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A problem of collision avoidance
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In this paper, collision avoidance between two vehicles of constant speed with limited turning radii, moving in a horizontal plane is investigated, where collision avoidance is viewed as a game by assuming that the operator of one vehicle has perfect knowledge of the state of the other.Abstract:
Collision avoidance between two vehicles of constant speed with limited turning radii, moving in a horizontal plane is investigated. Collision avoidance is viewed as a game by assuming that the operator of one vehicle has perfect knowledge of the state of the other, whereas the operator of the second vehicle is unaware of any impending danger. The situation envisioned is that of an encounter between a commercial aircraft and a small light aircraft. This worse case situation is examined to determine the conditions under which the commercial aircraft should execute a collision avoidance maneuver. Three different zones of vulnerability are defined and the boundaries, or barriers, between these zones are determined for a typical aircraft encounter. A discussion of the methods used to obtain the results as well as some of the salient features associated with the resultant barriers is included.read more
Citations
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A controllability minimum principle
TL;DR: In this paper, a controllability minimum principle and two associated transversality conditions are presented for nonlinear systems, where the goal is to generate a path that lies in the boundary of the set of points that are controllable to a target.
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Maximum-miss aircraft collision avoidance
TL;DR: In this paper, the authors used low-order dynamics to find small amplitude evasive maneuvers for both aircraft in near-miss configurations with short time-to-go, and found that the small amplitude maneuvers are optimal with respect to the low order dynamics and they combine longitudinal (speed) and normal (lift) accelerations.
Journal ArticleDOI
Optimal Collision-Avoidance Manoeuvres to Minimise Bunker Consumption under the Two-Ship Crossing Situation
Kang Zhou,Jihong Chen,Xiang Liu +2 more
TL;DR: In this paper, a collision-avoidance manoeuvring optimisation model is developed to minimize fuel consumption while assuring ships' operational safety, which can optimally determine when to begin collision avoidance actions, how to change courses, and what rudder angles are needed.
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Some Aspects of Collision Avoidance
TL;DR: S aspects of the problem of collision avoidance for two chicles are examined by hypothesizing certain rationales for the vehicle operators and then computing the sets of initial conditions for which collision can occur.
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Calculation of ship collision avoidance manoeuvres: A simplified approach
TL;DR: In this article, the moment at which a collision avoidance manoeuvre should be initiated in order to achieve a specific distance at the closest point of approach has been calculated based on the kinematics of encounter and simplified equations of motion.
References
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Book
Foundations of Optimal Control Theory
Ernest Bruce Lee,Lawrence Markus +1 more
TL;DR: This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research.
Journal ArticleDOI
A new technique for solving pursuit-evasion differential games
TL;DR: In this paper, a new method for finding the capture region and its internal structure is presented for a class of pursuit-evasion problems, and the optimal behavior is found for the two vehicles acting independently and then combined geometrically.
Book ChapterDOI
7 On the Geometry of Optimal Processes
TL;DR: In this paper, the authors investigate the geometry in state space of a dynamical system that behaves in an optimal fashion, defined by the requirement that an admissible rule render the minimum value of the cost associated with transfer between prescribed end states.