Automated packing systems:
Review of industrial implementations.
Paul F. Whelan
School of Electronic Engineering
Dublin City University
Dublin, Ireland.
Bruce G. Batchelor
Department of Computing Mathematics
University of Wales
Cardiff, Wales.
ABSTRACT
The problems involved in the automated packing and nesting of irregular shapes are not only of theoretical importance, but
have considerable industrial interest. The ability to manipulate objects under visual control is one of the key tasks in the
successful implementation of robotic, automated assembly and adaptive material handling systems. Such systems must be
capable of dealing with a wide range of variable products and of operating in industrial environments that are not overly
constrained. These systems will need to include the ability to manipulate arbitrary shapes in a flexible manner. Therefore, to
automate this part of the manufacturing process we need to develop automated material handling systems that combine
machine vision techniques and flexible packing strategies.
A rich theoretical background to the problems that occur in the automation of material handling can be found in operations
research, production engineering, systems engineering and automation, more specifically machine vision, literature. This work
has contributed towards the design of intelligent handling systems. This paper will review the application of these automated
material handling and packing techniques to industrial problems. The discussion will also highlight the systems integration
issues involved in these applications.
An outline of one such industrial application, the automated placement of shape templates on to leather hides, is also discussed.
The purpose of this system is to arrange shape templates on a leather hide in an efficient manner, so as to minimize the leather
waste, before they are automatically cut from the hide. These pieces are used in the furniture and car manufacturing industries
for the upholstery of high quality leather chairs and car seats. Currently this type of operation is semi-automated. The paper
will outline the problems involved in the full automation of such a procedure.
1. INTRODUCTION
Early research into determining optimal packing/nesting configurations can be traced back to Johannes Kepler in 1611 when he
tried to determine if the most efficient method of packing identical spheres was an arrangement now known as face-centred
cubic lattice. This consists of placing a bottom layer of spheres in a bounded region. Each successive layer is then arranged so
that the spheres occupy the gaps of the layer below (Stewart 1991; 1992). This is the arrangement greengrocers us to stack
oranges. Although the stacking of oranges in this way seems intuitive, researchers are still unable to prove that this stacking
configuration is the most efficient.
2. THE PACKING PROBLEM - AN OUTLINE OF CURRENT RESEARCH.
The field of operations research has been active in developing techniques for the automated packing/nesting of two and
three-dimensional shapes. Dowsland and Dowsland (1992) have recently reviewed the work done in this area. As well as
considering the application of operational research techniques to a full range of packing tasks, this review outlines the future
trends in packing research from this perspective. Sweeney and Paternoster (1992) also produced a recent review of the packing
problem. The authors have grouped the publications according to the three main solution methodologies, these are summarized
below:
•Sequential assignment heuristics, packing of patterns based on a set of assignment rules. The majority of heuristic
approaches consist of determining what order and orientation the pieces should be packed in.
•Single-pattern generating procedures such as dynamic programming based algorithms which try and reuse a single
'optimal' packing configuration. For example, in the two-dimensional rectangular packing problem the
solution is built up by considering partial solutions within smaller containing rectangles (Dowsland and
Dowsland 1992).
•Multi-pattern generating procedures such as linear programming
1
based approaches which consider the interaction
between patterns. This approach requires the solutions to be rounded and are, therefore, also heuristic in
nature. The packing task can be formulated as a binary integer problem in which a single variable represents
each possible piece position. For example a rectangle could be represented by a top left coordinate. A major
concern with this approach is the production of a physical design from the values of the variables in the
integer programming solution (Dowsland and Dowsland 1992).
A practical review of two and three-dimensional packing issues and solution methods can be found in Dowslands (1985) paper.
The majority of the applications outlined in this review are based on two-dimensional packing techniques. Many of the
three-dimensional problems are tackled by applying two-dimensional techniques on a layer by layer basis. Most published
work in the area of three-dimensional packing is limited due to its complexity, and the applications that are discussed tend to be
concerned with the loading of shipping containers. The paper also summarises some of the practical requirements in pallet
loading, these include:
• The stability of the loading stack.
