Simulation of Agent Movement with a Path Finding Feature Based on Modification of Physical Force Approach

Transcription

1 Simulation of Agent Movement with a Path Finding Feature Based on Modification of Physical Force Approach NURULAQILLA KHAMIS Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia, Jalan Semarak, Kuala Lumpur, MALAYSIA aqillakhamis@gmail.com HAZLINA SELAMAT Centre for Artificial Intelligence and Robotics, Universiti Teknologi Malaysia, Jalan Semarak, Kuala Lumpur, MALAYSIA hazlina@fke.utm.my RUBIYAH YUSOF Centre for Artificial Intelligence and Robotics, Universiti Teknologi Malaysia, Jalan Semarak, Kuala Lumpur, MALAYSIA rubiyah.kl@utm.my Abstract: Crowd modeling is the study of crowd behaviours and has been used by, for example, safety engineers and architectural designers in assessing crowd movements in buildings under normal and emergency situations. However, many existing crowd models neglect how agents in the crowd explore the environment to find the most suitable or optimal path towards their destinations. Therefore, the main purpose of this study is to present an agent-based crowd modeling approach by combining the social force model and the magnetic model that include detailed features of each agent. The agent-based model will be integrated with a path finding algorithm, the Dijkstra Algorithm, for optimal path selection towards the target destinations. Simulation results demonstrate that the proposed approach can perform plausible crowd movement in the simulated environment under normal situations. Key-Words: Agent based, physical force approach, path finding 1 Introduction Crowd modeling has attracted a tremendous research interest especially in computer graphics, animation, robotics and urban or building planning areas. In crowd modeling, the entities in the crowd, also known as agents, are embedded with certain levels of intelligence to interact and react with the simulated environment in order to imitate human movement. In computer graphics and animation research, crowd models are designed for gaming or movies. In [1], human perception to the surrounding, activities and actions are imitated. On the other hand, in [2], crowd modeling is used in urban or building planning as an important tool for architectural engineers and designers, as well as safety engineers to study crowd behaviour to assist or revitalize the design and crowd management plans before implementation. In developing crowd models, the type of modeling approach that suits the modeling objective must be considered. In order to represent the agent movement in the simulated model, various types of crowd models have been developed both at the macroscopic and microscopic levels. In the macroscopic approach, agents in the crowd are treated homogeneously by omitting individual internal and external characteristics such as the speeds, masses and positions. The objective is to study and analyze the flow of the crowd as been done in [3] [4]. Therefore, the macroscopic approach is more suitable in modeling large crowds, and including individual agent behaviors to interact in the simulated environment will require high computational demand, which may affect the simulation runtime performance. Meanwhile, the microscopic approach focuses on the heterogeneous character of agents in the crowd. Modelers are able to assign different levels of agent granularity details such as specified speeds, current positions, destinations, agent gazing angles etc. More intelligent or smart agent can be produced using this approach. Two types of microscopic models commonly used in crowd modeling are the cellular-based [5] and physical force-based [6][7] models. One of the cellular-based models, known as Cellular Automata (CA), has been introduced by [5] in 1999 and used in [8], [9] and [10]. Its runtime performance is indicated in discrete time, as the agent movements are represented such that the ISBN:

2 agents are hopping from one state, represented in grid, to another using a specific transition rule [5]. Although the implementation of CA model is simple and fast, scant agent interaction can be detailed out by using this model and rough agent movement can be visualized. In the physical force model, the movement of agents and the interactions between agents are based on the summation of resultant forces. This model have inspired many works, such as in [6], [11] and [12], for its capability to produce a collective type of crowd behaviors in crowd dynamics. In Helbing s work in [7], the model developed based on this approach is successful in representing crowd interaction and behavior during a panic situation such as arching and clogging [2, 7, 13] by including additional forces: a body force counteracting body compression and sliding friction force. Many researchers have applied this model to study the behavior and escape time of crowd for evacuation, emergency or panic situations [13]. This approach has also successfully simulated plausible agent movements in a panic situation. However, limited agents characteristic was included in this model, with the movement of agents being treated as particles without considering agent navigation and decision-making. The simulation performances alson gave no guarantee that the agents will not overlap with each other. In this paper, an agent-based crowd model with a modified physical force approach integrated with a path finding algorithm is proposed. The model considers only movement of the crowd in a normal situation. In Section 2, the development of agent model with a navigation or path-finding feature is described. Section 3 gives the comparative results between the proposed and existing models. Finally, the conclusions and future works are explained in the last section in this paper. 2 Agent Modeling In developing the model for agent s movement based on the physical force approach, this work is categorized into 2 stages: the basic agent movement model development in Stage 1 and the integration of a path finding features in Stage Agent Movement Model The agent s dynamics will be represented using the Newton s Second Law shown in Eq. (1), as introduced in [7]. Based on Eq. (1), the movement of the agent is influenced by three main forces, as shown in Eq. (2). These forces are the motivation force for the agent to move towards its target destination (, the interaction force with the other agent and obstacle ( and, respectively). in Eq. (2) is given as where, is the mass of the agent, is its desired speed in the direction, obtained by normalizing the vector agent position with the destination point. is the current speed adapted, at time,. According to Helbing s work in [7], the interaction force to repulse another agent,, in Eq. (2) is represented as where and represent large constants, denotes the distance difference between agent and in specified position, and. is the normalized vector point between the agents. The agents will touch each other if their distance, is smaller than the sum of agent body radius,. If the agents touch each other, Helbing has included additional forces, which are the body force counteracting body compression and the slide friction force. These additional two forces will represent agent s movement with a pushing behavior when modeling a crowd in panic or emergency situations. The interaction of an agent with an obstacle,, is treated analogously. The mathematical equations for the agent s repulsion force with the obstacle are given as (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) ISBN:

