The AAPF fault-tolerant method for small and complex product assembly

Abstract

Fault-tolerant control should be considered during assembly to ensure stability and efficiency of the assembly process. The paper proposes a fault-tolerant method to improve stability and efficiency during the assembly of small and complex products. The fault-tolerant method model was initially constructed, then an adaptive artificial potential field control algorithm (AAPF) was introduced to control related assembly tasks based on changes in assembly information. Next, active and passive fault tolerance methods were integrated using a least squares support vector machine (LS-SVM). Finally, the assembly of a 2P circuit breaker controller assembly with leakage protection was used as an example to verify the proposed assembly method. The experimental results demonstrated that the AAPF fault-tolerant method showed promising fault-tolerance capabilities for the assembly of small and complex products. Not only could it coordinate the number of tasks for each assembly robot, but it also effectively reduced the number of tasks that accumulated due to faults. The method proposed in this paper could effectively guarantee assembly stability and efficiency during small and complex product assembly.

Introduction

Because small and complex products have diverse parts and complicated assembly processes, improving the stability and efficiency of their assembly processes is important. Robot assembly of these products must not only have excellent operating efficiency but also have adequate stability. These requirements bring specific challenges to robot assembly control for these types of products. A robot assembly line (RAL), which combines principles of robotics and traditional assembly lines, can significantly reduce labor costs and improve production efficiency when compared to traditional production lines. ¹ For these reasons, RALs are highly valued by various manufacturing industries, and they have been extensively studied and applied. Past research into RALs primarily focused on optimizing the robot assembly sequence and the balance and flexibility of the assembly line, which could improve the robot assembly efficiency, reduce production costs, and quickly respond to rapidly changing market demands.^2–4 Nevertheless, when assembling small and complex products, an assembly system must have fault tolerance capability during the intricate assembly process, so the entire assembly system does not become paralyzed due to faults.

Therefore, improving the fault tolerance of an assembly process can improve the stability and efficiency of the assembly and is crucial for the rapid and efficient assembly of small and complex products. Existing fault-tolerant control methods primarily consist of active fault tolerance and passive fault tolerance methods. The former focuses on active fault diagnosis and feedback repair.

In contrast, the latter focuses on using the structural characteristics of the system itself. When a fault occurs, this control method relies on structural characteristics and combination methods to complete specific operational goals.^5,6 Many studies relating to the fault-tolerant control of assembly processes have already been performed.

Lopes and Camarinha-Matos ⁷ introduced an assembly supervision architecture to learn assembly planning strategies and domain knowledge of normal task execution to achieve efficient task distribution, assembly monitoring, and fault recovery in the assembly process. Chen et al. ⁸ proposed an assembly tilting strategy to diagnose assembly errors for the problem of position matching and used a binary search strategy to recover related errors during the assembly of electronic connectors. Majdzik et al. ⁹ focused on assembly failures caused by the assembly process, transportation, and mobile robots during battery assembly. They applied interval analyses to describe assembly failures as unknown discrete events and proposed a fault tolerance strategy for battery assembly. Wu and Ni ¹⁰ proposed a diagnosing method to diagnose faults on an automobile assembly line based on the triangular fuzzy v-support vector classifier and particle swarm algorithm. Hui et al. ¹¹ used a genetic algorithm and an ant colony algorithm to optimize the assembly path of complex products based on assembly path feedback. Lopes ¹² proposed a method for recovering from execution failures, which was based on analogies with previous failure recovery episodes, that was used to deal with complex assembly tasks during robotic flexible manufacturing. Du and Xi ¹³ developed diagnosis methodology to diagnose fixture faults in assembly processes and explored an improved particle swarm algorithm, based on simulated annealing and a selective neural network algorithm, for on-line identification. Zhang et al. ¹⁴ adopted a self-organizing feature mapping network (SOM) to realize the fault diagnosis of an automotive airbag assembly process. Cojocaru et al. ¹⁵ employed an efficient image analysis technique to obtain a real-time mechanism for detection of assembly faults. Wen et al. ¹⁶ developed a vision-based computer system to deal with online inspection of hose assemblies. Bastani et al. ¹⁷ proposed a spatially correlated Bayesian learning algorithm to diagnose faults of dimensional integrity in large product assemblies. Liu et al. ¹⁸ proposed a complicated product assembly variation analysis method based on a rigid–flexible vector loop that could determine the impact of each rigid and flexible part manufacturing error on product assembly variations. He et al. ¹⁹ proposed an assembly quality risk modeling approach, based on a reliability–quality–reliability chain, to improve the reliability of assembly processes, which could also improve the quality of the assembled products.

