Elsevier

Computer-Aided Design

Volumes 67–68, October 2015, Pages 58-86
Computer-Aided Design

Review
Review and taxonomies of assembly and disassembly path planning problems and approaches

https://doi.org/10.1016/j.cad.2015.05.001Get rights and content

Highlights

  • State-of-the-art review of the Assembly/Disassembly Path Planning (APP/DAPP) field.

  • New taxonomies for categorizing APP/DAPP problem types and solution methods.

  • Critical discussions on research trends, applications and open problems in APP/DAPP.

Abstract

Assembly Planning (AP) is one of the most important elements of process planning in manufacturing industries, and is defined as the process of creating a detailed assembly plan to craft a whole product from separate parts considering the final product geometry, available resources, fixture design, feeder and tool descriptions, etc. AP has three main subproblems: (1) Assembly Sequence Planning (ASP), in which a sequence of collision-free operations is computed for bringing assembly parts together, (2) Assembly Line Balancing (ALB), in which some groups of subassemblies are formed and assigned to assembly stations in a way that their workloads are balanced, and (3) Assembly Path Planning (APP), in which collision-free paths for adding parts to a subassembly are computed. Each of the above subproblems has a disassembly version, creating DASP, DALB, and DAPP problems. All of the above problems have proven to be either NP-hard or NP-Complete, and many researches have been conducted to solve them efficiently. While some surveys and reviews exist on the ASP/DASP and ALB/DALB problems, no comprehensive survey exists for APP/DAPP problems, despite their important role in the design process of products as invaluable tools for deploying concurrent engineering, end-of-life processing, maintenance and repair, and decreasing the cost and time of manufacturing products. This paper investigates the relations between the above six subproblems and reviews the state-of-the-art of the APP and DAPP problems and their solution approaches. Through two new taxonomies the properties and categories of APP/DAPP problems and solution approaches are identified and described, the characteristics and applications of the reviewed 60 most relevant works are exposed and analyzed comprehensively, and open problems in the field are identified.

Introduction

Assembly Planning (AP) is the process of creating a detailed assembly plan to craft a whole product from separate parts by taking into account the final product geometry, available resources to manufacture that product, fixture design, feeder and tool descriptions, etc. Assembly planning is one of the most important processes in manufacturing products since assembly processes use up to 50% of the total production time and more than 20% of the total manufacturing cost  [1]. So, efficient assembly plans can reduce manufacturing time and costs significantly. The Assembly Planning problem has been shown to be an NP-complete problem  [2] and covers three main subproblems: Assembly Sequence Planning, Assembly Line Balancing, and Assembly Path Planning.

The Assembly Sequence Planning (ASP) problem concerns with finding a sequence of collision-free operations o1,,on that bring the assembly parts p1,,pn together, having given the geometry of the final product A and the positions of parts in the final product. A systematic overview on the ASP is presented in  [3], which includes a survey of the elements of sequence planning, such as finding a feasible sequence, determining an optimal sequence according to one or more operational criteria, representing the space of feasible assembly sequences in different ways, applying search and optimization algorithms, and satisfying precedence constraints existing between subassemblies. The ASP problem is classified as an NP-hard problem and so cannot be solved in polynomial time  [4]. The complexity of finding an optimal sequence increases linearly with the size of the space of all potential assembly sequences in the case of exhaustive search. However, when all created sequences with the assembly sequence planner are linear and monotone, the number of assembly operations equals the number of parts, n, and therefore the total number of potential sequences is given by the permutations of parts, n!. Assuming that all the sequences created by the assembly sequence planner are monotone, the size of the solution space amounts to (2n2)!/(n1)!, and if non-monotone sequences are considered as well, the number of potential sequences will be infinite [5].