3 where denotes the distance between agent, with the obstacle, is the normalized direction perpendicular to the obstacle. From Helbing s model (also known as the Social Force model), a modifications in the interaction forces between agents,, and obstacle,, has been made. This proposed model includes a more specific agent characteristic, as given in Table 1, and conditions for the agent to repulse according to its surrounding. Helbing s work only considers the distance between an agent with other agents and obstacles before exerting the repulsion force but by including more detailed information on the agent s physical characteristics, a more realistic and natural agent movement can be performed. Table 1: Agent characteristic Characteristics Parameters Position Random distributed Mass, 50 kg (can varies) Walk speed Body Radius, Field of View, Comfort Area, Distance to repulse, Figure 1: Agent distance definition (from top view) By using the modified force model given in Eqs. (11) to (13), the conditions for the agent to repulse other agents or obstacles are defined. This includes its Field of View (FoV) and the agent s distance to repulse as given in Table 1 and depicted in Fig. 2. The agent will repulse if other agents are within the FoV,, and distance to repulse, x, i.e. in the region labeled 1 in Fig. 2. If the other agents are outside this region, i.e. they are in the region labeled 2 in Fig. 2, no repulsion force will be exerted ( = 0) as this is the region that an agent normally ignores other agents. for In this paper, the following mathematical model is proposed: (11) (12) (13) where, and are the social mass for agents i and j respectively. k is the repulsion constant. In this work, the interaction social mass for each agent is defined as unity since the initial assumption to prove the model operation is similar to the original social force model. From Eq. (11), represents the distance between agents, as depicted in Fig. 1. Figure 2: Agent operation to repulse On the other hand, the interaction force of an agent with an obstacle,, is given by Eq. (14). (14) (15) (16) where represents a constant value between the agent and the obstacle, is the distance between the agent position, and obstacle point,. is the normalize vector perpendicular between the agent and the obstacle. The condition for agent to perform repulsion force from obstacles is similar to that of the condition to repulse from other agents, described previously. Whilst Helbing s work in [7] ISBN:

4 is useful in simulating movements of agents in panic situations, it is rather complex. For normal situations, the proposed model is much simpler and since more physical characteristics of the agents are included in the model, the agents will perform more realistic and natural agent movements. 2.2 Path Finding The path finding algorithm integrated in the model described in Section 2.2 is the Dijkstra Algorithm. This algorithm [14] aims to find the shortest path from an origin to a destination by performing simple nodes calculations in all directions. The starting point (or node), called the initial node, is first assigned. For example, in Fig. 3, the initial node assigned is A. Another node, called the target node, B, is also assigned, as well as the distance values from the initial node and its neighbourhood. The number in each circle represents the node. The purpose of including this feature in the agent movement model is to guide an agent to navigate and move with optimal path towards the desired destination with a capability to evade other agents and obstacles at the same time. This ensures that the agent moves in a straight line from their current position towards the target destination without being impeded by other agents or obstacles. It also guarantees that the agent will bypass these agents or obstacles in the shortest path in its waypoints towards the target destination, as shown in an example in Fig. 5 where the black circle and the red star represent the agent and target destination respectively. Figure 5: (Left) agent without obstacle, (right) agent with obstacle Figure 3: Node assign The distances between the nodes are represented by numbers on the interconnecting lines, as shown in Fig. 4. In order to move from node A to B via the shortest path, the distance between each node from A will be calculated and the shortest distance will be chosen. From Fig. 4, the selected route is from node 1 to 6 via node 3. The chosen nodes will be marked as visited node and this visited node will not be checked again. 3 Simulation Results Matlab has been used to simulate the agent s movement. The simulated environment used in the simulation work is as shown in Fig. 6. There were 5 agents located at one side of an area with an obstacle that has a small opening. All the agents were to move towards a specified destination through the small opening on the right of the obstacle. The agents walk in a normal situation and try to reach their desired speed if there is no others agents/obstacle impede their pathways. By using the same physical parameters of the agents and experimental setting, comparisons are made between the Social Force model (given in Eqs. 2, 4 and 8) and the proposed model (given in Eqs. 2, 11 and 14) that also include the repulsion condition for each agent and the path finding feature using the Djikstra Algorithm. Figure 4: Nodes and distances ISBN:

