Real-time Crowd Movement On Large Scale Terrains

Transcription

1 Real-time Crowd Movement On Large Scale Terrains Wen Tang, Tao Ruan Wan* and Sanket Patel School of Computing and Mathematics, University of Teesside, Middlesbrough, United Kingdom *Department of Electronic Imaging and Media Communications, University of Bradford, Bradford, United Kingdom Figure 1: The movement of large crowds on large scale terrains can be generated using the integrated simulation framework. Abstract Crowds are described as complex adaptive systems in Artificial Intelligence. The generation of crowd in real-time simulations is beyond the manual design capability. In this paper, we present an integrated animation framework for simulating the adaptive movement behaviours of crowds on large terrains. A simulation system that is developed based on the framework can be used as a powerful animation and design tool to produce realistic crowd movements procedurally. The framework integrates efficient terrain rendering techniques and path planning algorithms to enable the simulation system to handle large terrain data sets and search optimal paths for crowds to progress on complex terrains. A novel local alignment algorithm is developed, which utilises a set of conventional behavioural rules to produce robust realtime coordinated motions of crowds with respect to environmental situations. Key words: autonomous virtual agents, procedure animation, real-time crowd simulation. 1. Introduction Described as complex adaptive systems in general AI studies, crowd of humans or animals presents intricate manner and adapts its immediate environmental situation instinctively. A simulation system that produces believable simulations of crowds in a realistic virtual environment can be a powerful complementary verification tool to create the realisation of the apparently complex adaptive behaviours of crowds. At the same time, the system also provides means for computer animation design since simulating large crowd behaviours is beyond the animator s manual design capability. Interactive simulations are important to many computer graphics applications, for example computer games. Crowd simulation involves many different aspects of computer graphics, such as visual representations and behaviour models of the crowd. One of the common unsolved tasks is to simulate the coordinated movement of a large crowd with respect to complex dynamic environments, involving not only the additional rendering cost, but also the position update

2 and collision detection test for the crowd. Real-time simulations for interactive systems, for example for computer games or collaborative virtual environments in the work place, would impose extra constraints to further complicate the process. In this paper we present a feasible virtual reality simulation framework that can handle the movements of crowds on large terrains in real time. The crowds are not only capable of performing a given motion task, but also can deal with new environmental situations profoundly on their own. Our simulation framework integrates real-time path planning algorithm to search optimal collision free paths for the crowds to progress on large complex terrains. A dynamic LOD data structure is used in order to render the terrains efficiently [2]. A rule-based system with spatial data structure is employed for locality queries and more importantly a novel local alignment algorithm is developed to produce realistic coordinated motion of crowds with ability to alter the motion state of each agent according to the immediate local environment. Given a large terrain in a 3D virtual environment and large crowds, the method produces robust simulations. Over 1,000 agents as simple graphics representations can be generated in real-time, while hundreds of agents represented as detailed mesh model of virtual characters can also be handled. The next section of the paper reviews related work in crowd simulation. In section three, we describe the implementations of terrain rendering algorithms. Crowd behaviour modelling based on our new local alignment algorithm and real-time path planning algorithms are presented in section four. Behavioural rules are presented in section five. The subsequent section shows simulation results. Finally, in section seven, we conclude the paper and present discussions on future work. 2. Related work Coordinated movements of a large crowd are best procedurally generated [1]. Procedure modelling techniques free animators from the need to specify every detail of each virtual agent s motion manually and allow the agent to determine its own actions extemporaneously. Grouped together by a large number of individuals and each of them maintaining its own motion state with the rest of the group accordingly, a crowd can be generally treated as a micro-structure system i.e. particle system [2]. Each of the particles in the crowd detects its environment and reacts intelligently. Depending on the fundamental algorithms used within a computer simulation system to describe the particles physical movements, different behavioural patterns can be exhibited by the crowd. As a whole, the combined behaviour of each individual in the crowd is a complex parallel-distributed system. Dynamic fluid models for simulating crowds are popular approaches used in Civil Engineering [3] [4]. Focused on motion flow descriptions, the fluid models may be sound from an engineering perspective, but computationally expensive and lack the descriptions of the behaviour characteristics of crowds. In computer graphics community, Reynolds proposed an approach that utilises simple rules that every micro-structure/agent/particle in the crowd has to follow [1]. This approach has been regarded as rule based simulation method and generated some interesting computer animations [5] for Hollywood feature films. Rules can be quite different depending on simulation tasks. Rule-based behaviour animation techniques can be used effectively to model the coordinated movements of a large crowd. In addition to behaviour rules, the movement of each agent in a large crowd has to be collision free with respect to the environment and to other nearby agents. Recently, real-time visualisation of densely populated urban environments has been reported [6]. A simple and fast collision detection algorithm is developed to handle the movements of virtual humans in an urban environment [6]. The method uses a look-up table with heights which can be used for preventing the virtual humans from colliding with buildings. The look-up table is also used for adjusting and determining the elevation of the virtual humans on the model without having to query the geometrical database. Our simulation is also produced by using a terrain height lookup table for determining and adjusting the elevation of virtual agents on the terrain surface. On the other hand, path searching and planning are needed for a crowd to navigate on large terrains. Our system utilises a spatial data structure to store the topology information of the large terrains for efficient locality queries. In addition to the data structures, a novel local alignment algorithm is developed for altering the motion behaviours of each agent according to its immediate local environment. According to the changes of the immediate local terrain topology, a crowd is expected to reorganise its motion behaviours accordingly. In order to manoeuvre through various environmental situations, a large crowd has to use the most optimal course which would lead the least energy cost for each agent in the crowd. It is evident that rendering for real-time crowd simulation becomes one of the major issues. We employ a binary tree data structure for real-time terrain generation [7] [8] [9]. Therefore, we are able to construct and render large complex terrains with continuous level of details by traversing through the binary triangle tree data structure. The integrated framework provides efficient and feasible methods for interactive crowd simulation.

