Formation Control of Small Unmanned Aerial Vehicles Using Virtual Leader and Point-to-Multipoint Communication

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1 Trans. Japan Soc. Aero. Space Sci. Vol. 5, No., pp. 3 9, Formation Control of Small Unmanne Aerial Vehicles Using Virtual Leaer an Point-to-Multipoint Communication y Takuma HINO an Takeshi TSUCHIYA Department of Aeronautics an Astronautics, The University of Tokyo, Tokyo, Japan (Receive December th, 9) In this paper, a simple but robust formation control scheme that can be applie to small unmanne aerial vehicles is propose. The propose formation control scheme is base on the virtual leaer approach, where formation members control their position in relationship to a common virtual leaer. The most istinguishing feature of the propose scheme is that only information on the virtual leaer is communicate between formation members. This feature gives the control scheme a extremely high robustness to communication failures an unit losses. Numerical simulation shows that the formation can be properly forme even if only 5% of the total communication succees. It is also shown that wingmen s position can be estimate to some extent, using the information communicate. Key Wors: Formation Control, Unmanne Aerial Vehicles, Point-to-Multipoint Communication. Introuction For the past two ecaes, formation flight of unmanne aerial vehicles (UAVs) has been one of the areas of great interest to researchers. UAVs varying greatly in size an weight have been evelope throughout the worl. They are effective in missions too risky or too costly for manne aerial vehicles to perform, Among the large number of UAVs evelope, those with wingspans aroun meters (i.e., small UAVs) are especially useful, as they o not require hangars to store or runways to take off or lan. However, the short cruise ranges of small UAVs restrict their fiels of application. One of the key ieas in overcoming this is the use of formation flight. Formation flight, commonly isplaye by flocks of migrating birs, can reuce inuce rag, leaing to longer cruise range. Also, formation flight has other useful aspects in terms of mission execution. First, mission capability is not lost by a single aircraft failure, as other members in the formation are able to carry on with the mission. Secon, for reconnaissance or search an rescue missions, the target area can be covere in a much shorter time if multiple vehicles are utilise. Therefore, mission execution by formations is particularly effective for time critical missions. For the above reasons, we will aress small UAVs as the target vehicle in this paper, as they will have greater benefit from it compare to their larger counterparts. Much research has alreay been one on formation flight. The effectiveness of formation flight has been escribe by Lissaman, ) Hummel ) an Shevell. 3) Lissaman an Hummel conucte theoretical analyses on formation flight of birs, while Shevell extene the use of Munk s stagger theorem from multi-planes to aircraft formations. Analysis Ó The Japan Society for Aeronautical an Space Sciences by Lissaman suggeste the existence of an ieal formation, where all formation members have equal benefit. Fowler ) evelope multiwing testbes which can be put insie win tunnels to emulate formation flight. The evelope testbes were use to obtain a aileron-to-yaw moel. Many formation control schemes have alreay been iscusse. Giulietti 5) gave an overview on formation control schemes for aircraft, an use the Dijkstra algorithm to form communication graphs. He also synthesize a formation reconfiguration scheme. Wolfe ) use a linearize aeroynamic moel of aircraft formation an synthesize a linear quaratic regulator to control it. Lewis 7) use virtual structures to control formations of groun-base robots. The fitting process of the virtual structure has a very high computational cost an was one using esktop computers, not robots. Virtual structures were also use by Ren, 9) where the target vehicles were spacecrafts. aras ) focuse on ecentralizing the controller an use vector fiels. y ecentralizing the controller, he obtaine a scheme with high robustness. However, much calculation (incluing ivision) an communication are require to compute the vector fiel. Pollini ) use wake sensing to estimate wingmen s position an synthesize a control scheme with no communication. Xi ) reuce communication between vehicles by setting a blin zone, where the units o not communicate with each other. Fax ) focuse on information exchange within the formation using graph theory. In formulating formation control schemes, some aspects must be kept in min. First, the scheme shoul be kept simple enough to be run on feeble computers onboar small UAVs; no complex fitting process require. This rules out approaches using virtual structure or potential/vector fiels. Secon, the scheme shoul not have point weaknesses. This rules out the common leaer-follower approach. Thir, the scheme shoul not rely too much on communication;

