Development of a Multi-Robot System for Pier Construction

Abstract

The construction industry is a challenging field for the application of robots. In particular, bridge construction, which involves many tasks at great heights, makes it difficult to implement robots. To construct a bridge, it is necessary to build numerous piers that can support the bridge deck. Pier construction involves a series of tasks including rebar connection, formwork installation, concrete pouring, formwork dismantling, and formwork reinstallation. These activities require working at heights, presenting a significant risk of falls. If bridge construction could be performed remotely using robots instead of relying on human labor, it would greatly contribute to the safety of bridge construction. This paper proposes a multi-robot system capable of remote operation and automation for rebar structure connection, concrete pouring, and concrete vibrating tasks in pier construction. The proposed multi-robot system for pier construction is composed of three robot systems. Each robot system consists of a robot arm mounted on a mobile robot that can move along rails. And to apply the proposed system to a construction site, it is essential to implement a compliance control algorithm that adapts to external forces. In this paper, we propose an admittance control that takes into account the weight of the tool for the compliance control of the proposed robot, which performs tasks by switching between various construction tools of different weights. Furthermore, we propose a synchronization control method for the multi-robot system to connect reinforcing structures. We validated the proposed algorithm through simulation. Furthermore, we developed a prototype of the proposed system to verify the feasibility of the suggested hardware design and control.

1. Introduction

Robotic systems tailored for the construction sector are actively under development worldwide, with the primary goal of enhancing safety, productivity, and operational efficiency. These systems span a wide range of applications, including robots designed for building inspections, pipeline inspections, 3D construction printing, bridge construction and even specialized underwater construction tasks [1,2,3,4,5,6,7,8,9,10,11,12].

Bridge construction, in particular, presents a unique challenge for the integration of robotic technology. This challenge primarily arises from the prevalence of high-altitude tasks, necessitating improvements in job safety and efficiency. A typical bridge consists of girders and piers, where the girder forms the upper structure of the bridge, while the pier serves as the foundational structure supporting the girder and transferring the bridge’s load downward. The construction of concrete piers typically involves a series of steps: connecting rebars, installing formwork, and pouring concrete. Due to height limitations for pouring concrete in a single operation, the construction process starts from the bottom of the pier and progresses upwards. This process includes a repetitive cycle of rebar connection, formwork installation, concrete pouring, formwork dismantling, and reinstallation. Such pier construction tasks demand work at significant heights and are susceptible to frequent fall-related accidents [12].

To mitigate risks, expedite construction timelines, and enhance quality, automated systems for pier construction are actively being developed, with partial automation integrated into the pier construction process. For instance, an automated climbing formwork system has been devised to autonomously disassemble and raise formwork, thus relieving workers from the hazardous task of dismantling and reinstalling formwork at considerable heights. However, many critical steps in the pier construction process, such as rebar structure connection, concrete pouring, and concrete vibrating, are still primarily per-formed by human workers. The full automation of these tasks remains a formidable challenge [12].

This paper introduces a multi-robot system designed to facilitate remote operation and automation for tasks involving rebar structure connection, concrete pouring, and concrete vibrating within pier construction. The proposed multi-robot system for pier construction comprises three distinct robot systems, each featuring a robot arm mounted on a mobile robot capable of rail-based movement. To successfully implement the proposed system on a construction site, it is crucial to incorporate a compliance control algorithm that adapts to external forces. In this paper, we present an innovative admittance control algorithm that accounts for the weight of the tool, ensuring precise compliance control for the proposed robot, which seamlessly switches between various construction tools of differing weights. Moreover, a prototype of the proposed system was developed, and its performance was validated through experiments to verify the suggested hardware design and control.

2. Multi-Robot System for Pier Construction

Bridge construction is a time-consuming process, leading to the development of various methods to streamline it. For example, Idaho State University is researching accelerated bridge construction in seismic regions. Their approach uses a new precast method involving structural steel tubes filled with concrete in plastic hinge zones, which act as seismic energy dissipating devices to enhance the structural performance of piers. Another innovative approach to reduce risks and improve construction efficiency includes the development of systems such as the Auto-Climbing Form System (ACS), which automatically raises formwork, and the Slip Form System, which allows continuous concrete pouring while gradually lifting the formwork [11,13].

