OPTIMAL PATH PLANNING ALGORITHMS IN VIRTUAL ENVIRONMENTS ROHAYANTI HASSAN UNIVERSITI TEKNOLOGI MALAYSIA

Transcription

1 OPTIMAL PATH PLANNING ALGORITHMS IN VIRTUAL ENVIRONMENTS ROHAYANTI HASSAN UNIVERSITI TEKNOLOGI MALAYSIA

2 OPTIMAL PATH PLANNING ALGORITHMS IN VIRTUAL ENVIRONMENTS ROHAYANTI HASSAN A thesis submitted in fulfilment of the requirements for the award of the degree of Master of Science (Computer Science) Faculty of Computer Science and Information System Universiti Teknologi Malaysia MAY 2006

3 Dedicated to my beloved Father, Mother, Brothers, Sisters, Abang and Teachers iii

4 iv ACKNOWLEDGEMENT All praise unto Allah for everything I have. I would like to thank the following persons who accompanied me during the time that I was working for this degree. Indeed, I am greatly indebted to my supervisor, Dr. Muhammad Shafie Abd. Latiff. I wish to thank him, who provided guidance, advice and support till the end of glorious successful work. My greatest acknowledgement is to my beloved mak and abah also to all my lovely brothers and sister. Thanks for their support and deep love. Not forgetting to abang, thank you so much on your truly patience and understanding. Special thanks to all the colleagues and friends at Universiti Teknologi Malaysia. Their support in providing insights, ideas and help made the thesis possible. Finally, the financial support by Ministry of Technology and Innovation is gratefully acknowledged.

5 v ABSTRACT Path planning algorithm is a common algorithm applied in many fields of research specifically in robotic, games and Virtual Environments (VEs). Meanwhile, VE is a cutting edge technology that can add realistic visualization of a real world. Interaction within a VE requires animated characters to participate in such a way that they are able to navigate as well as plan the tour. Normally, in a large virtual exhibition area, a visitor tours to multiple sites before reaching the final destination. This may lead to several problems such as collision with obstacles, time-consuming journey, inefficient searching process and high utilization of computer memory. The main aim of the research was to find an efficient route tour approach that combines path finding, path planning and path optimization algorithm. In relation to that, A* algorithm was used as a path finding technique to plan a collision-free-path journey from one location to another. A* algorithm was also incorporated with Cell Mapping technique to speed up the searching process. In addition, Extended Prim algorithm was applied to shorten the travelling time and a virtual exhibition area was used as a domain to execute and analyse the algorithms performances. The results show that the Extended Prim algorithm has succeeded in reducing the travelling time up to 60 percent. Furthermore, the results also revealed that the searching process and computer memory utilization significantly improved up to 22 percent and 55 percent, respectively. It was also found that the combination of A* algorithm and Cell Mapping technique can be applied to a wide range of VE s sizes.

6 vi ABSTRAK Algoritma perancangan laluan merupakan satu algoritma yang sering menjadi tumpuan bidang penyelidikan khususnya di dalam bidang robotik, permainan video dan persekitaran maya. Manakala, persekitaran maya pula adalah satu bidang teknologi terkini yang berupaya mentransformasikan dunia sebenar ke dalam bentuk visual. Di dalam persekitaran maya, lazimnya karakter animasi haruslah berupaya untuk merancang dan menentu arah laluan. Lazimnya, bagi persekitaran pameran maya berskala besar, pelawat akan mengunjungi banyak lokasi sebelum tiba ke destinasi yang terakhir. Situasi sedemikian akan mewujudkan beberapa masalah dalam perancangan laluan seperti perlanggaran dengan halangan, masa perjalanan yang panjang, diikuti dengan carian laluan yang tidak efisien dan penggunaan memori komputer yang tinggi. Justeru, penyelidikan ini bertujuan untuk mencari satu pendekatan carian perjalanan yang efisien dengan menggabungkan teknik pencarian laluan, perancangan laluan dan pengoptimuman laluan. Lanjutan daripada itu, algoritma A* dan teknik Cell Mapping telah digabungkan bagi meningkatkan prestasi carian. Manakala algoritma Extended Prim telah digunakan untuk menyelesaikan masalah pengoptimuman laluan dengan mengurangkan masa perjalanan. Persekitaran pameran maya telah dijadikan sebagai kes kajian bagi melaksana dan menguji algoritma ini. Hasil kajian membuktikan bahawa algoritma Extended Prim berjaya meminimakan masa perjalanan dengan pengurangan masa sebanyak 60 peratus. Manakala teknik Cell Mapping telah berjaya mengurangkan masa carian dan penggunaan memori komputer, masing-masing sebanyak 22 dan 55 peratus. Hasil kajian juga menunjukkan bahawa gabungan algoritma A* dan teknik Cell Mapping dapat diimplemen terhadap sebarang saiz persekitaran maya.