The Assembly Line Balancing (ALB) problem deals with partitioning the total assembly operations into a set of n elementary tasks oi(i=1,,n) with times ti, and assigning them to m assembly workstations wk(k=1,,m) such that in all workstations approximately equal assembly times are spent and the precedence constraints between operations are satisfied. Assuming that the set Sk of tasks is assigned to the workstation k, the assembly time of that workstation equals t(Sk)=jSktj. The ALB problem is also NP-hard  [6], and can be divided into two categories: Simple Assembly Line Balancing Problem (SALBP), and Generalized Assembly Line Balancing Problem (GALBP). SALBP is appropriate for modeling assembly lines with all their input parameters deterministically known, which produce a unique model of a single product (i.e., serial assembly lines)  [7]. On the other hand, GALBP is appropriate for balancing more complex lines such as parallel, U-shaped, mixed-shaped, and two-sided lines with stochastic dependent processing times  [8]. A survey on researches in ASP and SALBP that have applied soft computing approaches is presented in  [9], covering the years 2001 to 2011. Soft computing approaches are useful for ASP and ALB optimization because they are able to handle more complex and large size problems with numerous constraints.

The Assembly Path Planning (APP) problem considers generating sequences of positions for parts p1,,pn of a final product A with known geometries, from an initial (disassembled) position to the final (assembled) position, in the form of paths τ1,,τn that contain no collisions between assembled and disassembled parts and with obstacles o1,,or in a workspace W2 or 3. The APP problem inherently resembles the classic “Piano Movers’ Problem” in robot motion planning, which is simply described as moving a solid object in 3D space with six degrees of freedom amongst stationary obstacles, and has been proved to be PSPACE-hard and NP-Complete [10], [11], [12]. Therefore, APP has the same complexity of the general motion planning. Assembly paths are calculated based on the assembly sequences that are the output of the ASP problem. APP is an important phase of the broader Assembly Planning problem, because: (1) the solution of this problem can provide better feedback by CAD systems to designers  [13], (2) a good assembly path plan would ensure production of products that are more cost effective to manufacture and thus can influence the efficiency of the overall assembly planning process, and (3) a poor assembly path plan can increase the cost of manufacturing significantly and reduce the productivity since long part travel paths consume more time and energy. APP can be formulated as a motion planning problem  [14], [15] using the notion of Configuration Space (C-space) proposed by Lozano-Pérez in 1983  [16]. A configuration q is a minimal set of parameters defining the location of a mobile system in the world, and the configuration space C is the set of all configurations. In the case of a system M involving n mobile objects mi (e.g. the parts of the assembly), the Composite Configuration Space C is the Cartesian product of the configuration spaces of all the objects. That is, C=i=1ncmi;i=1,,n. Given the initial configuration qdis, the problem consists in finding a feasible path in C from qdis to a final assembled configuration qass.

Another closely related issue to the Assembly Planning is Disassembly Planning(DAP). Given the geometry of the final product and the resources to manufacture that product, Disassembly Planning creates a manufacturing plan for removing specific parts from a whole assembly. ‘Assembly by Disassembly’ is an important strategy for assembling since parts in an assembled state of a product have far more precedence and motion constraints than in a disassembled state of that product  [17]. These constraints drastically reduce the solution space size of the ASP and APP problems. According to this strategy, an assembly plan is obtained by disassembling a whole product into its constituting parts and then reversing the order of disassembly. When only geometric constraints are concerned and all parts are rigid, there is a bijection between assembly and disassembly sequences and paths, though this bijection does not remain correct when physics (e.g. gravity, friction) and motion control uncertainty are taken into account, or when some parts are deformable  [18] or toleranced  [19]. For example, disassembly of a part assembled by rivets is not simply the reverse of its assembly. DAP concerns with feasibly removing specific parts from a whole assembly, and is one of the important processes in product manufacturing since it is required for maintenance and repair of a product, is used in reverse and concurrent engineering, and has a major role in devising a proper design process.

A classification of DAP methods for disassembling of a component Ci from a product A is presented in  [20], according to the following criteria: (1) 1- vs. m-disassembly: Ci is m-disassemblable if multi-step translational motions are needed to remove it from A; (2) Direct vs. Indirect disassembly: Ci is directly disassemblable if it can be removed from A without removing other components; (3) Sequential vs. Parallel (non-sequential) disassembly: sequentiality refers to the maximum number of moving subassemblies with respect to one another in a disassembly method; (4) Monotonic vs. Non-monotonic disassembly: in monotonic disassembly the components are totally removed from A, and conversely, non-monotonic disassembly requires partial disassembly of one or more components; (5) Complete vs. Selective disassembly: complete disassembly occurs when all parts of the product A are disassembled; (6) Destructive vs. Non-destructive disassembly: the disassembly method is destructive when one or more components must be destroyed during the operation.

