Distributed Reactive Collision Avoidance - University of Washington

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University of Washington Abstract Distributed Reactive Collision Avoidance Emmett Lalish Chair of the Supervisory Committee: Professor Kristi A. Morgansen Aeronautics and Astronautics Collision avoidance is an important aspect of multivehicle coordination because it prevents vehicles from disrupting or destroying each other. The work contained in this dissertation concerns a novel approach to the n-vehicle collision avoidance problem. The vehicle model used here allows for three-dimensional movement and represents a wide range of vehicles. The algorithm works in conjunction with any desired controller to guarantee all vehicles remain free of collisions while attempting to follow their desired control. This algorithm is reactive and distributed, making it well-suited for real-time applications, and explicitly accounts for actuation limits. A robustness analysis is presented which provides a means to account for delays and unmodeled dynamics. Robustness to an adversarial vehicle is also presented.
TABLE OF CONTENTS Page List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Chapter 1: Introduction to Collision Avoidance . . . . . . . . . . . . . . . . . . 1 1.1 Definitions of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Introduction to DRCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter 2: Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter 3: Conflicts and Collisions . . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 4: DRCA Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.1 Deconfliction Maneuvers . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1.1 Constant-Speed Maneuver . . . . . . . . . . . . . . . . . . . . . . 25 4.1.2 Variable-Speed Maneuver . . . . . . . . . . . . . . . . . . . . . . 29 4.1.3 Heuristic Performance . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2 Deconfliction Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2.1 Control Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2.2 Guarantee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.3 Priority . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.4 Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2.5 Liveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Chapter 5: Robustness Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.1 Robust Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 Robust Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 i
Page 1 and 2: Distributed Reactive Collision Avoi
Page 3: In presenting this dissertation in
Page 7 and 8: LIST OF FIGURES Figure Number Page
Page 9 and 10: ACKNOWLEDGMENTS The author wishes t
Page 11 and 12: 1 Chapter 1 INTRODUCTION TO COLLISI
Page 13 and 14: 3 system state as time goes to infi
Page 15 and 16: 5 imum speed. The constant-speed un
Page 17 and 18: 7 in [12], where the rates of chang
Page 19 and 20: 9 hybrid system that describes each
Page 21 and 22: 11 at first to be the holy grail of
Page 23 and 24: 13 Chapter 2 PROBLEM STATEMENT The
Page 25 and 26: 15 ⎡ ⎤ ⎡ ⎤ r sˆt d ⎢ s
Page 27 and 28: 17 Chapter 3 CONFLICTS AND COLLISIO
Page 29 and 30: 19 where t is the time to closest a
Page 31 and 32: 21 Enter Desired Control Deconflict
Page 33 and 34: 23 must know a bound on the maximum
Page 35 and 36: 25 Figure 4.2: Example optimization
Page 37 and 38: 27 cone is enlarged from (3.9) to (
Page 39 and 40: 29 Theorem 2. For vehicle i of an n
Page 41 and 42: 31 Figure 4.4: Example optimization
Page 43 and 44: 33 Theorem 3. For vehicle i of an n
Page 45 and 46: 35 fashion. The goal then is to hav
Page 47 and 48: 37 v ĩ v e p t,ijˆt i v j p n,ij
Page 49 and 50: 39 Figure 4.8: Example of the contr
Page 51 and 52: 41 Because of the symmetry of the p
Page 53 and 54: 43 also ensures that there is a nei
Page 55 and 56:
45 to adjust their trajectories to
Page 57 and 58:
47 controllers. The goal of these c
Page 59 and 60:
49 of a complex multiplicative unce
Page 61 and 62:
51 Proof. A multiplicative uncertai
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53 u 1 u 2 θ γ v 2,max v 1,max Fi
Page 65 and 66:
55 speed (m/s) (a) 0.5 0.4 0.3 0.2
Page 67 and 68:
57 un (m/s 2 ) 0.2 0 (a) -0.2 0 5 1
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59 10 8 ‖˜r‖ − dsep (m) 6 4
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61 ‖˜r‖ − dsep (m) 4 2 0 (a)
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63 Table 6.1: Comparison of computa
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65 be stabilized with any of a vari
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67 the heuristic performance will b
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69 Chapter 7 CONCLUSION The primary
Page 81 and 82:
71 system of projecting everything
Page 83 and 84:
73 [11] G. Fasano, D. Accardo, and
Page 85 and 86:
75 [34] R. Skjetne, S. Moi, and T.
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Distributed Reactive Collision Avoidance - University of Washington

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