7 vii TABLE OF CONTENTS CHAPTER TITLE PAGE DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENT LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS iii iv v vi vii xi xiv xix 1 INTRODUCTION 1.1 Introduction Research Overview Motivation Statement of the problem Main goal Objectives Scope of the research Contribution of the study Thesis outline 8

8 viii 2 A REVIEW OF OPTIMUM PATH PLANNING 2.1 Introduction Optimum Path Planning in Virtual Environment Path Planning in Various Application, Related Problem and It s Current Method Environment geometry Limited Memory Real time performance Environment dynamic Optimum Path Planning Techniques Greedy algorithm Prim algorithm Genetic algorithm Other algorithm Navigating in Large Virtual Environment Summary 31 3 METHODOLOGY 3.1 Introduction Research Framework Phase 1: Literature Review Phase 2: Domain Development Phase 3: Model Development Phase 4: Implementation and Validation Summary 42 4 OPTIMAL PATH PLANNING MODEL 4.1 Introduction System Architecture of Virtual Optimal Tour 44

9 ix 4.3 Optimal Path Planning Path Searching Engine Discretisation of Environment Floor 47 Map Generation of obstacle nodes Cell Mapping Searching the path using A* 54 algorithm Character simulation: Directive Method Path Tour Engine Summary 62 5 EXPERIMENTAL RESULTS AND ANALYSIS OF EXTENDED PRIM 5.1 Introduction Extended Prim to Optimize Path Tour The Effect of Number of Nodes in Path Tour Position of Crowds in Optimum Path Tour Optimum Path Tour According to Room-order 79 Mode 5.5 Summary 81 6 EXPERIMENTAL RESULTS AND ANALYSIS OF CELL MAPPING TECHNIQUE 6.1 Introduction Utilization of Searching Area Experimental Analysis: Optimization Path Searching using Normal A* versus A* with Cell Mapping Technique 92

10 x 6.4 Experimental Analysis of Finding the Best Scale of 95 Cell Mapping A* with 60x60 Cell Mapping versus A* with x100 Cell Mapping in Virtual Exhibition A* with 60x60 Cell Mapping versus A* with x100 Cell Mapping in Virtual Exhibition Experimental Analysis of Finding the Best Scale of 105 Cell Mapping in Term of Increase Number of Path A* with 60x60 Cell Mapping versus A* with x100 Cell Mapping in Virtual Exhibition A* with 60x60 Cell Mapping versus A* with x100 Cell Mapping in Virtual Exhibition Summary CONCLUSION 114 REFERENCES

11 xi LIST OF TABLES TABLE NO. TITLE PAGE 2.1 Path Planning across Various Applications, Related 14 Problem and its Current Issue 2.2 Optimum Path Planning across Various Applications, Related Problem and its Current Issue Research of navigating in a large virtual environment The direction / velocity conversion table Table of weights containing path length of six nodes. Pick N1 as the first node to visit Percentage of reduction using Extended Prim algorithm over Prim algorithm in term of time Percentage of reduction using Extended Prim algorithm over Prim algorithm in term of path length Classification to determine the intermediate points 88

12 xii 6.2(a) Percentage of reduction using A* with 60x60 Cell Mapping over Normal A* of number of expanded nodes (b) Percentage of reduction using A* with 60x60 Cell Mapping over Normal A* in term of searching time (a) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 in term of expanded nodes (b) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 in term of searching time (a) Percentage of reduction using between A* with 60x60 Cell Mapping and using A* with 100x100 Cell Mapping over Normal A* in VE 2 in term of expanded nodes (b) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 2 in term of searching time (a) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 in term of expanded nodes (b) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 in term of searching time 108

13 xiii 6.6(a) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 2 in term of expanded nodes (b) Percentage of reduction using between A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 2 in term of searching time (a) Percentage of reduction between using A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 and VE 2 in term of expanded nodes (b) Percentage of reduction between using A* with 60x60 Cell Mapping and A* with 100x100 Cell Mapping over Normal A* in VE 1 and VE 2 in term of searching time 112