Table 1 provides a list of previous studies performed on this subject. It shows that active fault tolerance methods were adopted by many researchers, but few scholars focused on passive fault tolerance methods. According to previous research into fault-tolerance assemblies, active fault tolerance methods were much more effective than passive fault tolerance methods for fault detection and fault recovery, but they had finite inspection scales and were dependent on fault-tolerant algorithms proposed in previous studies. Passive fault tolerance methods had lower accuracy than active fault tolerance methods, but they had larger fault detection scales.

Table 1.

The review of the prior related research work.

Writer	Fault-tolerant method	Assembly product or purpose	Type of fault tolerance
Hui et al. 11	Genetic algorithm and ant algorithm, B-Rep filling algorithm	Complex product assembly	Passive fault tolerance
Wu and Ni 10	Triangular fuzzy v-support vector regression machine and particle swarm optimization	Car assembly	Active fault tolerance
Du and Xi 13	An improved particle swarm optimization with a simulated annealing-based selective neural network ensemble algorithm	Aircraft horizontal stabilizer assembly	Active fault tolerance
Zhang et al. 14	Self-organizing feature mapping network (SOM)	Automotive airbag assembly process	Active fault tolerance
Chen et al. 8	A tilt strategy and search strategies for error recovery	Mating of electronic connectors	Active fault tolerance
Wen et al. 16	A vision-based computer system	Hose assembly	Active fault tolerance
Majdzik et al. 9	A robust predictive fault-tolerant strategy	Battery assembly	Active fault tolerance
Bastani et al. 17	A spatially correlated Bayesian learning algorithm	Large product assembly	Active fault tolerance
Liu et al. 18	A complicated product assembly variation analysis method based on a rigid–flexible vector loop	Product with rigid–flexible hybrid construction	Active fault tolerance
Cojocaru et al. 15	Image analysis technique to obtain a real-time mechanism for detection of assembly faults	Small product assembly	Active fault tolerance

During assembly of small and complex products, assembly tasks are complicated and diverse and have relatively complex relationships with one another. A single fault tolerance mechanism cannot guarantee the stability of the system. Therefore, to improve assembly stability and the efficiency of small and complex product assembly, it is necessary to integrate active and passive fault tolerance methods, so the assembly process is not interrupted by unknown faults and has higher fault detection accuracy. This paper proposes a new fault-tolerant method that integrates active fault tolerance and passive fault tolerance methods to achieve stable and efficient assembly of small and complex products.

Overview of the methodology

This section provides a practical overview for identifying fault-tolerant methods of assembly for small and complex products. Before describing the fault-tolerant methodology, some assumptions were made:

1. Each robot could only perform two simple assembling actions, such as inserting, placing, turning, pressing, and bonding.

2. The sequence of the assembly tasks was known before the study began.

3. Each task could be finished by one kind of simple assembling action.

4. The time consumed by part transportation was not considered in this study.

The architecture of fault-tolerant methodology in assembly processes is shown in Figure 1, in which four modules are in series: Module I, Module II, Module III, and Module IV. Each module had a specific function. By communicating with each other, the four modules could carry out the fault-tolerant method in an assembly process.

Figure 1.

The architecture of fault-tolerant methodology.

Module I built the task quality model. Each task had its own quality, and task quality could be changed by the assembly condition. In this module, the artificial potential field (APF) theory ²⁰ was introduced to control the assembly process. In the APF theory, the quality affects the potential field force, and when the task quality was altered, the potential field force changed accordingly. Module II constructed the pheromone model according to the theory of the ant colony algorithm. ²¹ In this module, some condition parameters of the assembly affected the value of the pheromone, which was used to analyze the assembly condition and to alter the value of the task quality. Module III built the least squares support vector machine (LS-SVM) ²² model, which was used to analyze the information proposed by Module II. Module IV built the potential field boundary model. In this module, the potential field was constructed. When the boundary entry value of the task was sufficient, the task could enter the potential field. In the potential field, tasks were selected by the robots based on the value of the potential field force.

The assembly fault-tolerant control method

Traditional assembly methods divide the assembly of a product into many tasks according to the structure of the product. Products are also decomposed into multiple components, and each component is broken down into multiple sub-components. The assembly tasks of each component or sub-component are assigned to each corresponding assembly unit. Thus, the assembly tasks completed by each assembly unit are specified and irreplaceable. However, they also have significant dependence on each other. If an assembly unit or assembly task fails, the subsequent assembly units will stagnate, affecting the entire assembly process. In this paper, the division of assembly tasks was redesigned to improve the stability of the assembly process. Meanwhile, the assembly of a product is completed through a series of ordered assembly actions (such as inserting, placing, turning, pressing, bonding, and welding), and assembly tasks are completed by the required assembly actions. Assembly units can perform one or more assembly actions so that they have mutual dependencies and some amount of independence. Meanwhile, assembly units can be replaced with other units of the same type, so that the entire assembly has better passive fault tolerance and improves the stability of the assembly process.

Because the assembly process of a product can be divided into a set of assembly action combinations that occur in a particular order, a dynamic interaction relationship must be created between the assembly robots and the assembly tasks. Moreover, through dynamic monitoring of each assembly task, the assembly process has dynamic fault-tolerant control capabilities. Therefore, combining the artificial potential field (APF) control theory, ²⁰ the ant colony algorithm, ²¹ and the least squares support vector machine (LS-SVM), ²² an adaptive artificial potential field (AAPF) algorithm was developed to achieve the product assembly and effective fault-tolerant control of the assembly.

By controlling the mass values and the distances between objects in the potential field, the AAPF algorithm could control the interactions between objects. Additionally, during the assembly process, the number of tasks would maintain a dynamic balance during the assembly process, and the number of uncompleted tasks would not increase or decrease significantly. The LS-SVM algorithm was used to capture the changes in these data, then the obtained data were compared with previous training data to determine the operating status of the assembly system. If it estimated that there was a fault in the assembly process, the corresponding fault adjustment would be performed to ensure the stable operation of the assembly process. The assembly information of the tasks was set as a pheromone in the AAPF algorithm, and the potential field force was adjusted according to the value of the pheromone, which was applied to control the robots and the assembly tasks. Therefore, the combination of passive fault tolerance and active fault tolerance methods achieved by the AAPF algorithm made the assembly process more stable and reliable. The definition of the AAPF-related mathematical models is described in the next section.

Construction of the task quality model using AAPF theory

In AAPF theory, each assembly task has a corresponding mass. The value of a task’s mass is calculated as follows:

$$M_i=M{t}_i+S{w}_i-\mathrm{Dam}{p_i}_{,}$$

(1)

$$M{t}_i=\{\begin{array}{c}{e}^{{\lambda }_i}-\mathrm{tb}\times \mathrm{rep}{l}_i\hfill \\ \multicolumn{1}{c}{K\times e^{{\lambda }_i}-\mathrm{tb}\times \mathrm{rep}{l}_i}\end{array}\begin{array}{c}\mathrm{If}\mathrm{task}i\mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{task}\hfill \\ \multicolumn{1}{c}{\mathrm{If}\mathrm{task}i\mathrm{has}\mathrm{prior}\mathrm{tasks}}\end{array},$$

(2)

$$S_{\mathrm{Wi}}=1+\mathrm{tb}\times \mathrm{ad}{m}_{i,}$$

(3)

$$\mathrm{Dam}{p}_i=d{p}_i\times {{\mathrm{\Delta }}_{\mathrm{dp}}}_i.$$

(4)

In equation (2), $K=\underset{1}{\overset{u}{\Pi }}M{t}_j$ , where K is the product of the essential quality attributes of the predecessor tasks directly adjacent to task i, u is the number of tasks directly preceding task i, tb is the failure factor, repl_i is the quality dissipation factor of task i, and dp_i is damping variable. The initial value of dp_i is 0, and if task i is finished, the value of the dp_i is 1. Expressions for other parameters used in equations (2)–(4) are given next:

$$\mathrm{tb}=\{\begin{array}{c}1\mathrm{when}a\mathrm{fault}\mathrm{arises}\hfill \\ \multicolumn{1}{c}{0\mathrm{when}\mathrm{running}\mathrm{normally}}\end{array},$$

(5)

$$\mathrm{rep}{l}_i=l_{\mathrm{next}}/\mathrm{sum}.$$

(6)

In equation (6), l_next is the number of tasks succeeding task i, and sum is the total number of unfinished tasks. The value of the boundary attribute l_i of task i is shown in equation (7):

$${\mathrm{\lambda }}_i={\epsilon }_i/{\sum }_1^n{\epsilon }_i.$$

(7)

In equation (7), n is the number of tasks. Each task also has a corresponding task stimulus factor, e_i, and a task guidance factor, x_i.

$${\epsilon }_i={\gamma }_i\times {\xi }_i+1$$

(8)

$${\sigma }_i=1-1/(n-v)$$

(9)

In equation (8), g_i is the given priority coefficient of task i, and x_i is the task guidance factor of task i.

In equation (9), n is the number of assembly tasks, and v is the number of task i.

