Modeling and simulation of pedestrian dynamical behavior based on a fuzzy logic approach
Introduction
The modeling of pedestrian dynamics as an interdisciplinary research direction has attracted a wider interest of researchers and managers. The traffic capacity at the passage, characteristic features of normal and escape panics, and self-organization phenomena of crowds have been taken into account by architects and designers for optimization of limited traffic resources and formulation of urgent evacuation plans.
In order to understand complicated motion features of pedestrians, the important work is to build a suitable model for characterization of pedestrians’ behaviors. Many prior studies on pedestrian dynamics have presented various pedestrian (crowd) models. The state of art of the models is mainly based on the following three type of methods: macroscopic, mesoscopic and microscopic model. The first, which treats the crowds as a fluid or continuum, uses gas kinetics and hydrodynamics to describe large crowds [24], [25], [60]. The second, which doesn’t differentiate between individual pedestrians, focuses on describing part of global properties of pedestrians[21], [22]. The third, which can analyze and research individual behaviors with the interplay of pedestrians, always treats a pedestrian as a discrete individual driven by force, potential or utility [1], [5], [20]. In the last years much more attention has been focused on microscopic modeling, where the socio-psychological and complex interactions of individuals and environments are considered in the model. Examples of microscopic models are the social force model [18], [20], cellular automata model [5], [46], lattice gas model [38], [48], discrete choice model [1], agent-based model [41], and game theoretic model [4], [29]. As a kind of highly complex living organisms, the behaviors of a pedestrian are jointly determined by personal internal consciousness and external environments. It is difficult to propose a mathematic model describing and predicting a pedestrian’s behaviors accurately, especially given the complex interactions with surrounding environments.
The environmental effect is a critical factor in modeling of pedestrian dynamics, and it varies significantly over time and space. Researchers in various disciplines have made tremendous efforts to specify the stimuli of surrounding environments, including pedestrians, groups, obstacles, exits and so on, on pedestrian dynamic behaviors from different perspectives. The level of environmental stimuli is specified as physical force [18], [20], floor field [5], [46], drift (bias) [38], [48], utility [1], and payoff [4], [29] for quantitative evaluation of environmental factors in the previous studies. For example, Helbing et al. [18], [20] modeled the effects of surrounding pedestrians and walls as interaction forces which shows a negative exponential decline with distances. In mathematical terms, the change of pedestrian’s states is given by a classical Newtonian mechanics equation with precise environmental information such as distances, speeds, and directions. Schadschneider et al. [5], [46] introduced the concept of a floor field which is modified by the presence of pedestrians and obstacles. This allows the cellular automation model to take interactions between pedestrians and the geometry of the system into account in a unified and simple way. The floor field modifies the transition probabilities in such a way that a motion into the direction of larger fields is preferred. Antonini et al. [1] adopted the concept of ‘utility’ borrowed from economics to quantify the interactions between the decision maker and the other pedestrians in the scene as well as the dynamic aspects of the decision maker itself. The utility values of alternatives are then transformed into probabilities and each pedestrian’s movement is randomly selected according to these probabilities.
From a review of previous work, we noticed that these microscopic models are presented based on the promise that precise values of the complex interactions with surrounding environments such as speeds, directions and distances can be used in real time. The environmental effects on a pedestrian’s behaviors are evaluated quantitatively based on these precise environmental data. Actually, the information got from environments is perception-based information rather than measurement-based information in most situation. It is difficult to quantify the size of environmental stimuli in real-life scenarios because a pedestrian’s perceptions in a specific environment vary from one individual to another, and they are subjective in nature. Individuals have diverse perceptions when they are confronted with environmental interactions, and they may react subjectively to similar situations [14], [23], [43], [64]. Moreover, the inter-relationship between pedestrian’s dynamical behavior and pedestrian’s perception toward the surrounding environment is rarely considered in previous studies. The perception-based information is often neglected in this area of researches. As such, the urgency underlying the current study is to develop a useful model which can make full use of perception-based information and capture the relationship between the environmental design and the pedestrian’s perception.
To meet these goals, we employ a fuzzy logic approach in this study. The theory of fuzzy logic systems, inspired by the remarkable human capability, possesses the capability of operating on and reasoning with perception-based information [62], [63], [64]. Consider the intrinsic limitations of humans’ cognitive abilities for distinguishing detail and storing information, pedestrian’s perceptions toward surrounding environments are usually represented by natural language, which are inherently vague and imprecise. A fuzzy logic approach, compared with other methods, is highly robust in coping with the uncertainty and imprecision that are inherent in perception information. It also provides a scientific approach for the management of pervasive reality of fuzziness and vagueness in human cognition [63]. In addition, fuzzy logic also has the ability to utilize human experience and knowledge and imitate human thought processes [32]. For example, the near obstacle has a greater impact on the obstacle-avoiding behavior than the far. Using the fuzzy logic framework, the processes of pedestrian’s reasoning and decision making can be formulated by a set of simple and intuitive fuzzy rules, coupled with advantages of accessible input information and easily understandable output [62].
