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CU-Boulder ASEN 5519 - Flight Path Deconfliction of Autonomous UAVs

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American Institute of Aeronautics and Astronautics1Flight Path Deconfliction of Autonomous UAVsAdrian Stanley*QinetiQ, Thurleigh, Bedfordshire, MK44 2FQ, UKThis paper develops the deconfliction algorithms originally put forward by I. Hwang and C. Tomlin. This paper will recast the original two dimensional algorithm into a form that facilitates its use in three dimensional space. Additionally, this paper will extend the original algorithm to include maneuvers that will return the aircraft to their original flight path without initiating further conflicts. A quantitative result is also derived for the effects of a finite time for the deconfliction maneuver.Nomenclatureai= linear acceleration of aircraftD,p,q,ψ= cubic equation dummy variablesk = positive number denoting ratio of aircraft time on return maneuver to time to conflictn = positive number denoting ratio of aircraft speed on return maneuver to speed during deconflictionN = positive integer denoting number of aircraftR = minimum permissible aircraft separationri= aircraft positionri0= aircraft initial positionrmin, rmax= minimum/maximum radius bounding deconfliction maneuversS1ij= aircraft separation during 1stportion of deconfliction maneuverT = time to collisiont = timetcentre= time to centre of maneuvertmin= time to minimum separationu = deconfliction angle in 2-Du’ = deconfliction angle in 3-Dvi= aircraft velocityv’i= modified aircraft velocityv0i= aircraft velocity prior to deconfliction maneuverv3Di= aircraft velocity in 3-Dv2Di= aircraft velocity in x-y planevzi= z-component of aircraft velocityv1i= aircraft velocity through virtual conflict pointv1ai= aircraft velocity during 1stportion of deconfliction maneuverv1bi= aircraft velocity during 2ndportion of deconfliction maneuverv2i= aircraft velocity during return maneuvervmin, vmax= minimum/maximum aircraft velocities∆rij0= difference in aircraft initial positions∆tab= time elapsed between times ta and tb∆vij= difference in aircraft velocitiesγ= flight path angleλi= angle between aircraft flight path and virtual conflict pointµi= aircraft return maneuver angleρ= position of virtual conflictθi= heading angleτ= time of duration of maneuver *Aerospace Engineer, Autonomous Guidance and Telematics, QinetiQ Bedford, UKInfotech@Aerospace26 - 29 September 2005, Arlington, VirginiaAIAA 2005-6978Copyright © 2005 by QinetiQ Ltd. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.American Institute of Aeronautics and Astronautics2I. IntroductionS the level of autonomy given to Unmanned Aerial Vehicles (UAV) increases, so does the need for ever more reliable algorithms to ensure collision avoidance. Clearance and certification can be granted only if the procedures in place can be validated rigorously, i.e., they should be effective yet mathematically simple. Many studies have been completed and many techniques have been developed to address conflict identification and resolution. A comprehensive literature survey, performed in 2000 by Kuchar and Yang1, listed 68 different approaches to conflict detection and resolution. In 2002, Hwang and Tomlin2introduced a particularly simple algorithm for multiple conflict resolution, which is guaranteed to deconflict an arbitrary number of aircraft within a conflict zone. However, in the most general case the Hwang-Tomlin (HT) algorithm is incomplete, in that a further maneuver is required to return the aircraft to their original flight path. This paper describes the derivation of an additional maneuver and will show that no additional conflicts are generated subsequently. Furthermore, a number of extensions to the algorithm will be presented.This paper is divided into 6 main sections: Section II outlines the HT algorithm; Section III outlines the derivation of the “exact case” in vector form, thereby allowing the underlying geometry to become transparent; Section IV generalizes the “exact case” in to three dimensions; Section V describes the flight path return maneuver; and Section VI relaxes the assumption of an instantaneous acceleration and shows the results of allowing an acceleration over a finite time.II. The Hwang-Tomlin AlgorithmKuchar and Yang1, in their literature survey, classified deconfliction algorithms according to six main design factors: state propagation; state dimensions; conflict detection; conflict resolution; resolution maneuvers; and multiple conflicts. State propagation is concerned with whether a deterministic or probabilistic approach is taken to aircraft flight paths. Under this classification the HT algorithm is deterministic in projecting the flight path. State dimension is concerned with whether the deconfliction is performed in two or three dimensions. The HT algorithm is performed in two dimensions, but Hwang and Tomlin maintain that it is straightforward to generalize to three, as described in Section IV. Conflict detection is concerned with whether an explicit conflict detection procedure exists independently of the conflict resolution. The HT algorithm has a conflict detection procedure that specifies the minimum allowable separation before a conflict is deemed to have occurred. Conflict resolution is concerned with whether the resolution method is prescribed, optimal, force field, or manual. The HT algorithm is a protocol method, which is a combination of prescribed and optimized methods. Resolution maneuver is concerned with whether the maneuver involves a turn, a vertical maneuver, or a speed change. The HT algorithm involves turns and speed changes, but no vertical maneuvers. Finally, multiple conflict is concerned with whether the method deals with multiple aircraft at once or with pairs or individual aircraft. The HT algorithm can deconflict any number of aircraft simultaneously.The HT algorithm begins by obtaining a condition for deconflicting aircraft in a highly idealized scenario and then derives a condition for deconflicting more general and realistic scenarios by reducing them to the idealized case. It should be pointed out that in order to perform the maneuver, it is necessary for all aircraft to be cognizant of each others positions and velocities, i.e., co-operative. Consider a group of N aircraft confined to the x-y plane set to collide at the same point in space and time, i.e., the origin of the co-ordinate system. This will be referred to as the “exact case”. If the deconfliction maneuver occurs T seconds before


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CU-Boulder ASEN 5519 - Flight Path Deconfliction of Autonomous UAVs

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