Comprehensive Review of Robotized Freight Packing

Abstract

Background: This review addresses the emerging field of automated packing cells, which lies at the intersection of robotics and packing problems. Integrating these two fields is critical for optimizing logistics and e-commerce operations. The current literature focuses on packing problems or specific robotic applications without addressing their integration. Methods: To bridge this gap, we conducted a comprehensive review of 46 relevant studies, analyzing various dimensions, including the components of robotic packing cells, the types of packing problems, the solution approaches, and performance comparisons. Results: Our review reveals a significant trend towards addressing online packing problems, which reflects the dynamic nature of logistics operations where item information is often incomplete. We also identify several research gaps, such as the need for standardized terminologies, comprehensive methodologies, and the consideration of real-world constraints in robotic algorithms. Conclusions: This review uniquely integrates insights from robotics and packing problems, providing a structured framework for future research. It highlights the importance of considering practical robotic constraints. It proposes a research structure that enhances the reproducibility and comparability of results in real-world scenarios. By doing so, we aim to guide future research efforts and facilitate the development of more robust and practical automated packing systems.

1. Introduction

The fourth industrial revolution, characterized by the convergence of cutting-edge technologies, has ushered in a new era of logistics and packing processes. Logistics 4.0 has introduced innovative technologies such as automation, big data analytics, twin simulation, human-robot interaction, and autonomous vehicles. Within this context, 3D robotic packing has emerged as a cutting-edge solution, revolutionizing traditional packing methodologies and presenting novel opportunities for the industry [1].

In the dynamic world of e-commerce and logistics, efficient packing processes are crucial to optimizing shipping and storage operations. As the global e-commerce market continues to soar, with an increasing number of consumers opting for online shopping, the demand for efficient packing operations has never been more critical. E-commerce companies face immense pressure to deliver products to customers quickly and accurately, making 3D robotic packing an invaluable asset in this competitive landscape.

While human operators have traditionally handled packing processes, the rise of robotic technology has opened new horizons for automation in the packing domain. Robotic and human packing have several advantages and disadvantages that are mentioned below:

Working time: Robots can work uninterrupted for longer than humans, increasing productivity. While operators have fixed schedules, need resting time, and may get sick, robots can work 24 h a day, seven days a week, and have scheduled maintenance.

Costs: Operators have costs associated with their salaries and health insurance [2]; meanwhile, robots have costs related to their acquisition and maintenance. The cheaper option is case-dependent, and a financial analysis may be needed.

Space: Robots generally require more space to operate than human operators. Large space warehouses imply more (variable and fixed) costs.

Flexibility: Although robots’ flexibility has remarkably improved in the last years, human operators are still more flexible considering gripping and possible positions of the items within the container, mainly when irregular items are considered.

Integrality of goods: Robots are less likely to make mistakes than human operators, which can reduce the risk of damaged goods. Additionally, the programmability of robots enables the incorporation of regulatory constraints to ensure compliance with safety guidelines and standards. For example, robots can be programmed to avoid stacking poisons on top of food items [3].

The motivation for conducting this study stems from two key elements. First, automated packing cells emerge from the intersection of two fields: robotics and packing problems. No review specifically addresses the integration of packing and robotics in the literature. Existing reviews are focused either on packing problems [4,5] or on specific robotic applications, such as in the food industry [6,7,8] and leather handling [9]. Second, the dynamic nature of logistics and e-commerce necessitates exploring how robotic packing systems can adapt to the challenges within e-commerce operations. Therefore, this study aims to examine and organize the developments in robotic packing systems.

This study offers the following contributions. First, it is the first review to integrate robotics and packing problems by exploring robotic packing cells. Second, this study identifies research opportunities within this integration, providing guidance for future research in the field. Third, it proposes a research structure that will facilitate the comparison of proposed methodologies, enhancing reproducibility and the practical application of appealing methods in real-world scenarios.

Therefore, this manuscript aims to fill this research gap to indicate the advances, challenges, and prospects related to 3D packing with robots. Moreover, since this integration has boomed in recent years, publications related to this topic need a standard structure that allows researchers to compare their methodologies properly. For this reason, this manuscript proposes a structure for researching robotic packing.

This paper is organized as follows. Section 2 states the scope of this review and describes the methodological procedure used to compile the studies considered in this review. Section 3 provides a description of the components of robotic packing cells. Section 4 presents the classification and constraints of the packing problems. Section 5 describes the solution methods for solving the packing problems. Section 6 indicates how studies tend to compare the performance of the proposed approaches. Section 7 shows research gaps and possible directions for closing them. Finally, Section 8 presents the conclusions.

2. Scope and Methodology

Several research lines in automated activities related to handling 3D items with robots exist. The scope of this review exclusively focuses on the research line concerning the packing of 3D items within containers using robots. This scope includes different grades of human/robot interaction, i.e., collaborative robots (cobots) are considered. The research lines not covered in this review are picking (or order picking), rearrangement, and assembly.

The review methodology to establish the state of the art of 3D robotic packing was based on the ones proposed by [4,10]. First, the Scopus and Web of Science (WoS) databases were searched for the most relevant articles published in leading journals and refereed conference proceedings. Additionally, we expanded our search to include IEEE Xplore for engineering and technological advancements, Google Scholar for grey literature and articles not indexed in primary databases, and ProQuest for dissertations and theses. We combined specific and broad search terms, incorporating Boolean operators and truncation to refine our search results. The keywords covered various aspects of 3D robotic packing and related technologies. The primary keywords included: “3D robotic packing”, “robotic packaging”, “automated packing systems”, “industrial robotics”, and “Logistics 4.0”. These words were relevant to finding studies specifically focused on the packing process involving robotic systems in three dimensions, mentioned within the industrial sector. One of the example search queries in databases was (“3D robotic packing” OR “robotic packaging” OR “automated packing systems”) AND (“industrial robotics” OR “Logistics 4.0”). Relevant publications were those that did meet the scope and contributed significant information. This first inquiry identified the initial studies that approached 3D robotic packing. Then, a branching of manuscripts was performed using a breadth pruning approach with the cited references within the publications, i.e., the references of all considered publications were reviewed; if deemed relevant, they were included in the review, and their references are subsequently analyzed. This approach helps uncover additional relevant publications that might not have been found in the initial database search. This iterative procedure continued until no more suitable studies were found. Finally, a forward-looking search strategy was used to identify new research advances and incorporate these newly identified studies into the review, ensuring the literature review is up-to-date and comprehensive. This procedure was used to identify which publications cited the set of suitable publications. Figure 1 shows the stepwise elimination procedure, particularly those involving robotics and automation; several vital aspects are typically examined to ensure efficient and effective operation, such as Packing Algorithms, Robotic Systems and Components, Sensor Systems, Software Architecture, Packing Strategies, Physical Constraints, Environmental and Safety Constraints, Performance Metrics, Cost Considerations, and Application-Specific Requirements. These factors help ensure the 3D packing literature review is efficient, reliable, and suitable.

