UAV collision avoidance based on geometric approach

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1 Loughborough University Institutional Repository UV collision avoidance based on geoetric approach This ite was subitted to Loughborough University's Institutional Repository by the/an author. Citation: PRK, J.-W., O,. and TK, M.-J., UV collision avoidance based on geoetric approach. IN: Proceedings of the 2008 SICE nnual Conference, 20th-22nd ugust 2008, Tokyo, pp dditional Inforation: c 2008 IEEE. Personal use of this aterial is peritted. Perission fro IEEE ust be obtained for all other uses, in any current or future edia, including reprinting/republishing this aterial for advertising or prootional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted coponent of this work in other works. Metadata Record: Version: ccepted for publication Publisher: IEEE / c SICE Please cite the published version.

2 UV Collision voidance ased on Geoetric pproach Jung-Woo Park 1,yon-Dong Oh 2 and Min-Jea Tahk 3 1,2,3 School of Mechanical, erospace and Syste Engineering, Departent of erospace Engineering, Korea dvanced Institute of Science and Technology, Daejeon, Korea (Tel: ; E-ail: {jwpark; hdoh; fdcl.kaist.ac.kr) bstract: ethod of collision avoidance is described by using siple geoetric approach. Two UVs are dealt with and considered as point asses with constant velocity. This paper discusses en route aircraft which are assued to be linked by real tie data bases like DS-. With this data base, all UVs share the inforation each other. Calculating PC (Point of Closest pproach), we can evaluate the worst conflict condition between two UVs. This paper proposes one resolution aneuvering logic, which can be called Vector Sharing Resolution. In case of conflict, using iss distance vector in PC, we can decide the directions for two UVs to share the conflict region. With these directions, UVs are going to aneuver cooperatively. First of all, this paper describes soe 2-D conflict scenarios and then extends to 3-D conflict scenarios. Keywords: Vector Sharing Resolution, Cooperative collision avoidance, Point of Closest pproach (PC), Sphere protected zone. 1. INTRODUCTION There are any researches for Free Flight [1]. Many ethodologies and skills are published up to the present. For exaple, there are any studies accoplished that finding optial trajectories by using any optial theories, probabilistic odeling, applying potential field, and so on. Conflict can be defined as a predicted violation of a separation assurance standard [2]. So if the protected zone is violated, each UV should solve the violation using proper way to avoid the conflict. For the Free Flight, it is very essential task to understand geoetric relations between two UVs in a conflict. In this paper, using PC ethod[3], we calculate the iss distance vector of two UVs and the tie to take. If the agnitude of iss distance vector is saller than the iniu separation which should be guaranteed, it is considered as a conflict that can bring about collision between UVs. So this paper discusses a ethod to resolve the conflict, essentially to avoid the collision between soe pair of UVs by using siple geoetric sense. 2. SYSTEM MODELING In this paper, two UVs with constant velocities toward their goal positions are considered in a conflict condition when they are within a protected zone. Generally, aircraft s Protected Zone is currently sized by 5 ni (about 9.26 k) horizontally and 2000 ft (about 0.61 k) vertically [4], but for the siplistic, it is taken to be a sphere of specified radius about 5 ni in this paper. Initially the positions and velocities are assued to be infored by certain broadcasting systes like DS-, and the inforation fro such as GPS is assued to be quite exact. The point-ass equations of otion are derived with respect to a coordinate syste shown in Fig. 1. The point-ass UV equations are: 2 2 V = V + V V (1) x = V cos γ, y = V sin γ, z = Vsinθ = VV (2) g tanφ γ = V (3) where θ is UV s pitch angle, γ is heading angle, and φ is bank angle. To generate heading angle change, bank coand is given as an input, and pitch coand is given to generate pitch angle. The detail equations are: 1 φ = ( φ φ co ) (4) N 1 θ = ( θ θ co ) (5) M The equations consider the delay of actual UV s dynaics. It is shown that tie constant is assued to be N and M seconds for both dynaics at Eq. (4) and Eq. (5). V ( x, y, z) V V V V V V V ( x, y, z) ( x, y, z ) G G G ( x, y, z ) G G G Fig. 1 Geoetric view of basic conception of two UVs.

