Autonomous Mobile Robots for Enhancing Warehouse Logistics

Roadmap Overview

Warehouses are dynamic environments that have evolved into automated facilities designed to process, store, and ship products to customers around the world. These facilities play a key role in the logistics and supply chain networks for large-scale businesses. To meet the growing demands for speed and accuracy of today’s shipping expectations, significant advancements have been made to improve security, inventory management, storage optimization, climate control, and people management in warehouses. Figure 1 provides an overview of the basic processes that occur within a warehouse and points out some of the areas robotics are used to streamline product movement through the warehouse and enhance operational efficiency. 

Figure 1: Warehouse product movement workflow [1].

A lot of technology has been developed over the last several decades to optimize logistics and advance the operations within a warehouse. One of the largest challenges warehouses face is how to lift and transport heavy materials. Before the 1950s, this was primarily done through the use of carts on fixed rail systems or vehicles operated by humans. While these solutions helped to solve the transport problem, they introduced new issues around maintenance and fixed infrastructure as well as safety and training for employees and operators. In the 1950s, automated guided vehicles (AGVs) were introduced to warehouses. These vehicles were able to transport materials without the need for an operator, but still required the installation of a mechanism to guide the vehicles along a specified path. Initially, the guide was a set of wires that induced a magnetic field that would propel a cart along its path. This quickly evolved to utilize magnetic tape, optical strips, and eventually laser guidance. These systems are still in use today and provide a reliable mechanism to transport goods around a warehouse; however, they don't have the adaptability and intelligence needed for modern warehouse operations [4].

While AGVs were evolving, so was the field of robotics, specifically autonomous mobile robots (AMRs). AMRs are a class of robots that have the ability to sense their surroundings and intelligently navigate a dynamic environment to accomplish a task [6]. The first set of AMRs were developed by William Grey Walter in the 1940s and 1950s. He developed two robots named Elmer and Elsie for use in neurophysiology research. These robots were equipped with light and touch sensors, and eventually included the ability to sense sound and move around. Between the 1950s and 1990s, AMRs continued to evolve, but were primarily used in research and academia. The HelpMate was the first AMR that was commercially available. This robot was released in the 1990s and featured Sonar, infrared, and vision systems. The HelpMate was used to transport materials around medical facilities [3]. Now, companies like Amazon Robotics (formerly Kiva Systems) and inVia are developing advanced robotics to facilitate dynamic operations within a warehouse while reducing safety incidents and increasing productivity.

Figure 2: AMRs transporting shelves in a warehouse [2].

In this roadmap, we will attempt to address and characterize a technology aimed at reducing warehouse complexity in three key areas – storage optimization, product movement, and people management.

There are several different types of robots that are currently in use or being developed for warehouses today. Each type of robot has a specific function or a few specific functions within a warehouse. Table 1 provides an overview of the primary robots in use today.

Table 1: Warehouse Robotics

Type	Use Case	High Level Technologies
Robotic Arms	Loading or picking up boxes	* End-of-arm tools * Vacuum grippers * Joint actuators * Computer vision * Cameras * Sensors * Controller * Power systems
Packaging Robots	Packing and sealing boxes	* Boxing robotics * Labeling mechanics
Verification Robots	Scanning products and/or packages	* 3D scanners * Barcode/QR scanners
Autonomous Mobile Robots	* Lift and transport goods to humans * Optimize storage patterns	* LiDAR * Sensors * Digital Twins * Machine Learning * Optimization algorithms * Communications systems * Motor * Battery systems

Autonomous mobile robots and their use within warehouse systems will be the primary focus for our roadmap. These devices combine several advanced technologies to transport goods without the assistance of humans or guides. They help to reduce safety incidents, increase picking rates, and increase fulfillment rates within warehouses. Throughout the rest of this roadmap, we will do a comprehensive review of AMRs and their enabling technologies.

Design Structure Matrix (DSM) Allocation

We present here the DSM allocation of autonomous mobile robots and its tree. The company-wide initiative of warehouse automation is supported by the order management system, the inventory management system, and warehouse robots. Warehouse robots can be classified into autonomous mobile robots, robotic arms, packaging robots, and verification robots. We focus on the autonomous mobile robot for this roadmap, which is enabled by level 4 technologies in light blue, such as 3D mapping, digital twins, and route optimation algorithms. The DSM shows coupling between technologies; for example, the development of the lifter module is dependent on the performance of sensors, the controller, and the battery system.