2 Trans. Japan Soc. Aero. Space Sci. Vol. 5, No. the scheme shoul not require information on the entire formation. This again rules out the virtual structure approach. For these reasons, we choose to formulate a simple but robust control scheme base on the virtual leaer (VL) approach. Aitionally, point-to-multipoint (PMP) communication is utilise to reuce communication cost an increase robustness. This paper is organize as follows. In Section, the outline of the propose scheme is escribe. Following that, the stability an convergence of the propose scheme is given in Section 3. Numerical simulation results are iscusse in Section, an the paper is summarize in Section 5.. Control Scheme Outline The outline of the propose control scheme can be ivie into two phases: the local control phase an the communication phase. The etails of each phase are as follows... Local control phase Each member of the formation has it s own VL insie its computer, an the VL has the same ynamics as the UAV. oth the formation members an their VLs are controlle by a state feeback controller so that they keep a specifie relative position to each other. The VLs have an aitional control loop that enables them to track the esire course. For linear or locally linearize systems, this is written as t x m l;i x m f ;i " ¼ A # x m l;i A x m f ;i " # Kll K fl K lf K ff x m l;i x m f ;i! x l;i;targ x f ;i;targ ðþ an rawn as shown in Fig.. x m l;i an xm f ;i are the state vector of the ith unit an its VL after the mth communication roun, A is the system matrix, the control matrix, an the four K s are the feeback gains. x l;i;targ an x f ;i;targ are the target values for x m l;i an xm f ;i respectively. The feeback gains are chosen such that the system (incluing VL) is stable. Therefore, Reð k Þ ðk ¼ ; ;...Þ ðþ where k is the kth eigen value of the system... Communication phase In each communication roun, all formation members attempt to broacast information on their VL using pointto-multipoint communication. On receiving information, formation members moify their VL as x mþ:5 f ;j < ¼ xm f ;i þ xm f ;j : x m f ;j (communication succees) (communication fails) where the ith unit is the transmitter an jth unit the receiver, an x mþ:5 f ;j represents the intermeiate state between x m f ;j an xf mþ ;j. x f,i,targ - K f f K f l K l f x m f,i A /s ð3þ When all members have attempte to transmit information on their VL (en of communication roun), the superscript is incremente to m þ an each formation member continues to control their position as before. y repeating these steps, the VLs are ientical throughout the formation, an formation members are at the esire position from the VL. Hence, the formation itself takes the esire shape, heaing in the esire irection. Mathematical proof is given in the next section. As all formation members are ientical, the propose scheme has a higher robustness compare to the leaerfollower approach. Also, as only information on the VL is communicate (no information on actual position is require), high robustness against communication failures is obtaine. Furthermore, as communication is one using point-to-multipoint communication, the total number of transmissions is greatly reuce. 3. Stability, Convergence an Properties of Propose Scheme In this section, the stability an convergence of the propose scheme are explaine mathematically, an some brief comments are mae on interesting properties of the propose scheme. VL to track esire course 3. Control against new VL. Moify VL x l,i,targ - K l l x m l,i A /s Keep relative position Desire course (a) Local control. Communicate VL information (b) Communication Fig.. lock iagram of the state feeback controller. Fig.. Outline of propose scheme.