3 3. Generation of large terrains with BSP tree data structure Terrain is generated based on information extracted from a height-map, and then converted to a polygon mesh. Starting with a user defined size, the terrain is constructed by splitting the initial square structure into adjacent triangles with various sizes to represent terrain details. Triangles of different sizes are stored into binary tree data structure to represent various levels of details. The height of the terrain at a particular point is obtained by converting the grey scale value of the corresponding position on the height map. For a local area in a terrain, the more rumple it is, the more triangles are needed for its representation. During the simulation process, the terrain topology can be updated and continuously optimised according to camera movement and required graphics display frame rate There are basically two types of terrain image maps: the actual height map for the terrain and the terrain type map, for example green represents grass, yellow represents rock and blue as water. Figure 2 demonstrates a terrain example generated by our system and its wire frame representation. The top image of Figure 2 shows a terrain with mountain covered by snow at the high ground while low ground and flat areas are green with grass. A wire-framed representation is shown in the bottom image of Figure 2 to demonstrate that different level of details of the triangle mesh structures are used to construct the environment. Bigger and less detailed meshes are used for far distant mountain while finer meshes are for the areas closer to camera or more rumple ground. Since optimisation on terrain rendering would save necessary processes later on AI implementations, the terrain data has been further partitioned using an Octtree data structure. This data structure is a separate data structure to the binary triangle tree data structure and is used for detecting the camera position. Each of the tree nodes has a bounding box to be computed against view frustum for optimised view frustum culling. This second level rendering optimisation enables very high rendering frame rate at average of 60 FPS with a single object doing A* searching on the terrain. Simulating a crowd moving over a large terrain is basically a position update process which determines and adjusts the elevation of every agent of the crowd on the surface of the terrain and coordinates the movements of the agent groups in a cost effective way. In this case, the navigation problem has been reduced from six degrees of freedom to three. Calculating the contact points on the terrain for the agents by using collision detection algorithms can be a quite straightforward task, however this can be expensive and inefficient for interactive applications. A flat terrain surface with a constant altitude would make collision detection task trivial, but it lacks of realism. Although a terrain model specifies a surface in 3D space, it is essentially a 2D array of elevation data in nature due to the use of 2D terrain height maps. Any point located at (x,z) on the terrain map can be found by a lookup table referencing the 2D height map to find its height value. We simply implement a simulation solution by keeping the agents always above the ground using this simple intersection tests. 4 Coordinated movements of crowds and path planning 4.1 Path planning Figure 2. A terrain example generated by our system Navigating a large crowd on complex terrains means planning optimal paths for the crowd. Given a goal, agents of a crowd should be moving toward the goal in a cost effective way as we do in reality. Such movements