14 xiv LIST OF FIGURES FIGURE NO. TITLE PAGE 2.1 Star Trek: Armada Games (Davis, 2000) Runtime algorithm (Salomon et al., 2003) Algorithm of exploration paths (Andujar et al., 2004) D route planner configuration, (Al-Hassan and Vachtsevanos, 2002) Routes for two cases (Al-Hassan and Vachtsevanos, 2002) Research framework (a) Virtual Exhibition (b) Virtual Exhibition Examples of Object s data in Virtual Exhibition 2, room 3 38

15 xv 3.4 System Architecture of Virtual Optimal Tour Algorithm Testing and validation phase System architecture of virtual optimal tour User s input console Location of nodes to visit Optimal path planning configuration Framework for path searching engine (a) The discretisation space of floor map in Virtual Exhibition (b) The discretisation space of floor map in Virtual Exhibition (a) The search process between Nstart and Ndestination using 150x100 matrixes (red box) (b) The search process between Nstart and Ndestination using a small scale matrix and several stages Example of next node selection using Prim Example of next node selection using Extended Prim Animated character begin the tour at N1 67

16 xvi 5.2 Optimal path tour using Prim algorithm Optimal path tour using Extended Prim The effect of different number of nodes to visit in term of time The effect of different number of nodes to visit in term of path length The generated path tour as the number of nodes to visit increase Optimal path tour using Extended Prim with parameter crowd concern Path length performance with crowd and no crowd concern Optimal path tour using Extended Prim according to room order mode Path length performance according to room-order mode and none room-order mode Path searching using A* with no Cell Mapping technique Path searching using A* with Cell Mapping technique The structure of PreNodes_buffer Cell Mapping A* versus Normal A* in VE

17 xvii 6.5(a) Comparison result using Cell Mapping A* versus Normal A* in term of number of expanded nodes (b) Comparison result using Cell Mapping A* versus Normal A* in term of searching time A* with 60x60 Cell Mapping versus A* with100x100 Cell Mapping in VE (a) Comparison result using A* with 60x60 Cell Mapping versus A* with 100x100 Cell Mapping in term of number of expanded nodes in VE (b) Comparison result using A* with 60x60 Cell Mapping versus A* with 100x100 Cell Mapping in term of searching time in VE A path tour connecting six nodes using normal A* in Virtual Exhibition A* with 60x60 Cell Mapping versus A* with100x100 Cell Mapping in Virtual Exhibition (a) Comparison result using A* with 60x60 Cell Mapping versus A* with 100x100 Cell Mapping in term of number of expanded nodes in VE (b) Comparison result using A* with 60x60 Cell Mapping versus A* with 100x100 Cell Mapping in term of searching time in VE Path tour of six nodes in Virtual Exhibition 1 105

18 xviii 6.12 Path tour of ten nodes in Virtual Exhibition Path tour of fifteen nodes in Virtual Exhibition (a) Comparison result of path tour between six, ten and fifteen nodes in term of number of expanded nodes in Virtual Exhibition (b) Comparison result of path tour between six, ten and fifteen nodes in term of searching time in Virtual Exhibition Path tour of six nodes in Virtual Exhibition Path tour of ten nodes in Virtual Exhibition Path tour of fifteen nodes in Virtual Exhibition (a) Comparison result of path tour between six, ten and fifteen nodes in term of number of expanded nodes in Virtual Exhibition (b) Comparison result of path tour between six, ten and fifteen nodes in term of searching time in Virtual Exhibition Path from N6 to N5 searched using A* with 60x60 Cell Mapping versus A* with 100x100 Cell Mapping Path from N2 to N1 searched using Normal A* versus A* with 100x100 Cell Mapping 114

19 xix LIST OF ABBREVIATIONS AGV - Automated Guided Vehicles TSP - Traveling Salesman Problem PRM - Probabilistic Roadmap IDA* - Iterative Deepening A* BSP - Binary Space Partitioning RTS - Real Time Strategy SNA* - Synchronous Admissible A* GA - Genetic Algorithm MST - Minimum Spanning Tree BIP - Broadcast Incremental Power NP - Non Determine Problem

20 CHAPTER 1 INTRODUCTION 1.1 Introduction This chapter describes the organisation of whole thesis. The thesis emphasizes an optimal path planning algorithm for Virtual Environment. The optimal path planning algorithm is required in Virtual Environment to solve the wayfinding problems during navigation in Virtual Environment domain or virtual world. Section 1.2 discusses the motivation inspired this research. Section 1.3 lists the research problems. Section 1.4 states the research main goal, whereas Section 1.5 clarifies the research objectives. Meanwhile, Section 1.6 lists the research scope to restrict the research objectives. Section 1.7 discusses the contribution of this research and finally Section 1.8 gives a brief outline of this thesis. 1.2 Research Overview Path is a line on route along which something travels or moves. In between, path planning is the art of deciding the route to take, based on expressed in terms of

21 2 the current internal representation of the terrain. On one hand, path finding is the execution of this theoretical route, by translating the plan from the internal representation in terms of physical movement in an entity space. In the field of virtual environment or computer animation, path planning is an algorithm to find the path of motion. Path planning is also used to control motion. This research defines path planning as a deriving path to be taken by animated character from source to the destination by implementing some mathematical calculations or algorithms. Furthermore, an optimum path is a sequential path or known as path tour that meet several optimality criteria. Meanwhile, Virtual Environment has been identified as a technology to visualize an event and environment. Virtual Environment can be applied in various applications and described realistic visualization such as virtual museums, virtual stores as well as virtual exhibition. Virtual Environment is defined as a representation of actual world in three dimensional graphical worlds. It may consist of three main components i.e. space, crowd and movement or navigation. Many classical Artificial Intelligent (AI) planning problems involve navigation. Navigation may simply described as moving around the world, planning the routes, reaching desired destinations without bumping into things and so forth. Besides, navigation may consist of locomotion and way finding. Locomotion simply involves moving towards landmarks that are visible within the space, whereas way finding is the ability to plan efficient routes, find specific locations and recognize the destination when reaches (Darken and Sibert, 1996). Usually, interaction within a VE specifically in virtual exhibition area requires users to participate in such a way that, they are able to navigate as well as plan the tour. Thus, path planning is essential technique to optimize navigation in VE. The optimal tour may be defined as the generated paths that connect all desired destinations not only in a shortest distance but satisfy appropriate optimality criteria. Therefore, this research is aimed at integrating a path finding, path planning and path optimization algorithm to produce an efficient route tour for navigation of animated character in VE. The result is performed in simulation event and executed in virtual exhibition area.

22 3 The requirement of planning the optimal tour or navigation is obvious especially in complex environments such as a building with multiple floors and rooms as well as battlefields with a lot of obstacles and crowd. There are a lot of issues to produce an optimal route tour. The first one is to search the minimal path from one location to another location. On the other hand, for a workspace cluttered with obstacles, the real distance between two locations is actually the length of a collision-free path, and this information is not known prior to the search process. The path is generated using search algorithm. This thesis describes how the A* algorithm is used to compute the path where animated character is guided to reach the desired destination. The A* algorithm is chosen due to its heuristic admissibility guarantee to produce the best path if such path exist. Furthermore, the visit involves touring more than one site and another challenge is to generate an optimal traversing sequence through the user-specifies locations of interest. When there are several locations to traverse, the problem of determining an optimal traversing sequence involves the classical Travelling Salesman Problem (TSP), which is known as Nondetermine Problem (NP) - complete. For this reason, optimization is required and this thesis applies Prim algorithm as a solution. As the virtual world become larger, it will contain more objects and may entail problematical and complex searching algorithm. The algorithm searching area has to be synchronized to the size of the virtual world. A larger and dense searching area affects the searching performance, in term of high memory consumption. Therefore this thesis introduces Cell Mapping technique to enhance the searching algorithm to make it more flexible and to adapt in various layout as well as large scale VE. Inspired from above problems, a proper and effective route plan is essential for moving through the virtual world. As a solution, this thesis proposes the optimal path planner. The output of this path planner is a list of direction that will be converted into a motion for animated character. A directive method has been adopted as a technique to convert the motion animation. Initial conversion is in 2D motion. The users can simply identify the points or destinations they wish to visit

23 4 and the animated character will automatically guide them walking through the desired destinations. The rest of path generation is hidden from the user. In this thesis, several virtual exhibition areas have been developed as a domain for simulating the navigation of animated character. 1.3 Motivation One of the motivational factors inspired to further this research is a path planning as a core component in most game and virtual reality industry. As game and virtual reality become a commercially growing fast and a billion-dollar industry, a realistically gaming experience and visually interesting movement are important features to compete in market. Most of related applications adopt artificial intelligence techniques in path planning to produce the best route for the game character to move from starting point to the goal destination. Moreover motion planning algorithm is implemented in sophisticated camera techniques and realistic characters and objects features. It has also been used for designing better user interfaces and providing better navigation techniques specifically in VE. Furthermore, the importance of security in building design has been expressed by Atlas (1989). Generating different patterns of optimal paths will help the designer as well as the evaluator to design and evaluate the building structure in terms of security. The spatial design of a building affects the movement of occupants. In complex buildings with a large population, such as places of assembly, the movement of people towards the exits under emergency situations is a major concern. Traditionally the layout design is governed by the building fire codes. However, the building fire codes merely govern the design of the capacity of individual components, and do not guarantee that smooth egress will occur. Full-scale egress exercises may be needed to examine the layout arrangement in order to understand the layout problem. However, such exercises may be time-consuming, or may be impossible when the building has yet to be constructed. Therefore, a computer simulation or virtual environment technology