This methodology ensures the literature review is up-to-date and allows obtaining the main body of robotic 3D packing. After applying this methodology, 46 studies were left. Table 1 shows that most publications were research articles and that conference papers also play a significant role in knowledge dissemination, fostering discussion and collaboration among researchers. Figure 2 shows that robotic-packing-related publications have been booming in recent years, evidencing the influence of Logistic 4.0 on packing problems.

It is worth mentioning that the methodology used to collect relevant information only considered research publications. Therefore, the findings and insights of this review are biased toward these publications. This disclaimer is mentioned since most studies in 3D robotic packing are found in patents rather than research publications.

After collecting the main body of 3D robotic packing, the publications were analyzed regarding the physical layout, the packing problem, the solution methodologies for the packing problem, and the performance assessment shown in Figure 3. Therefore, the first step consisted of extracting the physical features of the layout of the packing cells. This overview involved elements such as the robot, conveyor, vision system, and end-effector gripper. Second, the studies were considered in the packing problem dimension to gain information about the problem types (according to state-of-the-art typologies) and constraints. Third, the studies were classified according to the solution methodology (mathematical models, heuristic algorithms, metaheuristics, machine learning models, hybrid algorithms, and preset patterns). Finally, the performance assessment was performed by classifying the manuscripts according to the instance types used (real test instances, classic data sets, and other test instances) and the comparison used (previous methodologies, diverse algorithm versions, and manual procedures).

3. Robotic Packing Cell

This section describes the general layout and the components identified in the reviewed studies. For this purpose, it is pertinent to define a robotic packing cell in general terms. In this manuscript, an automated packing cell consists of a configuration in which several items, equipment, areas, and at least one robot are grouped to perform a packing activity. The general structure of a cell consists of a picking area, objects to be packed, a robot, and a packing area. In the picking area, the objects to be packed lie (or arrive) before the packing procedure. This area may include a structure such as a table or a conveyor belt. The packing robot takes the objects from the picking area and positions them somewhere in the packing area. The packing area is usually a container, such as a box or a pallet.

Regarding the items to be packed, this study considers three-dimensional objects of any shape (regular and irregular). The most popular shape is the cuboid because it is the standard shape (even for containers) in logistics operations. Additionally, it is worth mentioning that homogeneous and heterogeneous scenarios are considered, i.e., cases in which there is only one type of item and cases in which there are several types of items.

Packing patterns can be built based on the available information about the to-be-packed items. The information is related to, among other features, their dimensions, shape, and order in the sequence of appearance (for example, when using a conveyor belt). It is considered an offline framework if all the information is known a priori to the packing activity. Otherwise, the framework is considered to be an online one. Packing methodologies use the items’ information to find packing patterns; therefore, the packing pattern’s utilization is expected to increase as more items’ information is available.

Notably, some robotic packing cells incorporate perception systems located at one or more positions within the cell. These systems are generally used to obtain information on the current state of the items (e.g., dimensions, position, and orientation) and the packing pattern (changes in the packing pattern throughout its construction).

The packing cell components identified in the reviewed studies are detailed below. Section 3.1 indicates the main features of the packing robots. Section 3.2 describes the identified process-specialized areas within the robotic packing cell. Section 3.3 presents the sensor or perception systems. Section 3.4 mentions the software architecture that integrates algorithms and components of the packing cells. Finally, in Section 3.5, some special situations are discussed.

3.1. Robots

Robots used in the packing process are diverse; however, they can be grouped according to several dimensions. This section aims to group the packing robots considering the available features from the reviewed studies.

The most common robot manufacturers found in the studies were KUKA [11,12,39,40,41,42], followed by Universal Robot [13,14,15,16,43] and IBM [17,18,55]. Most studies used mass-manufactured robots except for the one developed by [44]; they presented a robot prototype called UPSarm to pack boxes within truck containers.

Generally, packing robots have a fixed position within the working area; however, there were two studies in which the robot was on a mobile platform. Integrating a mobile platform allows the robot to increase its reach area, enabling it to perform more complex tasks. However, this integration could also mean increased task completion time due to the navigation (transportation) time. The studies that included a mobile platform were the ones developed by [40,45]. They used the mobile platform that allowed the robot to move from the picking to the packing area. Moreover, the robot could position itself differently within the picking/packing areas to facilitate the grasping/placement processes.

Most of the reviewed studies consider a single-arm robot; however, the studies developed by [19,20] have a different setup. The former contemplates a dual-arm industrial robot (Nextage) for a grocery packing environment. The latter uses two robots (UR3) to pack a bending item.

Packing robots are equipped with a device for grasping and placing cargo. All studies consider an end-effector device, which in this study is generically called a gripper. Robots have a maximum load capacity that limits the cargo’s weight the robots can handle. The reviewed studies generally used robots with a maximum load of less than 10 kg. For example, KUKA robots have a maximum load capacity ranging from 7 kg to 14 kg. Robots from Universal Robots have a maximum load capacity ranging from 3 kg (for the UR3) to 10 kg (for the UR10). The robots with the highest maximum load capacity in the reviewed studies are the STEP SR20E [30] and the ER20-robot [37], with a maximum load capacity of 20 kg. It is worth mentioning that within the robot’s maximum load capacity, the weight of the gripper must be considered. Four broad types of grippers were found in the reviewed studies (Table 2).

First, the suction or vacuum type grasps the items through vacuum generation (generally by an air compressor) and releases them by removing the vacuum. These grippers take the items from the top (although it is possible to grasp them from a side surface). The maximum weight the gripper can hold is limited by the vacuum generation and the strength of the suction cups (besides the cargo weight limit of the robots). The suction grippers could be preferred because they reduce collision chances with the packed items as long as the gripper’s size is smaller than the top surface of the item.

