An Efficient Transition Algorithm For Seamless Drone Multicasting
AAn Efficient Transition Algorithm For SeamlessDrone Multicasting
Wanqing TuSchool of Computer Science, The University of Auckland, New Zealand.Email: [email protected]
Abstract —Many drone-related applications (e.g., drone-aidedvideo capture, drone traffic and safety management) requiregroup communications between drones to efficiently disseminatedata or reliably deliver critical information, making use ofthe line-of-sight coverage of drones to realise services thatground devices may not be capable of. This paper studies high-performance yet resource-efficient mobile drone multicasting viatrajectory adjustment. We first analyse the trajectory adjustmentcondition to determine whether a straight-line trajectory isfully covered by the multicast or not, by conducting simplecomputation tasks and with controlled overhead traffic. We thenpropose the trajectory adjustment scheme to provide a newtrajectory with controlled travel distances. The ETTA algorithmis finally presented to apply the trajectory adjustment conditionand scheme to a drone transiting between forwarders whosecoverage do not overlap. The algorithm relies on multicastingforwarders, instead of additional transition forwarders, to fullycover the adjusted trajectory, helping to control interference andnetwork traffic load. Our NS2 simulation results demonstratethat ETTA, as compared to other mobile multicasts, can achieveguaranteed performance for drone receivers in a multicast withheavier traffic loads.
I. I
NTRODUCTION
To enable information to be delivered to a group of drones isessential for many drone-related applications and services, in-cluding drone safety monitoring, drone traffic management, airrescue assistance, surveillance operations, aerial video capturefor professional or entertainment purposes, etc. Multicastingbetween drones is an efficient communication method forsuch group applications, not only because it may deliverdata to multiple receivers with much less use of transmissionresources but also because it can deliver critical information(e.g., safety alarms, traffic schedules) reliably via multipleparallel paths. Moreover, drone multicasting is helpful in re-laying information for ground multicasting in which membersare not within line of sight of each other. In these groupapplications, drones often change their locations in orderto capture information from different angles, adjust line ofsight ranges between sky and ground, etc. This paper studiesmobile drone transitions in aerial multicasting, supporting thedevelopment of relevant drone applications.Mobile drone multicasting inherits the challenges faced bymobile multicasting on the ground: node transitions cause in-terrupted connections or increased interference. Conventionalground solutions enhance tree-based or mesh-based multi-casting protocols [1-2] to avoid interruption or interference.They however introduce considerable traffic overheads or complex maintenance for networks and their devices, makingthem unsuitable for drones that often have energy constraintsand computational limitations. More popular studies developgeographic multicasting [3-6]. In general, geographic multi-casting arranges group members into different physical zonesbased on their locations. Multicasting trees are establishedto connect different zones and broadcast is used within eachzone. Zone leaders manage members’ joining or leaving whichdecreases the requirement to adjust multicasting trees betweenzones, greatly reducing the incidence of interrupted mobileconnections and the associated interference and overheads.However, broadcasting unnecessarily spreads data to nodesthat do not belong to a group, wasting wireless bandwidthand device energy. Moreover, it is complicated to plan or formzones based on nodes’ physical locations.For drone-related multicasting, the literature mainly focuseson drone-to-earth applications (e.g., [7-8]) in which a dronedisseminates data to a set of ground users/devices. Multicast-ing between drones is rarely studied. The resource limitationsof drones and their wireless connections require handoveroperations to make light use of resources while guaranteeingseamless transitions. Therefore, drone transitions with lowtraffic overhead, controlled energy consumption, and simplecomputation tasks form our design target. Our transitiontakes advantage of the existence of multiple forwarders in amulticasting as well as an obstacle-free aerial communicationenvironment to achieve the expected transition performance. Inour system, straight-line trajectories are adopted with priorityto transfer drones, incurring short travel distances and lowtraffic overheads and hence benefitting resource efficiency.However, straight-line trajectories may not always be seam-less. We hence design a new algorithm - efficient transition viatrajectory adjustment (ETTA) to guide drones’ movement withcontrolled resource consumption. In detail, our contributionsinclude the following results. • Trajectory adjustment condition. We analyse the condi-tion when a straight-line trajectory is not