   

Figure 3: DSM Allocation and tree of Autonomous Mobile Robots

Roadmap Model using OPM

The OPM for warehouse automation and the role of autonomous mobile robots is shown below. In preparation for warehouse operations, inbound delivery to the warehouse is unloaded and stored in inventory shelves that are carried by AMRs. When a customer purchases a product on the e-commerce website, the order management system assigns an order to the warehouse, which initiates the picking and packaging processes: AMRs carry themselves to the fulfillment associate who picks the purchased products, packaging robots assist the fulfillment associate in packaging, packages are transported on conveyor belts as they are verified (scanned) by verification robots, and finally the outbound packages are loaded onto trucks by robotic arms and shipped out as outbound delivery. Throughout the process, the inventory management system tracks the inventory in the warehouse at the unloading, picking, and loading stages.

Figure 4: OPM for Warehouse Automation

Figures of Merit (FOM)

Below are key FOMs for autonomous mobile robots. Payload capacity, speed, and picking rate are FOMs that contribute to the efficiency of warehouse automation. Continuous operation time and failure rate determine the robustness of AMRs. Volume of AMR can also be a competitive metric as AMRs operate in warehouses that are limited in space. Learning time indicates the time it takes to train the AMR in a digital twin before deploying them into the physical warehouse.

Table 2: Figures of Merit (FOM)

Figure of Merit (FOM)	Unit	Description	Trend
Payload Capacity	[kg]	Total weight the AMR can carry (including items and shelves)	Increasing
Speed	[m/s]	Average speed of the AMR while carrying shelves inside the warehouse	Increasing
Volume	[m^3]	Volume of AMR (width x length x height)	Decreasing
Continuous Operation Time	[hrs]	Total time the AMR can operate in one full charge	Increasing
Picking Rate	[units / hr]	Number of units picked and delivered to fulfillment associate per hour	Increasing
Failure Rate	[times/ hr]	Number of times the AMR fails per hour	Decreasing
Learning Time	[hrs]	Total time it takes to train the AMR to operate in a warehouse	Undetermined

Following is the trend of payload capacity for AMRs by various manufacturers developed since 2006, where we can see a steady improvement in performance.

Figure 5: Trend of Payload Capacity

Alignment with Company Strategic Drivers

The following table contains the strategic drivers for our company, and how this roadmap aligns with our targets:

Table 3: Strategic Drivers

Strategic Drivers	Alignment Target
To develop an AMR that will optimize payload capacity and picking rate for increased productivity.	The 3AMR roadmap is aligned to this strategic driver. Increase payload capacity by 15% and picking rate by 10% per hour through improved AMR design while maintaining safety standards and guidelines. This directly enhances fulfillment speed and supports high-demand periods without the need for increased manpower.
To develop AMR software that enhances real-time inventory movement and visibility.	The 3AMR roadmap is aligned to this strategic driver. Achieve real-time, dynamic inventory movement with <1-second response time for task assignments. Enable synchronized task visibility across all AMRs, accessible remotely and on-site for warehouse management, with secure permissions.
To improve optimization and route planning algorithms resulting in enhanced operational efficiency and lower task completion times.	The 3AMR roadmap is aligned to this strategic driver. Implement adaptive route optimization models to reduce navigation times by 20%. This includes enhancing navigational accuracy and obstacle avoidance for more efficient warehouse flow.
To accelerate training and deployment time by investing in complementary digital twin technology.	The 3AMR roadmap is aligned to this strategic driver. Deploy digital twin technology to train AMRs to understand the layout and potential obstacles in a warehouse in a virtual environment prior to physical deployment. This will enable a reduction in training time by 25%, rapid scaling of AMRs, and efficient adaptation to warehouse layout changes. While the Digital Twin is an enabling technology, it is a key technology for improving training time and operational efficiency in the warehouse.