• The load bearing ability of the items in the stack.
• Ease of stacking.
• Air circulation requirements of certain products in a stack.
Carpenter and Dowsland (1985) expand on these system considerations. Dowsland (1985) also reviews some of the heuristic
approaches used for packing a given set of identical, and non-identical, rectangular items into a containing rectangle. This
extensive review covers the key areas in automated packing, such as optimality versus efficiency and the measurement of a
packing systems performance. The basic conclusion of the author is that although some very high packing densities have been
reported in the literature, as yet there is no generic heuristic approach that can be applied to the two-dimensional packing task.
Solutions reported tend to be very application specific.
1
This is a technique that is used to provide "a mathematical description (or model) of a real-life problem in which
something needs to be maximised (e.g. profits or security) or minimized (e.g. costs or risks)" (Devlin 1988). Optimization is
achieved by the suitable choice of a number of parameter values. This strategy makes much stronger demands on the program
structure when compared to heuristic techniques.
2.1 Packing of regular shapes.
The main emphasis of the early research into packing tended to concentrate on the well constrained problem of packing regular
shapes. This task usually consists of packing two-dimensional regular shapes into a well defined scene (the term scene is used,
in this paper, when referring to a region of space into which an arbitrary shape is placed), such as a rectangle (Chuang, Garey
and Johnson 1982; Brown 1971). The main industrial applications are in the area of pallet packing (Carpenter and Dowsland
1985) and container loading (Bischoff and Marriott 1990). Other applications include efficient VLSI design and automated
warehousing (Hall, Shell and Slutzky 1990).
2.2 Packing of irregular shapes.
More recently researchers in the field of engineering and science have begun to concentrate on the issues involved in the
packing of irregular shapes. Research in this area is constrained by the demands of a given application, so as to make the task
more manageable. Batchelor (1991) outlines a technique for the packing of complex shapes based on the use of the minimum
area bounding rectangle.
Qu and Sanders (1987) discuss a heuristic nesting algorithm for irregular parts and the factors affecting trim loss. The
application discussed is the cutting of a bill-of-materials from rectangular stock sheets. The author takes a systems approach to
the problem and produces some good results. These are discussed in the context of performance measurements which they
have developed. While the authors review the published work in this area, they make the important point that although a
number of techniques have been developed to enable the flexible packing of irregular shapes, very few of these have been
published due to commercial confidentiality. The approach described represents the irregular shapes in terms of a set of
non-overlapping rectangles. In fact the authors state that each of the parts in their study can be represented by no more than five
non-overlapping orthogonal rectangles. The system places each part in an orientation such that (a) its length > height and (b)
the largest complimentary (void) area is in the upper-right corner. The parts are then sorted by non-increasing part height. The
shapes are packed into a rectangular bounding region in a raster fashion, building up layers of intermeshed packed shapes. The
major disadvantage with this approach are (a) the use of rectangles to approximate the shape to be packed and (b) the
assumption that good packing patterns will be orthogonal.
Dori and Ben-Bassat (1984) investigate the nesting of shapes within a polygon rather than a rectangle. The authors discuss the
optimal packing of two-dimensional polygons with a view to minimizing waste. The algorithm is only applicable to the nesting
of congruent
2
convex figures. The problem involves cutting a number of similar but irregular pieces from a steel board, this is
referred to as the 'template-layout problem'. The authors decompose the task into two sub-problems. The first consists of the
optimal (minimal waste) circumscription of the original irregular shape by the most appropriate convex polygon. The
remaining problem consists of circumscribing the convex polygon by another polygon that can pave the plane, that is, cover the
plane by replications of the same figure without gaps or overlap. This is referred to as the paver polygon. Limitations of this
approach include the fact that it is only applicable to congruent convex figures and the assumption that the packing plane is
infinite, hence waste in the margin is not considered. Another limitation of this approach is that it can only be applied to
convex components with straight sides. Koroupi and Loftus (1991) address the issues raised by Dori and Ben-Bassat (1984),
by enclosing the component within a polygon so that the area added is minimal. The identical components, whether regular or
irregular, are then nested using paving techniques.