fully coveredby the multicasting system if a drone transits betweenforwarders that have overlapping coverage. The imple-mentation of such condition should be a fast yet resource-efficient process as it mostly requires to calculate Eu-clidean distance based on the 3-dimensional Pythagoreantheorem. • Efficient trajectory adjustment schemes. We design new a r X i v : . [ c s . N I] A ug rajectories to replace interrupted straight-line trajecto-ries for transitions between forwarders with or withoutoverlapping coverage. To balance the tradeoff betweenenabling a fast transition and controlling resource util-isation, these new trajectories are established to limitthe extra travel distance exceeding that of the origi-nal straight-line trajectory when drones move betweenforwarders with overlapping coverage, or to employ aminimal number of forwarders from the multicastingstructure that together can provide seamless coveragefor drones when they move between forwarders withoutoverlapping coverage. • The ETTA algorithm. It systematically combines thecondition and schemes of trajectory adjustment, sup-porting efficient yet seamless drone transitions in aerialmulticasting.Finally, we use NS2 simulations to evaluate our ETTA. Weobserve the average multicast delays, the average multicastthroughput, and the average mobile throughput in differentmulticasting networks. The results show that ETTA may admit more traffic load while guaranteeing the multicastingperformance for both mobile and stable drone receivers.II. R
ELATED S TUDIES
Wireless multicast with static group members focuses onimproving complex interference and limited wireless band-width. Early strategies avoid interference by utilising non-overlapping channels between nearby nodes (e.g., [9]) orby hopping nodes between different channels (e.g., [10]).Transmission scheduling is another well studied strategy thatefficiently utilises channel resources to gain more transmissionopportunities. Studies have scheduled transmission rates (e.g.,[11]), flow transmissions (e.g., [12]), etc. to enable a channelto accommodate more multicasts or to extend multicasts’coverage. External resources, such as licensed RF bands (e.g.,[13]) or wired network links (e.g., [14-15]), are also exploitedfor additional bandwidth.For mobile multicasting, many studies concern the reliableperformance received by mobile members. In [16], a tree mul-ticast is designed that assigns an ID to each multicasting node.Flows are forwarded in order of IDs. Interrupted connectivityis repaired by referring to the sparseness between IDs. Thecore-assisted mesh protocol [1] builds a shared multicast meshto maintain group connectivity when network routers movefrequently. It reverses the shortest unicast paths to form multi-casting paths on the shared mesh, supporting loop-free packetforwarding. Tree- or mesh-based mobile multicasting often re-quires complex operations to maintain connectivity, generatingconsiderable overheads to bandwidth-limited mobile networks.Geographic multicasting (e.g., [3]) improves this drawback bydividing group members into different zones. These zones areconnected via a multicasting. This multicasting structure doesnot change with nodes’ mobility because their movements donot cause zone movement. Within each zone, data is deliveredvia greedy forwarding. The geographic multicasting protocolin [4] computes a Steiner tree to connect zones. It carries concurrent multicasts for a higher delivery ratio, resulting inscalable delay performance even when network sizes increase.The work in [17] designs a virtual-zone-based structure tomanage group members. With the position information ofmulticasting nodes, it constructs a zone-based bidirectionaltree. The protocol uses zone depth to optimise tree structuresand integrates nodes’ location information with group membermanagement to enhance multicasting efficiency.For drone-related multicasting, in [7], drone-to-earth multicasttransmissions are developed by using filter bank multicar-rier. The proposal designs filter bank multicarrier with offsetquadrature amplitude modulation (offset-QAM) and hermitepolynomial-based prototype filtering, helping to manage thetradeoff between performance and spectral efficiency. In [8],drone trajectories are designed theoretically to minimise mis-sion completion time while ensuring each ground terminalto recover the file with a high probability. In general, whilemulticasting between drones is important to support manyemerging, it is however rarely studied in literature.III. E
FFICIENT T RANSITION V IA T RAJECTORY A DJUSTMENT (ETTA)In our drone multicasting system, we employ the link-controlled routing tree (LCRT) algorithm [14-15] (illustratedin Fig. 2 of Section III.B) to form interference-controlled pathsbetween drones. This section studies how to seamlessly transitdrones in a multicasting. We first explore drone transitionsbetween overlapping forwarders, i.e., two forwarders withoverlapping coverage. We then study transitions between non-overlapping forwarders, i.e., forwarders without overlappingcoverage. On this basis, the ETTA algorithm is presented.
A. Transitions Between Overlapping Forwarders
Drone m’s original location Drone m’s destination location
A BC DF A F B m T Fig. 1. Deriving the trajectory adjustment condition.
As mentioned, straight-line trajectories support fast dronetransitions and use resources efficiently. However, they maynot always be seamless. We use Fig. 1 to illustrate how todetermine whether a straight-line trajectory is seamless or notwhen the mobile drone m transits between two overlappingforwarders. In our system, as drones communicate via omni-directional antennas in sky space, we assume that a drone’stransmission range is a sphere with the radius of r . In Fig. 1,if m moves from A to B , let m ’s original and destinationorwarders be F A and F B , and the intersections of the straight-line trajectory with the coverage edges of F A and F B be C and D respectively. Denote the distances between A and B , A and C , and B and D as d ( AB ) , d ( AC ) , and d ( BD ) respectively.Theorem 1 gives the trajectory adjustment condition. Theorem 1.
For a drone m moving between two overlappingforwarders (shown in Fig. 1), the straight-line trajectory fromits origin A to its destination B is seamless if one of thefollowing conditions meets: 1) d ( AB ) ≤ d ( AC ) + d ( DB ) , or 2)when d ( AB ) > d ( AC ) + d ( DB ) , there exists a forwarder in themulticasting whose distances to C and D are both ≤ r .Otherwise, the straight-line trajectory needs to be adjusted. Proof.
We prove Theorem 1 by contradiction. When d ( AB ) ≤ d ( AC ) + d ( DB ) , suppose the straight line A → B is notseamless. Then, some part(s) of the straight-line trajectoryis(are) not covered by F A and F B . Let the length of theuncovered part(s) be l > . We have d ( AC ) + l + d ( DB ) = d ( AB ) ⇒ l = d ( AB ) − d ( AC ) − d ( DB ) . Since l > , wehave d ( AB ) > d ( AC ) + d ( DB ) . This contradicts d ( AB ) ≤ d ( AC ) + d ( DB ) . Therefore, when d ( AB ) ≤ d ( AC ) + d ( DB ) , thestraight-line trajectory does not need to be adjusted.When d ( AB ) > d ( AC ) + d ( DB ) , suppose there exists a mul-ticasting forwarder f whose distances to C and D are both ≤ r . If the straight-line trajectory is not seamless, there is atleast a point between C and D whose Euclidean distance to f is > r . This makes that C → D is not a straight line becausethe two ends C and D are both within the distance of r to f ,contradicting the fact that A → B is a straight line. Q.E.DThe implementation of Theorem 1 requires knowledge of theEuclidean coordinates of C and D , denoted as ( x C , y C , z C ) and ( x D , y D , z D ) respectively. As C is on the edge of F A ’stransmission range. We have ( x C − x F A ) + ( y C − y F A ) + ( z C − z F A ) = r . (1)Also, C is on the straight-line trajectory A → B , i.e., x C = x A + t ( x B − x A ) ,y C = y A + t ( y B − y A ) ,z C = z A + t ( z B − z A ) . (2)Inputting (2) into (1), we obtain t by solving the quadraticequation for t . Typically two distinct values of t will beobtained, defining two distinct points. The point closer to F B is C . Similarly, we obtain D ’s coordinates. Then, by Theorem 1,if A → B is seamless, m transits via this trajectory. Otherwise,a new trajectory is formed as below.When proposing a new trajectory, we try to control traveldistances and traffic overheads with computation of low com-plexity, allowing fast transitions with efficient use of resources(e.g., energy, bandwidth). The idea is to employ a location(denoted as T ), within the overlap of transmission rangesof F A and F B , to form a transition path A → T → B inside the combined coverage of F A and F B . Ideally, T should minimise