3 The relative distance is siply given as: = ( ) + ( ) + ( ) (6) rel R x x y y z z V c V With this relative distance, we can judge whether it is in a conflict condition or not. r 3. CONFLIICT DETECTION / RESOLUTION V r It is assued that two UVs are in an encounter with each other, and they are heading to their velocity direction which eans there s no sideslip for UVs. The geoetry is illustrated in Fig Conflict Detection When two UVs are getting closer, if we can calculate the iniu distance passed by each other, it can be judged whether collision can be occurred or not. For this, we can get the iss distance fro PC (Point of Closest pproach). The iss distance vector r is defined: r = cˆ ( r cˆ) (7) where r is the relative distance vector and ĉ is the unit vector in the direction of the relative velocity vector c fro UV to UV. Naturally we can know that the iss vector r and relative velocity vector c is orthogonal: r c = 0 (8) With the relation between r and r, we can calculate the tie to closest approach τ : r = r + c τ (9) With Eq. (8) and (9), finally we get: r c τ = c c (10) t the Eq. (10), when two of UVs are getting closer, τ > 0, and when two of UVs are getting further, τ < 0. Therefore, when τ > 0, we have to check whether there s a chance to have an event of conflict or not. Whenτ < 0, we can guess that there s no risk to have an event of collision at all. If the agnitude of r is less than specified iniu separation distance r safe considered in a conflict condition. - Conflict condition: r r r > 0 res = safe, two UVs are (11) where r res is the rest region after subtraction of r fro r safe. rres will be called Unresolved Region in this paper. Fig. 2 Relative otion of two UVs. 3.2 Conflict Resolution If r res > 0, conflict resolution aneuvering should be accoplished. In Fig. 2, we can intuitively know the direction where each of UVs has to go. UV ay turn to the left to avoid collision and UV ay turn to the left too. It can be easily figured out if we think about the otion of UVs with respect to the iss distance vector. To larger the iss distance, UV and have no choice except being headed for left. If UV akes a turn to the right, it takes a very long distance roundabout way or it collides with UV. The case of UV is also sae logic. To solve this proble, it is proposed that the conflict resolution aneuvering lies on the line of iss distance vector. This will be called as Vector Sharing Resolution in this paper and it is described in Fig. 3. In the Fig. 3, to share the unresolved region, two UVs should at least head for the direction of unit vector U and U. This indicates that this logic gives each UV a least direction to solve the conflict condition. Vector sharing resolution is achieved as defining the vector r and r VS VS in Fig. 3: - For UV V r res r = ( ) VS r V + V r (12) - For UV V r res r = ( ) VS r V + V r (13) - relation between r and r : VS VS r = r + r + r (14) safe VS VS y the eans of that the slower UV takes the ore sharing, the sharing is done. It is because slower UV can do avoidance aneuver ore than faster one with sae tie. Finally we get the unit vector U and U :

4 - For UV - For UV V τ r U U U V τ + r VS = V = r VS U τ + r (15) VS V τ + r VS V τ + r (16) V τ r VS r VS Fig. 3 Resolution Maneuvering. r If two UVs are going to have a direct head-on collision ( r = 0), by disturbance aking process we ake two UVs have non-zero iss distance vector. Detail is followed as: V ( h V) U = (17) V ( h V) where h is the unit vector of z-direction. In real flight, by certain aneuver of one of UVs, this proble can be resolved. dditionally, if it is doubt to the chattering or not coplete inforation fro DS-, we define certain region to be dealt with as zero iss distance region. 3.3 The Optial Maneuver to Resolve We can consider the optial proble to axiize the iss distance at the end of resolution aneuver. 1 2 in J = r (18) a 2 f where a is acceleration vector as input. Then we can derive the equation of ailtonian. = r iv ( t t) r i e (19) f f f where e is the unit vector of acceleration vector. Therefore we conclude that acceleration along the iss distance vector can iniize the ailtonian so that it can be the optial solution.[5] This is not sudden result. With the protected zone of sphere it is ost efficient to avoid each other along the iss distance vector since the iss distance vector is perpendicular to the velocity vector so that it axiize the iss distance with sae acceleration to apply the acceleration to the direction iss distance vector line. 3.4 pplication to the UV Dynaics We know the directions of now-going and odified. Now-going one is the direction of velocity V and odified one is the direction of U pplication to the UV Dynaics With these two vectors we can calculate the LOS (Line Of Sight) angle. For each UV, the LOS is defined: V U λ = signu(( V U ) z) arccos (20) V where subscript eans horizontal eleent. y the LOS angle found we decide the bank coand as an input. It is assued that each UV has its axiu bank angle of 45 degree. So with the axiu bank angle, we can calculate the axiu heading angle change for 1 second: g γ = ax, for 1 second and φ ax (21) V where g is the gravity acceleration and V is the horizontal velocity. Keeping on this result, the horizontal aneuver logic is followed as: Table 1 The orizontal Maneuver Options. Range of LOS angle ank Coand λ < γ ax φ = 45 γ λ γ ax γax ax co λ φco = 45 γ ax < λ φ = 45 co n UV can change the bank angle easily, so we set the tie constant N of 1 second in Eq. (4) pplication to the UV Dynaics With unit vector U for each UV, we can obtain the pitch angle required. Required pitch angle can be expressed as: U V θ req = arctan (22) U Vertical otion is hard to change fast. So we have to deal with the change of pitch angle carefully. t the vertical aneuver, we set the tie constant of M in Eq. (5) by the required pitch angle. Vertical aneuver logic is followed as: Table 2 The Vertical Maneuver Options. Required pitch angle Tie constant, M 0 < < 15 1 second θ req 15 < < 30 2 seconds θ req 30 < < 45 3 seconds θ req θ > 45 4 seconds req