Prasad and Somasundaram (1991) outline a heuristic based computer aided system that will allow the nesting of
irregular-shaped sheet-metal blanks. This paper also contains a comprehensive list of the practical constraints one must
consider in developing a packing system for sheet metal stamping operations. Constraints such as, bridge width, blank
separation, grain orientation, and the minimization of scrap. They also highlight the need to align the pressure centre of the
blank to be cut out with the axis of the press ram to reduce wear in the guideways of the press. Design requirements, such as
2
Figures of the same form and size, differing at most with respect to their orientation and position.
maximizing the strength of the part when subsequent bending is involved, are also considered.
Kothari and Klinkhachorn (1989) present a two-dimensional packing strategy capable of achieving dense packing of convex
polygon shapes. The techniques described have been applied to the stock cutting in the hardwood manufacturing industry. This
consists of efficiently cutting wooden pieces from a hardwood board so that the pieces are free of defects and aligned in the
direction of the grain. This last constraint is needed for strength and aesthetic reasons.
Albano and Sapuppo (1980) discuss a procedure which claims to produce an optimal arrangement of irregular pieces. Manual
and semi-automatic approaches to this nesting task are also discussed. The techniques described show how "the optimal
allocation of a set of irregular pieces can be transformed into the problem of finding an optimal path through a space of
problem states from the initial state to the goal state". The search approach developed makes certain assumptions about the
task; (a) the pieces are irregular polygons without holes and (b) that the bounding region is rectangular. Despite this, their
paper contains some excellent results. The main applications discussed is that of cloth layout and leather cutting.
Chung, Scott and Hillman (1990) developed an automated nesting system which determines how to cut regular or irregular
two-dimensional pieces from a regular or irregular shaped material. One of the application constraints that must be considered
is the fact that the material to be cut, an animal hide, contains defective regions. The problem of cutting defective animal hides
appears in the leather upholstery and shoe industry, for example. The approach taken implements an objected-orientated
representational scheme in conjunction with a heuristic search procedure to determine an efficient nesting position. The authors
concentrate on finding an "satisfactory solution" rather than trying to exhaust all possible packing positions for an optimal
solution. A solution is deemed "satisfactory" when its yield is better than or equal to the average of a human expert's solution.
The overall system has been evaluated by comparing its performance to that of a human expert, and an average yield difference
of within 5% has been claimed.
Cuninghame-Green (1989) considers the moving and nesting of irregular shapes within the context of some practical
applications such as leather cutting, for the manufacture of shoes, the efficient cutting of boards and the packing of chocolates.
In the case of the efficient cutting of the shoe leather patterns, the author outlines some of the applications constraints that
occur in practical applications of packing techniques. These include the isotropic constraints of grain matching. For example, if
the grain of the material requires that all the shapes to lie in the same orientation, then the resultant layout will waste 46% of
the material. Whereas, if the grain allows the shapes to be turned upside down, this figure is reduced to 33%. The interlocking
of the shapes can further reduce this figure. As well as developing his own approach based on what he calls "configuration
space obstacle or CSO" which shows the possible packing position for any pair of convex polygons in a given orientation, a
link is also made between the fundamental ideas behind motion planning (Sharir 1989) to automated packing. To deal with a
broader class of shapes, that is shapes other than convex polygons, two approaches are discussed. The first is based on the
concept of packing the convex hull of each irregular shape. This has the disadvantage that the shapes cannot be interlocked and
as such material can be wasted. The second approach requires the dissection of each irregular shape into convex polygons to
which the CSO approach is applied.
More recently Whelan and Batchelor (1991; 1992; 1993) have developed a system that will allow the packing of arbitrary
shapes into an arbitrary scene. This packing scheme consists of two major components:
(a) A geometric packer (GP), based upon the principles of mathematical morphology and which takes an
arbitrary shape in a given orientation and puts the shape into place, in that orientation (Whelan and
Batchelor 1991).
