Distributed Reactive Collision Avoidance - University of Washington

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4 ahead or time horizon so that the solution does not have to be recalculated often. Force field approaches use continuous feedback mechanisms to compute the control. Commonly, the force field between two vehicles is akin to the repulsion between two like-charged particles, however there are many possible alternatives for feedback schemes. These approaches are generally reactive, in that the control reacts to the current state of the system, rather than planning a trajectory ahead of time. The next differentiator between collision avoidance algorithms is their degree of centralization. Centralized means that all of the information about the vehicles is sent to a single server where the controls are calculated for each vehicle and sent back. The current air traffic control system uses centralization (with human operators), as do most optimization schemes. The other extreme is decentralization, in which no central server exists and each vehicle computes its own control based only on other vehicles within a particular range of itself. This situation is ideal from a computational perspective because there is a limit to how many vehicles can be within range at once, and therefore there is a limit to how much time the algorithm will take to run, regardless of the total number of vehicles involved. In between is a category termed distributed, in which there is still no central server and each vehicle computes its own control but may need more than local information to do so. In this case, computations scale with the number of vehicles involved (n), but the scaling is at least O(n) better than the centralized case, because now n separate processors are computing in parallel, rather than one server doing all the work. The vehicle model used in each formulation is also of utmost importance to the algorithm’s applicability to real systems. First, for collision avoidance to be nontrivial, the dynamics must be at least second order (acceleration-level control input), and the control inputs must be bounded to model the difficulties of overcoming inertia. Many vehicles (cars, ships, airplanes, etc.) have nonholonomic constraints, and as such are often modeled at a high level by unicycle dynamics. The inputs to this model are forward acceleration and heading rate (which is equivalent to acceleration normal to the velocity). All vehicles have a maximum speed, but some vehicles (notably airplanes) also have a positive min-
5 imum speed. The constant-speed unicycle is one of the most broadly applicable vehicle models because it is the most constrained (less constrained vehicles can still duplicate its movements, but not vice-versa). Ideally an algorithm should use all of the capabilities a vehicle has to offer, but still function under the constraints of a constant-speed unicycle if necessary. Another important aspect of a collision avoidance algorithm is whether it works for a heterogeneous group of vehicles. Heterogeneity can be due to differences in vehicle size, dynamics, speed range, control authority, etc. Many algorithms are developed for a homogeneous group of vehicles for convenience and ease of notation, but could be easily extended to a heterogeneous case. Others, especially constant-speed algorithms, can have difficultly generalizing from a homogeneous scenario. Another important consideration is that vehicle size, maximum speed, and control authority are often important parameters for the other vehicles in the system to know in order to properly avoid each other. In a homogeneous system these parameters are known implicitly because they are the same for every vehicle, but in a heterogeneous system, these parameters must be exchanged. Communication is the most obvious tool, though sensors could be employed to identify the vehicle type and compare it to some known list, the same way a captain can identify a sailboat or a ferry and infer their size and maneuverability. Until such technology is fully mature, heterogeneity may require some degree of inter-vehicle communication. A final aspect important to collision avoidance is liveness, which denotes the ability of the vehicles to attain their goals. Liveness is important to consider because one simple way to avoid collisions is to have everyone stop moving. While this method may avoid collisions, it is not useful because the vehicles cannot arrive at their destinations. This type of situation is called a deadlock. Another problem scenario is a livelock, where the vehicles continue to move, but in such a way that they cannot reach their goals.
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: 3 system state as time goes to infi
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
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
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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