Distributed Reactive Collision Avoidance - University of Washington

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12 without sacrificing safety. This framework also allows vehicles to be given different priorities, such that lower priority vehicles will make way for higher priority ones. This algorithm requires little (though nonzero) communication between vehicles, and can safely add new vehicles to the system as they reach sensor range. While the algorithm is distributed, it is not quite decentralized, in that all-to-all information is needed within a connected group. The information exchange can be easily implemented through a broadcast, and if there is enough bandwidth for vehicles to rebroadcast the information they receive, then a quasi-all-to-all topology can be achieved. The robustness analysis accounts for the corresponding time delays. Additionally, the algorithm can be run in a completely decentralized fashion, and while some of the guarantees no longer apply, simulations are given that demonstrate significant capability nonetheless. No homogeneity is required among the vehicles that make up the system. The DRCA algorithm allows the vehicles to perform completely different tasks and to have different size, speed, actuation limitations, and control gains. The remainder of this dissertation is organized as follows. The problem statement is given in Chapter 2, including the vehicle model. Specific definitions of collision and the collision cone are given in Chapter 3. In Chapter 4 the DRCA algorithm is described, which forms the bulk of the dissertation. A robustness analysis is given in Chapter 5. Finally, simulation results are presented in Chapter 6 and concluding remarks in Chapter 7.
13 Chapter 2 PROBLEM STATEMENT The work here presents a method for deconflicting n vehicles. Each vehicle has a nominal desired control input, u d (t), which comes from an arbitrary outer-loop controller. This controller is designed for the vehicle to perform a desired task, which could range from target tracking to waypoint navigation, to area searching, etc. The goal of the DRCA algorithm is to adjust the control input on each vehicle to guarantee collision avoidance while simultaneously staying close to the desired control input (keeping in mind that this desired control can change with time). For this approach to collision avoidance, the only vehicle states that matter are position and velocity. Orientations affect performance, as they often have bearing on the magnitude of acceleration available in a particular direction, but they do not affect the underlying concepts of conflict and collision. In this way, many different vehicle models work equivalently with this approach. To simplify the math, a simple vehicle model will be used for most of the following analysis: a 3D double integrator, which for the i th vehicle is given by ⎡ ⎤ ⎡ ⎤ r d i v i ⎢ v dt ⎣ i ⎥ ⎦ = ⎢ u ⎣ i ⎥ ⎦ , (2.1) Θ i Ω i Θ i where r i , v i , u i ∈ R 3 are the position, velocity, and control input, respectively. The matrix Θ i = [ˆt i , ˆn i , ˆb i ] defines the orientation and Ω i is the cross product matrix of the body rotation vector ω = [ω t , ω n , ω b ] T . The notation throughout this paper will use bold face for vectors, hats over unit-vectors, script capital letters for sets, standard capital letters for matrices and functions, and everything else is assumed scalar. Quantities subscripted with t, n, or b refer to the tangent, normal, or binormal direction, respectively.
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: 11 at first to be the holy grail of
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
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)
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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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