The automatic climbing formwork system for constructing the piers of a bridge automatically dismantles and lifts the formwork [12]. The automatic climbing formwork system automatically dismantles and lifts the formwork. The proposed multi-robot system for pier construction system is installed on the work platform at the top of this automatic climbing formwork system. Figure 1 is the design model of the proposed the multi-robot system for pier construction. It consists of a total of three identical robot systems, and each robot system is composed of a rail at the bottom, a mobile platform that can move along the rail, and a manipulator for tasks. Figure 2 shows the conceptual diagram of installing the multi-robot system for pier construction on the automatic climbing formwork system.

The target diameter of the pier column is 2 m, and the tool mounted on the manipulator has a maximum weight of 40 kg. A manipulator that meets these workspace and load requirements was selected. The specifications of the manipulator are shown in

Table 1. The specifications of the manipulator.

Manufacturer	Hyundai Robotics
Model	YS080
DOF	6 axes
Payload	80 kg
Body weight	645 kg

.

Each robot system moves on the rails to perform tasks such as ‘grabbing the upper rebar mesh and inserting it into the couplers installed on top of the lower rebar mesh’, ‘compressing the couplers to secure the upper and lower rebar meshes’, and ‘vibrating the concrete to remove air bubbles after concrete pouring’ [14,15,16]. Tool changes, required for each task, are conducted by coupling or decoupling the master side and tool side of the tool changer [17]. For the robot system to automatically or remotely change tools, the positional accuracy of the robot in relation to the tool’s location must ensure high precision. To address this, it is necessary to ensure the positional accuracy of the mobile platform. We have designed it to be constrained on the rails as shown in Figure 3 to prevent the mobile platform from tipping over or its position from being distorted. The mobile platform moves with a total of four driving wheels to prevent the driving wheels from losing contact with the rail due to obstacles like cement dropped on the rail. Each driving wheel is assisted by a guide wheel to prevent the robot system from tipping over or losing its posture during operation. Furthermore, for the recognition of the mobile robot’s position, a draw wire sensor was applied as illustrated in Figure 4, and the position of the mobile robot on the rail was estimated based on the length of the wire.

Because we use a draw wire, each robot must stay within its designated sector, with each robot covering a 120-degree section of the work area. The resolution of the draw wire sensor is 0.05 mm. Despite this, the position where the tool is placed can change due to vibrations from the work platform and debris from construction materials. The workbench where the tool station is installed is roughly machined, and to reduce weight, materials like mesh wire can be used for parts other than the framework. This may cause shaking during the robot’s movement. To resolve this issue, we propose an admittance control algorithm. We attached a Force/Torque (F/T) sensor to the end effector of a commercial manipulator to implement the admittance control algorithm. The specifications of the F/T sensor are listed in

Table 2. The specifications of the F/T sensor.

Manufacturer	ATI
Model	Omega160 IP65
Rated Fx, Fy	±2500 N
Rated Fz	±6250 N
Rated Tx, Ty	±400 Nm
Weight	7.26 kg
Diameter	165 mm
Height	65.9 mm

.

3. Control Algorithm

3.1. Admittance Control for Pier Construction Tasks

The application of admittance control technology in pier construction tasks is essential to prevent potential damage from interference and collisions between robots and construction materials. Specifically, during tool engagement, changes in the tool’s position can lead to misalignment between the master side and tool side of the tool changer, potentially causing coupling failures or damage from excessive force. Implementing admittance control allows for these issues to be smoothly managed within an allowable displacement range, adapting to external forces for gentle coupling.

Additionally, in tasks involving the coupling of rebar mesh, situations where three robot systems must simultaneously grasp and manipulate a single upper rebar mesh can lead to interference caused by positional errors or operational delays among the robots. Admittance control effectively mitigates such interference. Moreover, even as the crane holding the upper rebar mesh lowers the line, the robots can adapt without directly bearing the weight of the rebar mesh, thus preventing damage to the robots.

Consequently, admittance control is a key technology that enables robots to interact more agilely and safely with the external environment. This significantly expands the potential use of robots in complex tasks like pier construction, simultaneously enhancing both the work’s safety and efficiency.

Admittance control is extensively researched and applied in contact-intensive applications such as automated assembly using robots and human–robot collaboration [18,19,20]. However, advanced admittance control systems that require modifications to joint control are impractical for application in commercial industrial robots due to their complexity. We have developed a simpler admittance control that can be implemented in commercial industrial robots. Figure 5 illustrates the block diagram for applying admittance control to a commercial robot that requires position commands as input. This control strategy calculates the robot’s positional changes based on the readings from the Force/Torque (F/T) sensor, applying virtual stiffness along the x, y, and z axes to generate new commands for the robot to respond. Such calculations enable the robot to adapt flexibly to external forces, ensuring more stable task performance. Equations (1)–(3) define the positional changes for applying admittance on each axis. These equations correspond to the admittance model in Figure 5.

$${∆x=k}_x{f}_x-b_x{\dot{x}}_a$$

(1)

where

$∆x: the displacement on the x axis needed for compliance with the force$;

$x_a: actual position on the x axis$;

$k_x: stiffness coefficient on the x axis$;

$f_x: external force on the x axis$;

$b_x: damping coefficient on the x axis$.

$${∆y=k}_y{f}_y-b_y{\dot{y}}_a$$

(2)

where

$∆y: the displacement on the y axis needed for compliance with the force$;

$y_a: actual position on the y axis$;

$k_y: stiffness coefficient on the y axis$;

$f_y: external force on the y axis$;

$b_y: damping coefficient on the y axis$.

$${∆z=k}_z{f}_z-b_z{\dot{z}}_a$$

(3)

where

$∆z: the displacement on the z axis needed for compliance with the force$;

$z_a: actual position on the z axis$;

$k_z: stiffness coefficient on the z axis$;

$f_z: external force on the z axis$;

$b_z: damping coefficient on the z axis$.

Figure 6 is a diagram of frames related to admittance control. It is crucial that the F/T sensor’s readings are transformed based on the robot’s tool coordinate system, and the tool’s weight is also calculated and subtracted from the F/T sensor readings in the tool coordinate system. This exclusion of the tool’s weight and posture’s impact in the admittance control process allows the robot to perform accurate position adjustments and stable operations regardless of the tool’s weight or posture. The weight of the tool is measured in advance using the F/T sensor.

Equations (4)–(8) detail the compensation for the tool’s weight in the tool coordinate system based on the F/T sensor readings. In Equation (6), θ represents the angle of rotation around the z-axis due to the misalignment between the F/T sensor coordinates and the tool coordinates.

$${{}_T{}^{M}R=R}_z\left(\alpha \right)R_y\left(\beta \right)R_x\left(\gamma \right)$$

(4)

$${}^{T}Weight={}_T{}^M{R}^{-1}\times {}^{M}Weight$$

(5)

$${}^{T}F={}_S{}^T{R}_z\left(\theta \right)\times {}^{S}F$$

(6)

$${}^T\overline{F}={}^{T}F-{}^{T}Weight$$

(7)

$$\overline{F}=[f_x, f_y, f_z]$$

(8)

where

$\left\{T\right\}: Tool frame$;

$\left\{M\right\}: Mobile frame$;

$\left\{S\right\}: Sensor frame$;

$\alpha , \beta , \gamma : yaw, pitch, roll angle from \left\{M\right\} to \left\{T\right\}$;

${}_T{}^{M}R: Rotation Matrix from \left\{M\right\} to \left\{T\right\}$;

${}^T\overline{F}: Force F with Gravity Compensated$.

3.2. Synchronization Control

When the crane roughly positions the rebar mesh near the existing installation, the three robot systems precisely adjust the position of the rebar mesh. Subsequently, as the crane lowers the rebar, each rebar is secured to the couplers attached to the existing rebar mesh. For this purpose, the three robot systems need to synchronize after grasping the rebar mesh, allowing them to move the rebar mesh with a single joystick input based on global coordinates. Equations (9)–(18) represent the formula for converting joystick inputs to each robot’s coordinate system when manipulating the joystick based on global coordinates. With this, we implemented synchronization control by converting the joystick’s changes into each robot’s coordinate system and applying them to the position changes of the robots. Figure 7 depicts the coordinate systems related to synchronization control.

$${}^{G}P={[P_x, P_y, P_z]}^T$$

(9)

$${}^{R1}∆P_T={}_G{}^{R1}R·{}^G∆P$$

(10)

$${}_G{}^{R1}R={}_{R1}{}^G{R}^T$$

(11)

$${}_{R1}{}^{G}R=\left[\begin{array}{ccc}\mathrm{c}\mathrm{o}\mathrm{s}({\theta 1}_G+\pi )& -\mathrm{s}\mathrm{i}\mathrm{n}({\theta 1}_G+\pi )& 0\\ \mathrm{s}\mathrm{i}\mathrm{n}({\theta 1}_G+\pi )& \mathrm{c}\mathrm{o}\mathrm{s}({\theta 1}_G+\pi )& 0\\ 0& 0& 1\end{array}\right]$$