the extra travel distance exceeding that ofthe straight-line trajectory. Such a location is achievable by anexisting algorithm (e.g., [19]) to seek a point on the surface of the overlapping area that has the shortest distance to thestraight line A → B . However, this potentially increasescomputation delays and its energy consumption. Therefore,as illustrated by T in Fig. 1, we use the closest intersectionbetween the line A → F B and the edge of F B ’s coverage. T ’scoordinates can be represented as below, by the line functionbetween A and F B , x T = t ( x F B − x A ) + x A ,y T = t ( y F B − y A ) + y A ,z T = t ( z F B − z A ) + z A . (3)As T is on the edge of F B ’s coverage, we have ( x T − x F B ) +( y T − y F B ) + ( z T − z F B ) = r . Combining this equationwith (3), we can derive t and hence T ’s coordinates. The newtrajectory A → T → B is shown by the red lines in Fig. 1. B. Transitions Between Non-Overlapping Forwarders level 3level 2level 1level 0 01 23 4 567 86A BD
Fig. 2. An example of forming the LCRT tree and the ETTA trajectory.
Recall that, in our system, a multi-hop multicasting tree isestablished by the LCRT [14-15] algorithm to connect drones.As shown in Fig. 2, drones are assigned to different levelsbased on their shortest hop distances to the source (i.e., drone0 in Fig. 2). Then, from the second highest level (level 2 inFig. 2) to the second lowest level (level 1 in Fig. 2), at eachlevel, drones covering more forwarders/receivers at the imme-diately higher level are selected as forwarders with priority,until all forwarders/receivers at the immediately higher levelhave found their forwarders.When transiting between non-overlapping forwarders, in orderto form a seamless trajectory with controlled travel distanceto replace an interrupted straight-line trajectory (e.g., the bluedotted line in Fig. 2), our idea is to select a minimal number ofLCRT forwarders that overlap one by one to provide coveragealong the transition path. In detail, m generates an overlappinggraph to represent how LCRT forwarders’ coverage overlaps.LCRT forwarders are nodes on this graph. If two forwardersare overlapping, an edge between nodes representing the twoforwarders is added to the graph. Fig. 3 shows the overlappinggraph of the multicasting tree in Fig. 2.On this overlapping graph, each edge has a weight. Denote theweight of edge i ( i ∈ [0 , e − ) connecting two overlapping Fig. 3. The overlapping graph of the LCRT multicasting tree in Fig. 2. forwarders (say f (cid:48) and f (cid:48)(cid:48) ) as ω i , where e is the total numberof edges in the graph. For obtaining a short-delay trajectory, ω i is the Euclidean distance between f (cid:48) and f (cid:48)(cid:48) , namely, ω i = d f (cid:48) ,f (cid:48)(cid:48) = (cid:113) ( x f (cid:48) − x f (cid:48)(cid:48) ) + ( y f (cid:48) − y f (cid:48)(cid:48) ) + ( z f (cid:48) − z f (cid:48)(cid:48) ) , (4)where ( x f (cid:48) , y f (cid:48) , z f (cid:48) ) and ( x f (cid:48)(cid:48) , y f (cid:48)(cid:48) , z f (cid:48)(cid:48) ) are the coordinatesof f (cid:48) and f (cid:48)(cid:48) respectively. In Fig. 3, the red distance symbolsare edge weights achieved by (4). Via this weighted overlap-ping graph, by employing existing algorithms (e.g., Dijkstra’salgorithm, the A ∗ search algorithm), m searches the path thatconnects its original forwarder to its destination forwarderswith the lowest weight value.With the selected forwarders, m starts forming a seamlesstrajectory. Excluding the original and destination forwarders,we refer to all other selected forwarders as m ’s trajectoryforwarders. Suppose there are n trajectory forwarders withthe i th ( i ∈ [0 , n − ) one denoted as T F i . m calculates theintersections between the coverage edges of two overlappingtrajectory forwarders T F i and T F ( i +1) and between the cover-age edges of T F n and F B . Typically two distinct intersectionswill be obtained. The closer to m ’s destination B , called theeligible intersection (EI), is employed to form m ’s trajectory.In detail, m employs Theorem 1 to check the seamlessnessof the straight line between m ’s origin A and the first EI. Ifseamless, the straight line forms part of m ’s trajectory. If not, m employs the scheme in Section III.A to find the intersection T between the edge of T F ’s coverage and the straight lineconnecting A and T F . The trajectory ( A → T → the first EI)becomes a part of m ’s trajectory. Hereafter, for the remainingparts of m ’s trajectory, straight lines connecting consecutiveEIs are used. This is because two consecutive EIs are coveredby the same trajectory forwarder, ensuring that the straight linebetween them is seamless. The last part of m ’s trajectory isformed by the seamless straight line between the EI and B asboth locations are covered by F B .We use an example in Fig. 2 to show how to form such atrajectory. Based on the overlapping graph (Fig. 3), supposedrone 6 selects drones 3, 1, & D in the figure) between thecoverage edges of drones 1 &
5. By Theorem 1, drone 6decides that A → D is seamless and hence includes it as partof the trajectory. Now, as drone 1 overlaps with the destinationforwarder drone 5, D → B becomes the remaining part of thetrajectory. The red dotted arrow lines show the trajectory. C. The ETTA Algorithm
During establishing the multicasting tree, the selected LCRTforwarders exchange location information , and calculatesand exchanges their Euclidean distance to each other. Then,combining drone transition schemes between overlapping ornon-overlapping forwarders, we present the ETTA algorithm.————————————————————————— Algorithm 1 Efficient Transition via Trajectory Adjustment
Input:
Mobile drone m , m ’s origin ( A ) and destination ( B ), m ’s origin and destination forwarders F A and F B ;Output: m ’s ETTA transition trajectory from A to B .—————————————————————————1. m checks whether F A and F B are overlapping or not;2. If overlapping, by Theorem 1, m checks whether thestraight-line trajectory is seamless or not;3. If so, m transits via A → B directly; Exit.4. If not, m decides T to form a new seamless traje-ctory A → T → B to transit; Exit.5. If non-overlapping,6. m generates an overlapping graph for LCRT for-warders; m assigns weights to edges on the graph by (4);7. m employs Dijkstra’s or A ∗ algorithm to find apath with the minimum weight value; suppose n trajectoryforwarders on the path;8. m calculates the EI between the edges of thecoverage of T F and T F ;9. If the trajectory ( A → this current EI) is seamlessbased on Theorem 1, it becomes part of m ’s trajectory;10. Otherwise, m calculates T to form a new seam-less part of its trajectory, ( A → T → this current EI);11. i = 2 ;12. While i < n m calculates the EI between the edges of thecoverage of T F i and T F ( i +1) ; the straight line between thelast EI and this EI becomes part of m ’s trajectory; i = i + 1 ;14. m calculates the EI between the coverage edges of T F n and F B ; the straight line from the EI to B is the lastpart of m ’s trajectory; Exit.—————————————————————————IV. S IMULATION E VALUATIONSTABLE IS
IMULATION P ARAMETERS
Parameters Values Parameters Values