Pheromone settings

In an ant colony algorithm, the walking path of the ants is used to represent the feasible solution of the problem to be optimized. All paths of the entire ant colony constitute the solution space of the problem. Ants with shorter paths release much more pheromone. Hence, the concentration of pheromones accumulated on the shorter paths gradually increases, and the number of ants that choose the shorter path increases. Finally, the entire ant colony will focus on the best path because of positive feedback, and the corresponding solution is the optimal solution to the problem. Therefore, in the control strategy of the ant colony algorithm, the pheromone plays a significant role, guiding the ant colony to move through different paths based on its accumulation and dissipation.^21,23,24 According to this principle, the pheromone value τ_i of task i is calculated as follows:

$${\tau }_i=\mathrm{Cl}{r}_i\times \mathrm{Nu}{m}_i/\mathrm{sum}\times (1-\rho )\times {\xi }_i.$$

(10)

In equation (10), Clr_i is the task cleaning coefficient and is calculated using equation (11):

$$\mathrm{Cl}{r}_i=\{\begin{array}{c}\mathrm{tb}+1\mathrm{when}\mathrm{Nu}{m}_i<{\phi }_i\hfill \\ \multicolumn{1}{c}{\mathrm{Nu}{m}_i\times \mathrm{tb}+1\mathrm{when}\mathrm{Nu}{m}_i>{\phi }_i}\end{array}.$$

(11)

Equation (12) is used to obtain the quality regulator, adm_i, for task i:

$$\mathrm{ad}{\mathrm{m}}_i=\{\begin{array}{c}1\mathrm{when}\mathrm{running}\mathrm{normally}\hfill \\ \multicolumn{1}{c}{({{\tau }_i}^{\alpha }{{+}_i}^{\beta })/\sum _1^{\mathrm{sum}}{\tau }_i\mathrm{when}a\mathrm{fault}\mathrm{arises}}\end{array}$$

(12)

The values of α and β in equation (12) indicate the influence of the pheromone and the task stimulus factor on the task quality regulator. According to equations (1), (3), and (12), when the pheromone of the assembly task is altered, the quality value of each task in AAPF theory will change accordingly. Thus, the magnitude of the robot attraction to the assembly task is transformed, and a dynamic scheduling of assembly tasks is obtained.

Setting the potential field boundary

In AAPF theory, the influence of an assembly robot on an assembly task has a specific range; namely, there is a boundary between the assembly robot and the assembly task. If the task is within the boundary of the potential field, it will be affected by the gravity of the assembly robot. If it is outside the boundary, no matter how large the gravity of the robot is, the robot will not act on that assembly task. This boundary is called the potential field boundary. Each assembly task has a corresponding boundary entry value St_i.

$$S{t}_i=\mathrm{Ot}{l}_{i-1}\times {\lambda }_i$$

(13)

In equation (13), Otl_{i− 1} is the boundary coefficient of task i−1, which is the predecessor of task i. When the corresponding assembly task i−1 is completed, Otl_i−1 = 1. If it is not yet completed, Otl_i−1Î (0, 1).

$$\mathrm{Valv}=\min ({\lambda }_1,{\lambda }_2,\dots ,{\lambda }_n)$$

(14)

Valv is the entrance threshold of the potential field boundary. When Sti ≥ Valv, assembly tasks can pass through the potential field boundary.

When each assembly task enters the range of gravity of the assembly robot, each assembly robot generates a dynamic potential field force F_rti for assembly tasks:

$$F_{\mathrm{rti}}={\omega }_j\times M{r}_j\times M_i/d{r_{i-j}}^2.$$

(15)

In equation (15), w_j is the state parameter of the assembly robot, as defined in equation (16):

$${\omega }_j=\{\begin{array}{c}1\hfill \\ \multicolumn{1}{c}{-1}\end{array}\begin{array}{c}\mathrm{when}\mathrm{robot}j\mathrm{is}\mathrm{idle}\hfill \\ \multicolumn{1}{c}{\mathrm{when}\mathrm{robot}j\mathrm{is}\mathrm{in}\mathrm{the}\mathrm{assembling}\mathrm{state}}\end{array}.$$

(16)

When w_j = 1, F_rti is an attractive force and the corresponding task is attracted, but when w_j = −1, Frt_i is a repelling force that excludes the corresponding tasks.

