Distributed Reactive Collision Avoidance - University of Washington

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Chapter 6: Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.1 Variable Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.2 Preferential Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 6.3 Three-dimensional Avoidance . . . . . . . . . . . . . . . . . . . . . . . . 58 6.4 Heuristic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.5 Computational Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.6 Formations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 6.7 Comparison to an SGT Algorithm . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 ii
LIST OF FIGURES Figure Number Page 1.1 Air traffic control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.1 Geometric definition of the collision cone. . . . . . . . . . . . . . . . . . . 18 4.1 Flow chart of the DRCA algorithm. . . . . . . . . . . . . . . . . . . . . . 21 4.2 Example optimization of a constant-speed maneuver. . . . . . . . . . . . . 25 4.3 Example of an infeasible constant-speed maneuver problem. . . . . . . . . 30 4.4 Example optimization of a variable-speed maneuver. . . . . . . . . . . . . 31 4.5 Example of an infeasible variable-speed maneuver problem. . . . . . . . . 34 4.6 Block diagram of the deconfliction maintenance controller. . . . . . . . . . 36 4.7 Geometry of the conflict measures p t and p n . . . . . . . . . . . . . . . . . 37 4.8 Example of the control function, F . . . . . . . . . . . . . . . . . . . . . . 39 5.1 Geometry of worst case adversary . . . . . . . . . . . . . . . . . . . . . . 53 6.1 Five vehicle simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.2 Excess separation of vehicles in Fig. 6.1. . . . . . . . . . . . . . . . . . . . 55 6.3 Preferential routing comparison for three vehicles. . . . . . . . . . . . . . . 57 6.4 Three-dimensional collision avoidance. . . . . . . . . . . . . . . . . . . . 58 6.5 Excess separation of vehicles in Fig. 6.4. . . . . . . . . . . . . . . . . . . . 59 6.6 Comparison of the constant and variable-speed deconfliction maneuvers. . . 60 6.7 Merging two groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.8 Fifty-vehicle swarm avoiding a static obstacle. . . . . . . . . . . . . . . . . 64 6.9 Collision avoidance of 32 aircraft using the DRCA algorithm. . . . . . . . 66 6.10 Collision avoidance of two perpendicular flows. . . . . . . . . . . . . . . . 68 6.11 Excess separation for vehicles in 6.10. . . . . . . . . . . . . . . . . . . . . 68 iii
Page 1 and 2: Distributed Reactive Collision Avoi
Page 3 and 4: In presenting this dissertation in
Page 5: TABLE OF CONTENTS Page List of Figu
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
Page 69 and 70:
59 10 8 ‖˜r‖ − dsep (m) 6 4
Page 71 and 72:
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
Page 79 and 80:
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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