DAP covers three main subproblems: Disassembly Sequence Planning, Disassembly Line Balancing, and Disassembly Path Planning, all of which are either NP-hard or NP-complete:

The Disassembly Sequence Planning (DASP) problem computes a sequence of collision-free operations that remove the assembly parts from the final product, having given the geometry of the final product and the positions of parts in the final product. A survey on this subproblem is presented in  [21], which covers topics such as different ways of representing the space of feasible disassembly sequences; component-oriented approaches that consider automatic path generation, motion and stability analyses and collision detection; product-oriented approaches that perform automatic analyses of the ability to decompose a product from its assembly drawing; and the hierarchical-tree approach which is based on the inverse Material Requirement Planning (MRP) and relates disassembly processes to the hierarchical product structure.

The Disassembly Line Balancing (DALB) problem optimally assigns the required disassembly operations of a product to disassembly stations so that the precedence constraints between operations are satisfied. DALB is necessary when some returned products are disassembled in order to recycle and remanufacture that product. Many papers on this topic have been published to date, for example, Scholl has presented a comprehensive textbook on this problem  [22].

The Disassembly Path Planning (DAPP) problem computes the path for separating a part from a sub-assembly, having given the geometry of the final product, the positions of parts in the final product, and the space in which the assembly operation is performed. Given the initial configuration qass, the DAPP tries to find a feasible path in the composite configuration space C from qass to a final disassembled configuration qdis. However, the difference between the DAPP and standard path planning problems is that the final disassembled configuration may not be precisely specified, but implicitly defined by the distances between parts. Like APP, DAPP is an important and useful tool for designing assembly/disassembly processes and reducing manufacturing time and cost.

APP and DAPP problems are tightly related to four more specific and limited problems, which can be solved if solutions to the APP and DAPP are found. These problems are Motion Stability, Assembly Maintainability, Selective Disassembly Planning, and Partitioning. Among these problems, only the Motion Stability Problem is related to both APP and DAPP problems, and the others are closely related only to the DAPP problem.

  • (1)

    Motion stability problem deals with identifying the presence and time of occurrence of instability of an assembly during (dis)assembly part motions. The first algorithm presented for analyzing the stability of a number of blocks and solving the set of contact forces in the assembly of rigid blocks was presented in 1970 by Blum et al.  [23]. Boneschanscher et al. considered the situation in which physical and insertion forces are present in the assembly process and developed a semi-heuristic algorithm to determine the stability of sub-assemblies  [24]. An investigation of the computational complexity of stability of polygons was presented in  [25]. Also, optimum locations of fixels (fixturing points) for assemblies were determined by the potential energy minimization principle in  [26]. For identifying the set of orientations under which an assembly is stable when gravity is considered, Mattikalli et al.  [27], [28] developed linear programming approaches. Mosemann et al. first created an AND/OR assembly graph in  [29] and then analyzed the stability of the subassemblies at each node of the AND/OR assembly graph in  [30]. Recently, Rakshit and Akella have presented an approach for the motion stability analysis of mechanical parts disassembly in the presence of physical forces such as gravity and friction  [18].

  • (2)

    Assembly maintainability problem investigates the possibility of removing a particular part from an assembly without changing positions and orientations of other parts, and finds such a path if one exists. Before 1995, Assembly Maintainability was labor intensive and heavily relied on humans in providing access paths for parts through using either physical mock-ups or computer animations with CAD models. However, Chang and Li presented an automated approach in 1995 to replace this manual process and demonstrated the feasibility of using an automated assembly maintainability system  [31]. Although both the Assembly Maintainability and DAPP problems have the same goal of finding paths for disassembling a product, they differ in that DAPP focuses on finding disassembly paths only at certain straight directions, but the Assembly Maintainability problem accommodates complex straight or curved part removal motions. The Assembly Maintainability problem can be reduced to the “piano movers” problem, and since it is NP-complete the Assembly Maintainability problem is also NP-complete.

