1 INTRODUCTION

With the rapid development of China's underground space engineering and intelligent construction, higher requirements are imposed on the internal structure utilization and construction quality. Traditional casting methods in tunnel and underground space engineering suffer from slow phased operations and quality control challenges, delaying tunnel construction. Prefabricated assembly structures, featuring factory prefabrication and on-site assembly, offer high standardization, rapid construction, and precision, better meeting the development needs (Jiang, 2018; Lü et al., 2019; Zhu, 2019). However, due to difficulties in lifting fully prefabricated components, underground space constraints, and strict assembly precision requirements, there are limited reports on the intelligent assembly of tunnel prefabricated components using smart devices and robotics. As the demand for efficient prefabricated assembly increases, installation robots show great application potential.

Inspired by the multilegged movement of spiders in confined spaces, a hydraulically actuated arc parts installation robot adopts a multilimbed design, which is suitable for operation under arc components. Equipped with a dual-layer adjustment mechanism for coarse and fine positioning, the robot requires an efficient hierarchical motion allocation strategy due to the complexity of the adjustment system and hydraulic actuation constraints, to ensure precise and reliable workpiece attitude adjustments.

To enhance the operational efficiency of robots, many researchers optimize robotic motion parameters to improve trajectory performance. Yu et al. (2018) used a cosine-form adaptive genetic algorithm for time-optimal planning; Kang et al. (2017) proposed an energy-optimal method for two-wheeled robots; Kim and Kim (2014) applied Pontryagin's minimum principle for a three-wheeled robot. However, these optimization-based methods mainly address kinematic or task-space constraints, ignoring congested environments and heavy-load dynamics.

Moreover, high-precision synchronous control of hydraulic adjustment mechanisms is crucial for precise posture adjustment, especially under parameter uncertainties and disturbances. Prior research on hydraulic system synchronization includes deriving ideal transfer functions (Jiang et al., 2008), tuning proportional-integral-derivative (PID) parameters with genetic algorithms (Chen & Pan, 2022; Yang et al., 2014), and combining fuzzy logic, PID, and decoupling algorithms (Chen & Pan, 2022; Han, 2008; Liu et al., 2021; Yao et al., 2018; Zhang & Zhao, 2021). But these either lack multisystem coordination or suffer from complex controllers and parameter tuning.

To overcome these issues, this study leverages active disturbance rejection control (ADRC). ADRC has been effective in systems with unpredictable delays, like power plant dedusting (Sun et al., 2022), and in simplifying controller tuning for first-order plus time delay models (Sun et al., 2021). We transform parameter, modeling, and disturbance uncertainties into a “total disturbance” rejection problem. Designing a controller with a simple structure, strong disturbance rejection, and high robustness can enhance multihydraulic system synchronization and prevent engineering accidents, which is significant for large-scale industrial applications.

With a focus on the current research status and engineering requirements, this study proposes a motion planning and control method for assembly robots of arc parts in shield tunnels. Initially, inverse models for the attitude adjustment and hydraulic systems are established, laying a theoretical foundation for subsequent research. Subsequently, with considerations for flow optimization of heavy-duty systems, external uncertainties are transformed into a total disturbance rejection problem, enabling attitude adjustment and stable control of heavy-duty hydraulic systems. Numerical simulation results demonstrate that the proposed method exhibits excellent convergence and anti-interference capabilities under complex working conditions. Relying on the tunnel project of Shanghai Airport Link, a prototype has been developed and applied in engineering practice. Field data reveal that this method significantly improves the assembly efficiency and accuracy of curved components in tunnels, providing a practical exemplar for the engineering application of intelligent tunnel assembly technology.

2 PROBLEM DESCRIPTION

The JCXSG-11 section of the Shanghai Rail Transit Airport Link Line Project is located in the Pudong New Area of Shanghai. The segment tunnel adopts a single-tube double-track arrangement, with an outer tunnel segment diameter of 13.6 m, an inner diameter of 12.5 m, a segment thickness of 0.55 m, and a ring width of 2 m. The internal structure is fully prefabricated, as shown in Figure 1, and consists of five main components: arc parts, central partition walls, transverse brackets, cable troughs on both sides, and evacuation platforms. The arc part has a length of 9.5 m, a height of 2.834 m, a width of 2 m, and a weight of 36.35 tons per section.

As shown in Figure 2, to achieve attitude adjustment of arc parts in confined spaces, the multilegged configuration of the walk-through assembling robot for arc parts (W-ARa) ingeniously leverages the hollowed-out sections of the arc parts to navigate safely within restricted areas. Once the workpiece to be installed is placed on the robot, the robot transports it to the target location and performs attitude adjustments. Given the robot's complex structure, numerous hydraulic actuators, and heavy load capacity, coordinating the movement of multiple hydraulic actuators and ensuring precise cylinder execution for a given target pose presents a significant challenge. This requires developing an effective coordination and allocation strategy for the parallel hydraulic system across both upper and lower layers, taking into account environmental and structural constraints, as well as the load pressure limitations of the hydraulic system. By framing this planning problem as an optimization problem and targeting load pressure optimization, the method aims to achieve both attitude adjustment and the installation tasks of the arc parts.

The mathematical model describing the relationship between the installation system, its load, and the target attitude angles is critical. The forward kinematic model represents the actual pose of the installation system's load plane, thereby ensuring the accuracy of attitude adjustments. Conversely, the inverse kinematic model calculates the corresponding motions of each hydraulic system based on the target pose, providing guidance for adjusting the system to achieve the specified target attitude.

Simultaneously, the system is affected by various factors during operation, including environmental changes, unknown external disturbances, variations in the properties of hydraulic oil due to temperature fluctuations, and the manufacturing, assembly, and installation precision of hydraulic system components. These factors contribute to poor synchronization of the walking system in the installation machine. Synchronization directly impacts the operational stability of the system and the installation accuracy; in severe cases, it may lead to engineering failures. Achieving high-precision synchronous control of the upper and lower parallel hydraulic cylinder systems under actual working conditions is thus a critical issue addressed in this study.

3 W-ARa STRUCTURE AND DYNAMIC MODEL

The traversing arc parts intelligent installation machine is composed of a main frame assembly, subframe assembly, fine-tuning platform assembly, operation platform with stair guardrails, hydraulic system, and intelligent control system. The equipment features a dual-frame step-through design, with overall dimensions of 6530 mm × 3200 mm × 2609 mm (length × width × height) and a total weight of 35 tons. The design scheme of the W-ARa is shown in Figure 3.

As the core structure of the installation robot, the attitude adjustment mechanism must ensure that the motion of actuators (i.e., hydraulic cylinder piston rods) enables the six degrees of freedom movement of the load workpiece within the tunnel's confined space, thereby accomplishing the attitude adjustment task. Inspired by legged robots, the mechanism is divided into upper and lower layers. The lower layer coordinates the movement of the piston rods of the hydraulic cylinders connected to each leg, while the upper layer works with four hydraulic cylinder piston rods. Together, these achieve vertical lifting and axial rotation of the load workpiece. The rotational angles of the workpiece around the axis are independently controlled by a set of rotation angle adjustment cylinders. Additionally, to ensure that the installation robot and the load workpiece always remain aligned with the tunnel's central axis, a central axis adjustment cylinder is incorporated into the design. This configuration ensures precise attitude adjustment and alignment within the tunnel's constrained environment.

Corresponding to the mechanical structure, the right side illustrates the entire electrical components and their control framework, including hydraulic cylinder actuators, multiple sensors, controllers, and a monitoring platform. All fundamental motion control tasks are handled within the programmable logic controller, while the industrial personal computer is responsible for executing motion planning and computing the synchronization control algorithms.

3.1 Dynamic modeling of W-ARa

To achieve the adjustment of a given attitude angle, it is necessary to model the robot system. Due to the large number of actuators involved in the system and the rigid structural composition of the installation robot, certain deformations may occur in the space, making it difficult to represent the system using an exact mathematical model. Therefore, when modeling the system, the following assumptions are made:

• 1.

  The hydraulic cylinder piston rods of the upper and lower layers for attitude adjustment only have motion along the vertical direction, with no rotational degrees of freedom between the piston rods. That is, the load workpiece only undergoes translational displacement along the z-axis, and rotational degrees of freedom exist only in the x and y axes.

• 2.

  Lateral forces do not affect the entire system, meaning that the direction of force output always remains along the axis of the piston rods.

• 3.

  The axial deformation caused by the rigid connection of the robot body is neglected.

• 4.

  The relative sliding between the load workpiece and the supporting plane of the load is neglected.

For the installation robot used in this study, the model structure diagram reveals that the upper and lower layers are decoupled. Specifically, we have $$ , $$ . The overall mechanical schematic of the system can be abstracted as shown in Figure 4.

In Figure 4, the coordinate system $$ is established at the center of the bottom plane of the installation robot system; the coordinate system $$ represents the centroid of the upper attitude adjustment system, and $$ represents the centroid of the load workpiece. Specifically, we have $$ as the rotation angle of the load workpiece around the $$ -axis, $$ as the rotation angle around the $$ -axis, which corresponds to the allocation of the upper attitude adjustment platform. θx2 represents the rotation angle of the connection platform around the $$ -axis, and $$ represents the rotation around the $$ -axis, which corresponds to the allocation of the lower attitude adjustment platform. The vertical displacement of the hydraulic cylinder piston rods in both the upper and lower layers is represented by $$ , where $$ denotes the upper and lower layers, respectively, and $$ denotes the sequence number of the hydraulic cylinders in each layer.

For the simplified model of the installation robot attitude adjustment shown in Figure 4, the analysis is carried out based on Newton's second law and the rigid body rotation law. For the upper and lower systems, we have the following equations:

$$$$ (1)

    $$$$ (2)

The variables are defined as follows: $$ represents the force exerted by each hydraulic cylinder in the upper and lower layers; $$ is the load mass in the hydraulic systems of both layers; $$ and $$ are the moments of inertia of the load workpiece around the $$ -axis and $$ -axis, respectively; $$ and $$ are the distances from the hydraulic cylinder body to the $$ -axis and $$ -axis, respectively, for the four hydraulic cylinders in the upper attitude adjustment system when the piston rods are not extended (i.e., the initial state of the system); $$ and $$ are the moments of inertia of the connection platform around the $$ -axis and $$ -axis, respectively; and $$ and $$ are the distances from the hydraulic cylinder body to the $$ -axis and $$ -axis, respectively, for the hydraulic cylinders in the lower attitude adjustment system at the initial state.

The dynamic equations for the vertical motion of the piston rods in the upper and lower hydraulic cylinders are as follows:

  $$$$ (3)

The variables are defined as follows: $$ is the effective area of the piston rod side of the $$ -th layer hydraulic cylinder; $$ is the load of the $$ -th hydraulic cylinder; $$ is the mass of the piston rod in the upper hydraulic system; $$ is the viscous damping coefficient of the hydraulic system; and $$ is the displacement of the $$ -th hydraulic cylinder piston rod.

Due to the displacement of the piston rod, the action point of the system will experience a certain amount of offset. In the ideal case, the offset is much smaller than the dimensions of the workpiece and the installation robot structure, so the offset of the piston rod can be neglected. After the load system generates a deflection angle, the position vectors of the piston rods in the upper and lower layers of the installation robot system are denoted as $$ , $$ . These can be expressed as:

$$$$ (4)

The displacement of the piston rods in the upper and lower hydraulic cylinders is given by $$ , where dxi and dyi represent the center distances of the hydraulic cylinders in the upper and lower attitude adjustment systems, respectively, and $$ and $$ are the direction factors corresponding to $$ and $$ for the upper and lower hydraulic cylinders, respectively.

Based on the positioning information of the four sets of hydraulic cylinders in the upper and lower layers, three force application points are selected for each set, namely $$ . These six points form the minimum set that determines the attitude of the load workpiece. The values are extracted and defined as $$ , $$ . The relationships between $$ and $$ are given by:

$$$$ (5)

Based on this, the positions of the fourth hydraulic cylinders in each layer can be linearly represented as:

$$$$ (6)

For simplicity, let $$ , then Equation ( 6) can be expressed as $$ . Furthermore, $$ and $$ can be represented as:

$$$$ (7)

The forces on the piston rods of the upper and lower hydraulic systems are defined as $$ , $$ .

