Layered-Cost-Map-Based Traffic Management for Multiple AMRs via a DDS

Abstract

A traffic management system can be used to control multiple automated mobile robots (AMRs) effectively. This paper proposes traffic management for multiple AMRs based on a layered cost map in ROS 2 for multiple purposes. Using the layered cost map, the new concepts of a prohibition filter, lane filter, fleet layer, and region filter are proposed and implemented. The prohibition filter can help a user set an area that would prohibit an AMR from trespassing. The lane filter can help set one-way directions based on an angle image. The fleet layer can help AMRs share their locations via the traffic management server. The region filter requests for or receives an exclusive area, which can be occupied by only one AMR from the traffic management server. Multiple AMRs communicate via a data distribution service (DDS), which is shared by topics in the same DDS domain. The traffic management server in the domain sends or receives topics to each of the AMRs. The experiments of AMRs under the proposed traffic management show the effectiveness of our approach.

1. Introduction

Traffic management is essential for an automated mobile robot (AMR) to perform tasks effectively. A typical example of a fixed task is that an AMR starts from a point (the origin) and performs a set of tasks at the destination points. While operating multiple AMRs, a set of traffic rules can help operate multiple AMRs in a factory or warehouse. For example, when human workers and AMRs coexist in a factory or warehouse, it would be more efficient for the AMRs to perform tasks based on the right-hand traffic rule when the AMRs pass through the corridor with humans. In this case, if the corridor is divided into two passages and a one-way passage is introduced in one of the passages, the AMR can be forced to take the right-hand route in that passage. It is common for multiple AMRs to get stuck in a deadlock. Unlike an automated guided vehicle (AGV), which follows a set path that is similar to a railroad track, an AMR does not possess a specific traffic management algorithm as there are no fixed paths. Thus, if two or more AMRs enter a narrow passage, where only one AMR can pass, at the same time, they fall into a deadlock state, which needs to be manually removed by a human traffic manager. In addition, when one AMR performs a task in a specific area and another AMR performs a task that interferes with the working AMR, the efficiency of the working AMR is reduced. If the AMR that arrives first has a high task priority, an extreme case may occur, e.g., the next AMR would not complete the task within the set time and conduct the mission typically. To cope with the traffic management of multiple AMRs, a layered cost map based on the data distribution service (DDS) is proposed.

This paper aims to present a simple and elegant way to manage multiple AMRs. In particular, we propose a novel traffic management approach to coordinate multiple AMRs, which builds on a layered cost map in the robot operating system (ROS) 2. Our traffic management server manipulates the layered cost map in an elegant way by encoding specific functions as a collective stack on the layered cost map. Research activities for only one AMR via cost maps for path planning have been studied  [1,2,3,4,5]. However, traffic management for multiple AMRs has not been extensively studied yet. This is the first approach for the traffic management of the multiple-robot system via cost maps in ROS. Our novel concepts of prohibition and lane filters allow the user to set a prohibited area and a one-way driving rule, respectively. The fleet layer is used to effectively avoid collision among AMRs sharing information with the DDS. To effectively operate multiple AMRs, the region filter is used to reserve an area for only one AMR, whereas the remaining AMRs can wait outside of the area. Experiments with real AMRs have been performed to validate the proposed algorithms of the prohibition filter, lane filter, fleet layer, and region filter.

2. Related Works

Over the past years, several studies have focused on the traffic management of AGVs. To resolve collision and deadlock, the transport road network has been applied to divide non-overlapping zones [6]. The path planning for quay and rail-mounted gantry cranes with AGVs has been integrated with the mixed-integer programming model based on path optimization, integrated scheduling, conflicts, and deadlock [7]. For highly scalable management, AGVs autonomously execute pick-up and delivery operations based on a fully decentralized control algorithm [8,9]. Considering time constraints, a traffic management method with a virtual network map has been added to the planning process [10]. A hierarchical layer control architecture has been adopted for the traffic management of AGVs [11]. Using ROS, an experiment has been conducted to verify a solution to the scheduling deadlock problem using the rotational anti-deadlock algorithm [12]. A self-adaptive traffic management model with behavior trees and reinforcement learning (RL) has been proposed to make optimal decisions to cope with diverse, dynamic, and complex situations [13].