This technology roadmap encompasses the design and software enhancements required to improve AMR efficiency in a warehouse. Without training and optimization algorithms, AMRs would not be autonomous. Similarly, any design that enables a robot to transport goods around a warehouse is in scope.

Positioning of Company vs. Competition

The images and table below show examples of AMRs available on the market today along with representative data points for key figures of merit that AMRs are evaluated upon.

Figure 6: Commercially available AMRs

Table 3: Current Competition in AMRs

Company	Robot	Date Released	Load Capacity (kg)	Volume (m^3)	Load Capacity / Volume (kg/m^3)	Weight (kg)	Load Capacity / Weight	Speed (m/s)	Battery Life (hr)	Battery Charge Time (hr)
Kiva/Amazon Robotics	DU 1000	2006	450	0.14	3,333	110	4.09	1.39	*	*
Kiva/Amazon Robotics	The Hercules	2017	567	0.09	6,631	340	1.67	*	*	*
Kiva/Amazon Robotics	The Pegasus	2018	560	0.09	6,550	60	9.33	*	*	*
Kiva/Amazon Robotics	Titan	2023	1,134	*	*	*	*	*	*	*
Kiva/Amazon Robotics	Atlas	2014	340	*	*	*	*	*	*	*
Zebra Robotics	Fetch 100 Flex	2020	75	0.48	154	91	0.83	1.74	9	3
Zebra Robotics	Fetch 100 Connect	2023	57	0.15	375	74	0.77	1.50	9	3
Zebra Robotics	Fetch100 Shelf	2021	78	0.48	161	91	0.86	1.75	9	3
Rockwell Automation	Otto 100	2015	150	0.13	1,173	93	1.61	2.00	6	0.3
Rockwell Automation	Otto 600	2022	600	0.24	2,551	290	2.07	1.40	*	0.5
Rockwell Automation	Otto 1200	2023	1,200	0.39	3,053	4,200	0.29	1.50	*	0.5
Rockwell Automation	Otto 1500	2015	1,900	0.82	2,305	820	2.32	2.00	10	1
GreyOrange	Ranger Uplift	2024	1,000	0.41	2,426	300	8.09	2	*	*
Konica Minolta	MiR100	2015	100	0.18	553	65	1.54	1.50	10	3
Konica Minolta	MiR200	2017	200	0.18	1,107	65	3.08	1.50	10	3
Konica Minolta	MiR500	2018	500	0.40	1,258	230	2.17	2.00	8	1
Konica Minolta	MiR250	2020	250	0.14	1,796	94	2.66	2.00	20	1
Scallog	Boby	2021	600	0.29	2,051	150	4.00	1.50	14	2.5

*This data is not publically available and is most likely a trade secret.

We have plotted the tradespace of battery life and load capacity below. The utopia point is top right. We observe the Pareto Front in the gray-dotted line, where we see an inverse relationship between battery life and load capacity. We also note that aside from those on the Pareto Front, most models are cluttered around 5-10 hours of battery life and less than 500kg of load capacity. Because AMRs operate in a warehouse where the charging stations are readily available, 10 hours might suffice; future emphasis may be on increasing load capacity or vehicle speed.

Technical Model

Based on our company strategic drivers and competition, we formulated a morphological matrix of key design decisions. Perception is how the AMR recognizes surrounding obstacles. Load interface is how items are carried; many AMR applications in the warehouse use shelves. Management of the AMR fleet can be centralized or decentralized. Communication can be wi-fi or Bluetooth. Although many route optimization algorithms are widely used, we choose the most common three algorithms. Battery size and charging power affect the continuous operation time and charging time of the AMR.

Table 4: Morphological Matrix

Design Decisions	Option 1	Option 2	Option 3
Perception	LiDAR	Radar	Camera
Load interface	Lifting shelves	Carrying bins	Towing cart
Fleet management system	Centralized	Decentralized
Communication system	Wi-fi	Bluetooth
Route optimization system	A* algorithm	D* Lite algorithm	Dijkstra’s algorithm
Battery size [kWh]	2	4	8
Charging power [kW]	4	6	8

To understand the sensitivity of FOMs to the decisions made in the morphological matrix, we derived technical models for two key FOMs: picking rate and continuous operation time.