During the assembly process, V_task represents the number of tasks that can be completed at one time. When assembly failures occur, some tasks cannot be completed quickly, resulting in an accumulation of unfinished tasks. Therefore, to prevent too many assembly tasks from entering the field, a time interval, Interval, is applied to control the generation of tasks outside the boundary. Interval₀ is the time interval during normal assembly.

$$\mathrm{Interval}=\{\begin{array}{c}\mathrm{Interval}0\mathrm{sum}<V\_\mathrm{task}\hfill \\ \multicolumn{1}{c}{2\times \mathrm{Interval}0\mathrm{sum}>V\_\mathrm{task}}\end{array}$$

(17)

The LS-SVM model

In support vector machines, a non-linear mapping function is applied to map samples from a low-dimensional feature space to a high-dimensional feature space, and the optimal classification surface is constructed in this high-dimensional feature space. The LS-SVM model applies equality constraints instead of inequality constraints and takes the second norm of the error as the loss function of the optimization goal. The classification decision function of the LS-SVM model is given in equation (18)^25–27:

$$y\left(x\right)=\mathrm{sign}[\sum _{j=1}^l{\delta }_j\phi {\left(x_j\right)}^T\phi \left(x\right)+b]$$

(18)

In equation (18), x_j is input information, y(x) is output information, δ_j (j = 1,…,l) is the Lagrange multiplier, φ(.) is a non-linear mapping function from the input space to the high-dimensional feature space, and b is the bias.

$\mathrm{Kx},x_j=\phi {\left(x_j\right)}^T\phi \left(x\right)$ is defined as the kernel function of the least squares support vector machine, and a radial basis function (RBF) is introduced as the kernel function. The radial basis kernel function is as follows:

$$\mathrm{Kx},x_j=e^{[-\frac{x-{x_j}^2}{2{\sigma }^2}]}.$$

(19)

In equation (19), s² is a parameter of the radial basis function (RBF). During the assembly processes, the relevant data for each task in the regular assembly process are first extracted, the LS-SVM model is trained, relevant data are extracted in real-time during the assembly process, and the LS-SVM model is used to judge the assembly state, which is applied as part of the active fault tolerance control.

The AAPF algorithm

1. Each assembly task and its corresponding boundary coefficient, Otl_i, are initialized (Otl_i∈ (0, 1)), and φ_i is set to 5. Using the given priority coefficient, γ_i, and by setting the boundary attributes to their initial states, the task excitation factors, λ_i, are calculated.

2. Each assembly robot starts to receive assembly tasks, then w_j is set to 1, the potential field boundary is opened, the threshold of the boundary entrance, Valv, is calculated, and Valv = min(λ₁, λ₂,…, λ_n). Then the boundary entry value, St_i, of each assembly task is calculated.

3. The values of St_i and Valv are compared for each task. If the value of St_i is higher than Valv, the corresponding task i enters the potential field boundary.

4. Each assembly robot selects tasks that enter the potential field by calculating the quality, M, of each task and the corresponding potential field force, Frit_i. A robot selects the task with the maximum potential field force. When the robot obtains the corresponding assembly task, then ω_j = −1 for that robot; this generates a repulsive force for unselected tasks, and these unselected tasks are expelled from the potential field boundary.

5. When task i is completed, its corresponding boundary coefficient, Otl_i, is set to 1, and the initial value of the preceding task’s (task i−1) boundary coefficient, Otl_i−1, is reset (Otl_i−1∈ (0, 1)). Then the robot that completed the assembly task receives the assembly instructions again, and ω_j is reset to 1.

6. Steps (3)–(5) are repeated until the entire product assembly is completed. Meanwhile, the LS-SVM model is used to analyze whether the entire assembly process is normal. If it is healthy, the LS-SVM model sends a message value of tb = 0. If a fault occurs, it sends a message value of tb = 1.

7. When tb = 1, the pheromone, τ_i, of each task, the quality conversion factor of task i, and the task quality attenuation factor are calculated. Then the quality and Frit_i are recalculated, and the robot reselects assembly tasks to minimize the impact of failures.

8. When the LS-SVM model detects that the data of each task return to normal, it sends a message value of tb = 0, and the entire system returns to the normal assembly state. The system cycles through steps (3)–(6) until the required number of assembled products is obtained.

Experimental analysis

To verify the proposed fault tolerance method of robot assembly, the assembly of a 2P circuit breaker controller with leakage protection was experimentally analyzed. The processor of the computer used in this experiment was an Intel(R) Core(TM) i5-6200U CPU @ 2.30 GHz 2.40 GHz, with 4G memory. The experimental platform was Matlab R2016b.

The specific structure of the 2P circuit breaker controller with leakage protection and its parts are shown in Figure 2. Disassembling and analyzing the 2P circuit breaker controller with leakage protection indicated that there were 45 assembly tasks that must be performed to assemble the product. Each task was represented by a corresponding letter. The constraint relationships between tasks are shown in Figure 3. The label I/PT means the task could be finished by robot Rcf, which could perform inserting and placing assembly functions. The label R/PR means the task could be completed by robot Rxy, which could perform turning and pressing assembly functions. The label W/S means the task could be carried out by robot Rnh, which could perform bonding and welding assembly functions. The number next to each label represents the time required to complete the assembly task. During the assembly of the product, six assembly functions were required: inserting, placing, rotating, pressing, sticking, and welding. Each modular robot could only perform two assembly functions, so in the assembly processes, at least three robots with different functions must be applied to assemble the 2P circuit breaker with leakage protection. The corresponding relationships between the robots and the assembly tasks are shown in Table 2.

Figure 2.

2P circuit breaker with leakage protection.

Figure 3.

Relationships among assembly tasks of the 2P circuit breaker with leakage protection.

Table 2.

Assembly tasks corresponding to each assembly robot.

Robot type	Corresponding assembly tasks
Rcf	A11 J11 J21 A21 D11 H11 H21 D21 M32 D13 K12 D23 I14 K13 I24 I15 M36 I26
Rxy	A12 B11 C21 C11 B21 K11 H13 H23 M33 E34 M35 I25 I28 A22
Rnh	G11 A11 G21 L31 M31 B12 E12 E22 F13 F23M34 K14 E35

A variety of faults may occur during an assembly process, but no matter what kinds of faults occur, they will cause an accumulation of the assembly tasks that will affect the assembly process. Therefore, the proposed passive fault-tolerant control method should ensure that a process will not become paralyzed when faults occur. It can also clear the accumulation of tasks to a certain extent to improve the assembly efficiency. In this experimental analysis, the faults were classified into two types: assembly robot failure and logistics transportation failure, which are discussed from the perspective of passive fault-tolerant control and active fault-tolerant control.

To analyze the problems presented above, the models proposed in the “The assembly fault-tolerant control method” section were applied in Matlab programs to analyze the assembly process. The calculation steps are shown in Figure 4.

Figure 4.

The calculation process of the AAPF algorithm.

Passive fault-tolerant control analysis

For the passive fault-tolerant control analysis, the fault tolerance degree of the assembly process was analyzed according to the characteristics of the faults. The conditions of the tasks that had faults were also analyzed. The specific experimental data are shown in Figures 5 and 6. When assembly logistics failures occurred, the relative robots had to be in a saturated state to eliminate the accumulated tasks in the assembly process. If one type of assembly robot failed (in this experimental analysis, the robot Rh02 failed), assembly robots of the same type selected the assembly tasks of the failed robot and kept the system in a saturated assembly state to meet the requirements of assembly efficiency and reduce the accumulation of tasks. In summary, it was observed that the assembly method automatically adjusted the number of assembly tasks for each assembly robot when faults occurred so that the stability of the assembly process was maintained. Therefore, the system had the ability of passive fault tolerance.

Figure 5.

The completion condition of each robot for the failure of assembly logistics: (a) frequency = 100, (b) frequency = 200, (c) frequency = 400, and (d) frequency = 500.

Figure 6.

The completion condition of each robot for the failure of an assembly robot: (a) frequency = 100, (b) frequency = 200, (c) frequency = 400, (d) frequency = 500.

Figures 7 and 8 show that when an assembly failure occurred, a task accumulation phenomenon occurred for some assembly tasks, such as for task A11 or F13. Some tasks were consistent with the normal state; hence, the passive fault-tolerant control could coordinate the assembly workload of each assembly robot, but it could not completely coordinate all the assembly tasks. Assembly tasks would eventually accumulate in the assembly process, blocking the logistics channel and affecting the assembly process. Therefore, while performing passive fault-tolerant control, it was also necessary to apply an active fault-tolerant control method to coordinate the number of tasks and to ensure that when a fault occurred, the assembly efficiency of the entire assembly system could be improved when compared to using only passive fault tolerance control.

Figure 7.

Changes in the number of assembly tasks caused by robot failure: (a) change in the number of tasks A11 when the robot fails, (b) change in the number of tasks L31 when the robot fails, (c) changes in the number of tasks F13 when the robot fails, and (d) change in the number of tasks I25 when the robot fails.

Figure 8.

Changes in the number of assembly tasks caused by logistics failures: (a) change in the number of tasks A11 during logistics failure, (b) changes in the number of tasks L31 during logistics failure, (c) changes in the number of tasks F13 in the event of a logistics failure, and (d) change in the number of tasks I25 during logistics failure.

Analysis of active fault tolerance control

Although passive fault tolerance methods were applied in the assembly process, some assembly tasks could still not be completed in time when a fault occurred, which affected the operation of the assembly. Therefore, in the process of fault-tolerant control, it was necessary to monitor the assembly state actively so that if a fault occurred, it could be corrected in time. In the design of this assembly method, the changes in assembly data were captured by a LS-SVM model, which determined the operation assembly of the assembly system. If it was judged that a fault had occurred, the system carried out the corresponding fault adjustment mechanism, and information for the assembly tasks was collected. Some judging parameters used in the LS-SVM model are summarized in the following equations:

$$x_1=\sum _{i=1}^n{a}_i,$$

(20)

$$x_2=\mathrm{maxA},$$

(21)

$$x_3=\sum _{i=1}^n{a}_i/n,$$

(22)

$$x_4=maxA-\sum _{i=1}^n{a}_i/n.$$

(23)

In equations (20)–(23), n is the number of tasks finished in the real-time assembly, a_i is the real assembly time of task i, and A is the array of a_i. The variables x₁, x₂, x₃, and x₄ represent the feature parameters, where x₁ is the total number of tasks finished in the real-time assembly, x₂ is the maximum value in array A, x₃ is the mean value of the real-time task number, and x₄ is the value of the difference between x₂ and x₃. The feature parameter array is extracted as follows: X=[x₁, x₂, x₃, x₄].

To verify the accuracy of the assembly data analysis performed by the LS-SVM model, 200 sets of assembly data were introduced for analysis and verification. These data included information about normal assembly operation, failures in the assembly, and fault recovery, expressed using array A and array X, which are shown in Table 3.

Table 3.

Assembly monitoring data.

Assembly numbers	Some data in A of the array					Partial data of array X
						x 1	x 2	x 3	x 4
1	1	1	1	1	…	12	1	0.266667	0.733333
2	1	1	1	1	…	12	1	0.266667	0.733333
3	0	0	1	0	…	13	1	0.288889	0.711111
4	0	0	0	0	…	12	1	0.266667	0.733333
…	…	…	…	…	…	…	…	…	…
18	1	1	1	1	…	12	1	0.266666667	0.733333333
19	0	0	1	0	…	13	1	0.288888889	0.711111111
20	30	0	0	0	…	162	31	3.6	27.4
21	30	0	0	0	…	158	31	3.511111	27.48889
22	30	0	0	0	…	153	30	3.4	26.6
23	28	0	0	0	…	150	29	3.333333	25.66667
24	28	0	0	0	…	148	29	3.288889	25.71111
25	28	1	1	1	…	157	29	3.488889	25.51111
26	28	1	1	1	…	155	29	3.444444	25.55556
…	…	…	…	…	…	…	…	…	…
98	4	1	1	0	…	29	5	0.644444	4.355556
99	4	1	1	0	…	27	5	0.6	4.4
100	4	1	0	0	…	24	5	0.533333	4.466667
101	4	1	0	0	…	23	5	0.511111	4.488889
102	4	1	0	0	…	21	5	0.466667	4.533333
103	2	1	0	0	…	18	5	0.4	4.6
104	2	1	0	0	…	16	5	0.355556	4.644444
105	2	1	0	0	…	16	4	0.355556	3.644444
106	2	0	0	0	…	16	4	0.355556	3.644444
…	…	…	…	…	…	…	…	…	…
193	1	1	1	1	…	12	1	0.266667	0.733333
194	1	1	1	1	…	12	1	0.266667	0.733333
195	0	0	1	0	…	13	1	0.288889	0.711111
196	0	0	0	0	…	12	1	0.266667	0.733333
197	0	0	0	0	…	8	1	0.177778	0.822222
198	0	0	0	0	…	9	1	0.2	0.8
199	0	0	0	0	…	6	1	0.133333	0.866667
200	0	0	0	0	…	4	1	0.088889	0.911111

The LS-SVM model analyzed the data in Table 3, and the corresponding classification results are shown in Figure 9. After the LS-SVM analysis, the LS-SVM model would provide a signal value = 1 or −1. When the result was 1, it meant that the assembly system was in regular operation or recovering to regular operation, and the corresponding value of tb was 0. When the result was −1, it indicated that the system was in fault, and the corresponding value of tb was 1.

Figure 9.

Data analysis results of the LS-SVM model.

In Figure 9, the two curves represent the judging results generated by the data of array X and array A. The resulting curve produced by array X can be observed. From the 18th to the 24th assembly of the product, the assembly process is in fault, so the signal value = −1 and the corresponding value of tb = 1. The system consequently responded to the failure, and in the 102nd through the 108th assembly of the product, the assembly fault was eliminated and the assembly process returned to a normal state. The resulting curve obtained from array X is consistent with the assembly state described in Table 3, whereas the curve generated by array A could not be used to accurately determine the assembly state of the assembly process.

When tb = 1, the system could perform active fault-tolerant control of the faults and could manage the accumulation of tasks caused by the fault to ensure an orderly operation of the assembly system. In the experimental analysis, the fault handling ability of the active fault tolerance was analyzed when a failure occurred during an assembly of 1000 products. The relevant results of active fault tolerance were also compared with passive fault tolerance.

The comparative analysis results shown in Figures 5, 6, and 10 indicate that, for active fault tolerance control, the number of the finished tasks for each robot was essentially the same as for passive fault tolerance control. Therefore, when considering the number of completed assembly tasks, active fault tolerance control and passive fault tolerance control produced essentially the same results. By saturating the assembly states of the existing robots, the number of accumulated tasks caused by faults can be minimized.

Figure 10.

Task completion of each robot under active fault tolerance control: (a) logistics fault, frequency = 200, (b) logistics fault, frequency = 500, (c) robot fault, frequency = 200, and (d) robot fault, frequency = 500.

Figures 11 and 12 indicate that active fault-tolerant control is more effective than passive fault-tolerant control for eliminating the task accumulation caused by faults and keeping the task within the required number for normal assembly. Therefore, when a fault occurs, in addition to effectively coordinating the number of assembly tasks of each assembly robot, active fault-tolerant control can also find the tasks with a large accumulation and coordinate each assembly robot to eliminate the task accumulation. It ensures that no clogging occurs during the overall assembly process and makes the assembly process efficient. Figure 13 shows that during normal assembly, the number of assembled products was 123. However, under the robot failure status, the assembled product number was 45 with the application of passive fault tolerance control and 50 with the application of active fault tolerance control. When the logistics failures occurred, the assembled product number was 62 with the application of the passive fault tolerance control and 72 with the application of active fault tolerance control.

Figure 11.

Change in the number of assembly tasks selected for robot faults under active fault tolerance control: (a) change in the number of tasks A11 when the robot fails, (b) change in the number of tasks L31 when the robot fails, (c) change in the number of tasks F13 when the robot fails, and (d) change in the number of tasks I25 when the robot fails.

Figure 12.

Changes in the number of assembly tasks selected for assembly logistics failures under active fault tolerance control: (a) change in the number of tasks A11 during logistics failure, (b) changes in the number of tasks L31 during logistics failure, (c) change in the number of tasks F13 in the event of a logistics failure, and (d) change in the number of tasks I25 during logistics failure.

Figure 13.

The number of assembled products under corresponding control methods when a failure occurs: (a) compared with normal assembly, when the robot fails, the number of assembled products under the relevant control method and (b) compared with normal assembly, the number of assembled products under relevant control methods when logistics failures occur.

Figure 14 shows that during the normal assembly of 10,000 products, the number of assembled products was 1248. However, when the logistics failures occurred, the number of assembled products with passive fault tolerance control was 642, and the number of assembled products with active fault tolerance control was 1210. Therefore, not only can active fault-tolerant control effectively reduce the accumulation of assembly tasks caused by failures, but it can also prevent the assembly process from generating assembly fluctuations, ensuring the stability of the assembly system.

Figure 14.

The number of assembled products for the corresponding control method when assembling 10,000 products and a logistics failure occurs.

Conclusions

1. The division of assembly tasks based on assembly actions allows assembly robots not only to replace each other in the assembly process but also to maintain a certain independence. The AAPF fault-tolerant method has better passive fault tolerance performance in the assembly of small and complex products. It can improve the stability of the assembly process when a fault occurs.

2. In the AAPF algorithm, the pheromone was calculated by the application of the assembly data during the assembly of small and complex products, and the control of some assembly parameters could be realized by adjusting its value.

3. By the application of the LS-SVM model, the AAPF algorithm could achieve both passive fault-tolerant control and active fault-tolerant control of the assembly. Through experimental analysis, it was demonstrated that the AAPF algorithm could not only coordinate the number of assembly tasks of each assembly robot but also effectively reduce the number of assembly tasks that accumulated because of the faults. Therefore, the combination of active fault-tolerant and passive fault-tolerant control could effectively ensure the stability and effectiveness of the assembly.

4. It is very important to analyze the assembly information accurately when using the AAPF algorithm, but the collection of assembly information is vast and complex during an assembly process. This complexity brings challenges to the LS-SVM method, so the analysis performance of the LS-SVM model will need to be improved in future work.

5. The fault-tolerant method proposed in this paper was used to describe only one type of assembled product. When two or more kinds of assembled products must be assembled, the method will not be effective. Therefore, the fault-tolerance of multi-type product assembling will also be studied in future work.