The second most used gripper type uses lateral paddles (or fingers). These grippers work as clamps to grasp and release the items from the sides. Therefore, the weight of the items is limited by the closing force of the paddles. It is worth mentioning that this force may damage items in situations where the items are fragile. A disadvantage of these grippers is that their use is more collision-prone or tends to leave unwanted gaps in the packing pattern.

The third gripper type found in the reviewed studies consists of upper and lower paddles. This gripper type is unusual since only two studies considered them. The first one was developed by [21], who used it to avoid the disadvantage of lateral paddle grippers. The lower finger could slide back to place boxes in the desired locations. The other study was developed by [44], who used a gripper with one upper palm and two lower paddles. The lower paddles could extend (to grasp the boxes) and retract (to release the boxes).

Finally, the fourth gripper type uses an electromagnet at the wrist of the robot. It was found in the study developed by [45]. This gripper requires the items to be magnetic or attached to a magnetically attracted material. The authors used the latter strategy by placing a ferromagnetic sheet on the upper surface of the items (boxes). It is worth mentioning that the authors used this strategy to simulate a suction gripper.

3.2. Process-Specialized Areas

A general layout consists of mainly two process-specialized areas related to picking and packing. These areas must be within the robot’s working space to manipulate the items. The picking area is where the small items lie before they are packed into the container. The placement area is where the container is located and where the packing pattern is built.

Picking areas of the reviewed studies can be classified according to two criteria: the item’s availability for picking and obstacles within the picking area. The former refers to whether all items are available for picking or not. The latter is associated with the presence or absence of obstacles, such as the container walls in which the items lie.

Table 3 indicates that most studies have focused on cases in which there are no obstacles and not all items can be reached by the robot; i.e., items arrive at the picking area one at a time or in groups. This choice likely stems from the prevalence of this particular real-world scenario. This scheme for the picking area includes staging areas [17,18], preparation tables [22,44], conveyors, and mockup conveyors (items are placed into a picking position) [23,51]. On the other hand, the least used format is the one with obstacles, and the robot can only reach some items [24].

Some studies have focused on the scenario in which all items are available for picking with and without obstacles. In the former case, researchers have used box-type containers [12,15,40,42]. Meanwhile, in the latter case, researchers have used tables, other pallets, and the floor in which all items lay close to the robot.

Packing areas are generally associated with containers where the packing pattern is built. Table 4 shows that the most common placement containers are pallets. These containers are flat, portable platforms without physical walls or roofs. Therefore, the stability of the packing pattern only depends on the stability provided by the stacked items. Moreover, the absence of walls makes them less collision-prone for the robot than all containers. The second most common placement containers are boxes, distinguished for having walls. The walls can provide stability (or contact points) to the packing pattern; however, they can cause some collisions with the robot in the packing process.

The less common placement containers are crucibles [25,46], wheeled carts [26,37], and truck containers [44]. These containers have walls like boxes but differ in shape (crucibles) and access for the robot. Truck containers are packed through one side while carts are packed through one side and from the top.

Besides picking and packing areas, some studies consider other process-specialized areas. Some reviewed studies contemplated the Buffer area associated with the buffer constraint (see Section 4.2.3). In this area, the items can be temporarily stored during the packing process [16,27,41,44].

Other studies contemplated areas used to measure the items [17,18] or prepare them [23,44]. In the former, the items’ features, such as dimensions and weight, are determined manually or with other devices. In the latter, the items are adjusted to a suitable picking orientation for the packing robot.

Finally, some studies included a temporal storage area where items could be placed if they would not fit in the packing area [2,28]. The placement of an item in this area generally marks the end of the packing process, and a new container has to be used.

3.3. Sensor Systems

Several reviewed studies incorporated sensor systems to identify the items’ position, size, and orientation. RGB-D (Red, Green, Blue + Depth) sensors were the most common systems. The two most popular RGB-D sensor manufacturers in the reviewed studies were Intel Real Sense and Asus. The following models of Intel Real Sense were found: SR300 [13,41,42], D435 [14,15,24], and D435i [16,43]. The only model of Asus found in the reviewed studies is the Xtion Pro Live [29,45].

Researchers have also used light beams (including lasers) to determine more precisely the items’ dimensions [17,18] and surface heights [21,25,46].

The sensor systems are located in several sections of the physical layout of the packing cell. Five sections were found in the reviewed studies: on the packing robot, in the general work environment, and in the picking, packing, and detailing areas. It is worth clarifying that sensors in the work environment can simultaneously obtain information about picking and packing areas and even the robot [14,29].

The number of sections in which sensor systems were located varied among studies; however, the maximum number of areas with sensors was three. Table 5 shows in which and how many layout sections the reviewed studies used sensor systems. This table shows that sensor systems are usually located in two sections and have been mainly located to monitor the items and the picking and packing areas.

Ref. [47] proposed a particular sensor system in the picking area to monitor the incoming items on a conveyor. The system had two sensors in the picking area, one for the last item on the conveyor and the other for some items behind it. This scheme can be used to obtain information on future items that will be packed. This information can improve the packing pattern’s utilization.

Some studies used sensor systems that focused on the item. These sensors were used to gain more accurate information on the items, like their dimensions [17,18] or their surface. In the last case, the sensor was generally located between the picking and packing areas. This information was used along with the information obtained with other sensors that focused on the packing [24,25,46] and picking [12,30] areas to improve the efficiency of the packing process or to guarantee vertical stability. For example, the items’ bottom and the packing pattern’s top surfaces can be scanned to identify the best positioning options. This strategy is advantageous when irregular items are considered.

Table 5 shows that several studies did not use or specify the focus of the perception systems. The main reason for not using a sensor system was that several studies did not need them because they focused on simulations. Computational simulations allow working with perfect information; therefore, all information related to the items’ position, dimension, and orientation (at least in the picking area) is known. This situation makes sensors unnecessary since sensors are essentially used to gather information.

3.4. Software Architecture

A software architecture is a high-level design and organization of a software system. The architecture is essential to the software development process because it shows all the components, their tasks, and how they are integrated. The software architecture improves the understanding of a system with several components, as happens in applications of 3D robotic packing. Unfortunately, several reviewed studies did not clearly explain all the architecture used in the study. However, this situation has been improving with the inclusion of diagrams [12,14,16] and more detailed descriptions [15,29].

