A Study of Mobile Robot Motion Planning ■I HI IN D u b l in C ity U n iv e r s it y Ollscoil Chathair Bhaile Atha Cliath By Bang Wang B. Sc., M. Sc. A Dissertation Presented in Fulfilment of the Requirements for the Ph. D. Degree Supervisors Prof. Michael Ryan Mr. Charlie Daly School of Computer Applications December 1994 Declaration I hereby certify that this material, which I submit for assessment on the programme of study leading to the award of Ph. D. degree in Computer Applications, is entirely my own work and lias not been taken from the work of others save and to the extent that such work is cited and acknowledged within the text of my work. Date: / Bang Wang Acknowledgements I would like to express my heartfelt gratitude to my supervisors: Prof. Michael Ryan and Mr. Charlie Daly whose help, supervision and guidance were invaluable during my period of study. I would also like to express my gratitude to Dr. Michael Scott for his proof reading of this thesis and for his invaluable comments and suggestions. I would also like to thank Dr. Alan Smeaton, Dr. Heather Ruskin, Dr. James Power for their help whilst I was studying in the School of Computer Applications. Sincere thanks are also expressed to the technicians of the School, Mr. Jim Doyle and Mr. Eamonn McGonigle, for all their invaluable help they gave me. I would also like to thank all my fellow postgraduate students at the School, but I would like to especially mention Gary Leeson, Barry O’Connell, Micheal Padden, Colmdn McSweeney, Donal Murray, who helped me understand Ireland, improve my English, and provided much needed support over the last couple of years. I would also like to thank my good friend, Dr. Jun Yan, for his guidance to this research. Without his suggestions and ideas, I would not have been able to complete this thesis. Finally, I would like to extend my gratitude to the School of Computer Applications for its financial and other support given to me, and which has given me the opportunity to learn and experience Western (especially Irish) culture. A Study of Mobile Robot Motion Planning Bang Wang B. Sc., M. Sc. Abstracts This thesis studies motion planning for mobile robots in various environments. The basic tools for the research are the configuration space and the visibility graph. A new approach is developed which generates a smoothed minimum time path. The difference between this and the Minimum Time Path at Visibility Node (MTPVN) is that there is more clearance between the robot and the obstacles, and so it is safer. The accessibility graph plays an important role in motion planning for a massless mobile robot in dynamic environments. It can generate a minimum time motion in 0(n2»log(n)) computation time, where n is the number of vertices of all the polygonal obstacles. If the robot is not considered to be massless (that is, it requires time to accelerate), the space time approach becomes a 3D problem which requires exponential time and memory. A new approach is presented here based on the improved accessibility polygon and improved accessibility graph, which generates a minimum time motion for a mobile robot with mass in O((n+k)2»log(n+k)) time, where n is the number of vertices of the obstacles and k is the number of obstacles. Since k is much less than n, so the computation time for this approach is almost the same as the accessibility graph approach. The accessibility graph approach is extended to solve motion planning for robots in three dimensional environments. The three dimensional accessibility graph is constructed based on the concept of the accessibility polyhedron. Based on the properties of minimum time motion, an approach is proposed to search the three dimensional accessibility graph to generate the minimum time motion. Motion planning in binary image representation environment is also studied. Fuzzy logic based digital image processing has been studied. The concept of Fuzzy Principal Index Of Area Coverage (PIOAC) is proposed to recognise and match objects in consecutive images. Experiments show that PIOAC is useful in recognising objects. The visibility graph of a binary image representation environment is very inefficient, so the approach usually used to plan the motion for such an environment is the quadtree approach. In this research, polygonizing an obstacle is proposed. The approaches developed for various environments can be used to solve the motion planning problem without any modification. A simulation system is designed to simulate the approaches. Table of Contents 1. Introduction .......................................................................................................................1 1.1 The Basic Problem of Motion Planning............................................................................. 2 1.2 Motion Planning Environments........................................................................................... 4 1.3 Classification of Motion Planning........................................................................................5 1.4 Scope of the Thesis.................................................................................................................. 7 2. L i t e r a t u r e R e v i e w .....................................................................................................................9 2.1 Introduction..............................................................................................................................9 2.2 Geometrical Planning....................... 10 2.2.1 Configuration Space..................................................................................................................11 2.2.2 Visibility Graph.........................................................................................................................12 2.2.3 Voronoi Diagram Approach.................................................................................................... 16 2.2.4 Freeway Approach.................................................................................................................... 17 2.2.5 Potential Field Function Approach................................................................................. 19 2.2.6 Exact Cell Decomposition Approach..................................................................................... 23 2.2.7 Approximate Cell Decomposition Approach........................................................................25 2.3 Dynamic Planning...................................................................................................... 27 2.4 Motion Planning in Dynamic Environments...................................................................28 2.4.1 Hardness Results....................................................................................................................... 28 2.4.2 Space Time Approach.............................................................................................................. 29 2.4.3 Divide and Conquer Strategy...................................................... 38 2.4.4 Accessibility graph....................................................................................................................39 2.4.5 Collision Avoidance with Moving Obstacles........................................................................41 2.4.6 Collision Detection Among Moving Objects................................................... 42 2.5 Fuzzy Logic M ethods............................................................................................................43 2.5.1 Fuzzy Logic Methods for Mobile Robots Navigation....................................................... 43 2,5.2 Fuzzy Logic Methods for Digital Image Processing.........................................................45 2.6 Neural Networks for Mobile Robots Navigation...........................................................45 2.7 Summary.................................................................... 47 3. S h o r t e s t P a t h P l a n n i n g .............................................................................................. 50 3.1 Introduction............................................................................................................................ 50 3.2 Configuration Space..............................................................................................................51 3.2.1 Definition of Configuration Space.................. 51 3.2.2 Obstacles in Configuration Space......................................................................................53 3.3 Visibility Graph..................................................................................................................... 58 3.3.1 Definition of the Visibility Graph......................................................................................58 3.3.2 Graph Search Algorithms...................................................... .......60 3.3.3 Acceleration of Graph Search............................................................................................(SI 3.3.4 Smoothing the Path............................................................................................................ 66 4. M in im u m T im e P a t h P l a n n i n g ...................................................................................73 4.1 Introduction............................... 73 4.2 Dynamic Planning.................................................................................................................74 4.2.1 Mathematical