Fuzzy inference system-assisted human-aware navigation framework based on enhanced potential field
Abstract
With the advent of Autonomous Mobile Robots (AMRs) in public areas such as malls and airports, their harmonious coexistence with humans is crucial. AMRs must operate in a manner that ensures human safety, comfort, and acceptability to reduce stress. This is called Human Aware Navigation. This study introduces a framework for AMR navigation that prioritizes safety and human comfort in such environments, utilizing an enhanced Potential Field approach augmented by Fuzzy Inference Systems. To achieve a smooth AMR trajectory, the framework employs these systems based on AMR, human, and obstacle information. The proposed approach is tested across various scenarios, including complex, cluttered environments that mimic practical situations. Simulation results demonstrate that AMRs using the proposed method navigate human-rich environments safely and comfortably while mitigating common issues associated with Potential Field-based approaches, such as local minima and obstacles near the goal.
Keywords
1. INTRODUCTION
Asimov's first law of robotics[1] explicitly states that "A robot may not injure a human being or, through inaction, allow a human being to come to harm", serving as a foundational principle in human-robot interaction. While this rule primarily concerns physical harm, the significance of safeguarding a person's psychological well-being cannot be understated. Currently, there is no established technology allowing robots to interpret the human mind, but research has been ongoing since the early 2000s to understand how robot actions may influence human psychological safety[2].
Traditionally, robots, especially Autonomous Mobile Robots (AMRs), have been utilized in factories and warehouses due to their efficiency in handling repetitive tasks[3]. However, recent years have witnessed the widespread deployment of AMRs in diverse settings, including restaurants[4,5], airports[6,7], and hospitals[3,8]. Surprisingly, despite the presence of humans in these environments, AMRs have often operated without due consideration for human safety. Nevertheless, some researchers[9,10] have concentrated on two generalized levels of safety: (ⅰ) physical safety, which involves avoiding collisions with humans; and (ⅱ) psychological safety, which entails adhering to specific human norms, such as maintaining a safe distance from humans[9] and refraining from navigating certain areas near humans[10]. To mitigate the risk of collision with humans and alleviate human discomfort caused by AMRs' operation, proper navigation approaches for the AMRs are required.
In a typical AMR setup, the core components are often referred to as the "3P's", which play a critical role in its functionality[11]: Perception, Prediction, and Path planning. Here, perception represents mapping the AMR's surrounding environment, while prediction involves forecasting the future states of all the agents within that environment. Finally, path planning focuses on determining the safe course of action for the AMR to reach its next state. Scholars have frequently explored the interplay of these three components in the context of AMRs. For instance, Mateus et al. proposed a vision-based perception approach employing deep convoluted neural networks[12] for pedestrian detection. Their work featured a convolutional neural network-based aggregate channel features detector for pedestrian detection, alongside using asymmetric Gaussian functions to model human-aware constraints. The path planning was accomplished using the A* algorithm. Similarly, Bruckschen et al. delved into prediction, considering how humans navigate based on observations from the AMR and prior knowledge of human interactions with objects[13]. Hansen et al. developed an adaptive method for detecting a person's interest in interacting with the robot, relying on case-based reasoning and two-dimensional (2D) laser range measurements[14]. They further incorporated a time-dependent cost map for planning the AMR's path based on human future movement. In other works, such as the research by Ah et al.[15], a Probabilistic Road Map (PRM)-based algorithm was employed for the global path planner, while deep reinforcement learning was used for the local planner. The results obtained after evaluation with different environments and pedestrian behaviors exhibited improved AMR navigation with a reduced likelihood of colliding with humans.
In previous studies, it has become evident that the 3P's are intricately interconnected. However, the focus of this work predominantly centers on AMR's path planning, emphasizing the critical aspect of collision-free navigation while assuming the successful attainment of perception and prediction. In the domain of path planning research, diverse conditions and considerations have been employed by different researchers in designing their algorithms, encompassing aspects such as the nature of humans, algorithms, Human-Aware Navigation (HAN) models, and environmental factors. A summary of these variations is presented in Table 1.