3 Aug. T. HINO an T. TSUCHIYA: Formation Control of Small UAV Using Virtual Leaers an PMP Communication Stability an convergence The stability of the local control is assure by Eq. (). This equation assures that after sufficient time, each formation member is at a specifie relative position to the VL, while the VL tracks the esire course. Thus, only the convergence of the scheme remains to be shown. For the formation to converge into the esire shape, the VL must converge into a single point. The egree of convergence can be evaluate by the maximum istance between the VL s state vectors after the mth communication roun m : m ðtþ ¼maxx m f ;i ðtþ xm f ;j ðtþ ðþ i;j where t is the time elapse from the mth communication roun. Aitionally, the VL s state vector is expresse as a sum of normalize eigen vectors v k : m i;k x m f ;i ðtþ ¼X k jv k j¼ m i;k v k expð k tþ in the above equation is the coefficient for the ith unit after the mth communication roun. The suffix i is not require for the eigen vectors, as all units use the same feeback gain an the eigen vectors are ientical between units. We prove the following theorem relate to m. (Theorem) m is monotonically non-increasing, therefore ð5þ ðþ mþ m ðm ¼ ; ; ;...Þ ð7þ (Proof) We again ivie the proof accoring to the phases escribe in the previous section Local control phase From Eq. (), the istance between VL s state vectors at time t after the en of the mth communication roun is, x m f ;i ðtþ xm f ;j ðtþ ¼ X m i;k m j;k v k exp k t k X m i;k m j;kjv k jj exp k tj k X m i;k m j;k k ¼ x m f ;i ðþ xm f ;j ðþ ðþ Therefore, m ðtþ ¼maxx m i;j f ;i ðtþ xm f ;j ðtþ maxx m f ;i ðþ xm f ;j ðþ i;j ¼ m ðþ 3... Communication phase Let S k be the set of units the kth unit succees in transmitting ata to. Using Eq. (3) an triangle inequality, the istance between VLs becomes ð9þ x mþ:5 f ;j x mþ:5 f ;k Therefore, xm f ;j xm f ;k ðj; k S i Þ xm f ;j þ xm f ;i >< xm f ;k ðj S i ; k S i Þ ¼ xm f ;j xm f ;k ðj S i ; k ¼ iþ >: x m f ;j xm f ;k ðj; k S i Þ xm f ;j xm f ;k ðj; k S i Þ xm f ;j xm f ;k þ xm f ;i xm f ;k >< ðj S i ; k S i Þ ðþ xm f ;j xm f ;k ðj S i ; k ¼ iþ >: x m f ;j xm f ;k ðj; k S i Þ ¼ m mþ m ðþ ðþ From Eqs. (9) an (), m is prove to be monotonically non-increasing. (En of proof) From the above theorem, the formation will converge into the esire shape as long as sufficient communication succees between units so that m converges to. Whether the communication within the formation allows it to converge can be iscusse using the ajacency matrix H m an its prouct: H p;q H p H pþ H q H q ¼ Yq H m ð3þ m¼p The ith row, jth column entry of H m is if communication from the ith unit to the jth unit succees in the mth communication roun an if it fails (iagonal entries are always ). The ith row, jth column entry of H p;q is equal to the number of communication paths from the ith unit to the jth unit that exist between the pth communication roun an qth communication roun. The following hypothesis regaring convergence is establishe. (Hypothesis) m will converge to zero if, for all natural numbers p, there exists a finite number r such that matrix H p;pþr has at least one row in which all entries are non-zero. In other wors, there is always a unit within the formation whose VL information is passe on to every formation member within r communication rouns. This is a very straight forwar, intuitively correct hypothesis, but is yet to be mathematically proven. Instea, we show that the hypothesis hols using Monte-Carlo simulation. Communication networks with up to units are ranomly create an evaluate to etermine whether or not m converges to zero. The minimum istance

4 Trans. Japan Soc. Aero. Space Sci. Vol. 5, No. δ m δ m Fig.. Fig. 3. Communication rouns r exists r oes not exist m for fixe communication networks. r exists r oes not exist Communication rouns m for communication with stochastic factor. between VLs is initially set to. an, cases are evaluate. The transition of m for fixe communication is shown in Fig. 3; each unit is able to sen information to the same units in every communication roun. Note that the graph is ouble logarithmic. There is a clear ifference between the cases where r exists (re bol lines) an those where it oes not (blue ashe lines). When r exists, m continuously ecreases until the computational limit, whereas when r oes not exist, m levels off at a value far higher than the computational limit. The same tren can be seen for communication with stochastic factors: communication between units fails from time to time, which is shown in Fig.. Out of the, cases evaluate, none of the cases violate the hypothesis. Therefore, at this moment, the hypothesis can be sai to be analytically true. 3.. Properties 3... Flexibility of operation The propose scheme is extremely flexible in terms of operation. As formation members control themselves accoring to the VL, they o not necessarily require knowlege on number of members an overall formation shape. Therefore, the control scheme is extremely robust in that:. Units can be easily ae to or remove from the formation.. Unit an communication failures o not affect other formation members. 