3.5. Special Cases

Two studies contemplated the human-robot interaction (collaborative robot or cobot) in the packing process. Ref. [29] used a cobot for packing irregular items within a box, and ref. [45] used a cobot for box palletizing. The concept of collaborative robots started to gain traction in recent years, considerably later than noncollaborative robots. This situation explains the low number of studies that consider cobots.

Robots and cobots have several advantages and disadvantages in packing applications. Robots generally have a larger payload capacity than cobots due to the safety constraints integrated into cobots. These constraints may also limit, in some cases, the working speeds. Additionally, the packing process is generally repetitive and predictable (a robot-favored scenario), at least in the homogeneous case, i.e., when the items are identical. However, some packing tasks can have higher complexity, making cobots a better option due to their flexibility. For example, when irregular items are handled, the packing pattern’s stability is highly complex, and human input can facilitate this process.

Another special case that is worth mentioning is the use of simulations. Some studies used simulations, others used physical experiments, and others used both. Physical and simulated environments have features that can make them a better option for an application depending on the study’s objective. Physical environments are more accurate since they are subjected to natural forces that may impact the result of a process. On the other hand, simulations depend on models representing those forces, and some use simplifications that may distort the results. These models can take high computation times if not simplified enough, making the simulation slower than reality. However, simulations can use elementary models that allow many iterations to be carried out in a fraction of a physical experiment’s time.

It is worth mentioning that simulations and physical environments are not mutually exclusive; a packing application may benefit from both schemes. Both schemes can be used to validate and optimize the robotic packing system. For example, an application may use a simulation environment to plan and design the automated packing system, validate, optimize algorithms (including the robot kinematics), and analyze the impact of changes within the packing cell. On the other hand, the physical environment can be used to verify the actual system’s functionality and identify elements to improve.

Simulators found in the reviewed studies are URSARSim [39], MATLAB-Robotics Toolbox [48], Klamp’t [49], V-Rep [40], Blender [42], pyBullet [14,31,53], Unity [36], and Bullet [32]. Besides these simulators, some studies have developed simulation setups [22,50].

4. Packing

This section explains the most relevant aspects of the packing considered in the reviewed studies. The reviewed studies are organized according to cutting and packing classifications (Section 4.1) and their constraints (Section 4.2).

4.1. Typologies

Packing problems form part of the broader area called Cutting and Packing (C&P). These problems are considered to have fundamental similarities in their structure: there is a set of small items that are assigned to a set of large objects (containers) and satisfy the containment and non-overlapping constraints [4,56,57]. The former constraint states that the small items must entirely lie within the large objects. The latter constraint indicates that the small items must not overlap.

Ref. [56] proposed a typology whose purpose was to unify several versions of C&P problems that appeared in the literature with different names but with the same structure. This typology has four criteria (dimensionality, kind of assignment, assortment of large objects, and assortment of small items). It classifies C&P problems with four entrances, one for each criterion. For example, 1/V/I/R is a one-dimensional problem in which the whole set of small items must be assigned to a subset of identical large objects. The small items consist of a few item types, each with many items.

Ref. [57] proposed an improved typology based on the one presented by [56]. The newer typology has five criteria (dimensionality, kind of assignment, assortment of small items, assortment of large objects, and shape of small items). It has been broadly accepted by the scientific community, possibly due to the use of names commonly used in the jargon of the C&P community. Considering only the kind of assignment and the assortment of small items criteria, the authors classified the pure C&P problems into broad groups called Basic Problem Types. Moreover, if, besides the previous criteria, the assortment of large objects criterion is considered, then the C&P problems are classified into more specific groups called Intermediate Problem Types. Finally, if all criteria are considered, the C&P problems are classified into Refined Problem Types.

This typology contemplates that some problems do not fit the two, four, or five criteria groups and constitute exceptional cases or variations. The studies considered in this review are classified according to the typology proposed by [57] to determine the trends and gaps related to the addressed packing problems.

4.1.1. Basic Problem Types

The Basic Problem Types are obtained by identifying the type of assignment and the assortment of small items criteria. The first criterion distinguishes between output maximization and input minimization. The former implies that the quantity of large objects (containers) is insufficient to accommodate all small items; therefore, the objective is to maximize the utilization of the containers. On the other hand, the latter means there are enough large objects to accommodate all small items; the objective is to minimize the number of containers used. The second criterion indicates whether the small items are identical, can be grouped into a few types with each type having a significant demand, or are grouped into several types with each type having a low demand.

The classification into the Basic Problem Types is shown in Figure 4. It is worth noting that several reviewed studies did not clearly state the packing problem they were tackling. Therefore, the classification was performed according to the information in the methodology description, the application context, and the performed tests.

Two studies were classified as Bin Packing Problems and shared a particular feature regarding the container. In the studies developed by [25,46], the container was a crucible allowed to be filled more than its top as long as the small items (polycrystalline silicon nuggets) were stable. This situation could be interpreted as an Open Dimension Problem; however, the authors of this review consider it insufficient to catalog them as such. Therefore, these studies are deemed to have containers of fixed dimensions. Two studies were not classified within the Basic Problem Types shown in Figure 4. These studies were developed by [20,50], who focused on packing a single item. These studies are of input minimization since all items are packed. However, the assortment of small items is unclear to this manuscript’s authors. Therefore, these studies are considered special cases or variations of packing problems.

In real applications in logistic centers and warehouses, the robotic packing cells tend to focus on packing all items, i.e., input-minimization. However, Figure 4 shows that several studies are framed under the output-maximization scheme. This situation occurs because some studies limit their experiments to the packing of a single container, and the packing process ends when no more items can be placed within the container. Therefore, these problems are classified as output-maximization problems.

4.1.2. Intermediate Problem Types and the Other Criteria

Following the typology proposed by [57], the reviewed studies are further cataloged into the Intermediate Problem Types by considering the assortment of large objects criterion. Table 6 shows the Intermediate Problem Types found in the reviewed studies according to the type of assignment criterion. This table indicates that the 3D packing problems associated with robotic packing tend to address single (IIPP, SLOPP, and SKP) or identical large objects (SSSCSP and SBSBPP). The study developed by [23] was the only study that addressed a weakly heterogeneous assortment of large objects. They solved MBSBPP instances for a logistics company implementing a GRASP algorithm.

The scope of this review established the dimensionality (first criterion of the improved typology) to 3D. Therefore, the remaining criterion (shape of small items) is addressed next. This criterion distinguishes between regular and irregular items (see Table 7). The former includes, among others, cylinders, balls, and boxes; meanwhile, the latter indicates arbitrary shapes. Within the studies that addressed regular-shaped items, boxes are by far the most common, possibly due to their vast applications in the logistics industry. In fact, only the study developed by [50] considered cylinders besides boxes. They proposed a placement-position search technique to pack the objects near the corner of the container.

4.1.3. Online and Offline Packing Problems

Finally, packing problems can be classified based on the availability of item information, distinguishing between offline and online problems [4]. In offline problems, all item information is available beforehand, while in online problems, the information is incomplete. Table 8 shows that more studies have considered the online version of packing problems than the offline version. This trend indicates that research on automated packing cells focuses more on scenarios where there may be uncertainty in the dimensions of the items to be packed. Such scenarios are frequently encountered in logistics and transportation centers driven by e-commerce, where different items must be packed, grouped, and shipped to various destinations.

It is worth mentioning that the study developed by [27] introduced two problem variations called Nondeterministically Ordered Packing (NDOP) and Quasi-Online Packing (QOP). The former assures that a packing plan exists for every possible order of arrival of a given set of items. The latter consists of packing the items one at a time as they arrive, i.e., it is embedded in an online packing framework.

4.2. Constraints

Ref. [58] comprehensively reviewed constraints applied in the container loading process and classified them into five categories (container-related constraints, item-related constraints, cargo-related constraints, positioning constraints, and load-related constraints). These constraints have been accepted and generalized to other packing applications. However, ref. [59] proposed a more practical classification with two groups. The first one is the safety constraints related to the integrity of the cargo and the safety of the operators. The second one is the logistic constraints associated with operational decisions that do not depend on the physical features of the items and containers. The constraints found in the reviewed studies are detailed according to this last classification.

4.2.1. Safety Constraints

Regarding the safety constraints, none of the studies considered the weight limit constraint. The study developed by [17] was the only study that assessed the weight distribution constraint by conditioning that heavy items must be placed at the bottom of the container and light items on top of the heavy ones. This constraint is suitable to the study’s context: grocery packing.

The orientation constraint is more relevant for boxes than for other shapes because arbitrary shapes can be symmetric [29,50] or can have multiple orientations [14,15]. For this reason, this constraint is discussed considering the studies that only handled boxes. The most common approach was only to allow two orientations obtained by a 90° rotation around the vertical axis, consistent with how the robot picks the boxes up. These two orientations are limited because grasping or placing boxes from a different surface than the top can cause difficulties associated with the grippers and the robot kinematic. For example, in some cases, the robot may push the items instead of grasping them from one of the item’s sides, or the robot could collide with the structure in which the items lie.

Other approaches for the orientation constraint are discussed below. The study developed by [48] was the only one that used a single orientation for the pieces. They palletized boxes grabbed from a conveyor belt with a simple packing approach that exploits the circumstance of identical boxes and a single orientation of the boxes. An interesting strategy regarding orientation management consisted of allowing the packing algorithm to consider several (or all six) possible orientations of the boxes; however, the boxes were manually pre-oriented in a previous area before the robot took them [23,26]. An unusual strategy was presented by [33], who limited the number of orientations by the degrees of freedom of the robotic arm and imposed that the box’s largest dimension cannot be aligned with the arm’s vertical axis. Thus, the two box’s orientations are not considered.

The stacking constraint refers to avoiding damaging the packed boxes and protecting the goods within the boxes. The studies developed by [2,54] were the only studies that considered toxicity and fragility constraints. The former is associated with how suitable a box is near others, considering its contents’ toxicity. The latter refers to the load-bearing strength (pressure or weight that a box supports on top) and whether the contents will be damaged in the event of a fall from the top.

The physical positioning constraint is an unusual constraint found in three studies. Ref. [50] proposed a placement-position search technique to place an item in the corner of the container. Refs. [25,46] tackled the robotic packing of polycrystalline silicon nuggets into crucibles, which adopted a packing construction based on the dimensions of the nuggets. First, the bed layer consisted of small gravel-sized nuggets. Then, an alternate filling process was followed until the crucible was full. This process involved placing large nuggets near the crucible’s wall and smaller nuggets in the inner part of the crucible.

The last safety constraint is associated with the stability of the small items in the packing pattern. This constraint distinguishes vertical (or static) and horizontal (or dynamic) stability [59]. The former addresses the stability of the items when the container is not moving, i.e., the stability of the packing pattern (when in construction and finished) subdued to the gravity force. The latter addresses the stability of the items when the container is moving, i.e., the stability in the transportation in which the items are subdued to accelerations in different directions.

None of the reviewed studies addressed the horizontal stability constraint; however, there are different approaches concerning the vertical stability constraint. Some studies did not consider the vertical stability constraint because it was not needed in the study’s application. For example, ref. [54] pointed out that the pallet (container) can be secured with strapping and wrapping machines in industrial applications. Moreover, refs. [20,50] packed a single item; therefore, the stability constraint was unnecessary. However, it is worth mentioning that in the study developed by [20], the object did not easily fit within the container, but it was flexible. Therefore, they used another robot to guarantee the position and stability of the item in the packing process. Another situation where the stability constraint is not required consists of packing only one layer of items, i.e., without stacking items above others [29,40].

The vertical stability can indirectly be considered by using layer construction. This strategy can be used when the boxes (small items) are identical [22] or when they share the same height [28]. Furthermore, besides the stability of the boxes (individually), some studies use layer construction to improve the stability of the whole packing by alternating packing layers. The alternating layers are obtained by different packing layers [52] or by packing a rotated packing layer [21,34].

Considering the studies that handled boxes, unfortunately, some of them did not clearly state the strategy used to incorporate the vertical stability constraint; however, the following strategies were spotted: first, the full-support constraint, i.e., all the area of the base of a box is supported by the other boxes or the container’s floor [23]. Another strategy to incorporate vertical stability when the items are boxes is a more technical approach (since it is based on physics). It seeks to guarantee that the center of mass of each box lies within the convex hull of support points [30,47]. Finally, the last found strategy was using heightmaps, a two-dimensional representation of the height of a three-dimensional surface [16,43].

Vertical stability is challenging to incorporate into the solution methodologies when handling irregular items due to the estimation of stable poses of these items in the landscape that forms other items. The complexity of these conditions has made researchers resort to various approaches to consider the vertical stability constraint with irregular items. Ref. [49] used force and torque balances that required a convex programming solver to validate whether an arrangement is stable. Ref. [31] developed an algorithm that creates a belief space representation of the world and updates it according to the observations taken. This procedure allows the algorithm to estimate the changes in the packing pattern.

The most usual strategy to consider vertical stability when handling irregular items is constantly monitoring the packing pattern. This monitoring can be performed by raster methods [19], line representation of heights [25,46], or heightmaps [14,15]. It is worth noting that the monitoring requires sensors or cameras that perceive depth.

4.2.2. Logistic Constraints

Regarding the logistic constraints, the reviewed studies only considered complexity constraints, i.e., constraints that reflect technological and human limitations. These constraints in the scope of this review are associated with robot-packable patterns that include guillotine packing patterns and collision avoidance. Several studies did not consider the collision avoidance constraint or did not clearly state the strategy to achieve it [24,26,32]. Other studies indirectly considered it by limiting the rotation of the boxes to the vertical axis [12], grasping several items with the gripper at once (instead of one) [34], performing guillotine packing patterns [18], using different types of grippers [19], or using a large robot and trajectory path with top-down loading motions that was hardly going to cause a collision [23,25,46].

Researchers who have tackled robotic 3D packing have used several strategies to handle the collision avoidance constraint. When the items are boxes, the most common strategy is oversizing them to overcome the uncertainty associated with the exact size and position of the item, the vision system, and the picking point [16,17,18,35]. This strategy tends to leave gaps between the packed items. Another strategy consists of packing in a far-to-near fashion from the robot. Zhao et al. in [30,47] achieved this packing method by implementing a reward function for collision-free trajectories. Another strategy is to modify the trajectory path by creating artificial (dummy) points the robot has to reach [22,28].

When irregular items are handled, the most common strategy for avoiding collisions is using heightmaps in which possible placement areas are validated for collision considering the nearby landscape [14,15,49].

A strategy for collision avoidance suitable for regular and irregular items consists of sampling the trajectory to obtain several steps. Then, each step was subdued to a collision check in which possible collisions between the robot (including the carrying item) and environment obstacles (packed items and container) were detected. This approach was used by [11,27,44].

The scope of this review also addresses approaches that contemplate human-robot interaction. In these cases, collision detection is crucial in protecting the integrity of the people near the working robot. Therefore, this constraint is managed with robust perception systems that constantly monitor the robot’s movements and the environment [29,45].

It is worth mentioning that some studies allowed (or even wanted) collisions instead of avoiding them to successfully achieve a desired packing pattern. Ref. [20] used the collisions between the flexible item to be packed and the container to perform the bending of the item. Shome et al. in [41,42] allowed collisions when the items were pushed to the desired position.

4.2.3. Automatic Environment Constraints

Besides the safety and logistic constraints, some additional constraints appear in robotic packing cells. The most resounding constraints are buffering, deletion, and repacking. The first one allows items to be temporarily stored in a holding area before being packed into the container. This technique enables the packing decision to be taken later. Therefore, the packing utilization and flexibility of the packing process may improve at the expense of increasing the task’s time and the problem’s complexity. The utilization may increase because there are more positioning options, and a better option may be chosen. On the other hand, the time may increase because more robot movements are required to move items from the picking area to the buffer area and from the buffer area to the packing area.

The second constraint consists of not packing some incoming items or removing some packed items from the packing pattern. Generally, the removed items are packed in a subsequent container. Finally, the last constraint allows the packed items (typically the last ones) to be rearranged.

None of the studies considered the deletion constraint. The buffer constraint was considered only by four studies. Refs. [16,27,43] adopted a k-buffering, i.e., a variable size buffer. Although these methodologies allow a considerable value for k, it is worth mentioning that it is limited by the robot’s reach and the space and location of the buffer in real applications. Ref. [43] realized a sensibility analysis of the buffer size (maximum number of items in the holding area). They showed how the container’s utilization increases as the buffer’s size increases. The other study that contemplated this constraint was the one developed by [44], who used a buffer of 12 boxes in a container loading framework.

The repacking constraint was only considered by [16]. They used a staging area as the buffer and a temporary storage area for repacking procedures. When their methodology detected an arrangement that improved the packing density, the items that needed repositioning were unpacked from the pallet to the staging area and repacked into a better position.

5. Solution Methodologies

Finding optimal solutions to the 3D packing problem with robots is challenging due to the complexity and combinatorial nature of the task. This complexity is increased in an online framework due to incomplete information about the items. Furthermore, since 3D robotic packing is related to real-time application, all systems must provide fast results. Therefore, researchers have focused more on efficient solutions, i.e., high-quality solutions obtained in a reasonable time. This situation is evidenced in that the preferred methodologies are heuristics and algorithms based on machine learning (see Table 9).

Heuristics are the most preferred methodology to solve the packing problem within robotic packing cells. These methodologies are characterized by being fast (low execution time) and their simple structure. In the case of robotic packing cells, heuristics are closely related to how the packing task develops. The packing task consists of iteratively adding items into a container while ensuring some practical constraints until the container is complete or until there are no more items to pack. This structure also describes the procedure that constructive heuristics follow.

The most relevant aspects in which heuristics differ are the selection of the item to pack (including their orientation) and the position in which the items will be packed. These decisions can vary in the order they are taken. In the offline framework, some researchers prefer first to choose a position and then choose the item to pack [39], or vice versa. However, in an online framework, item selection usually is not necessary, and the heuristic focuses on choosing the best position for the standby item (into the cargo space or buffer).

The item and position selections are based on different prioritization criteria and representations. The most known prioritization criterion is associated with the Deepest Bottom Left (DBL) strategy, in which items are placed starting at the deepest bottom left corner, and the packing pattern is built towards the opposite corner [19]. However, there are more complex prioritization criteria, such as choosing the positions closer to the container’s corners [23].