5 Figure 6: Experiment setting Fig. 7 and Fig. 8 show the trajectories of all the agents from their initial positions towards the target destination using the original Social Force model and the proposed model respectively. By comparing the agents trajectories in Fig. 7 and Fig. 8, it can be observed that the proposed model produced smoother trajectories compared to the Social Force model. Agents in the proposed model imitate the behavior of human better in the sense that they repulse before being in contact with other agents. This is because the proposed model includes a specific condition to repulse whereas the Social Force model treat each agent as a particle that only start to repulse when the agent make a body contact with other agents, which gives a better representation of a crowd in a panic or emergency situation where this kind of contacts is unavoidable. However, in a normal situation, the proposed model gives a better representation of human movements. When the time taken by the agents to reach their destinations are compared, Table 2 shows that 60% of the agents in the proposed model take shorter time to reach the destination compared to those in the Social Force model. This may be caused by the optimal path finding features that have been integrated in the proposed model. Table 2: Time taken to reach destination Agent Original Social Modified Force Model, (s) Model (s) Agent Agent Agent Agent Agent Figure 7: Agents trajectory original model These comparisons show that our proposed model is successful in simulating a more realistic and smooth agent trajectory compared to the original model. Figure 8: Agents trajectory modified model 4 Conclusions and Future Works The paper compares two agent movement models based on the physical force approach. A modification of the original Social Force model has been proposed. The modified model include a repulsion condition and a path finding feature for the agent that also allows more physical characteristics of the agent to be included for a more realistic simulation of agent movement. The comparison between the original Social Force model and modified version has been made. Simulation results show that proposed model is capable of producing a more realistic and smooth agent trajectory. The agents also take shorter duration to reach the target destination. ISBN:

6 Future work will include social interaction of agents moving in a group. By including this factor into the model, more complex agent dynamic can be analyzed. References: [1] D. Terzopoulos, Artificial life for computer graphics, Commun.ACM, Vol. 42, no. 8, pp , Aug [2] N. Waldu, P. Gattermann, H. Knoflacher, and M. Schreckenberg, Pedestrian and evacuation dynamics Springer Verlag, [3] S. Chenney, Flow tiles, in Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation. Eurographic Association, 2004, pp [4] T.M. Kisko, R. Francis and C. Nobel, Evacnet4 users guide, University of Florida, [5] V. J Blue and J.L Adler, Cellular automata microsimulation of bidirectional pedestrian flows, Transportation Research Record: Journal of the Transportation Research Board, Vol. 1678, no. 1, pp , [6] S. Okazaki and S. Matsushita, A study of simulation model for pedestrian movement with evacuation and queuing, in International Conference on Engineering for Crowd Safety, 1993, pp [7] D. Helbing, I. Farkas and T. Vicsek, Simulating dynamical features of escape panic, Nature, Vol. 407, no. 6803, pp , [8] Z. Zarita and E. A. Lim, Refined cellular automata model for tawaf simulation, [9] Y.-C. Peng and C.-I.Chou, Simulation of pedestrian flow through a t-intersection: A multi floor field cellular automata approach, Computer Physics Communications, Vol. 182, no. 1, pp , [10] P. Shao, A more realistic simulation of pedestrian based on cellular automata, in Open-source Software for Scientific Computation (OSSC), 2009 IEEE International Workshop on. IEEE, 2009, pp [11] M. Moussaid, N. Perozo, S. Garnier, D. Helbing and G. Theraulaz, The walking behaviour of pedestrian social groups and its impact on crowd dynamics, PloS one, Vol. 5, no. 4, p. e10047, [12] K. Teknomo, Microscopic pedestrian flow characteristics: Development of an image processing data collection and simulation model, Diss. Tohoku Univ, [13] S. Zhou, D. Chen, W. Cai, L. Luo, M. Y. H. Low, F. Tian, V. S. H. Tay, D. W. S. Ong and B. D. Hamilton, Crowd modelling and simulation technologies, ACM Transactions on Modeling and Computer Simulation (TOMACS), Vol. 20, no. 4, p. 20, [14] M. Sniedovich, Dijkstra algorithm revisited: the dynamic programming connexion, Control and cybernetics, Vol. 35, no. 3, p. 599, ISBN: