Jtam.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 46, 4, pp. 909-916, Warsaw 2008 ON A METHOD OF TARGET DETECTION AND TRACKING USED IN AIR DEFENCE Jan W. Osiecki Military Academy of Technology, Warsaw, Poland e-mail: osewoj@wp.pl Konrad Stefański Kielce University of Technology, Kielce, Poland e-mail: konrad@poczta.fm The work discusses a new approach to the control of motion of the gy- roscope axle with an in-built optical system responsible for detection and tracking of aerial targets emitting infrared radiation. The method, which has been presentedby the authors at numerous conferences on the subject, requires using phase trajectories of control errors. Key words: gyroscope, scanning, phase trajectories 1. General information The work discusses the operation of a short-range anti-aircraft missile fired from a mobile launcher mounted on a vehicle or a naval ship. The launching takes placeduringmotion of the vehicle or vessel.The study focuses on apassi- ve self-guidance system used for targets emitting thermal (infrared) radiation, which are ”seen” by a missile as light spots (at a longer distance) or light patches (at a closer distance). An object to be attacked by a missile should be intercepted by the built-in optical system before themissile is launched. It may be difficult, however, to select the precise moment of missile firing (after an image of the target is perceived in the optical system)when the launcher is moving or the base, onwhich the operator stands, is moving.Modern systems for scanning or searching through the space and detecting the target are used to facilitate the manual operation (Krzysztofik and Osiecki, 2000; [7]; Voigt, 1977). Scanning heads are used in ground-air and air-air missiles. 910 J.W. Osiecki, K. Stefański The aim of thework is to present and analyse an efficient system for space scanning used in a rocket head. After the object to be attacked is detected basing on the emitted infrared radiation, it can be tracked while the missile realises the first loop of the self-guidance process (Osiecki and Stefański, 2003, 2004). Fig. 1. The proposed system responsible for space scanning and target tracking The proposed system responsible for space scanning and target tracking operates according to theprinciple shown inFig.1.Theoptical unit ismounted in the gyroscope axle with three degrees of freedom (Fig.2: dΦ/dt = n = = const). The unit with the gyroscope and the control circuit is mounted on board of an aerial vehicle such as a missile or another unmanned aerial vehicle. The systemoperation canbedivided into three stages. Stage I is conventio- nally termed the space patrolling. The aerial vehicle with a scanning-tracking system on board moves in the surveillance zone with a programmed motion. The motion program will not be discussed here, as it is the subject of a se- parate strategy. When the target is intercepted, i.e. when it is at a presumed viewposition, the program responsible for scanning the space anddetermining the angular coordinates of the target is switched on. In stage III, the target is tracked and, if necessary, destroyed. In stage II, the direction of the gyroscope axle is controlled according to a pre-determinedprogramof space scanningand target tracking, both inaclosed system, basing on themethoddescribed inHsu andMeyer (1970), Osiecki and Stefański (2003, 2004), Stefański (2004), which uses the deviation trajectories tending to zero. On a method of target detection... 911 Fig. 2. A diagram of the gyroscope suspended on Cardan’s joint The equations ofmotion of the optical unitmounted on the gyroscope axle are given: a) for rosette scanning (Fig.4a) ψ(t)= asin(̟1t)sin(̟t) η(t)= asin(̟1t)cos(̟t) (1.1) b) for spiral scanning (Fig.4b) ψ(t)= (a− bt)cos(̟t) η(t)= (a− bt)sin(ωt) (1.2) c) for multi-loop spiral scanning (Fig.4c) ψ(t) = (a− bt)cos(ωt)+0.1acos(80̟t) (1.3) η(t)= (a− bt)sin(ωt)+0.1asin(80ωt) The motions are realised through control applying the following system of equations describing motion of the gyroscope axle, 0η (Nizioł, 2005), see Fig.1 912 J.W. Osiecki, K. Stefański JBϑ̈+ 1 2 JB(β̇ +̟Z) 2 sin2ϑ−J0n(β̇ +ωZ)cosϑ+JB ˙̟X cosβ + −JB̟Xβ̇ sinβ − 1 2 JB̟ 2 X sin 2β sin2ϑ−J0nωX sinβ sinϑ+ = JBωX(β̇ +ωZ)cos2ϑsinβ = MB (1.4) JB(β̈ +̟Z)cos 2ϑ−JB(β̇ +ωZ)ϑ̇sin2ϑ+J0nϑ̇cosϑ+ − 1 2 JBω̇X sinβ sin2ϑ−JBωXβ̇ cosβcos 2ϑ−JBωXϑ̇sinβcos2ϑ+ +J0nωX cosβcosϑ+JBϑ̇ωX sinβ + 1 2 JBω 2 X sin2β + + 1 2 JB(β̇ +ωZ)ωX cosβ sin2ϑ− 1 2 JBω 2 X sin2β sin 2ϑ = MC and M0 = MB −Jϑ̈ M0 = MC −Jβ̈ Figure 3 shows a block diagram of the control system, which is uniform for scanning and tracking (stages II and III). At the moment the target is intercepted, the system begins either taking the target bearings or tracking it. The bearings can be taken only if the distant target practically does not move in relation to the system founded on the ground. When the tracking mode is selected, it is necessary that the switch-over be done in the system determining