The cost map is often used for obstacle avoidance in robot navigation. The obstacle depicts a high cost value based on its location and speed in the cost map. The cost map generally helps navigation by separating dynamic obstacles from static ones. A typical dynamic obstacle can be defined for a person who walks across the robot’s path [14,15,16,17,18,19,20,21]. Predicting the patterns of pedestrians and reflecting them in the cost map can help further reduce the deadlocks between the robots and humans. Several studies have been presented in which human behavior is predicted and reflected in the cost map [22]. The social robot placement not to interfere with human workers could be modeled and reflected in the cost map [23]. Few studies have accurately predicted the human trajectory using deep inverse RL [24,25]. Moreover, the cost map has been used to coordinate multiple robots [18]. Ellis et al. proposed risk-averse Bayesian reward learning for autonomous navigation from human demonstration [26].

Sivaprakasam et al. have investigated a scenario in which the robot navigates to an optimized path by reflecting the terrain in the cost map [27]. In an off-road environment, the robot calculates the cost of the path so that it can successfully pass to avoid obstacles with a high probability. Ugur and Bebek [28] presented the motion planning of the exploration rover based on a real-time cost map using a depth field and color image data to pass through rugged terrain. Similarly, a study [29] proposed an approach that divides terrain into paths and assigns each of the paths with a cost for path planning in a Mars-like environment. In an indoor environment, a robot created a 3D octomap using wheel odometry, a 2D laser, and an RGB-D camera to pass through the terrain so that the robot can move up and down the slope, avoiding the stairs, arriving at a set destination [30]. Moreover, Regier et al. presented an approach in which a robot analyzed the density of regions (rather than the terrain) to pass through a region that was not dense [31].

3. Methods

3.1. Data Distribution Service

In a distributed system environment, a DDS [32] is data-centric. All the participating AMRs in the DDS domain are allowed to be data publishers and subscribers, as shown in Figure 1. Other participating AMRs can read the data written by any of the AMRs in the same DDS domain. In the DDS, the standard data type is described by a topic name and value pair topic = <name, value>. All the data are virtually stored in a global data space. The global data space may be in a distributed set of hardware units or the local memory of individual robots. A topic is transmitted in a multicast manner to share data reliably. To identify which topics are involved, an identifier, e.g., a namespace, is prefixed to the topic name in the following style: $/namespace/topic$. A namespace corresponds to the name of an AMR.

In this paper, a single centralized traffic management server is applied to set the configurations of AMRs. To this end, the DDS enables the traffic management server to simultaneously send static or user-defined maps as topics to multiple AMRs. In contrast to AMRs that pre-download maps, the participating AMRs in the DDS can share maps via the traffic management. Moreover, AMRs can communicate with each other to share information about their positions or occupied regions. All the AMRs send their position information to the single traffic management server with the DDS topic in real time to avoid collision. A ticket that includes the robot and region information is shared bidirectionally between the AMRs and the traffic management server to control the region occupation.

