by Chiu, Kit Chau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 90-92). / Abstracts in English and Chinese. / ABSTRACT --- p.02 / 摘要 --- p.04 / ACKNOWLEDGEMENTS --- p.06 / TABLE OF CONTENTS --- p.07 / LIST OF FIGURES --- p.10 / LIST OF TABLES --- p.12 / Chapter 1 --- INTRODUCTION --- p.13 / Chapter 1.1 --- Application with formation flying --- p.14 / Chapter 1.2 --- Previous work --- p.16 / Chapter 1.3 --- The present work --- p.18 / Chapter 1.4 --- Thesis outline --- p.19 / Chapter 2 --- OPTIMIZATION IN DESIRED TRAJECTORY --- p.21 / Chapter 2.1 --- Problem formulation --- p.21 / Chapter 2.1.1 --- System model --- p.21 / Chapter 2.1.2 --- System constraints --- p.22 / Chapter 2.1.3 --- Cost function of the system --- p.23 / Chapter 2.2 --- Reformation as optimal control problem --- p.23 / Chapter 2.2.1 --- Polynomial form for input --- p.24 / Chapter 2.2.2 --- Problem simplification --- p.26 / Chapter 2.3 --- Numerical case studies --- p.27 / Chapter 2.3.1 --- Case study 2-1: Equal weightings in all units and directions --- p.27 / Chapter 2.3.2 --- Case study 2-2: Equal weightings in all directions but different weightings in control units --- p.30 / Chapter 2.3.3 --- Case 2-3: Different weightings in x-y-z directions but equal weightings in all control units --- p.33 / Chapter 2.4 --- Chapter summary --- p.35 / Chapter 3 --- OBSTACLE AVOIDANCE --- p.36 / Chapter 3.1 --- Additions of obstacle constraints --- p.36 / Chapter 3.2 --- Simulation case studies --- p.37 / Chapter 3.2.1 --- Case study 3-1: No obstacle --- p.38 / Chapter 3.2.2 --- Case study 3-2: Single obstacles --- p.40 / Chapter 3.2.3 --- Case study 3-3: Two obstacles --- p.42 / Chapter 3.2.4 --- Case study 3-4: Two obstacles and optimal velocity --- p.48 / Chapter 3.3 --- Chapter summary --- p.51 / Chapter 4 --- FUZZY INTERACTIVE FORCE BETWEEN ELEMENTS --- p.52 / Chapter 4.1 --- Region of repulsive force --- p.52 / Chapter 4.2 --- Region of attractive force --- p.53 / Chapter 4.3 --- Beyond the attractive region --- p.53 / Chapter 4.4 --- Interactive force as function of separation --- p.54 / Chapter 4.5 --- Fuzzy mapping --- p.55 / Chapter 4.6 --- Chapter summary --- p.58 / Chapter 5 --- VIRTUAL LEADER --- p.59 / Chapter 5.1 --- Virtual leader --- p.59 / Chapter 5.2 --- Two maneuverable elements and two virtual leaders --- p.60 / Chapter 5.3 --- Rotational Trajectories for the two virtual leaders --- p.61 / Chapter 5.4 --- Chapter summary --- p.65 / Chapter 6 --- OPIMIZATION BY INTERACTIVE FORCE --- p.66 / Chapter 6.1 --- Narrow channel passage --- p.66 / Chapter 6.2 --- Interactive forces --- p.68 / Chapter 6.3 --- Definition of interactive force --- p.69 / Chapter 6.4 --- Formulation as optimization problem --- p.71 / Chapter 6.4.1 --- Parameterization of f1 and f2 --- p.71 / Chapter 6.4.2 --- Reformulated optimization problem --- p.73 / Chapter 6.5 --- Simulation results --- p.74 / Chapter 6.6 --- Chapter summary --- p.77 / Chapter 7 --- MODIFICATION IN OBSTACLE --- p.78 / Chapter 7.1 --- Modification for interactive force --- p.78 / Chapter 7.2 --- Modification in obstacle description --- p.79 / Chapter 7.3 --- """Shortest distance"" between control unit and obstacle" --- p.80 / Chapter 7.4 --- Simulation case studies --- p.81 / Chapter 7.4.1 --- Case study 7-1: Single triangular obstacle --- p.81 / Chapter 7.4.2 --- Case study 7-2: Two triangular obstacles --- p.83 / Chapter 7.5 --- Chapter summary --- p.85 / Chapter 8 --- Conclusions and future works --- p.86 / Chapter 8.1 --- Conclusions --- p.86 / Chapter 8.2 --- Future works --- p.88 / Chapter 8.2.1 --- Fuzzy mapping --- p.88 / Chapter 8.2.2 --- Intrinsic parameters and properties --- p.89 / BIBLIOGRAPHY --- p.90