower crane, Journal of Computing in Civil Engineering 16 (1) (2002) 76 – 81. [15] K. Lin, C. Haas, Multiple heavy lifts optimization, Journal of Construction Engineering and Management 122 (4) (1996) 354 – 362. [16] M.S. Ali, N.R. Babu, K. Varghese, Collision free path planning of cooperative crane manipulators using genetic algorithm, Journal of Computing in Civil Engineering 19 (2) (2005) 182 – 193. [17] P.L. Sivakumar, K. Varghese, N.R. Babu, Automated path planning of cooperative crane lifts using heuristic search, Journal of Computing in Civil Engineering 17 (3) (2003) 197 – 207. [18] S.C. Kang, E. Miranda, Physics based model for simulating the dynamics of tower cranes, Proceeding of Xth International Conference on Computing in Civil and Building Engineering (ICCCBE), Weimar Germany2004 (June). [19] R.R. Lipman, K.A. Reed, Using VRML in construction industry applications, Symposium on Virtual Reality Modeling Language, Monterey, CA2000 (February). [20] E. Amatucci, R. Bostelman, N. Dagalakis, T. Tsai, Summary of modeling and simulation for NIST RoboCrane applications, Proceedings of the 1997 Deneb International Simulation Conference and Technology Showcase, Detroit, MI, September 29-October 3, 1997. [21] W. Stone, K. Reed, P. Chang, L. Pfeffer, A. Jacoff, NIST research toward construction site integration and automation, Journal of Aerospace Engineering 12 (2) (1999) 50 – 57. [22] L.Y. Liu, Construction crane operation simulation, Proceeding of Computing in Civil Engineering, 1995, pp. 1420 – 1426. [23] J.T. O’Connor, P.V. Dharwadkar, K. Varghese, T.M. Gatton, Graphical visualization for planning heavy lifts, First Congress on Computing in Civil Engineering, ASCE, Washington, DC, 1994 (June). [24] L.E. Bernold, S.J. Lorenc, E. Luces, On-line assistance for crane operators, Journal of Computing in Civil Engineering 11 (4) (1997) 248 – 259. [25] L. Cousineau, N. Miura, Construction Robots: The Search for New Building Technology in Japan, ASCE Press, 1998. [26] K.M. Liston, M. Fischer, J. Kunz, 4D annotator: a visual decision support tool for construction planners, Computing in Civil Engineering, Proceedings of International Computing Congress, Boston, 1998 (October), pp. 330 – 341. [27] B. Koo, M. Fischer, Feasibility study of 4D CAD in commercial construction, Journal of Construction Engineering and Management 126 (4) (2000) 251 – 260.

[28] V.R. Kamat, J.C. Martinez, General-purpose 3D animation with VITASCOPE, Proceedings of the 2004 Winter Simulation Conference, Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, 2004. [29] J.C. Latombe, Robot Motion Planning, Kluwer Academic Publishers, Boston, 1991. [30] N.M. Phater, The MOLOG project, Cadcentre Pipeline 11 (3) (2001). [31] M.S. Ali, D. Ajmal, N.R. Babu, K. Varghese, Offline path planning of cooperative manipulators using co-evolutionary generic algorithm, Proceedings of 19th International Symposium on Automation and Robotics in Construction, Washington, D.C., 2002 (September), pp. 415 – 424. [32] R.R. Lipman, K.A. Reed, Using VRML in construction industry applications, Web3D, VRML 2000 Symposium Proceedings, Monterey California, 2000 (February), pp. 1 – 7. [33] M.L. Chui, A virtual reality environment for construction simulation, Proceedings of the 17th IAARC International Symposium on Automation and Robotics (ISARC), Taipei, Taiwan, 2000 (September), pp. 1147 – 1152. [34] C. Bennett, S. Ditlinger, Bechtel automated lift planning system, Proceeding of Robotics for Challenging Environments, New Mexico, 1996 (June), pp. 401 – 409. [35] J. Denavit, R.S. Hartenberg, A kinematic notation for lower-pair mechanism based on matrices, Journal of Applied Mechanics (1955) 215 – 221. [36] S.C. Kang, E. Miranda, Automated simulation of the erection activities in virtual construction, Proceeding of Xth International Conference on Computing in Civil and Building Engineering (ICCCBE), Weimar Germany 2004 (June). [37] L.E. Kavraki, J.C. Latombe, Probabilistic roadmaps for robot path planning, Practical Motion Planning in Robotics: Current Approaches and Future Directions, John Wiley, 1998, pp. 33 – 53. [38] M.C. Lin, J.F. Canny, A fast algorithm for incremental distance calculation, IEEE International Conference on Robotics and Automation, Sacramento, California, 1991 (September), pp. 1008 – 1014. [39] J.T. Klosowski, J.S. Mitchell, H. Sowizral, K. Zikan, Efficient collision detection using bounding volume hierarchies of k-DOPs, IEEE Transactions on Visualization and Computer Graphics 4 (1) (1998) 21 – 36. [40] G. Sanchez, J.C. Latombe, Using a PRM planner to compare centralized and decoupled planning for multi-robot systems, Proceeding of IEEE International Conference on Robotics and Automation, Washing D.C. 2002.