3.2. Layered Cost Map

The cost map encodes the cost of individual grid cells as a gray scale value in a discrete fashion (Figure 2). Our AMRs utilize the cost of each cell so that the AMRs move toward the path with the lowest cost. AMR planning is categorized into global planning, which does not consider dynamic obstacles, and local planning, which considers dynamic obstacles. The algorithm using the cost map, known as the dynamic window approach (DWA) for local planning, is adopted in this paper. This algorithm is positioned as the primary planning algorithm of ROS 1 and ROS 2, considering its strength that the computational cost is extremely low. The cost map expresses objects or spaces that AMRs should avoid with regard to the cost. The layered cost map is expressed using the OR operation by stacking multiple cost maps for obstacles and spaces [33]. Like ROS 1, ROS 2 provides the layered cost map as a plugin library. Once a plugin library is created, a plugin is referenced for global and local planners. The most basic layer is the static map, which receives a map drawn from simultaneous localization and mapping (SLAM). It helps AMRs avoid walls and static obstacles. Although static and dynamic obstacles are reflected as a form of cost values, AMRs may approach very closely those obstacles. To increase the separation distance for navigation planning, it is necessary to express an area around the obstacle with a lower cost value than the obstacle cost to provide buffer areas before the collision. The inflation layer represents this area. One of our goals is to help multiple AMRs proceed to their destinations without collision; thus, the fleet layer is designed to share the locations among the AMRs. In addition, the master cost map grid stacks separate layers, including the static map layer, prohibition filter, lane filter, fleet layer, region filter, and inflation layer. The prohibition filter, lane filter, fleet layer, and region filter are stacked for no-trespassing, one-way, and collision avoidance, and exclusive areas, respectively.

3.2.1. Filters

Let us consider an area where high-risk locations exist without obstacles for AMRs. Such an area can be designated as a prohibited area by a user-defined image to prevent AMRs from passing through it. As AMRs are prevented from trespassing on this area, the cost map layer is named the prohibition filter. The cost exhibits a maximum level of 254. If necessary, it can be reduced to a non-maximum level so that the AMR can flexibly trespass on the area when it needs to avoid dynamic obstacles. We designate a prohibition filter by adding the filter part as a suffix because a separate map is required. In contrast to a static map, we call the map the prohibition filter mask map. Similar to the static map, the mask map is transmitted from a separate map server and delivered to the topic—/prohibition_mask. The prohibition filter is then created from the mask map and is overlapped with the existing lower-cost map layers using the OR operation. As shown in Figure 2, the mask map is created with the static map by adding the prohibited area marked in black.

AMRs can effectively pass through a long and narrow passageway with pedestrians or other AMRs simultaneously if AMRs are regulated according to right-hand traffic. The lane filter is in charge of enforcing such a traffic rule. The lane filter uses a map server that requires a separate mask map file to send maps as topics—/lane_mask. However, one difference is that it receives a 16-bit map file to set directions. The lane filter map server is designed to receive the 16-bit map file to set the 16-bit direction cost map. Similar to the mask map of the prohibition filter, the 16-bit mask map is converted to a cost map. The cost can be dynamically adjusted according to the yaw angle of the AMR, as described in Algorithm 1.

Algorithm 1 Lane filter

Input: ∠ robot; the yaw angle of the robot    ∠ lane; pixel color value in range 0 to 35,999 Output: Cost functionGetCost(∠ robot $,\angle$ lane)    Wait for the response of the action server    if $0.4\le cos\left({\angle }_{\mathrm{robot}}-{\angle }_{\mathrm{lane}}\right)\le 1.0$ then        Cost = 0    else if $-1.0\le cos\left({\angle }_{\mathrm{robot}}-{\angle }_{\mathrm{lane}}\right)\le -0.4$ then        Cost = 254    else        Cost = 128    end if    return Cost end function

In a multi-AMR system, there could be limits on the number of AMRs in a particular area. For example, if two AMRs enter a narrow road, which is challenging to pass simultaneously, they may enter a deadlock situation. To cope with this situation, the region filter can be designed to prevent deadlock when multiple AMRs enter the same area simultaneously. The region is represented by the convex hull. The convex hull region is configured with a set of vertices, which defines an array type in the YAML file. The configuration of the region filter is obtained using the text-based parameter file. The region list includes x and y coordinate vectors with [double, double] type. When an AMR enters a pre-designated area by setting an exclusive area in the cost map, it changes the free space to an occupied space, prohibiting other AMRs; thus, we define the layer as the region filter. In the region filter, when one AMR enters the exclusive area, the information must be reflected in the cost map of other AMRs; thus, location sharing among AMRs is required. The region filter communicates with the region filter server to reserve or release the region. The region filter in an AMR requests a ticket with a topic—/ticket—from the region filter server to enter the region. The region filter returns the ticket with the topic—/ticket—to the region filter server to leave the region. The region filter server responds to the region filter of each AMR based on robot ID and region ID to identify the AMRs and regions. The region filter is implemented by Algorithm 2.

Algorithm 2 Region filter

ticket: robot $ID$, region $ID$, return value   AMR side: Upon entering the region: if Is AMR in the inflation region then    response=reserveRegion(robot $ID$, region $ID$)    if response==Success then       Perform the given task    end if end if Upon leaving the region: if Is AMR leaving out of the inflation region then    response=releaseRegion(robot $ID$, region $ID$)    if response==Success then       Send the release to the region filter server    end if end if   Region filter server side: functionreserveRegion(robot $ID$, region $ID$)    region_info=SearchAMR(robot $ID$, region $ID$)    if region_info==empty then       AllocateAMR(robot $ID$, region $ID$)       return Success    end if end function functionreleaseRegion(robot $ID$, region $ID$)    region_info=SearchAMR(robot $ID$, region $ID$)    if region_info!=empty then       DeallocateAMR(robot $ID$, region $ID$)       return Success    end if end function

3.2.2. Fleet Layer

We use a layer that adjusts the surrounding cost map based on the locations of AMRs to prevent collision with other AMRs. It is named the fleet layer since it does not require a separate map. A total of N AMRs share their locations as the coordinate transforms topic—/multi_robot. Each AMR then marks the position of the other AMR in the cost map with a high cost value, i.e., a 2D circle-shaped cost plus the inflated cost, which is bell-shaped in 3D. As a result, each robot can avoid the collision. Collision avoidance is based on the basic DWA. This algorithm has been widely used for a single AMR owing to its simplicity and low computational cost. The DWA is a cost-map-based algorithm that is effective for static obstacle avoidance. When dynamic obstacles in front of an AMR are recognized, they can be reflected in the cost map. To reflect multiple AMRs with high cost values, it is necessary to collect the pose information of each AMR as a topic—/robotname/pose—in the multi-robot server.

All filters and the layer are summarized in

Table 1. Summary of filters and a layer.

Category	Function	Type
Prohibition filter	To prevent AMRs from trespassing on an area	8-bit image
Lane filter	To set AMRs’ driving direction	16-bit image
Fleet layer	To share the position of each AMR	None
Region filter	To occupy an area exclusively	Parameter text file

according to the function and type.

4. Experimental Results

4.1. Hardware Settings

For this study, the AMR (for testing) was developed by Hyundai Robotics (Figure 3). The AMR is equipped with a differential drive for wheel control, Wi-Fi for DDS, sensors for tracking, and potentially peripheral I/O for delivery. The differential drive is an all-in-one motor. The brushless motor, motor drive on the controller area network (CAN), wheel, and tire are included in the differential drive. The tracking sensor comprises a 2D lidar scanner for positional sensing and adaptive Monte Carlo localization (AMCL). Note that the lidar scanner has a 270-degree sensing range with a blind spot. The peripheral I/O can connect to the rotatable or prismatic type of the actuator. The goal is to use the AMR for factory transportation or simple delivery services provided to hotel customers. The robot software platform is ROS 2 Eloquent, and the DDS library is FastDDS (https://github.com/eProsima/Fast-DDS (accessed on 30 June 2022)). All experiments were conducted with uncovered AMRs.