Regarding space representation, researchers have used techniques such as maximal spaces [23], residual spaces [39], and height maps [16]. The first two relate to cuboid sub-containers, which are created or modified as more items are placed within the container. The last one uses a 2D grid, where each cell represents the height of the packed items.

Heuristics are scenario dependent; i.e., the satisfactory performance on a scenario does not necessarily transfer to other scenarios. For this reason, researchers have been focusing on developing more flexible (intelligent) algorithms that can adapt to a much more comprehensive range of scenarios. Therefore, machine-learning approaches have gained popularity among researchers. These approaches return fast solutions; however, they take considerable time in their training [30]. Moreover, these methods require a deep understanding of the problem to extract useful information that the algorithms can use.

Machine Learning approaches can be used for boxes and irregular-shaped items. In the former case, for example, ref. [12] formulated the packing problem as a Markov Decision Process (MDP) and used the actor-critic architecture. The goal was to maximize the space utilization ratio of the container, achieving a trade-off between exploration and exploitation. This actor-critic architecture contains a neuronal network that predicts the probability of each action and a value function that evaluates the state. In the latter case, ref. [31] developed the Sample Algorithm (SA) to solve problems with partially observed states and deterministic action effects. The objective is to minimize the entropy of the packed grocery items. Moreover, ref. [30] proposed a machine-learning algorithm for packing arbitrarily shaped items with partial observations.

Other less-used methods are discussed next. Mathematical programming techniques aim to find optimal solutions (minimizing the waste or maximizing the utilization) by deciding the items’ positions within the container considering practical constraints. Generally, solving a problem through mathematical programming is computationally demanding, and, depending on the problem size, it can take considerable time.

Ref. [54] proposed a mixed integer programming model for solving the 3D palletizing problem with diverse cardboard box sizes, considering the pallet’s capacity and box dimension, orientation, and sequence. The objective function is related to minimizing the operation time. Ref. [26] formulated a 3D stacking problem including practical-robotic constraint and vertical stability of the packages in an online framework. This formulation was solved using dynamic programming in an MPC (Model Predictive Control) framework with adaptative windows.

Predetermined patterns are found when the packed items are boxes and computed before the packing process begins. These patterns consist of several layers that usually repeat until the container is full. These patterns appear when there is a single box type in the whole container [41] or at least in each layer [52].

Metaheuristics leverage their ability to explore complex search spaces and find high-quality solutions. Several metaheuristic approaches solve offline packing problems. However, these algorithms are often not adaptable to online packing problems due to incomplete item information. Only two studies consider a metaheuristic approach. Ref. [23] used a Greedy Randomized Adaptative Search Procedure (GRASP) algorithm to solve the MBSBPP in an offline framework. This algorithm did not consider additional constraints related to the robot; however, in [60] they analyzed the feasibility of the packing patterns due to the inverse kinematic of the manipulator. Ref. [24] employed a Differential Evolution (DE) algorithm known for its effectiveness in other optimization problems. The algorithm is based on iteratively moving objects around in the container until a local optimum is reached. The algorithm uses a differential update rule to move objects; i.e., each object’s movement is based on the others in the container.

Finally, an interesting approach is using mathematical models and metaheuristics, i.e., matheuristic. Ref. [33] proposed a matheuristic consisting of two rolling-horizon mixed integer linear programming (MILP) and heuristics (First Fit and Best Fit) to obtain an optimal or near-optimal solution.

6. Instances and Performance Comparisons

The methodologies proposed in the reviewed studies to solve robotic 3D packing need to be evaluated to identify in which scenarios they perform better. Moreover, methodologies should be compared to determine their strengths and limitations in a given scenario. The evaluations and comparisons enable the validity and credibility of research findings. Furthermore, these procedures enhance research transparency and encourage knowledge sharing and peer validation, improving the state-of-the-art solutions for 3D packing problems.

Methodologies are tested on a set of instances whose origin may vary. Table 10 shows that in 3D robotic packing, the most common instance type, comes from real-life applications, followed by randomly generated instances and instances obtained from other studies (data sets). This situation indicates that several studies are application-dependent. Furthermore, some real-life applications are not detailed enough to be used by other studies (probably due to confidentiality agreements), which limits the comparisons between methodologies.

The most appropriate way to compare the performance of methodologies is by comparing their results over the same instances. Some instances of the online framework of the packing problem that have been proposed are CUT-1, CUT-2, and RS [32]. In CUT-1 and CUT-2, items are generated by sequentially “cutting” the bin into pre-defined item types; therefore, the items can be arranged into a perfect packing pattern. Meanwhile, in the RS, the sequence of items is randomly generated. These instances are relatively new but widely used [16,43,47].

Ref. [61] proposed some that have been used by other researchers in the robotic 3D packing community [11,33]. These instances consist of various-size cuboid items divided into nine classes. The first five classes consist of a single bin size and five item types. The items’ dimensions are randomly generated according to uniform distributions. The sixth, seventh, and eighth classes have different bin sizes, and the item’s dimensions are obtained with uniform distributions. The last class is generated by cutting the bin into smaller parts.

Irregular-shape instances can be found in some challenges, such as the one organized by Amazon (Amazon Picking Challenge). These challenges aim to foster innovation and advancements in robotic systems capable of picking and packing items from shelves or bins. Participants are asked to develop autonomous robots that can navigate warehouse environments, identify and grasp specific items, and place them accurately into containers or onto conveyors [27,62].

Since the most common instance type was not classic data sets (widely used instances by other researchers), it is worth analyzing how the reviewed studies compared their methodologies. Table 11 shows that most studies do not compare their methodologies or compare them with other versions of the methodologies by changing some procedures or parameters. This situation is concerning since, in this way, it is hard to identify the strengths or limitations of methodologies. This concern is deepened because few studies compare their methodologies with previous works.

The robotic 3D packing pretends to replace or complement the packing operation performed by humans. Therefore, some studies compared their methodologies to manual operation in terms of efficiency [32,45].

7. Final Remarks

The number of publications on robotic 3D packing is limited but has increased in recent years (Figure 2). This situation indicates that this field is booming, and more publications are expected in the coming years. The following notes may guide upcoming studies focusing on unexplored areas.