Comparison of related works
Ref. | Nature of human | HAN model considered | Algorithm | Advantages | Disadvantages |
[16] | Static | PR | PRM | Fast path planning compared to A* | Consideration of only static human and PR |
[17] | Dynamic | PR | A* | Natural behavior of AMR, reduced planning time, time-dependent cost map | Consideration of PR only, planning timeout, computational burden |
[18] | Dynamic | PR, FV | A* | Natural behavior of AMR, time-dependent cost map | Planning time-out, higher computational burden compared to [17] |
[19] | Static | PR, FV, BS | APF | Smooth path compared to A*, no path planning timeout | Local minima and GNRON, consideration of only static human |
The "nature of human" category relates to whether the human's position and heading exhibit changes over time. Meanwhile, the HAN model encompasses various constraints, including considerations such as respecting the human's intimate zone [Proxemics (PR)], avoiding navigation in the human's frontal space [Field of View (FV)], or refraining from traversing the area immediately behind the human [Back Space (BS)].
For instance, in the research conducted by Korkmaz et al., emphasis was placed on utilizing the A* algorithm as a primary planner, introducing a dynamic path planning method for HAN[16]. Their comparison between A* and PRM as navigation bases revealed that PRM could function as a quicker planner for HAN in comparison to A*. However, it often resulted in longer travel distances, steering the AMR away from humans. Notably, they did not consider that human moves over time and solely relied on PR. Moreover, the paths generated by both A* and PRM were found to be significantly influenced by the number of nodes[16,20]. Attempts to reduce the number of nodes in the A* map to alleviate computational burdens could compromise the path's smoothness. Similarly, Kirby et al. implemented a conventional A* path planner enhanced with social conventions, such as passing humans on the right[21]. Additionally, Kollmitz et al. designed a time-dependent deterministic planner using A*, which accounted for human motion[17]. However, this method solely relied on PR for navigation. They introduced a planning timeout within the algorithm, allowing it to stop after a fixed time and return the least-cost path to the destination. While this aids in timely algorithm termination, it occasionally yields sub-optimal paths or no path at all. Nonetheless, this algorithm ensures the AMR exhibits natural behaviors, such as avoiding close proximity to humans,
waiting for humans to pass, and adjusting its path in response to humans. Moreover, Briamonte et al. explored the application of the time-dependent deterministic A* path planning method for AMRs navigating in confined spaces around groups of humans, incorporating considerations of PR and FV[18]. However, their study observed longer navigation times compared to[17]. In another study by Sampathkumar et al., the authors adopted the Artificial Potential Field (APF) for path planning, integrating human-associated factors through adjustable coefficients[19]. They optimized the path planning model using a genetic algorithm, fine-tuning coefficients such as scaling factors and Potential Field (PF) orders to minimize the AMR's path length while adhering to human-prescribed rules. Despite these improvements, their APF-based approach still encountered challenges related to local minima and difficulties reaching goals due to nearby obstacles, termed as goal non-reachable with obstacle nearby (GNRON) issues[22]. In short, the aforementioned studies include some level of limitations, such as a lack of consideration of sufficient human factors or human movement, planning timeout, or navigation issues (local minima and GNRON).
In light of these considerations, this work employs Enhanced PF (EPF)[23] as the foundational path planning technique. Furthermore, three human factors (PR, BS, and FV) are considered in this study, along with no planning timeout. The integration of EPF with HAN effectively addresses the limitations of APF while adhering to the principles of HAN in the AMR navigation. Additionally, the coefficients of EPF highly govern the behavior of AMRs. Hence, this research incorporates a Fuzzy Inference System (FIS) to dynamically adjust the coefficients within the HAN-EPF framework based on the system knowledge. This adaptive coefficient adjustment equips AMRs to effectively navigate within dynamically changing environments, accommodating the presence of humans with PR, BS, and FV considered human factors. The efficacy of the proposed approach is subsequently evaluated based on the AMR's ability to navigate to its destination while strictly adhering to HAN constraints, ensuring proper human-robot interaction and safety.
Overall, the main contributions of this work are
● To design a diverse human factors-employed HAN framework based on EPF that effectively overcomes local minima and GNRON issues.
● To employ the FISs to adaptively determine coefficients that enable the AMR to safely navigate in a dynamically changing human-rich environment.