4 deliver a sense of intelligence. Many actions could be taken when agents are navigating on a large complex terrain, for example, avoiding rivers, high mountains, and rough ground etc. The instinct reactions of the agents to their environment would make crowd simulations believable and realistic. At a global level, a modified A* path planning algorithm is used for searching an obstacle free path with the least cost for the agents from a starting point to the goal point. In order to find an optimal path as quickly as precisely as possible, a general A* algorithm normally works on fine defined lattices that cove the region of the algorithm searches for. The grid-system will be based upon points distributed with linear distances in a square format. Each point will have a maximum of eight neighbouring points as shown in Figure 3. Arrows indicate the search directions. If one particular point is deactivated then connection to the point direction is made invalid (the dark shaded cell), for example in a case where there is an obstacle or at a point on the terrain is too high to make an economic movement or in contrast, the point is under a water level. The simulation framework takes advantage of the grid nature of the terrain height map which suits well for the A* algorithm to perform. Details of the A* algorithms are described the reference [10]. Two node lists are created representing the map locations and costs. One is called OPEN list and another set called CLOSED. Each time through the main loop, the program selects the best element from OPEN, which is the node with the lowest cost, and then looks at its neighbours. The searched node is put into the CLOSE set, and the program then put any unvisited neighbours into the OPEN set. The cost of a node is the sum of the current cost of walking from the start to that node and the heuristic estimation of the cost from the node to the goal. The bottom image of Figure 3 demonstrates an A* search example. For a specific large terrain, a grid mesh that has the same size as the terrain is attached to the terrain mesh. The grids consist of all the areas in which the agents can move into. We can design a highly optimised grid according to the need of a specific simulation to cover only minimal amount of polygons or otherwise to encode the grid with more polygon details in order to produce more accurate agent movements. Grid points of areas which are covered by water or at high ground are deactivated as shown in Figure 4, so that search connections to these areas are invalid, therefore restricting the movements of the agents in a predefined process. Figure 4: Grid points representing the areas covered by water or high ground are restricted areas for agent movements. Figure 3: An A* grid with an agent current position (the dot) and its eight neighbouring cells (shaded area) and an A* search example 4.2 A local alignment algorithm for movement adjustments Figure 5: A group of agents following a searched path. A path found by the A* algorithm, indicated as the line in Figure 5, is assigned to a selected leader of a crowd, and rest of the members of the crowd following the leader s action based on a set of behaviour rules. A set of sub-goals shown as boxes along the path, are

5 assigned at a threshold distance along the entire path. The inserted subgoals are used to speed up the simulations since not only the path searching algorithm can work progressively to achieve real-time search procedure, but also as agents need to manoeuvre through different terrain situations, sub-goals allow the assessment of the immediate local situation of the agents to be carried out. A balance between the efficiency and accuracy of the algorithm has to be taken into account. Too many subgoals could slow down the decision making process as the program performs local alignment calculations around each subgoal. In contrast, few subgoals would lead erroneous or unrealistic movements of the crowd. Each subgoal is a vector of small magnitude. The x- and z- local axis at the vertex of the subgoal defines a tangent plane of the terrain surface at the subgoal. We define a height limit threshold that is considered to be too energy inefficient for the agents to move into. The local alignment algorithm is designed to scan a circular area around the subgoal covered by the tangent plane and compare the magnitude of the vector. The magnitude of the scanning vector will be increased at each iteration step until it finds the height that is equal or greater than the height limit threshold. Depending on the area that is available to accommodate the agent group to move into, the agents in the crowd will need to recoordinate and adjust their positions and movements. For example, during the navigation the crowd encounters a narrow valley along the path, this happens when the magnitude of the subgoal vector in the opposite direction is equal or smaller than the current direction vector as shown in Figure 6, the agents in the crowd will need to re-coordinate their positions and movements in order to pass the valley. On the other hand, navigating on an open field, the agents of the crowd will occupy a larger area than when they were passing through a narrow valley Figure 6: Displacement of subgoals Motion coordinations of crowds are implemented by using a set of simple navigation rules. Agents are constrained by the rules to move around the centre of the sub-goals along the path. 5. Group Behaviour Modelling 5.1 Behaviour rules A set of simple navigation rules that each agent in the crowd has to follow is defined as the follows: Separation Steering to avoid collision by maintaining a certain separation distance from other agents in its proximity. Alignment Steering towards the average heading of local group members. Each agent aligns itself with other agents in its immediate proximity. Cohesion Steering toward the average position of local group members. An agent groups together with other agents in its immediate proximity Avoidance Steering to move away from local obstacles or enemies. Agents steer away from obstacles and avoid collisions within their immediate proximity. 5.2 Locality query The most troublesome source of computational effort for crowd simulations is the cost of locality queries between agents for collision avoidance. Although simple rules are implemented to guide the agents movement, locality queries of a spatially explicit multi-agent system have an asymptotic complexity of o(n 2 ), when each agent has to detect every other agent in the group. A spatial data structure known as quad-tree has been used to sort the agents in crowds to accelerate locality queries. The agents are pre-sorted based on their location in space, so that the rule-based system can quickly find which agents are in a given neighbourhood without having to examine every agent in the entire population of the crowd. Each of the agents maintains its own proximity around its sub-goal. When an agent within a group passes through one sub-goal to another, one more rule is added to change the movement of the agent by moving it with a desired velocity soon after it enters into the proximity of the next sub-goal, therefore, the agent group navigates dynamically. As shown in Figure 7, running cross a narrow valley, a huge crowd will decrease the distances between agents within the crowd and slow its velocity down, so that each agent checks its goal next to the current goal, if the radius of the tangent of the next goal is smaller then the current then it

6 reduces its speed and decreases it s distance to a threshold. A 2D grid of the same size as the height field map is used to create cells with a unique cell value for each of the cells across the map. During the simulation, the locality query is performed by a function, which identifies all of the cells and examines each of the agents in each of these cells. The cells consist of a single pointer to a double linked list of proxy objects, which contains the x and z coordinates of a location, and a pointer to the agent. Given a minimum separation distance and a maximum density, the number of agents within a given area is bounded. Therefore using spatial subdivision techniques, the locality query problem has been accelerated from o(n 2 ) to o(nk), where n is the total number of agents and k is the bound. 6. Simulation results and discussions Figure 7 demonstrates a number of screen snapshots of the crowd simulation: Figure7a shows two groups of agents with 350 agents in each of the groups at 63 FPS simulation frame rate on an open ground. Spatial subdivision in the crowd would increase the simulation frame rate 16 times faster than the native o(n 2 ) locality query implementation. At the beginning of the simulation, agents are distributed into cells based on their initial positions. A grid of size consisting of 4096 cells is used. As shown in the following table, rendering speed is depending on many factors such as the number of obstacles placed in the environment and the complexity of the terrain structures. When avoiding obstacles and crossing narrow valleys, the agents in the crowds have to readjust their positions and speed. Figure 7b shows 1,000 agents avoiding a single obstacle, in this case, the frame rate is reduced from 20 FPS (frame /second) to 13 FPS. As shown in Figure 7 c, with 1,000 agents crossing a narrow valley, the frame rate is further reduced to 9 FPS. The following Table shows a real-time profile of the simulation system, which demonstrates the average, minimum, and maximum percentage of a frame rate spent on each process. Table : Simulation Profile Average Minimum Maximum Name FPS OpenGL display function Render terrain Render obstacles Render agents Statistic text rendering Update agent Over 50 % of the processing power has been spent on graphics rendering, while the second process overhead is the update of the agents movement behaviours. Rendering agents using detailed character models will add considerable process overhead to the system so do the animations of the model, as shown in Figure 1, two examples of crowd simulation generated by our simulation system. The virtual characters shown on the left image of Figure 1 are represented by using single mesh character models with textures and the two groups of agents shown on the right image of Figure 1 are rendered as mesh model without textures..simulating coordinated motions of 700 agents rendered as animated humanoid models would result a 2 FPS simulation frame rate, which is much slower compared with simple graphics representations i.e. boxes. This has indicated that new graphical representation methods are needed for real-time large crowd simulation. Another candidate solution is the animated billboards, which is essentially an image-based rendering technique. An image-based rendering method for visualising crowds in real-time has been reported recently, which renders the agents as animated impostors [11]. We will test this method and adapt it into our system. 7. Conclusion Producing realistic and robust results of crowd simulation in real-time is always a challenging task. The simulation framework described in this paper is able to simulate coordinated movement of large crowds on complex terrains with the desired frame rate. The steering behaviours listed above are implemented as simple FSMs (Final State Machines), which perform state transitions and maintain the knowledge information about herding of each agent in a crowd. The dynamic level of detail of the terrain enabled a nature integration of path planning algorithm that has been implemented here. Dynamic relocating obstacles at run time will cause the navigation path to be recalculated, this can be achieved in two ways :one is to temporarily remove the A* node at the position of the obstacles hence the search algorithm would consider the node and a small region around it is inaccessible, the second way is simply to allocate very high cost values for the nodes beneath the obstacles to cause the movements to the areas too expensive to the agents. Our novel local alignment