1. Picking rate of AMR

The picking rate of AMR represents its effectiveness in warehouse automation and is defined by (1.1). Using additional definitions provided by (1.2) to (1.5), the equation for the picking rate can be derived as described in (1.6). Here, we assume that all AMRs start their trip from the storage area and travel to the fulfillment associate, and that they return to the storage area once the picking is complete. The partial derivatives of the picking rate with respect to each variable can be calculated as shown in (1.7) to (1.13). A list of variables used in equations is also provided below.

   

To visualize the sensitivity of the picking rate on key variables, the partial derivatives were normalized and their results were plotted on a tornado chart. Because operation data is not publicly available, we assumed the following values: continuous operation time T_op = 9 [hrs], charging time T_chg= 1 [hr], distance of each trip d_i = 500 [m], plan time t_plan = 10 [s], wait time t_wait = 30 [s], associate's item collection time t_assoc = 5 [s], number of items picked N = 45 [units], and average speed V_i = 1.5 [m/s]. We see that increasing average speed and decreasing distance traveled by AMR has the most impact on improving the picking rate. Improving continuous operation time and reducing charging speed are also effective strategies.

2. Continuous operation time

Continuous operation time is the total time the AMR can operate in one single charge and affects the picking rate, as mentioned above. Using the definition provided by (2.1) and some additional descriptions (2.2) to (2.4), we derive the equation for continuous operation time as shown in (2.5). Partial derivatives are calculated in (2.6) to (2.11), accompanied by a list of variables.

   

Similarly, the partial derivatives are normalized and plotted on a tornado chart. Sensitivity is calculated here based on Kiva/Amazon Robotics "The Pegasus" whose weight M = 60 [kg] and max load capacity m = 560 [kg]. The results show that increasing battery capacity, battery efficiency, and motor efficiency improves continuous operation time. We also note that although suggested from the tornado chart, we will not decrease payload or average speed as they negatively impact the efficiency of the overall warehouse automation.

Key Publications, Presentations, and Patents

The following are a representative set of patents and papers that have contributed to the overall development of AMRs:
1. Patient #US 7,402,018 B2 – Inventory System with Mobile Drive Unit and Inventory Holder
2. Patient #US 7,873,469 B2– System and Method for Maneuvering a Mobile Drive Unit
3. Patent #US 8,280,547 B2 – Method and System for Transporting Inventory Items
4. Martins, V. F., Silva, F. J. G., & Monteiro, F. (2021). A Digital Twin Approach for the Improvement of an Autonomous Mobile Robot's (AMR) Operating Environment: A Case Study. Retrieved October 29, 2024, from https://www.researchgate.net/publication/356528334
5. Nilsson, N. J. (1984). Shakey the robot. AI Center, SRI International. Retrieved November 1, 2024, from https://www.cs.sfu.ca/~vaughan/teaching/415/papers/shakey.pdf

Patent: Inventory System with Mobile Drive Unit and Inventory Holder
Patent #: US 7,402,018 B2
Date of Patent: Jul. 22, 2008
Patent Owner: Amazon Technologies Inc (formerly Kiva Systems, Inc.)
CPC Classification:
- International Classification: B62B II/00
- US Classification: 414/331.06.211/95. 28.047.35

Details: Patent US 7,402,018 B2 describes a system for transporting inventory that includes an inventory holder and a mobile drive unit. It is designed for environments like warehouses and manufacturing facilities. The system operates by using the mobile drive unit to autonomously dock with the inventory holder and transport it to specified locations within a workspace. The patent shows figures explaining the system configuration and includes process flow diagrams and descriptions to explain how the system operates once it wirelessly receives orders which trigger a series of commands.
Relevancy: This system is relevant because of its ability to streamline operations in automated environments, reduce labor costs, improve warehouse efficiency, and adapt to dynamic inventory demands, which addresses many limitations of traditional, rigid automated inventory systems that are not scalable. The system can also be operated with minimal human effort.

Patent: System and Method for Maneuvering a Mobile Drive Unit
Patent #: US 7,873,469 B2
Date of Patent: Jan. 18, 2011
Patent Owner: Amazon Technologies Inc (formerly Kiva Systems, Inc.)
CPC Classification:
- International Classification: G01C 21/32
- US Classification: 701/209; 701/202; 340/988, 995.19

Details: Patent US 7,873,469 B2 describes a procedure for navigation of a mobile drive unit. There are several workflows outlined in the patent - how to generate and reserve a route once a task has been received, how to proceed on the route reserving small segments at a time, and how to reroute if a segment is already reserved by another unit. It includes a series of procedural diagrams that outline each step in the routing and maneuvering process. Additionally, there is a series of illustrations demonstrating the layout of a warehouse and various hypothetical routes and situations.

Relevancy: Effectively navigating a space is critical to the function of AMRs in a warehouse. This patent describes a procedure that allows AMRs to navigate through a warehouse on an optimized path without running into other AMRs. This helps increase picking rates and decrease failures.

Patent: Method and System for Transporting Inventory Items
Patent #: US 8,280,547 B2
Date of Patent: Oct. 2, 2012
Patent Owner: Amazon Technologies Inc (formerly Kiva Systems, Inc.)
CPC Classification:
- International Classification: G06F 7700
- US Classification: 700/214
Details: Patent US 8,280,547 B2 describes a method and system designed to autonomously navigate to transport inventory with the mobile drive unit. The drive unit can move to a specific point with the inventory holder either attached or supported. It determines the inventory holder’s location and checks if it deviates beyond a set tolerance from the desired point. If the deviation is too large, the mobile drive unit moves to a new position, docks with the inventory holder, and then returns to the intended location.
Relevancy: This patent is relevant as it addresses the system’s ability to ensure precise positioning and movement of inventory within a warehouse or fulfillment center, which is crucial for efficient operations. By automatically correcting deviations in the inventory holder’s location, the system maintains organized flow and minimizes human intervention, thereby increasing the accuracy, speed, and reliability of inventory management in automated environments.

Paper: Shakey the Robot
Author(s): N J Nilsson
Organization: Artificial Intelligence Center

Details: This paper is a compilation of excerpts from Stanford Research Insititute that describe the development and abilities of a mobile robot named Shakey (the second Shakey system) between 1966 and 1972. The excerpts cover Shakey’s key components (hardware and software), “world model” (a model that represented Shakey's surroundings), low-level actions, intermediate-level actions, STRIPS (the Stanford Research Insititute Problem Solver which enabled Shakey to generate plans to accomplish tasks), vision routines, ability to extract patterns from previous plans and apply learnings to new plans, as well as Shakey’s limitations. Experiments near the end of the paper further describe Shakey’s ability to navigate and handle obstacles as well as perform simple tasks.
Relevancy: This paper has played a major role in the evolution and development of autonomous robots. It laid the ground work autonomous navigation and reasoning in robots. This paper has been cited approximately 1,273 times according to google scholar and continues to be a reference point for researchers and scientists in robotics and artificial intelligence today.
Citation: Nilsson, N. J. (1984). Shakey the robot. AI Center, SRI International. Retrieved November 1, 2024, from https://www.cs.sfu.ca/~vaughan/teaching/415/papers/shakey.pdf

Paper: A Digital Twin Approach for the Improvement of an Autonomous Mobile Robots (AMR’s) Operating Environment—A Case Study
Author(s): P Staczek, J Pizon, W Danilczuk, and A Gola
Organization: Lublin University of Technology

Details: This paper provides various examples of the use of digital twins of AMRs and their operating environments in production and logistics. It also introduces a case study of a digital twin that is used to determine the effectiveness of implementing a new AMR to the shop floor and to adjust AMR settings and shop floor configurations to achieve smooth operation.
Relevancy: A digital twin is especially useful in a logistics environment where physical testing can suspend or interfere with operations. Its ability to recreate the environment allows simultaneous, repeated tests on various AMR designs, such as optimization of the navigation and localization algorithms. The digital twin can also assist the warehouse operator in simulating the effect of introducing or updating AMRs on operations, for example, predicting the picking rate of an AMR.
Citation: Stączek, P., Pizoń, J., Danilczuk, W., & Gola, A. (2021). A digital twin approach for the improvement of an autonomous mobile robot's (AMR) operating environment—a case study. Sensors, 21(23), 7830. https://doi.org/10.3390/s21237830

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