3. No irect communication is require between all formation members (both tight an sprea-out formations can be controlle by the same scheme).. Multiple formations sharing VL information can be controlle together Total communication cost The propose scheme uses point-to-multipoint communication. Thus, the total number of transmissions mae per communication roun for a formation of n units is n ¼ OðnÞ. However, if conventional point-to-point communication is use, the total number of transmissions is nc ¼ Oðn Þ, an orer higher than the propose scheme VL an formation centre of gravity matching After the VLs have converge, its motion can be mae to match that of the centre of gravity of the formation using aequate gain selection. When the VLs have converge into a single point x f, the equation of motion for the centre of gravity of the formation x C.G. is given as t x C.G. ¼ " X n x m # l;i x f t n i¼ x f xc.g. A ¼ A x f " K # ll K fl xc.g. K lf K ff x f ðþ The target vector has been omitte for simplicity. For x C.G. to be ientical to x f ; A K ll K fl ¼ A K ff K lf, ðk ll K lf þ K fl K ff Þ¼ ð5þ The above equation is not obligatory, but helps in efining formations an controlling them.. Numerical Simulation To verify the performance of the propose formation control scheme, numerical simulation using a simple two-imensional moel is performe... Numerical moel The equation of motion for the numerical moel use in the simulation is 3 3 V sin x e y V cos e 7 t V 5 ¼ C t t þ C r j r j ðþ 7 V sin 5 r where is the wheelbase, an C t, C r are coefficients regaring the two control inputs t an r. Their values are liste in Table. Other symbols are efine as in Fig. 5. To make the moel more realistic, upper bouns, lower bouns an rate limits have been applie to the control inputs. The limits an other important simulation parameters are also liste in Table. To enable calculation using the computers onboar small UAVs, we use a linearize moel, which is obtaine by linearizing the above moel aroun trim spee V an trim heaing as

5 Aug. T. HINO an T. TSUCHIYA: Formation Control of Small UAV Using Virtual Leaers an PMP Communication 7 Table. Moel parameters. Parameter Unit Value Wheelbase m. C t C r G/ra.5 Control upate Hz 5 Communication Hz Input limits t upper limit G. t lower limit G : t rate limit G/s 5. r upper limit ra. r lower limit ra : r rate limit ra/s 5. Measurement noise (STD) Position m.3 Spee m/s.3 Heaing ra. Disturbances (STD) Force G. Moment Gm.3 δ r y e x e V, δt Θ Fig. 5. Numerical moel use Formation Formation Formation 3 Fig.. Desire formations. [m] x sin V cos x y 7 t v 5 ¼ cos V sin y v 5 þ C t 7 V 5 t r ð7þ where x ¼ x e sin t ðþ y ¼ y e V cos t ð9þ v ¼ V V ðþ ¼ ðþ In the following simulations, the trim spee an heaing are set as V ¼ :5 [m/s] an ¼ [ra], respectively. Aitionally, all state variables (x e ; y e ; V; ) are assume to be observable in the simulation... Simulation scenarios Five units are to form the formations shown in Fig. (numbers insie the rectangles are unit numbers) uner the following cases. Case Form formation when 5% of total communications succees. Case Unit loss (unit no. ) at t ¼ 5 s when 5% of total communications succees. Case 3 Merge formations an 3 into formation at t ¼ 5 s when 5% of total communications succee. No communications between formations an 3 before they are merge. Case Divie formation into formations an 3 at t ¼ 5 s when 5% of total communications succee. No communications between formations an 3 after separation..3. Simulation results The simulation results using feeback gain 3 :5 :5 :5 K ll K fl :5 ¼ 7 ðþ K lf K ff :5 : :5 : 5 :5 : :55 :

6 Trans. Japan Soc. Aero. Space Sci. Vol. 5, No (b) x e position error (c) y e position error (a) Overview 3 5 Fig. 7. Simulation results (Case ). Change Formation (b) x e position error (c) y e position error (a) Overview 3 5 Fig. 9. Simulation results (Case 3) Unit Failure (b) x e position error (c) y e position error (a) Overview 3 5 Fig.. Simulation results (Case ). Change Formation (b) x e position error (c) y e position error (a) Overview 3 5 Fig.. Simulation results (Case ). are shown in Figs. 7. The position errors in the figures are the ifferences between the actual position of units an their targete position within the formation. In each case, the formation settles into the esire shape, with a maximum position error of : [m]. This is an