7 algorithm that allows agents to handle their immediate environmental situation enables the simulation more realistic. Implementing rule-based AI system for simulations of these kinds is reasonably straightforward. However, when adding more complex behaviours, well planned and designed object-orientated data structures will greatly optimise the system performance. As described in the previous sections, it is problematic to simulate large numbers of agents in complex virtual environments. Communications between the agents and the agents groups can be also included into the simulation. There is a need for further research work in this area. References [1] Reynolds, C. W. (1987) Flocks, Herds, and Schools: A Distributed Behavioural Model, in Computer Graphics, 21(4) (SIGGRAPH '87 Conference Proceedings) pages [2] W. T. Reeves, Particle Systems - A Technique for Modeling a Class of Fuzzy Objects, Computer Graphics, vol. 17, no. 3, pp , [3] Ford, L. R and Fulkerson, D.R, Flows in Network, Princeton University Press, Princeton [4] Fukui, M and Ishibashi, Y, (1999) Self-organized Phase Transitions in CA-models for Pedestrians, J. Phys. Soc. Japan, 8: , 1999 [5] Batman Returns, (feature film) Director: Tim Burton, Producer: Warner Brothers. 1992: [6] F. Tecchia and Y.Chrysanthou, Real-time Visualisation of Densely Populated Urban Environments: a Simple and Fast Algorithm for Collision Detection, Eurographics UK, Swansee, April [7] H. Hoppe. View-dependent refinement of progressive meshes, In SIGGRAPH 97 Conference Proceeding, August 1997.pp [8] W.T Reeves, Approximate and Probabilistic Algorithms for Shading and Rendering Structured Particle Systems, Computer Graphics, vol. 19, no. 3, pp , [9] P. Lindstrom, D. Koller, W. Ribarsky, N. Faust, and G. A. Turner, Real-time Continuous Level of Detial Rendering of Height Fields. In SIGGRAPH 96 Conference Proceedings, pp , August [10] Game programming gems 2, edited by Mark A. DeLoura. Hingham, Mass: Charles River Media, August [11] F. Tecchia, C. Loscos and Y. Chrysanthou. Image- Based Crowd Rendering. IEEE Computer Graphics and Applications, volume 22, number 2, March-April 2002.

8 (a) (b) (c ) Figure 7: Simulation screen snapshots: a): two agent groups with 350 members in each of the groups moving towards the same goal. b). 1,000 agents moving with obstacle avoidance. c). 1,000 agents moving pass narrow valley.