The paper is structured as follows: Section 2 lays the groundwork by defining frames and providing a concise overview of the EPF and FISs. Section 3 elaborates on the integration of HAN principles into the EPF framework and outlines the design of the FISs. In Section 4, the authors present and explore simulation results aimed at validating the performance of the proposed approach. Finally, Section 5 offers concluding remarks on this work.
2. PRELIMINARIES
2.1. Definition of frames and states
To describe the motion of the AMR, the reference frames, as shown in Figure 1, are established. The inertial frame is represented by
The positions of the AMR, human, obstacle, and the AMR's destination in the inertial frame are denoted as
where
Here,
2.2. Enhanced potential field
The APF serves as a widely adopted method for robot collision avoidance owing to its mathematical efficiency and its capability to generate smooth obstacle-avoiding trajectories. This approach comprises two primary components: attraction and repulsion. An AMR is steered toward its destination by an attractive PF while being simultaneously pushed away from environmental obstacles through repulsive PFs. Consequently, a net PF emerges, which is the sum of both attractive and repulsive PFs, influencing the AMR's motion. The total potential function, denoted as
where
Here,
Note that the attractive and repulsive PFs are found by
where
Note that
where
where
Note that
where
Here,
2.3. Fuzzy inference system
A FIS is an approach that employs a rule base and fuzzy set theory[24] to map inputs to outputs, as shown in Figure 2. When numerical data is input into the FIS, it undergoes a transformation into fuzzy inputs through fuzzification. This process involves assigning a degree of membership to each Membership Function (MF) corresponding to the numeric value. An MF precisely defines the degree to which an input value belongs to a fuzzy set. It maps input values from a precise domain onto a scale of the degree of membership, mostly ranging between 0 and 1. This scale indicates how strongly an element is associated with the set, allowing for a smooth transition between membership and non-membership states. Subsequently, the inference unit derives outputs based on user-defined rules, typically expressed in linguistic form; for example, "If Input 1 is Category 1 AND Input 2 is Category 2, then Output is Category 3". These outputs are associated with varying degrees of membership within output MFs. Finally, a process called defuzzification is employed to convert these fuzzy outputs back into numerical outputs. In this study, Mamdani-type FISs[24] are used and are referred to as FIS. One of the key advantages of FIS-based systems is their capacity to provide explainability, which can be attributed to the linguistically defined rules and MFs[25].
3. METHODOLOGY
3.1. Human aware navigation
HAN represents the convergence of robot motion planning and human-robot interactions[9]. While the primary aim of robot motion planning is to guide the robot to its destination, HAN prioritizes AMR's ability to minimize stress and prevent harm to humans. Therefore, it can be defined as "navigation of the AMRs based on human-centered PFs, aiming to minimize discomfort and prevent harm"[19].
Human discomfort stemming from AMRs can arise from various sources, including the robot's appearance, unnatural movement, production of discomforting noise, close proximity to humans, and failure to adhere to cultural norms[9]. Kruse et al. classified discomfort in HAN into three main categories: human comfort, AMR naturalness, and AMR sociability[9]. Human comfort revolves around ensuring maximum comfort and safety for humans in the presence of AMRs. Examples include AMRs maintaining a specified distance from humans at all times and refraining from traversing specific spaces near humans. AMR naturalness entails the robot's movement resembling that of humans, such as following smooth trajectories and having a friendly appearance, thereby enhancing acceptance. AMR sociability implies that the robot should adhere to cultural norms, such as traveling on a specific side (left/right) of humans depending on the country and overtaking humans along a certain direction. Among these categories, this work primarily focuses on human comfort concerning AMR navigation, as the robot's appearance and noise levels are not significantly related to its navigation. Safety takes precedence in this context.
This study introduces three important terms in HAN: PR, FV, and BS, as shown in Figure 3. PR signifies that the AMR must not only maintain a predetermined relative distance from humans at all times but also avoid collisions with them. BS denotes the region behind the human, where the presence of the AMR may cause discomfort to humans when traversing. FV represents the region in front of the human where the AMR could potentially obstruct the human's path. Consequently, a successful HAN planner must ensure that the AMR avoids these defined regions.
3.2. Proposed approach: HAN-EPF
3.2.1. Definitions of HAN factors
The primary focus of this study centers on the integration of factors associated with humans into the navigation of the AMR. To streamline collision-free path planning, it is assumed that the relative positions of humans with respect to the AMR are known, as this information can be obtained through optical or infrared sensors equipped with perception algorithms. Similarly, the relative position information of obstacles is obtained through lidar sensors. Note that obstacles are represented as a collection of points resembling cloud points. Data from the sensor, in the form of cloud points, is utilized to outline the boundaries of obstacles within the sensor's range. To account for HAN factors related to humans, this work introduces virtual cloud points surrounding a human. These virtual points are positioned along the perimeters of the HAN factors. To illustrate the formation of these virtual cloud points, Figure 4 depicts a parametric representation of the HAN factors in relation to a human, as introduced in the previous section.
The threshold distance for PR can vary considerably, depending on factors such as human age, the type of social interaction, and cultural norms[26]. However, in this work, PR is treated as a constant
where
To generate a specific virtual cloud point within the FV region, denoted as
3.2.2. Formulation of HAN-EPF
To account for human comfort in the AMR's navigation, an additional repulsive PF term is incorporated into the total PF. Consequently, the total PF of the HAN-EPF is expressed as
where
where
It is important to note that, at any given time step, only the closest virtual cloud point related to human factors and the closest obstacle point are considered. For instance, in Figure 5, all the HAN factors are detected in the left figure. However, the AMR is closer to FV than PR and BS. Hence, only FV is considered when generating
The HAN-EPF contains several unknown parameters, but the dominant factors influencing the AMR's collision avoidance behavior are the coefficients
Note that
3.3. Preliminary study for understanding HAN-EPF
Before designing the FISs for the scaling factors, it is crucial to gain insights into how these scaling factors influence the AMR's behavior. This foundational understanding is essential for creating the MFs and rules for the proposed FISs. To achieve this, preliminary simulation studies were conducted to investigate the AMR's behavior in terms of its path length and relative distance from obstacles during avoidance maneuvers, with a focus on changes in the scaling factors. These preliminary results serve as the basis for designing the proposed FIS and help to establish reasonable ranges for the scaling factors. The simulation parameters introduced in Section 4 were utilized for these preliminary studies. Note that the coefficient
Figure 6. AMR's trajectory with very small
Due to the dominant attractive PF compared to the repulsive PF, the AMR is not effectively repelled from the obstacle. Consequently, when
It is noteworthy that the appropriate range for
3.4. FIS design
This study employs three FISs to determine the coefficient
For each input and output of the FISs, three MFs are considered, which are Low, Medium, and High. In particular, this work considers two sets of the MFs, as shown in Figure 9. The first set of the MFs in Figure 9 (left) is used for the inputs of all three FISs. These MFs normalize input numeric values within the range of 0 to 1. This normalization allows the FISs to be applicable across different environments and AMR velocities, provided that the maximum values are known. For FIS 1, the output uses the first set of MFs. On the other hand, the outputs of FIS 2 and FIS 3 use the second set of MFs defined in Figure 9 (right). The range of these output MFs, ranging from 0.01 to 55, is determined based on the preliminary studies described in the previous section.
The next step in designing the FISs is to build the rules that define the relationship between the inputs and outputs for each FIS, aiming to achieve the desired behavior of the AMR. As stated previously, FIS 1 determines the magnitude of the attractive PF. For example, if the AMR is in close proximity to obstacles or humans while being far from the goal position, it is desirable for the AMR to generate a smaller attractive PF than the repulsive one to avoid collisions, even if the relative distance to the goal is large. Conversely, if the AMR is far from both the destination and obstacles, it should generate a large attractive PF, which corresponds to a large value of
Rule matrix for FIS 1
Relative distance to the goal | ||||
LOW | MEDIUM | HIGH | ||
LOW | Medium | Medium | Low | |
Relative distance to the obstacle | MEDIUM | Medium | Medium | High |
HIGH | High | High | High |
The next step in designing the FISs is to establish the rules for FIS 2, which determines
Rule matrix for FIS 2
Relative distance to the obstacle | ||||
LOW | MEDIUM | HIGH | ||
LOW | Low | Low | Low | |
Relative angle to obstacle | MEDIUM | Low | Medium | Medium |
HIGH | High | High | High |
Similar to FIS 2, FIS 3's rule matrix is designed to govern the desired avoidance maneuver of the AMR with respect to humans. For instance, when the AMR is in close proximity to a human and the relative velocity is high, a significant repulsive PF is needed. In such a case, where the human is approaching the AMR's direction, the AMR should have the capability to maneuver without violating HAN rules. This significant repulsive PF can be generated by setting
Rule matrix for FIS 3
Relative distance to the virtual cloud point | ||||
LOW | MEDIUM | HIGH | ||
LOW | Low | Low | Low | |
Relative velocity to human | MEDIUM | Low | Medium | Medium |
HIGH | High | High | High |
The entire process is summarized in the flowchart, as shown in Figure 10. Initially, once the parameters are defined, the human positional information is utilized to generate the virtual cloud points. Concurrently, the parameters used in the calculations concerning the AMR frame are inputted into the FIS to derive the outputs:
4. SIMULATION STUDIES
To validate the effectiveness and the performance of the proposed approach, simulation studies are performed, considering different environments using the parameters listed in Table 5.
Simulation parameters for the proposed HAN-EPF approach
Description | Value (unit) |
Time interval, | |
Order of potential, | |
Distance of influence, | |
Collision threshold distance | |
Repulsive field rotational angle, | |
Sensing range | |
Maximum AMR velocity | |
Maximum human velocity | |
Proxemics range, | |
Back space range, | |
Back space width, | |
Field of view angle, | |
Field of view range, |
To make the simulation realistic, the maximum human velocity is limited to
4.1. Scenario 1
In this scenario, the AMR maneuvers in an environment designed to introduce challenges such as local minima, GNRON, and the presence of a moving human. The environment includes a circular obstacle placed to block the AMR's head-on, causing a local minima issue, and a rectangular obstacle positioned near the destination position to create a GNRON issue. The parameters for the position information of the AMR and human are listed in Table 6.
Simulation parameters - Scenario 1
Description | Value (unit) |
AMR start position | |
AMR destination position | |
Human start position |
Figure 11 (left) shows the AMR's trajectory in Scenario 1, demonstrating that the AMR adaptively avoids both the obstacle and the human during its travel. Also, Figure 11 (right) provides a visual representation of the scenario, highlighting that the AMR successfully maintains a relative distance greater than the collision threshold value of 0.5 m from both obstacles and the human. The closest relative distance between the AMR and the obstacle (purple dot) is 1.6 m, while the closest distance to the virtual cloud points (red dot) is 1.07 m. Furthermore, Figure 12 shows a close-up view of the AMR's interaction with the human. At
Figure 11. AMR's trajectory and relative distance from the AMR to obstacles and humans (Scenario 1).
4.2. Scenario 2
Scenario 2 presents a more complex environment compared to Scenario 1, involving obstacles and moving humans. This environment consists of two humans, one in motion and the other rotating to change gaze, along with three obstacles. The parameters related to the positions of the AMR and human are given in Table 7.
Simulation parameters - Scenario 2
Description | Value (unit) |
AMR start position | |
AMR destination position | |
Human-1 start position | |
Human-2 start position |
Figure 13 displays the trajectory traveled by the AMR in Scenario 2. Despite facing two humans simultaneously near a static obstacle, the AMR adeptly navigates through this complex situation. Following this maneuver, the AMR safely reaches its destination while avoiding two static obstacles. Figure 13 (right) provides a visual representation of the relative distance between the AMR, obstacles, and humans. It can be observed that the closest relative distance between the AMR and the obstacles and the virtual cloud points are
Figure 13. AMR's trajectory and relative distance from the AMR to obstacles and humans (Scenario 2).
Figure 14 (top left) depicts the initial encounter between the AMR and human-1, who starts to rotate the AMR approaches. The AMR spends a significant portion of time navigating close to the FV of human-1, primarily because of the continuous rotation of their gaze. In response, the AMR adjusts its path, avoiding human-1 and subsequently encountering a rectangular obstacle near
4.3. Scenario 3
Scenario 3 considers a more realistic environment, resembling an airport setting with various humans and infrastructure-like obstacles. Circular obstacle-1 and circular obstacle-2 can be envisioned as pillars in an airport hallway, with humans following the convention of moving along the right side. In addition, there are two rectangular obstacles that represent passenger waiting regions. The simulation includes six human agents, and their positions are listed in Table 8.
Simulation parameters - Scenario 3
Description | Value (unit) |
AMR start position | |
AMR destination position | |
Human-1 start position | |
Human-2 start position | |
Human-3 start position | |
Human-4 start position | |
Human-5 start position | |
Human-6 start position |
From Figure 15 (right), one can observe that throughout the simulation, the AMR never crosses the collision threshold. The minimum relative distance between the AMR and obstacles, as well as the virtual cloud points around humans, are
Figure 15. AMR's trajectory and relative distance from the AMR to obstacles and humans (Scenario 3).
Figure 16. AMR's trajectories near obstacles and humans (Scenario 3): (top left) 10.5 s, (top right) 14.5 s, (middle left) 20 s, (middle right) 35 s, (bottom left) 45 s, and (bottom right) 65 s.
To summarize the findings of the simulation study, the closest relative distances from the AMR to humans and obstacles obtained are tabulated in Table 9. Upon comparing various scenarios, it is observed that the relative distance from the AMR to humans is smaller than the distance from the AMR to obstacles. Since humans are moving, unlike static obstacles, during the operation of the AMR, there is a high possibility that the AMR navigates around humans closely. Furthermore, it is observed that the AMR comes closest to both humans and obstacles in Scenario 3 compared to the others. These results are natural as the AMR must navigate in a complex environment, dealing with dynamically moving humans and multiple static obstacles. Despite these challenges, it is noteworthy that in all scenarios, the AMR adeptly navigates to the destination position without violating any HAN constraints.
Closest relative distance from the AMR to humans and obstacles for each scenario
Scenario | Closest distance to human (m) | Closest distance to obstacles (m) |
Scenario 1 | ||
Scenario 2 | ||
Scenario 3 |
5. CONCLUSIONS
In this study, the authors introduce a HAN approach for AMRs through the integration of an EPF framework, referred to as HAN-EPF. The HAN-EPF method is designed by incorporating a repulsive PF that considers the impact of social constraints on human comfort during navigation. The concept of virtual cloud points is introduced when the AMR detects a human presence, effectively addressing these social constraints and ensuring safe and respectful interactions with humans. To simplify parameter selection, the coefficients of the repulsive PF are redefined in terms of the coefficient of the attractive PF and analyzed based on minimum relative distances and travel distances. Three FISs are employed to adaptively determine these redefined coefficients, guided by the design of MFs and rules based on analysis results. The approach's validation through simulation studies in diverse scenarios demonstrates effective AMR navigation, adherence to HAN rules, and avoidance of collisions with obstacles. Summarizing the important contributions of this work:
● Introducing the EPF as a foundational method for path planning, considering human factors, specifically PR, BS, and FV.
● Designing the FISs for the determination of the EPF's coefficients, assisting the AMR in successfully navigating in a human-populated environment that undergoes continuous changes.
In the future, the integration of a global planner alongside HAN-EPF as a local planner will be considered. This exploration involves testing this combined setup in environments characterized by an increased number of static obstacles.
Additionally, future plans involve delving into parameter optimization for the developed FISs using learning capabilities offered by optimization algorithms to achieve optimal routes for AMRs while adhering to the principles of the HAN framework.
DECLARATIONS
Authors' contributions
Made substantial contributions to the conceptualization, methodology, and analysis: Sampathkumar SK, Choi D, Kim D
Contributed to approach validation, software simulation, and writing - original draft preparation: Sampathkumar SK, Choi D
Contributed to the investigation, supervision, and writing - review and preparation: Kim D
Availability of data and materials
Not applicable.
Financial support and sponsorship
None.
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2024.
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How to Cite
Sampathkumar, S. K.; Choi, D.; Kim, D. Fuzzy inference system-assisted human-aware navigation framework based on enhanced potential field. Complex Eng. Syst. 2024, 4, 3. http://dx.doi.org/10.20517/ces.2023.34
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