$$$$ (8)

where $$ represents the load gravity matrix for the upper and lower hydraulic systems, which is explicitly given as $$ . $$ is the moment arm matrix of $$ , and its value can be expressed as:

$$$$ (9)

where $$ represents the load inertia matrix for the upper and lower hydraulic systems, which is explicitly given as:

$$$$ (10)

The system of equations derived from the above can be obtained as:

$$$$ (11)

where $$ is the resultant external force matrix, which is explicitly expressed as:

$$$$

where $$ is the viscous damping coefficient matrix for the hydraulic cylinders. The viscous damping coefficient $$ for both the upper and lower hydraulic systems is taken to be the same, and its expression is: $$ . $$ represents the mass matrix of the hydraulic cylinder piston rods, and its expression is:

$$$$

The mechanical model of the hydraulic system, expressed by Equations (8) and (11), establishes the relationship between the displacement of each hydraulic cylinder and its corresponding attitude angle. During the attitude adjustment of the load, the actual displacement of the hydraulic cylinder piston rods depends on factors such as the load, the input pressure to the hydraulic system, and the installation dimensions of the cylinders. When solving for a specific load and target attitude angle, the main challenge is to allocate the corresponding upper and lower layer attitude angles while minimizing the input pressure of the entire hydraulic system. The system model established herein provides the foundation for solving this problem.

4 HIERARCHICAL ALLOCATION ALGORITHM

5 ANALYSIS OF SIMULATION AND EXPERIMENT RESULTS

From the established system dynamics model, it can be observed that assuming the installation machine is initially in a horizontal state, when a given attitude angle is provided, it is necessary to find a set of cylinder displacement solutions that minimize the system pressure while satisfying Equation (13). This will ultimately achieve the goal of attitude adjustment. Therefore, the inverse solution using the proposed pressure optimization algorithm is key to obtaining the optimal allocation strategy. To verify the established system model and the optimal allocation strategy for motion planning, a simulation verification is performed on the W-ARa.

The process of simulation verification is as follows: Given four attitude angle examples to be adjusted, the solution is performed based on the linearly weighted decreasing particle swarm optimization algorithm. First, random variables generated in the population are used as the displacement values for the upper-layer hydraulic cylinders, yielding the corresponding $$ and $$ . Subsequently, the required adjustment angles $$ and $$ for the lower hydraulic system are determined, and the displacement values for the lower hydraulic cylinders are obtained. Using the established installation machine system dynamics model, the system input hydraulic pressure for each feasible solution set is calculated, and its minimum value is retained. Through continuous iterations of the algorithm, the solution is found that minimizes the input hydraulic pressure for the installation machine system and provides the displacement values for the upper and lower hydraulic cylinders.

Since the displacement values of the lower hydraulic cylinders correspond to the upper-layer variables, the variables are set as the four displacement values of the upper-layer hydraulic cylinders. Therefore, the optimization particle is 4-dimensional. The parameter search space corresponds to the stroke of the hydraulic cylinder's piston rod. The population size is set to $$ , the learning factors are $$ and $$ , the final and initial inertia weights are $$ and $$ , and the number of iterations is $$ . The attitude angles for the given simulation examples are as follows: Instance NO.1 $$ , Instance NO.2 $$ , and Instance NO.3 $$ . The corresponding calculation results are shown in Table 1.

In the solving process, the convergence of load pressure is crucial. Through numerical calculations and iterative operations, the system can obtain a load pressure value that closely approximates the real-world situation. In Figure 5, the displacement of the piston rods of each hydraulic cylinder in the hydraulic system can be clearly seen. Through continuous optimization and solving, the system can more accurately predict the performance and operating state of the hydraulic system, providing better assurance and support for the hydraulic system in practical applications.

The system pressure convergence process, as shown in Figure 5, indicates that when the LDW-PSO algorithm is applied to solve the three sets of simulation examples, the load pressure of the entire hydraulic system converges rapidly. By utilizing the proposed optimal distribution strategy, the displacement values of the hydraulic cylinder pistons in the upper and lower systems corresponding to the given attitude angles can be determined quickly. This highlights the efficiency of the optimal distribution strategy.

Taking Example No.2 as an instance, the iteration process is analyzed, and the displacement of the hydraulic cylinders throughout the iterative process is plotted in the corresponding plane, as shown in Figure 6.

By plotting the positions of the actuator pistons during the iterative process of the simulation, as shown in Figure 6, it can be seen that, throughout the algorithm's iterations, the four action points of the upper hydraulic system consistently remain on the same plane. This result meets the constraints specified in the motion planning strategy, demonstrating the validity of the system model and the effectiveness of the proposed optimization-based motion planning method for the installation robot. After adjusting the posture of a curved workpiece, the task time required for assembly is 5 min. Based on this, the computation time for each instance is calculated as a percentage of the total task time to highlight its efficiency. The solution times for the three instances are shown in Table 2.

To enable the installation robot to effectively track the displacement of the pistons in each actuated hydraulic cylinder, a parallel arrangement of hydraulic cylinders is considered. Using the upper or lower parallel dual hydraulic systems as an example, a linear expanded state observer is designed based on the ADRC theory. This observer monitors and compensates for the system's total disturbances in real-time. The system's control framework is then established by combining linear feedback control with dual-error feedback, enabling synchronized control of the parallel hydraulic systems. Additionally, to validate the system through joint simulation, as shown in Figure 7, a semiphysical simulation model of the installation robot's hydraulic system is developed on the AMESim platform and integrated with Matlab/Simulink for co-simulation as shown in Figure 8.

In the process of building the parallel hydraulic system model, combined with the actual working conditions, there are differences in the setting of the main parameters of the two hydraulic systems and the load size, to simulate the actual system of production and processing accuracy of the different impacts, the main parameter settings as shown in Table 3.

Comparative simulations of the control results based on linear ADRC (LADRC) and PID control were conducted. The tracking simulation results of the dual hydraulic system for the given reference signal, as well as the synchronization error simulation results, are shown in Figure 9.

The variation curves of piston velocity, pressure in both chambers of the hydraulic cylinders, and flow rate under the synchronization control strategy based on LADRC for the dual hydraulic system are presented in Figure 10. The simulation results demonstrate that, under varying preset load pressures and in the presence of noise, the dual-cylinder system with LADRC control can quickly and accurately track the reference signal after a brief oscillation. Moreover, the synchronization accuracy achieved after the system stabilizes is superior to that obtained with PID control.

To verify the disturbance rejection capability of the system while closely simulating real operating conditions, external time-varying random noise was introduced after 80 s. Figure 11 shows that, even with the presence of time-varying random disturbances, the system maintains good tracking performance of the reference signal. Moreover, the synchronization control strategy based on LADRC exhibits smaller fluctuations and higher synchronization accuracy. As shown in Figure 12, under the LADRC-based synchronization control strategy, the combined effect of different preset pressures applied to the piston ends and random disturbances leads to slight differences in flow rate between the two hydraulic systems. Nevertheless, even under fluctuating conditions, the flow rates of the parallel hydraulic systems remain highly synchronized, with limited fluctuation amplitude. This demonstrates effective suppression of unknown time-varying disturbances to a certain extent, further validating the superior synchronization control performance of the proposed controller for dual hydraulic systems.

The assembly control accuracy of the arcuate components is defined by the relative deviation from the previous arcuate component. Assembly accuracy requirements for field testing are shown in Table 4, and the application photos are presented in Figure 13.

As shown in Figure 14, this paper counts the 1–50 ring arc parts installation quality acceptance data, of which the horizontal misalignment, the gap between the blocks and the center line deviation meets the installation requirements, the vertical misalignment appear two rings of values beyond, the overall installation quality pass rate is high.

6 CONCLUSIONS

The currently proposed method still has some limitations, which may restrict its adaptability to highly dynamic or unstructured environments due to its heavy reliance on predefined system parameters. In addition, the system offers high scalability and adaptability. Within the system load range, the modularity of the system and the flexible design of the control architecture make it possible to adapt the system to a wide range of geometries and sizes of arc parts beyond the Shanghai Airport project by adjusting the relevant parameters in the motion planning and control strategy.

AUTHOR CONTRIBUTIONS

Quan Xiao: Conceptualization; methodology; writing. Guofei Xiang: Conceptualization; methodology; writing. Liang Liao: Methodology. Lai Wei: Methodology. Hongli Wang: Methodology. Songyi Dian: Conceptualization.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.