(12)

$${}^{R2}∆P_T={}_G{}^{R2}R·{}^G∆P$$

(13)

$${}_G{}^{R2}R={}_{R2}{}^G{R}^T$$

(14)

$${}_{R2}{}^{G}R=\left[\begin{array}{ccc}\mathrm{c}\mathrm{o}\mathrm{s}({\theta 2}_G+\pi )& -\mathrm{s}\mathrm{i}\mathrm{n}({\theta 2}_G+\pi )& 0\\ \mathrm{s}\mathrm{i}\mathrm{n}({\theta 2}_G+\pi )& \mathrm{c}\mathrm{o}\mathrm{s}({\theta 2}_G+\pi )& 0\\ 0& 0& 1\end{array}\right]$$

(15)

$${}^{R3}∆P_T={}_G{}^{R3}R·{}^G∆P$$

(16)

$${}_G{}^{R3}R={}_{R3}{}^G{R}^T$$

(17)

$${}_{R3}{}^{G}R=\left[\begin{array}{ccc}\mathrm{c}\mathrm{o}\mathrm{s}({\theta 3}_G+\pi )& -\mathrm{s}\mathrm{i}\mathrm{n}({\theta 3}_G+\pi )& 0\\ \mathrm{s}\mathrm{i}\mathrm{n}({\theta 3}_G+\pi )& \mathrm{c}\mathrm{o}\mathrm{s}({\theta 3}_G+\pi )& 0\\ 0& 0& 1\end{array}\right]$$

(18)

where

${}^{G}P: Position of the Upper Rebar mesh in the global frame \left\{G\right\};$

${}^G∆P: Position displacement of the Upper Rebar mesh in the global frame \left\{G\right\}$;

${}^{R1}∆P_T: Position displacement of the Robot 1’s tool in the Robot 1’s frame \left\{R1\right\}$;

${}^{R2}∆P_T: Position displacement of the Robot 2’s tool in the Robot 1’s frame \left\{R2\right\}$;

${}^{R3}∆P_T: Position displacement of the Robot 3’s tool in the Robot 1’s frame \left\{R3\right\}$.

Figure 7. Coordinate systems related to synchronization control.

Figure 7. Coordinate systems related to synchronization control.

4. Simulation

To verify the admittance control algorithm designed for pier construction tasks, this study developed a dynamic simulation environment, illustrated in Figure 8, utilizing the RecurDyn (2023) simulator and MATLAB (R2023a). RecurDyn, as a dynamic simulation tool, offers seamless integration with MATLAB Simulink, facilitating the application of control algorithms and the analysis of dynamic behaviors. The multi-robot system for the pier construction model and the rebar mesh were applied in the RecurDyn simulator as shown in Figure 9. The rebar mesh, with a weight of 856 kg, is configured to move via a cylindrical joint, and the grippers of the three robot systems are attached to the rebar mesh through spherical joints. Each robot system features a degree of freedom configuration with 1 DOF for the mobile robot and 6 DOF for the manipulator joints, totaling 7 DOF. Within MATLAB, the position values for the cylindrical joint of the rebar mesh and the 7 DOF for each robot system are inputted. The force at the junction between the robot and the rebar mesh, along with the position values for each joint, are then outputted to MATLAB. To generate position commands for each joint in the RecurDyn-implemented robot system, features were developed to include inverse kinematics, a joint-specific position profile generator, and feedback on the posture and position of the end-effector through forward kinematics. The implemented simulator was tested to ensure that the robots reacted compliantly to forces as per the admittance algorithm when the rebar mesh was moved vertically.

Figure 10 illustrates the simulation results. When the rebar mesh is moved, as shown in Figure 10a in the simulator, a significant force is applied to the robot system if it does not move. However, it was observed that by moving the robot system compliantly with the force through admittance control, as shown in Figure 10b, a lesser force is applied.

5. Experiment

To verify the mechanical mechanism and control performance of our proposed system, we developed a prototype of the mobile manipulation system for pier construction, as depicted in Figure 11. The robot system consists of a bottom rail, a mobile platform capable of moving along the rail, and a manipulator for performing tasks, as seen in the figure. The end-effector of the manipulator is equipped with an F/T sensor, with the tool side of the tool changer attached to the F/T sensor. The tool changer allows for the interchangeability of tools according to the task requirements. Furthermore, the external forces acting on the working tool can be sensed through the F/T sensor.