5 s pitch angle changes, the horizontal velocity and the vertical velocity also change. The velocity eleent change is described as: V = V sinθ and V = V cosθ (23) V 4. NUMERICL RESULTS The conflict detection and resolution algorith discussed in previous sections are evaluated in two saple encounter scenario in this section. Siulation has been accoplished with initial inforation about position and velocity for both UVs. Two UVs are assued to head toward their goal position. nd the integrated positions and velocities have been treated as broadcasted inforation. Miniu separation distance is 5 ni (about 9.26 k) as defined. lso it is assued that the interval for updating the inforation fro DS- is 1 sec. etween the intervals, UVs aneuver with the coands for bank and pitch during 1 sec. It is for the consistent aneuvering not to change the bank and pitch angle suddenly during the conflict resolution. ll siulations for 2-D and 3-D are accoplished assuing all scenarios are non-cooperative cases since it is easier to avoid each other cooperatively so that the non-cooperative aneuver guarantees the successful conflict resolution of the cooperative cases D Conflict Scenario Table 3 Proble Definition for 2-D. Initial Position (0,0,0) k UV Initial Velocity (150,150,0) /s Goal position (75,75.,0) k Initial Position (0,100,0) k UV Initial Velocity (150,-145,0) /s Goal position (75,27.5,0) k - Results for 2-D Fig. 5 Relative distance. Fig. 6 ank angle profile for Own UV. Own UV turns to the right to avoid the conflict. Trajectory is expected pattern and the relative distance also never invades the iniu separation region. On the way to the guidance for hoing, avoidance guidance is applied. During the hoing guidance, the sudden angle(bank) change occurs. ut it can be odified in real by using PNG guidance D Conflict Scenario Table 4 Proble Definition for 3-D. Initial Position (0,0,0) k UV Initial Velocity (150,100,10) /s Goal position (30,20,2) k Initial Position (30,0,0) k UV Initial Velocity (-150,90,10) /s Goal position (0,18,2) k - Results for 3-D Fig. 4 Trajectories of both UVs. Fig. 7 Trajectories of both UVs.

6 study starts with the calculation of iss distance fro PC. In case of pair-wise conflict resolution, the UV just aneuvers with the coend to resolve the conflict region directly. owever, in case of ultiple conflict resolution, all trajectories of UVs should be dealt with. Fig. 8 Relative distance. Fig. 10 Conception of ultiple conflict resolution. Fig. 9 ank angle profile for Own UV. Fro the siulation, we can see that horizontal and vertical aneuvers work well. In orizontal, own UV turn to the left and changes the altitude down. These results are also expected pattern to resolve the conflict effectively. 5. CONCLUSION Collision avoidance can be done by accoplishing the conflict resolution algorith described in this study. Keeping and not losing the iniu separation distance, we settle up the conflict between UVs. There are ethodologies and skills developed to avoid the conflict. The geoetric approach is also one of the ways. In this paper, using geoetric ethod, the conflict resolution aneuver is accoplished successfully. Using PC ethod, the algorith for conflict detection and resolution is induced by intuition siply. ut there are still tasks to solve in the future. This paper deals with siple dynaics for the UVs. More realistic and well approached dynaics are needed, especially in the pitch dynaics. nd ultiple collision avoidance algorith should be issued. Even though vector sharing resolution is one of any resolution algoriths for collision avoidance, it gives just one possibility to resolve the conflict. 6. FUTURE WORK One conception is considered for the ultiple collision avoidance. The algorith described in this In the Fig. 10, the strea vectors for own UV are described. oth drawings are at the tie when the closest intruder is faced with. In the first case(left), own UV can resolve all conflict with all intruders one by one by applying the algorith for the pair-wise conflict resolution. ut, in the second case(right), own UV should consider all intruders at the sae tie since own UV cannot resolve the conflict by using pair-wise conflict resolution algorith. Therefore in that situation, first, we calculate the artificial center of two intruders, second, consider two intruders as one intruder and, finally, apply the algorith as described in this paper. Then, the global conflict resolution is accoplished. For ultiple conflict resolution, the rate of updating the inforation fro DS- should be fast and own UV ay aneuver agilely. More the intruders are, ore coplicated algorith should be considered. Therefore the progress for ultiple conflict resolution should be dealt with carefully, and the enough evaluation is needed. It is the direction of this study. REFERENCES [1] Lee C. Yang and Jaes K. Kuchar, Prototype Conflict lerting Syste for Free Flight, erican Institute of eronautics and stronautics, Inc., [2] Wallace E. Kelly III, Rockwell Collins, Cedar Rapids, and Iowa, Conflict Detection and lerting for Separation ssurance Systes, Digital vionics Systes Conference, St. Louis, [3] Jiy Krozel and Mark Peters, Strategic Conflict Detection and Resolution for Free Flight, Seagull technology, Inc., [4] Douglas R. Isaacson and einz Erzberger, Design of Conflict Detection lgorith for The Center/Tracon utoation Syste, NS es Research Center, [5].W.MERZ, Maxiu-Miss ircraft Collision voidance, Dynaics and Control, Vol. 1, pp , 1991.