The novelty of this study is the proposing of the fuzzy logic based pedestrian model, which can incorporate efficiently human experience and knowledge and pedestrian’s perceptions toward surrounding environments into the modeling process. The main contribution of this paper are briefly summarized as follows: (i) A fuzzy logic-based microscopic pedestrian model is proposed to simulate pedestrian dynamic behaviors. The model differs from other models in that it can take full advantage of human experience and knowledge and perceptual information obtained from interaction with surrounding environments, which are widely available and extremely useful, and often neglected in this area of researches. (ii) The effects of complex interactions with surrounding environments on pedestrian dynamics are considered qualitatively during the modeling process. The model describes different influences affecting individual pedestrian motions by a few simple fuzzy logic rules. The local obstacle-avoiding behavior, regional path-searching behavior and global goal-seeking behavior are modeled as fuzzy inference systems with predefined input and output variables. These behaviors are adopted to guide pedestrians to avoid the front obstacles, select the lowest negative energy path, and move in direction of their goals, respectively. At each step, the decisions of turning angle and movement speed are determined by the integration of intermediate results of three behaviors with the weighted average method. (iii) Weighting’s assignment principles are designed to adjust weighting factors of three behaviors automatically rather than assign arbitrary fixed values in advance. This enables a pedestrian to avoid potential conflicts and make reasonable decisions in complex situations. (iv) The characteristics of three common crowd organization forms, i.e. crowd evacuation, unidirectional and bidirectional pedestrian flows, are investigated by using the fuzzy logic model. Self-organization phenomena, including ‘arching and clogging’, ‘faster-is-slower effect’ and ‘lane formation’, are reproduced by simulations of the proposed model. The fundamental diagrams of speed-density and density-flow are also investigated in a quantitative way. It is expected to be useful to the exit and hallway design of buildings. (v) The effects of walking habits on the traffic efficiency of bidirectional pedestrian flows are also performed.
The organization of this paper is as follows: Section 2 provides an overview of related works. In Section 3, the architecture of the proposed fuzzy logic model is presented. The detailed implementation methods of the local obstacle-avoiding behavior, regional path-searching behavior, global goal-seeking behavior, and weighting’s assignment principle are described in this section; The validation and simulation of the proposed model are discussed in Section 4; Finally, Section 5 concludes the paper with remarks for future works.
Section snippets
Background of microscopic pedestrian behavior models
Over the years, researchers have constructed various microscopic models to approximate and simulate pedestrian dynamical behaviors in normal and panic scenarios. Examples of microscopic models are the social force model [18], [20], [51], cellular automata model [5], [13], [46], lattice gas model [38], [48], discrete choice model [1], [30], agent-based model [41], and game theoretic model [4], [29], which have been proposed to investigate characteristics of crowd evacuation, bidirectional
Model description
In this section, we first introduce a method of representation of physical space which plays a central role in the modeling and simulations. Then, we present the architecture and elements of the fuzzy logic-based pedestrian model. Pedestrian dynamic behaviors are determined by integration of local obstacle-avoiding behavior, regional path-searching behavior and global goal-seeking behavior with mutable weighting factors at three different scopes. Three elementary behaviors and the weighting’s
Simulations and results
Once the fuzzy logic-based pedestrian model has been established, we can use it to predict pedestrian dynamics and then discover crowd’s characteristic features and collective phenomena in different scenarios. But before that, the effectiveness of the proposed model must be validated. General methods used to validate the pedestrian models include the computer simulations and controllable real experiments. For the computer simulations, a commonly used strategy is to compare with the well-known
Conclusion
The main contribution of this paper is the proposing of a new model for pedestrian dynamical behaviors by using a fuzzy logic approach. First, a pedestrian’s visual field is divided into five sectors by radial-based discretization method. The decisions of turning angle and movement speed of each step are made by integration of the intermediate results of local obstacle-avoiding behavior, regional path-searching behavior and global goal-seek behavior with mutable weighting factors. The weighting
Acknowledgments
This work is supported by National Natural Science Foundation of China (No. 61322307 and No. 61233001).
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