4.2. Prohibition Filter

As shown in Figure 4, a single AMR starts from the origin and reaches the destination point across the desk, which has four slender legs. The left part of the figure shows the AMR passing under the desk. As the cost map in the non-applied prohibition filter shows four groups of tiny dots of high cost values at the four legs, the AMR goes through the relatively low cost under the desk. In contrast, the prohibition filter prevents the AMR from the global or local planning under the desk. Keeping the desk area to preset a high cost value, the AMR moves away from the desk, even though the lidar sensor detects only four legs.

4.3. Lane Filter

To test the lane filter, we try to have two AMRs to leave their starting points and reach the destination points. As shown in Figure 5, three boxes are located together at the center of the white rectangular area. There are two designated direction areas, which are divided by three boxes. The back and front parts of the three boxes are set in the right and left directions, respectively. The path between the starting and destination points is straight; hence, the AMRs can drive along the straight direction without the filter. However, the AMRs turn around the three boxes and finally reach their destinations under the lane filter. Based on the analysis of the cost map of each AMR shown in Figure 6, it is found that lane areas depend on the cost maps. For AMR A, the cost of the front lane increases as the direction cosine between AMR A and the lane directions is negative since AMR A faces the right direction. For AMR B, the opposite-direction cosine is applied. Although U-shaped navigation planning is inefficient with regard to energy- or time-based planning, AMRs are forced to drive one way under the lane filter.

4.4. Fleet Layer

As shown in Figure 7, two AMRs start from their origins to reach the origins of the opponents. To avoid the collision, each AMR receives the position of the opponent AMR. Then, the fleet layer draws the opponent AMR based on the circle-shaped cost map (see Figure 8). To navigate with low-cost values, AMRs analyze global and local navigation planning while avoiding high-cost locations. As a result, the two AMRs avoid the collision.

To compare the fleet layer to the AMR detection by the lidar, the cost maps of AMR A and B estimated by the lidar are presented in Figure 9. First of all, it is found that the radius of the opponent’s AMR keeps changing. Moreover, we find that the opponent AMR is not moving anymore after turning against the other due to the limited lidar sensing angle, as shown in the third part of Figure 9.

4.5. Region Filter

4.5.1. Narrow Path

As shown in Figure 10, multiple AMRs should pass through the narrow path whose width can only accommodate a single AMR. Two AMRs may inevitably collide with each other or stop infinitely, with deadlock. Once the destinations are set to the opposite locations of two AMRs, they shall perform global navigation planning. Providing a higher priority with an AMR for passing through the path, the cost of the narrow path region can be differently set. Analyzing cost maps in Figure 11, AMR A and B try to drive the diagonally positioned goals through the narrow path. First, the narrow path opens for AMR B, which has a higher priority. After AMR B arrives at the designated goal, AMR A starts passing through the path when the narrow path lowers the cost for AMR A.

4.5.2. Exclusive Working Area

We consider an AMR working in a designated area where other AMRs are prohibited. Regarding the area as an exclusive working region, the AMR can use the place while reserving it to the region filter server. As shown in the first image of Figure 12, two AMRs try to enter the exclusive working area, which is surrounded by six yellow boxes attached to the white wall. As shown in the second image, AMR B with higher priority enters the area, and AMR A waits around the U-shaped area. After finishing the task, AMR B leaves the area, and AMR B finally enters the area and performs the given task. In the beginning, from AMR A’s point of view, the exclusive working area is the prohibition area (see Figure 13) since AMR A has a lower priority. After AMR B leaves the area, the region filter server releases the area from the prohibition area to a free area for AMR A.

5. Conclusions

In our approach, a layered cost map is proposed to achieve the traffic management of AMRs. In particular, a DDS is adopted to share maps or reserve tickets. We successfully demonstrate a single AMR tested with regard to the prohibition filter and two AMRs tested with regard to the one-way directions, narrow paths, and exclusive working areas in real-world situations. All demonstrations show that the filters and layer are easy to implement but effective without other mathematical algorithms. All the layers are experimentally validated with real-world AMRs. The video of the experimental results is available at: https://youtu.be/M--RUWZmbow/ (accessed on 30 June 2022).