(b) An heuristic packer (HP), which is concerned with the ordering and alignment of shapes prior to applying them
to the geometric packer. This component also deals with other general considerations, such as the
conflict in problem constraints and the measurement of packing performance. In addition, it deals with
practical constraints, such as the effects of the robot gripper on the packing strategy, packing in the
presence of defective regions, and isotropic ("grain" in the material being handled) and pattern matching
(Whelan and Batchelor 1992; 1993).
3. PACKING TECHNIQUES IN INDUSTRIAL SYSTEMS.
Lately a growing number of researchers have begun to develop industrial systems that deal with the more difficult robotic tasks
(Lee 1989). One such application of this new generation of 'intelligent robotics' is the automated packing (nesting) of parts in
an assembly process. Applications of these systems include the automated assembly of small components under visual control
(Van der Heijden 1985), air motor assembly (Adept 1991), automated gasket and carburettor mating (Shoureshi et al 1989)
and automatic shirt collar assembly (Delgrange and Maouche 1989).
Automated packing/nesting and automated assembly are closely related tasks. In the majority of assembly systems, the parts
only fit together in certain ways, dependant on their shapes, and they can only be moved into their fitting positions in ways that
are also dependent on their shape. This shape-dependent part-fitting is a key feature in any assembly application (Malcolm and
Smithers 1990). A primary source of difficulty in automated assembly is the uncertainty in the relative position of the parts
being assembled. This uncertainty can be significantly reduced by the use of vision and tactile sensors.
Hall, Slutzky and Shell (1989) give a good overview of the application of part nesting in intelligent robotic packaging and
processing systems, as well as outlining robotic game playing systems and actual solutions to a number of industrial problems.
A system for the automated palletizing of randomly arriving parcels, has been developed by the authors. In the development of
such industrial systems, the authors have taken account of the some of the various systems issues involved in such a design. In
such a system, heuristics are necessary to deal with the interlocking and intermeshing of the boxes on the pallets as well as
dealing with the toxicity and crushability of the boxes contents. Other areas of related research include the work of Jain and
Donath (1989), in which they discuss the development and implementation of a knowledge based system for three-dimensional
automated assembly tasks, under robotic control.
Hoffman (1989) examines eliminating the requirement to hand tune specific assembly tasks in an automation environment.
Hitakawa (1988) outlines the development of a SONY flexible automatic assembly system suitable for small-quantity batch
production. Philip Chen (1991) tackles the problem of trying to find all the feasible assembly sequences for a set of n parts that
construct a mechanical object. Kak et al (1986) outline the development of a knowledge based robotic assembly cell. This cell
is used in the sensory guided part mating of three-dimensional objects. Ayache and Faugeras's (1986) paper discusses the
development of a robotic system under machine vision control. This system carries out the automated picking and placement of
partially overlapping industrial parts. The system is based on the generation and recursive evaluation of hypotheses for object
recognition.
When faced with a specific application requirement, it is always well worthwhile analysing the problem from a systems
engineering perspective. By adopting a systems approach, the maximum use is made of problem-specific "contextual"
information, derived, for example, from the nature of the product being handled, the process used to manufacture it and the
special features of the manufacturing environment. By doing so, the complexity of the application is hopefully reduced. For
example, it may be found that, by mechanically restricting the orientation and the order of arrival of objects considered by the
packing system, the problem can be simplified. In fact, by taking heed of such constraints, in a practical packing application,
the procedure might well reduce to a standard, well-tried technique. It is our belief that in packing, as happens so often
elsewhere, systems considerations are always worth investigating. Table 1 summarizes some of the practical considerations
found in the industrial implementation of automated packing systems, that if considered within a systems engineering
framework, can often reduce the complexity of a given application.
Although the application of robotics and vision to parts assembly has great potential (Harrington and Sackett 1987) and will
strongly influence the competitiveness of the European community, it is currently lacking in industry. This has been recognized
by the European community through its funding of major projects such as ESPRIT, BRITE and more specifically the
EUREKA projects that fall under the umbrella term FAMOS
3
. The FAMOS-EUREKA projects have targeted one of the
3
A German acronym for Flexible Automated Assembly Systems.