7.1. Limitations

As stated in Section 2, this study considers publications but does not include patents. Given these developments’ novelty and real-world applications, the number of patents related to robotic packing cell systems is substantial. Additionally, this review is biased toward the problems addressed in the publications, which may only partially reflect the impact across some industries where robotic packing cells can be used. Many studies focus on issues encountered in e-commerce, where the heterogeneity of objects to be packed is high. However, some manufacturing industries have low heterogeneity; homogeneous cases (where objects are identical) can occur. While homogeneous packing problems are less challenging from a packing perspective than heterogeneous ones, they still represent significant practical applications in specific industries. This review may only partially capture these homogeneous scenarios, emphasizing the need for further research to encompass a broader range of industrial applications.

7.2. Managerial Implications

Integrating robotic systems can significantly enhance efficiency and accuracy in logistics operations, which is crucial for meeting e-commerce demands. Managers should invest in flexible robots that adapt to dynamic environments with incomplete item information, improving responsiveness. While robotic systems have higher initial costs, they can reduce long-term operational expenses by minimizing labor costs and increasing productivity. Careful cost-benefit analyses are necessary to justify these investments. These analyses should contemplate scaling operations to meet varying demand levels. Additionally, robots require more space than human workers, necessitating optimized warehouse layouts.

Strategic planning is critical when considering the implementation of robotic systems. The type of packing problem to be solved, the nature of the merchandise and containers, and the system layout must be carefully considered. Identifying the most suitable robots for the task and designing a layout that includes a perception system, picking zone, packing zone, merchandise, and robot are crucial steps. These elements must be well-organized to optimize the layout distribution. By addressing these factors, organizations can significantly enhance their operational performance and gain a competitive edge in the logistics and e-commerce sectors.

7.3. Research Opportunities

More research is needed on the layout of packing cells and the development of equipment selection guides. Current studies often do not specify the reasons for choosing specific robots, particularly in simulations where various robots could be selected. Additionally, the structures that allow robots greater reachability, such as mobile platforms or reel systems, need further exploration. This research would help set up packing cells properly, optimizing robot performance and efficiency.

Further investigation is required into the maximum velocities and accelerations that suction-type grippers can handle while ensuring object retention. While suction-type grippers are preferred for their simplicity and suitability for common warehouse materials, more information on their performance limits is needed [52]. This research would help design more reliable and efficient grippers for various packing applications.

Research is necessary to develop a clear strategy for determining the number and positions of cameras and sensors in packing cells. Some studies use multiple sensors for the same area. However, the impact of varying the number of cameras still needs to be discovered [13,15]. Accurate perception systems are crucial for assessing objects’ shape, position, and orientation. This research would improve the reliability and replicability of robotic packing systems.

More attention should be paid to the software architecture of robotic packing cells, integrating all modules, such as packing optimization, perception systems, and robot kinematics. A well-designed software architecture, including a Fault Recovery Module, is essential for detecting, responding to, and overcoming operational failures. This research would facilitate the development and operational efficiency of robotic packing cells.

Further research is needed to find the best human-robot configurations for packing activities. Despite increasing implementation in various industries, only some studies have considered cobots in robotic packing. Exploring schemes where human operators assist in picking or packing tasks would enhance the effectiveness of cobots in avoiding collisions and ensuring proper handling. This research would optimize human-robot collaboration in packing processes.

Research should address the bias toward handling regular shapes in packing problems, as fewer publications focus on irregular shapes [56,57]. While recent studies have started to close this gap, more attention is needed on multiple container systems, particularly heterogeneous ones. Sensor systems must recognize container dimensions, positions, and orientations accurately. This research would enhance the versatility and application of robotic packing cells in various industries.

More studies should address automatic environment constraints such as buffering, repacking, and deletion in robotic packing. Future research should focus on k-bounded packing spaces, where algorithms decide which container to use based on physical limitations. This research would improve the efficiency and adaptability of robotic packing cells in dynamic environments.

Comparative research on algorithm performance is necessary, using classic database instances found in ESICUP and OR-Library for offline frameworks. There are no classic databases for online frameworks, likely due to recent interest in this area. Establishing a repository for these instances would facilitate performance comparison and improve the robustness of packing algorithms. This research would standardize algorithm evaluation and enhance the development of effective packing solutions.

7.4. Structure for Future Research

For effective communication in future studies on robotic packing, the packing problem must be clearly stated, including the objective function and constraints, and classified according to the most recent typologies. The equipment and layout used in the study must be clearly described. The architecture of the robotic packing software should be included and explained, detailing all algorithms used in the system (packing, perception systems, robot operation). Videographic evidence is suggested to facilitate understanding, showing one or several operation cycles of the system [16,23,31,47].

8. Conclusions

The growing research interest in robotic 3D packing is evidenced by the increasing number of publications, indicating that this area is booming and likely to see continued expansion. The reviewed studies highlight a significant focus on online packing problems, emphasizing the need to address scenarios where item information is incomplete, a common challenge in dynamic logistics and e-commerce environments.

This review uniquely integrates insights from robotics and packing problems, providing a structured framework bridging the gap between these traditionally separate fields. Integrating robotic systems into logistics operations can significantly enhance efficiency and accuracy, which is crucial for meeting the demands of e-commerce. Managers should consider investing in flexible robots capable of adapting to dynamic environments and incomplete item information, supported by careful cost-benefit analyses and strategic planning.

While this review has identified several research gaps, it is important to note their practical implications. The need for standardized terminologies, comprehensive methodologies, and the consideration of real-world constraints in robotic algorithms are not just academic concerns but are crucial for the effective implementation of robotic 3D packing systems. Future research should focus on developing equipment selection guides, exploring the maximum capabilities of suction-type grippers, and establishing clear strategies for sensor placement and software architecture. The review also highlights the potential for improved human-robot collaboration through more extensive research and implementation of cobots. There is a need to explore the best human-robot configurations for packing activities to enhance efficiency and safety.

Furthermore, the reviewed studies reveal a bias toward handling regular shapes, such as boxes and single-container systems. Future research should address the challenges of packing irregular shapes and multi-container systems, particularly in heterogeneous environments. The practical applications and industrial relevance of the findings and methodologies discussed in this review underscore the importance of continued research and development in robotic 3D packing. By providing a structured approach to integrating robotics with packing problems, this review aims to facilitate the development of more robust and practical automated packing systems for various industrial applications.