To prevent interference with cables during the movement of the robot system, a cable rail was installed so that the cable could follow the rail. In Figure 11, it is possible to observe the cable bending and unfolding in accordance with the movement of the mobile platform. The robot system, as shown in Figure 12, was restrained to the rail through guide wheels to prevent overturning or posture distortion. The control algorithms for the mobile platform and the operation software for the manipulator were loaded onto a control PC to implement the control functionality of the mobile manipulation system.

Firstly, tests were conducted using this prototype to verify whether the proposed system could navigate stably without overturning and whether position control based on wire sensors was feasible. To intuitively control the mobile robot, the position of the mobile robot is defined in a 360-degree angle with respect to the center of the circle formed by the three rails. To achieve this, the wire sensors were estimated at angles relative to the center of the circle.

We conducted a test to drive the robot system back and forth between two points on the rail using this experimental setup. Smooth desired trajectories for moving to the two positions on the rails were generated using a profile generator. A trapezoidal velocity profile considering the target position and current position was generated and applied as a feedforward input. The position error was compensated for using a PID controller with anti-windup applied [12].

To track the desired values, position control tests were performed by receiving feedback on the position using the draw wire sensor values. The draw wire sensor value was converted to the position (in degrees) of the robot on the rail and applied accordingly.

Figure 13 and Figure 14 depict graphs of the experimental results, showing smooth motion between the 25° and 90° points on the rail for both the position and velocity of the robot. Additionally, we confirmed stability throughout the motion, observing no deviation from the rails during operation and no tilting of the platform at the start or stop of motion.

Next, we conducted load compliance tests and arbitrary external force compliance tests for the admittance control proposed in this study.

For the load compliance test, a 10 kg load was attached to the F/T sensor, and the robot’s compliance behavior in the direction of gravity was tested when the end-effector’s orientation was pitched at 90 degrees and 45 degrees, respectively. Even with changes in the end-effector’s orientation, as observed in Figure 15 and Figure 16, it can be confirmed that the robot complied with the direction of gravity. Additionally, as shown in Figure 17, we applied force to the load cell to confirm that the robot compliantly operates in the direction of the applied force.

We confirmed that the robot responds compliantly in the direction of the force applied to the load cell, even when the end-effector orientation changes.

Following that, we conducted the tool coupling test for the proposed robot system. Figure 18 demonstrates the proposed robot system moving the mobile platform in the tool unattached state, operating the manipulator to couple the tool, and performing tasks in the working posture. The order of the figures is from left to right and from top to bottom. When coupling the tool, there was not a perfect alignment between the master side of the tool changer and the tool side. However, by applying admittance control, we were able to couple smoothly without coupling failure or excessive load.

Finally, we conducted a synchronization control test based on global coordinates while three robots simultaneously handled the rebar mesh specimens. During this test, we applied admittance control to compensate for interference between robots and to ensure compliance with the additional load imposed on the robots when lowering the specimens with the crane. In Figure 19, it can be observed that three robots are gripping the rebar specimen and performing synchronized motion.

6. Conclusions

In this study, we proposed a multi-robot system capable of remote operation and automation for reinforcing bar connection, concrete pouring, and concrete vibrating tasks in pier construction. The robot system consists of a mobile platform that can move along the bottom rails, and a manipulator for performing tasks. The system is designed to handle tasks such as gripping the upper rebar mesh and inserting it into the coupler attached to the upper part of the lower rebar mesh, compressing the coupler to fix the upper and lower rebar meshes, and vibrating the concrete to remove air bubbles after pouring. To perform these tasks, appropriate tool changers are required. To successfully apply the proposed system to construction sites, it is essential to implement compliant control algorithms that adapt to external forces. Due to significant differences in the shape and weight of the task tools, admittance control must exclude the influence of the task tools. In this study, we proposed admittance control that excludes the influence of task tools and verified through simulation that compliant behavior to external forces is achievable. Furthermore, we developed a prototype of the proposed system to confirm the mechanical structure and control performance. Through testing, we confirmed the stability of the mobile platform during operation, without derailing from the rails or tilting at the start and stop points. Additionally, we verified the capability of the prototype to comply with external forces and to integrate with task tools. Furthermore, we proposed a synchronization control method for the multi-robot system to connect the rebar structures and validated its feasibility through rebar handling tests. Future work will involve testing for multi-collaborative tasks using the prototype.