acceptable value, consiering measurement noise an other isturbances. Figure 7 (Case ) emonstrates the robustness of the control scheme to communication failures, where the formation is successfully forme even if only 5% of the communication succees. The flexibility an robustness to unit failures of the propose metho can also be seen in cases. In case, units are not affecte by unit s failure at t ¼ 5 [s], an continues on as if nothing happene. In cases 3 an, the formations are successfully merge or ivie. From the simulation results, it can be conclue that the propose formation control scheme satisfies the requirements given in Section I... Wingman estimation Numerical simulation tests reveale the possibility of estimating wingman s position using only VL information. This is because the motions of the VL s an formation members are linke by feeback gains K fl an K lf, shown in Fig.. Therefore, VL information contains information on the formation member that sent it. If the estimation of the wingman s position can actually be one using VL information, it can be use for collision avoiance without the nee of communicating its own position. The estimation results uner % communication success are shown in Fig.. It can be seen that the wingman s position is estimate to some extent (maximum error :5 [m]), but not yet enough for practical use. Further testing an improvement of the estimation metho are require for the estimate values to be use for collision avoiance. 5. Conclusion In this paper, a low-calculation cost formation control scheme robust against communication failures an unit losses is propose. The convergence an stability of the propose scheme is shown mathematically an numerically. The performance of the propose scheme is evaluate by numerical simulation. Numerical simulation results show that the formation can be properly forme even if only 5% of the total communication succees. Aitionally, numerical simulation reveals the possibility of estimating the wingman s position from the VL information receive.

7 Aug. T. HINO an T. TSUCHIYA: Formation Control of Small UAV Using Virtual Leaers an PMP Communication (a) x e estimation error (b) y e estimation error Unit 's etimate of Unit Unit 's etimate of Unit 3 Unit 3's etimate of Unit Unit 's etimate of Unit 5 Unit 5's etimate of Unit Fig.. Wingman position estimation uner % communication success. For future stuies, the propose scheme will be use to control formations of UAVs. Several steps must be taken before real flight tests by UAVs are possible. The authors are currently preparing for tests using raio-controlle carbase autonomous groun test vehicles. Along sie this preparation, numerical simulations using UAVs will be carrie out to etermine feeback gains. After these two steps are complete, real flight tests will be performe. Flight tests are targete for spring. Aitionally, measures to acquire the wingman s position will be introuce. The most feasible measure is to use visual cues; as the wingman s position shoul be possible even if no communication exists. The estimate position of the wingman using VL information will be use to support this. References ) Lissaman, P.. S. an Shollenberger, C. A.: Formation Flight of irs, Science, (97), pp ) Hummel, D.: Aeroynamic Aspects of Formation Flight in irs, J. Theor. iol., (93), pp ) Shevell, R. S.: Funamentals of Flight, n e., Prentice Hall, Unite States of America, 9. ) Fowler, J. M. an D Anrea, R.: A Formation Flight Experiment, IEEE Control Systems Magazine, 3 (3), pp ) Giulietti, F., Pollini, L. an Innocenti, M.: Autonomous Formation Flight, IEEE Control Systems Magazine,, (), pp. 3. ) Wolfe, J. D., Chichka, D. F. an Speyer, J. L.: Decentralize Controllers for Unmanne Aerial Vehicle Formation Flight, Guiance, Navigation an Control Conference, AIAA Paper , 99. 7) Lewis, M. A. an Tan, K.-H.: High Precision Formation Control of Mobile Robots Using Virtual Structures, Autonomous Robots, (997), pp ) aras, J. S., Tan, X. an Hovareshti, P.: Decentralize Control of Autonomous Vehicles, Proceeings of the n IEEE Conference on Decision an Control, 3, pp ) Ren, W. an ear, R. W.: Virtual Structure ase Spacecraft Formation Control with Formation Feeback, AIAA Guiance, Navigation, an Control Conference an Exhibit, AIAA Paper 93,. ) Pollini, L., Giulietti, F. an Innocenti, M.: Sensorless Formation Flight, AIAA Guiance, Navigation, an Control Conference an Exhibit, AIAA Paper 35,. ) Xi, X. an Abe, E. H.: Formation Control with Virtual Leaers an Reuce Communications, Proceeings of the th IEEE Conference on Decision an Control, an the European Control Conference, 5, pp. 5. ) Fax, J. A. an Murray, R. M.: Information Flow an Cooperative Control of Vehicle Formation, IEEE Trans. Automatic Control, 9 (), pp. 5 7.