  • (3)

    Selective disassembly planning problem tries to generate a sequence of parts removal required to disassemble a certain ‘target’ part from an assembly. This operation is necessary when the target part has reached its expected end of life or because it fails to function properly in the simulation of maintenance operations. Two subproblems must be solved to generate a selective disassembly plan: the DASP and DAPP problems  [32]. Because these two subproblems are NP-complete, the general Selective Disassembly Planning problem is also NP-complete.

  • (4)

    Partitioning problem concerns with finding a proper subset S of a rigid parts assembly A and a direction d such that the complementing subsets S and AS do not collide with each other when the subassembly S is moved as a rigid body along d. The partitioning problem is NP-complete for two-handed monotone assembly plans (i.e. when the given assembly can be partitioned into two complementing subsets each treated as a rigid body without intermediate placement of subassemblies) and arbitrary direction  [33], [34].

Fig. 1 illustrates the relations between the main six problems of ASP, ALB, APP, DASP, DALB, and DAPP, together with their short descriptions and the objective functions that have been considered and optimized in the literature for each problem. Note the logical sequence of ASPALBAPP and DASPDALBDAPP shown in the figure, as the output of a problem can be the input information for its succeeding problem.

Surprisingly, while some surveys and reviews exist on the ASP/DASP and ALB/DALB problems, the APP/DAPP problems or solution methods have not received due attention despite their important role in the design process of products as invaluable tools for deploying concurrent engineering, end-of-life processing, maintenance, repair, and decreasing the cost and time of manufacturing products. Therefore, regarding the importance of the APP/DAPP problems and the vast body of research conducted on these topics on one hand, and the lack of a consolidated and unifying framework or a proper categorization of the problems and solution approaches of the APP/DAPP problems on the other hand, developing a comprehensive survey and classification seems indispensable.

Trying to address this issue, in this paper we present a state-of-the-art review on the APP and DAPP problems and their solution approaches. Also, through two new detailed taxonomies, properties and categories of APP/DAPP problems and solution methods are identified and described, and their characteristics and applications in the reviewed literature are exposed broadly. The proposed taxonomies cover the main aspects of APP/DAPP problems and solutions, as described below:

APP/DAPP problems taxonomy: The first step in defining an APP/DAPP problem is to obtain information on the structure of the assembly and its parts, and then construct a comprehensive model for establishing assumptions and expressing the parts, the assembly, and the relationship between parts in the assembly. Once a model has been built, the nature of the assembly can be identified and analyzed. Therefore, the taxonomy of APP/DAPP problems has two main aspects:

  • Problem model, which includes assumptions about the considered components in the assembly, dimensions, tolerances, geometry, rigidity, and various geometrical, physical and mechanical constraints of the assembly and its parts, as well as the allowed movements during the assembly/disassembly operation, and the objective function of the model. These features are further described in Section  2.1.

  • Problem nature, which expresses the inherent features of the (dis)assembly problem stemmed from the geometrical structure of the assembly, such as number of parts, sequentiality, monotonicity, linearity, coherence and scale. These features are further described in Section  2.2.

APP/DAPP solution methods taxonomy: Given a sequence for assembling/disassembling parts to/from an assembly (obtained by solving an ASP/DASP problem), a solution to the APP/DAPP problem is a set of plans for the motions of some or all parts of the assembly from their initial to final configurations. This can be done using several path/motion planning methods which are selected according to their characteristics, nature, and ability in satisfying the assumptions and constraints of the problem model. APP/DAPP solution methods can be studied from two aspects:

  • Solution approach, which is the course of action the planner adopts for finding (dis)assembly paths and coming up with a total (dis)assembly plan that solves the APP/DAPP problem. The approach could be Graph-based, Grid-based, Sampling-based, Space Decomposition, or Interactive, as described in Section  3.1.