the signals p and r by introducing other deviations, i.e. replacing e0 with eu = ϑ−θp, e1 with eu1 = ϑ̇− θ̇p, e2 with ev = β −σp and e3 with ev1 = β̇ − σ̇p, where θp(t) and σp(t) represent the angular coordinates of the moving target. There exist a number of design solutions (mechanisms) as well as algori- thms responsible for scanning. We shall focus on the design of a mirror lens (Fig.1) fixed on the gyroscope axle and consider different yet uniform algori- thms realising its scanning and tracking motions. The space scanning paths can be described with the general formula ϑ = a1(t)sin(ω1t)+a2(t)cos(ω2t) (1.5) η = b1(t)cos(ω1t)+ b2(t)sin(ω2t) The formula describes the desired signals given at the input of the control system of the optical coordinator axle in the missile head. The control is realised in a closed system. On a method of target detection... 913 Fig. 3. A block diagram of scanning and tracing a target Different scanning paths can be obtained, and the shape depends on the value of the following ratios: a1/a2, b1/b2 and ω2/ω1. Three examplary shapes of scanningpaths,whichareaxial and symmetrical [ai = bi], are shown inFigs. 4a, 4b and 4c, and these are: anArchimedean spiral, amulti-loop spiral and a rosette, respectively. When the scanning is performed along a rosette-shaped path, the number of the rosette leaves will be different, depending on the ratio ω2/omega1 < 0. When the ratio is ω2/ω1 = n2/n1, where n1 and n2 are natural prime numberswith regard to each other, the sum n1+n2 is equal to the sum of the rosette leaves. 2. Summary and conclusion The system proposed above uses a gyroscope with three degrees of freedom and an optical unit built in the gyroscope axle, which receives infrared si- gnals sent by the target. Different algorithms can be applied to scan a large surveillance area. As soon as the first signals are received, i.e. the target is perceived as a light spot, the optical axis is directed towards the spot centre so that the target coordinates can be determined irrespective of the radia- tion energy distribution. The system of control is efficient even if the target 914 J.W. Osiecki, K. Stefański Fig. 4. Results of a digital simulation of tracing a target (m =0.8kg, d =0.08m, M0 =500khm 2/s2, J = md2/16kgm2/s2, J0 =2J, bb = bc =0.001kgm 2/s2, n =600rad/s, v0 =300m/s, D =500m, a = b =1.2rad, ω =16πrad/s, ω1 =20ω/3,mobile base: ωx =0.2sin(2πt)rad/s, ωz =0.5cos(5πt)rad/s) On a method of target detection... 915 changes its position with high speed. After the spot centre is established, the system switches over to the tracking mode, which enables observation of the moving target. The system satisfies all the formulated requirements. Controlling the gyroscope axle is not complicated, the scanning time until the target is intercepted is short and the tracking is characterised by high precision. References 1. Hsu J.C., Meyer A.U., 1970, Modern Control Principles and Applications, McGraw-Hill B.C. 2. Krzysztofik I., Osiecki J., 2000, On a certain mechanism of space scan- ning with an optical target coordinator, 17th National Conference for Rese- archers and Academics on the Theory of Machines and Mechanisms, Warsaw- Jachranka, Conference Proceedings, 505-510 3. Nizioł J., 2005,Dynamics of Gyroscopes. Technical Mechanics. Vol. II: Dyna- mics of Mechanical Systems, J. Nizioł (Edit.), IPPTPanWarsaw, 474-558 4. Osiecki J.W., StefańskiK., 2003,Applyingphase trajectories to control the bearing-taking system,9thNational Conference for Researchers andAcademics on the Automation and Application of Control and Communications Systems, Gdynia, Conference Proceedings ”Automation and Application of Control and Communications Systems”, 2, ISBN 83-87280-60-7, 421-428 5. Osiecki J.W., Stefański K., 2004, The method of automatic optical space scanning and target tracking, Scientific Bulletin of the Rzeszów University of Technology No. 213, Mechanics Bulletin No. 63, Avionics, 2, Rzeszów, ISSN 0209-2689, 421-428 6. Stefański K., 2004, A space scanning system for identifying and tracking aerial targets, 5th International Conference on Armaments ”Scientific Aspects of Armament Engineering”, Waplewo, Conference Proceedings, 939-943 7. US Patent No. 4,030,807 8. VoigtA., 1977,Optical ScanningApparatus withTwoMirrorsRotatableAbout a Common Axis, USPatentNo. 4,039,246 –Aug. 2, 1977 (assigned byGeneral Dynamic Corporation, Pamona, Calif.) 916 J.W. Osiecki, K. Stefański O pewnej metodzie wyszukiwania i śledzenia celu w obronie powietrznej Streszczenie Wpracy przedstawionometodę sterowania ruchemosi giroskopu z umieszczonym w niej układem optycznym dla wykrywania i śledzenia celów powietrznych, emitują- cychpromieniowaniewzakresiepodczerwieni.Nawiązujedowcześniejszychwystąpień autorównakonferencjach i przedstawiadalszy rozwójmetody.Metoda sterowaniapo- lega na wykorzystaniu trajektorii fazowych uchybów sterowania. Manuscript received April 14, 2008; accepted for print August 20, 2008