Distributed Reactive Collision Avoidance - University of Washington

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20 Chapter 4 DRCA ALGORITHM The DRCA algorithm uses a two-step process: a deconfliction maneuver and a deconfliction maintenance phase. The guarantees of n-vehicle collision avoidance rest upon three results. The first is that a deconfliction maneuver will keep the vehicles from colliding so long as they are each separated by at least a given bound. The second is that this deconfliction maneuver will result in a conflict-free state for the vehicles. The final result is that once a group of vehicles is conflict-free, the deconfliction maintenance controller will keep them that way. These steps yield the flow chart for the DRCA algorithm that is shown in Fig. 4.1. When the vehicles are sufficiently separated, no avoidance is necessary, so the vehicles can simply use their desired control. The deconfliction maintenance phase also takes the desired control into account, though there is no guarantee that it is followed at all times. In general, vehicles will not all see each other at the same time and perform one synchronous maneuver. Rather, they must avoid each other as they come into sensing/communication range (this will be referred to as communication from here on since some communication is required even if sensing is used). This maneuver does not require all-to-all communication, but does require some assumptions about connectivity and separation in order for the full collision avoidance guarantees to hold. However, if these assumptions are relaxed, the DRCA algorithm will still function as a high-performance heuristic, albeit without the full safety guarantee. The first step of the DRCA algorithm is to decide when a vehicle needs to perform its deconfliction maneuver. Let D be the set of vehicles who are currently deconflicting (either performing the deconfliction maneuver or deconfliction maintenance). Define a binary
21 Enter Desired Control Deconfliction Maintenance Yes Yes Separated No Conflict−Free No Deconfliction Maneuver Figure 4.1: Flow chart of the DRCA algorithm. condition, χ i : D → {true,false}, which designates that the separation between vehicle i and the vehicles in D is enough to guarantee that vehicle i can avoid those vehicles. This condition will be derived later. Define a second binary condition, ξ i (D), which designates when vehicle i executes avoidance. The condition ξ i can be chosen for a longer or shorter look-ahead, but at the crossover point, χ i must be true. The DRCA algorithm causes vehicle i to follow its desired control until ξ i (D) becomes false. At this point vehicle i becomes a member of D and performs its deconfliction maneuver, which amounts to choosing a conflict-free velocity vector, broadcasting it to the group, and then accelerating to attain it as quickly as possible. Once this vehicle attains a conflict-free state with the other vehicles in D, it switches to deconfliction maintenance. The other vehicles in D that are already performing deconfliction maintenance avoid this new vehicle using its broadcast velocity instead of its actual velocity until its maneuver is complete. Conceptually, this method is akin to a turn signal, where the new vehicle tells the group how it will be accelerating, and the group can then work around that decision. As such, each vehicle will see no conflicts with a newly added member of the group. To implement this algorithm, each vehicle in D must be able to broadcast to all the other vehicles
Page 1 and 2: Distributed Reactive Collision Avoi
Page 3 and 4: In presenting this dissertation in
Page 5 and 6: TABLE OF CONTENTS Page List of Figu
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: 19 where t is the time to closest a
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
Page 63 and 64: 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)
Page 73 and 74: 63 Table 6.1: Comparison of computa
Page 75 and 76: 65 be stabilized with any of a vari
Page 77 and 78: 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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