  • Solution nature, which refers to inherent properties of the solution methods, such as mode, scope and completeness. Section  3.2 presents detailed explanations about these features.

The key benefits of these taxonomies are:

  • 1.

    They are efficient and consistent representations of the sizeable volume of research and information in the APP/DAPP field.

  • 2.

    They incorporate and provide essential keywords and their hierarchical structures in all important concepts within the APP/DAPP field.

  • 3.

    They highlight the main features of many researches in the literature and attribute various characteristics to them though not directly and explicitly mentioned in the original articles.

  • 4.

    They provide sufficient knowledge and guidance for understanding and directly finding correct and exact information about researches on each aspect of APP/DAPP problems and solution methods.

  • 5.

    Through using comprehensive frameworks of the taxonomies and the discussions provided, readers can identify research gaps in APP/DAPP problems formulation and solution and thereby initiate novel researches in this field.

In this paper, along with describing the above two taxonomies, the APP/DAPP literature has been critically reviewed to sufficient details and all industrial or puzzle-like applications mentioned in the reviewed papers are reported in a table, together with a summary of their main features. The survey revealed some remarkable facts about research on APP/DAPP, such as: (1) Assembly of flexible parts has been hardly addressed; (2) Assembling tools, hands, or fixtures have mostly been ignored in planning assembly sequences and paths; (3) There are few solution methods that can handle non-monotone, nonlinear, non-sequential, and incoherent assembly planning problems; and (4) About 65% of the studied 119 examples were actual or simulated industrial assemblies and the rest were puzzle-like, theoretical problems. Other interesting facts are presented through the discussions presented in Section  4, where some analyses regarding the proportion of works on APP/DAPP solution approaches and their chronological trends, as well as open problems in the field are also presented. Finally, conclusions are provided in Section  5. Additionally, due to the abundance of acronyms coined for various solution methods, we have tabulated all the acronyms used in this article in Appendix.

Section snippets

Taxonomy of APP/DAPP problems

In this section we present a taxonomy for the main features of APP/DAPP problems and review the articles that have dealt with these features. Fig. 2 illustrates the taxonomy with its two main aspects of problem model and problem nature.

Taxonomy of APP/DAPP solution methods

In this section, we present a taxonomy of APP/DAPP Solution Methods and survey the articles that have dealt with each feature of the taxonomy. As shown in Fig. 9, the taxonomy of APP/DAPP Solution Methods covers the two aspects of Approaches and Nature of solution methods.

Discussion

In this section some observations and analyses are presented related to the in-depth review and taxonomies of the previous sections, which deal with the frequency, applicability, and trends of solution approaches and their nature (mainly in terms of completeness), as well as industrial or synthesized applications for which APP/DAPP problems have been proposed, and finally some open problems and research areas in the field of (dis)assembly path planning.

Conclusions

Assembly and Disassembly Planning are two fundamental problems in any manufacturing industry, which in addition to their significant importance and impact on manufacturing and assembling operations, give better insight to part and product designers in creating more cost-effective products in manufacturability and maintainability respects. Assembly and Disassembly Planning problems encompass three main subproblems: ASP/DASP, ALB/DALB, and APP/DAPP. While survey papers exist for the first two

References (111)

  • D. Lee et al.

    Path planning for micro part assembly by using active stereo vision with a rotational mirror

    Sensors Actuators A

    (2013)
  • J.S. Carlson et al.

    Non-nominal path planning for robust robotic assembly

    J Manuf Syst

    (2013)
  • R.H. Wilson et al.

    Geometric reasoning about mechanical assembly

    Artificial Intelligence

    (1994)
  • X. Jin et al.

    An analysis of the assembly path planning of decelerator based on virtual technology

    Phys Procedia

    (2012)
  • C. Pan

    Integrating CAD files and automatic assembly sequence planning

    (2005)
  • P. Jiménez

    Survey on assembly sequencing: a combinatorial and geometrical perspective

    J Intell Manuf

    (2013)
  • H. Lv et al.