24 5 can be used to overcome these weaknesses to simulate the egress pattern, and also can assist building designer and facility manager to plan the optimum spatial arrangement as well as to manage the crowd flow during emergency situations. On the other hand, in many areas of manufacturing such as machine layout, motion planning and mechatronics, the requirement for an optimum path is evident. The optimal path planning has an impact in improving efficiency and throughput such as PCB assembly. For example, system based on free range robots has indicated that a robot which is able to move along the optimum path saves energy and yields higher output. A similar requirement for optimum path planning exists in the electronic industry in the printed circuit board (PCB) assembly process. PCB assembly consists of placing electronics devices on a board to create a bigger component. Time reduction which leads to an increase in production depends very much, whether in improving quality or productivity, on the sequence of component insertions. 1.4 Statement of The Problem The main problem of this study is to produce the optimal route tour that satisfies the optimum cost for animated character travelling in large VE. Followed by this problem, the following questions have to be satisfied. i) How to plan a collision free path in VE? ii) What are the parameters that satisfy an optimum cost of route tour? iii) How to simulate the animated character to follow the route tour? iv) How to apply a small-scale algorithm into a large-scale environment?

25 6 1.5 Main Goal The main goal of this research is to produce an efficient optimal path planning algorithm in large Virtual Environment. 1.6 The Objective The objectives of this research are as follows: i. To analyse current path finding, path planning and optimisation algorithm which accommodate in virtual environment. ii. To generate the best path from one location to another location without colliding with obstacles in the environment. iii. To produce the optimal tour path that traverses all desired locations. iv. To produce a solution in applying a small-scale optimal path planning algorithm into a large scale of virtual environment. 1.7 Scope of the research The research includes the following areas: i. This research implements Prim algorithm to optimize the route tour. Moreover the research mostly concentrates on shortest distance and

26 7 mode in selection the node sequence as parameters concern to produce an optimal route tour. ii. A* algorithm is implemented to generate the collision free path and executed in offline mode. iii. Cell mapping technique is used to enhance the small-scale searching algorithm in order to be applied into any expandable virtual world. iv. The directive method is used to convert generated optimal route tour into a list of direction in order to move and simulate the animated character. 1.8 Contribution of The Study The research produces several contributions. Generally, the research proposes an optimal path planning algorithm which is a hybrid technique between Extended Prim algorithm and A* algorithm with Cell Mapping technique. This hybrid algorithm is used to solve path optimisation problem in any scale of VE. The contributions of this research are as follows: i. The Extended Prim algorithm as an optimisation algorithm has reduced the number of iterations in producing an optimal sequence of nodes. Therefore, Extended Prim algorithm has shortened the travel time. ii. Furthermore, the research has merged A* algorithm with Cell Mapping technique which using windowing search concept to produce an efficient and adaptive searching algorithm that can accommodate its implementation into a flexible large-scale VE. The

27 8 Cell Mapping technique has maintained the search window matrix in a small scale. Hence the search process becomes efficient when the domain of searching area becomes larger. iii. A* algorithm with Cell Mapping technique has reduced the number of expanded nodes to increase the usage of computer memory. iv. A* algorithm with Cell Mapping technique has also reduced the searching time. 1.9 Thesis Outline This section presents how this thesis is organized in different chapters. Chapter 2 presents a critical review of the literature related to the topic area of path planning in virtual environment. It discusses related problems arise with current methods and solutions. Within the path planning, it includes the discussion on how to produce an optimal path in a larger virtual environment. Chapter 3 is the wide description of research methodology, which provides a rich discussion about the flow of this research that how actually this research has been divided into different phases and how the operational and experimental work has been carried out. Chapter 4 presents the overall Model of Optimal Path Planner. The purpose and function of every process or module in the model is described in detail. Chapter 5 demonstrates the implementation and experimental analysis of optimization in path touring. It includes the discussion and summary of the results finding using this new algorithm. Meanwhile, Chapter 6 presents the Cell Mapping technique to accompany A* algorithm in searching the path. This chapter discusses this new technique is capable to improve the path searching in term of lower number of expanded nodes and searching time. Finally, Chapter 7 concludes the thesis by proposing future work and the possibility for the enhancement of knowledge in the field of virtual environments, computer animation and all related field.