    An assembly sequence planning approach with a discrete particle swarm optimization algorithm

    Int J Adv Manuf Technol

    (2010)
  • R.M. Marian

    Optimisation of assembly sequences using genetic algorithms

    (2003)
  • L. Capacho Betancourt

    Asalbp: The alternative subgraphs assembly line balancing problem. formalization and resolution procedures

    (2007)
  • S.Ö. Tasan et al.

    Improving the genetic algorithms performance in simple assembly line balancing

  • M.F.F. Rashid et al.

    A review on assembly sequence planning and assembly line balancing optimisation using soft computing approaches

    Int J Adv Manuf Technol

    (2012)
  • Reif JH. Complexity of the mover’s problem and generalizations extended abstract. In: Proceedings of The 20th annual...
  • J. Canny

    The complexity of robot motion planning

    (1988)
  • L. Zhang et al.

    D-Plan: Efficient collision-free path computation for part removal and disassembly

    J Comput-Aided Des Appl

    (2008)
  • J.-C. Latombe

    Robot motion planning

    (1991)
  • S.M. LaValle

    Planning algorithms

    (2006)
  • T. Lozano-Perez

    Spatial planning: A configuration space approach

    IEEE Trans. Comput.

    (1983)
  • D. Halperin et al.

    A general framework for assembly planning: The motion space approach

    Algorithmica

    (2000)
  • S. Rakshit et al.

    The influence of motion path and assembly sequence on the stability of assemblies

    Robot Sci Syst

    (2013)
  • H. Srinivasan et al.

    A framework for virtual disassembly analysis

    J Intell Manuf

    (1997)
  • A.J. Lambert

    Disassembly sequencing: A survey

    Int J Prod Res

    (2003)
  • A. Scholl

    Balancing and sequencing of assembly lines

    (1999)
  • Blum M, Griffith A, Neumann B. A stability test for configurations of blocks, Artificial Intelligence Memo No. 188,...
  • Boneschanscher N, Van Der Drift H, Buckley SJ, Taylor RH. Subassembly stability. In: Aaai, 1988, p....
  • Palmer RS. Computational complexity of motion and stability of polygons. In: Cornell University,...
  • Wolter JD, Trinkle JC. Automatic selection of fixture points for frictionless assemblies. In: Proceedings of IEEE...
  • R. Mattikalli et al.

    Finding all stable orientations of assemblies with friction

    IEEE Trans. Robot. Autom.

    (1996)
  • R. Mattikalli et al.

    Gravitational stability of frictionless assemblies

    IEEE Trans. Robot. Autom.

    (1995)
  • H. Mosemann et al.

    Stability analysis of assemblies considering friction

    IEEE Trans. Robot. Autom.

    (1997)
  • Mosemann H, Rohrdanz F, Wahl F. Assembly stability as a constraint for assembly sequence planning. In: Proceedings of...
  • Chang H, Li T-Y. Assembly maintainability study with motion planning. In: Proceedings of IEEE international conference...
  • I. Aguinaga et al.

    Path-planning techniques for the simulation of disassembly tasks

    Assem Autom

    (2007)
  • R.H. Wilson et al.

    Two-handed assembly sequencing

    Int J Robot Res

    (1995)
  • Haicheng L, Yuan L, Jianfeng Y, Yuan Z. Path planning algorithm for assembly of complex product based on V-map and ant...
  • Lee S, Moradi H. Disassembly sequencing and assembly sequence verification using force flow networks. In: Proceedings...
  • C. Hui et al.

    Efficient method of assembly sequence planning based on GAAA and optimizing by assembly path feedback for complex product

    Int J Adv Manuf Technol

    (2009)
  • J. Cortés et al.

    Disassembly path planning for complex articulated objects

    IEEE Trans Robot

    (2008)
  • Ferré E, Laumond J-P, Arechavaleta G, Estevès C. Progresses in assembly path planning, In: Int. conf. on product...
  • Coutee AS. Virtual assembly and disassembly analysis: An exploration into virtual object interactions and haptic...
  • T. Lim et al.

    Haptic virtual reality assembly–moving towards real engineering applications

  • Cited by (133)

    View all citing articles on Scopus

    This paper has been recommended for acceptance by Ming C. Lin.

    View full text