Frequency 2.4GHz Propagation model Free spaceDimensions 3D Transmission power 15dBmNumber of 1 Wireless channel 54Mbpschannels data rateReceive -80dBm MAC protocol 802.11thresholdAntenna Omnidirectional Simulation time 200santenna The location information may be obtainable for example via a GPSreceiver. Research studies (e.g., [21]) also proposed good schemes to locatenodes in mobile ad-hoc networks. e conduct experimental studies with the discrete eventnetwork simulator NS2.35 [18] to compare four multicastingschemes when they handle mobile group members:
LCRT [14-15] that does not provide transition support for mobile groupmembers;
T-LCRT that enhances LCRT by selecting droneson the multicasting tree to support mobile transition. A dronereceiver may forward data to a mobile drone when it is closeto this receiver;
EGMP [17], a geographic multicasting, thatgroups drones into zones and connects these zones via a bi-directional tree;
ETTA , i.e., our algorithm that supports dronetransitions by only using forwarders on the multicasting tree.Table I lists common settings used in our simulations. Weevaluate the following performance for the four schemes. Ourresults plotted are the mean values of 20 simulation runs. • Average multicast delay (AMD).
AM D = AD i n , i ∈ [0 , n − , where AD i is the average packet delay at the i th drone receiver, and n is the total number of dronereceivers in the group. • Average multicast throughput (AMT).
AM T = AT i n , i ∈ [0 , n − , where AT i is the average data throughput atthe i th drone receiver. A. Evaluation of Small-Group Mobile Multicasting
We first conduct a small-group simulation with 9 drones. Thereis 1 mobile drone which moves a distance of 102.6 metersat a speed of 10m/s during the multicasting. We vary thenetwork traffic load from 512Kbit/s to 2.176Mbit/s to observethe four schemes. Fig. 4 shows the AMD performance. LCRTand ETTA achieve shorter AMDs than T-LCRT and EGMPdo. This is because T-LCRT and EGMP employ nodes thatare not forwarders on the multicasting structure as transitionforwarders for the mobile drone, while ETTA makes use ofmulticasting forwarders to handover the mobile drone andLCRT does not implement any handover process. The employ-ment of transition forwarders that are not on the multicastingstructure generates extra traffic to the system, prolonging themulticasting delays of T-LCRT and EGMP. Between T-LCRTand EGMP, T-LCRT issues control traffic to the system inorder to determine suitable transition forwarders. This extratraffic load worsens AMD for T-LCRT as compared to EGMP.Both LCRT and ETTA achieve all AMDs under 150ms in thissimulation. The slight AMD difference is due to the fact thatthey calculate AMDs based on different packets: the AMDof LCRT does not take those packets dropped during mobiletransition into account while ETTA calculates the AMDs basedon all transmitted packets.Fig. 5 plots the AMT performance. ETTA achieves the highestAMT because it attempts to transit the mobile drone byplanning trajectories fully covered by the LCRT tree. ETTAtrajectories are formed by multicasting forwarders and henceno extra traffic is generated to the system. Also, such trajec-tories are planned using LCRT forwarders’ coordinates thatare obtained when establishing the LCRT tree, generatinglittle control traffic to the system. For LCRT, it has thelowest AMT because the mobile drone does not receivedata during its movement. EGMP and T-LCRT both employ
Network Traffic Load (Mbit/s) A v e r age M u l t i c a s t D e l a y ( s ) LCRTT-LCRTEGMPETTA
Fig. 4. Comparison of AMDs in the small-group simulation.
Network Traffic Load (Mbit/s) A v e r age M u l t i c a s t T h r oughpu t ( % ) LCRTT-LCRTEGMPETTA
Fig. 5. Comparison of AMTs in the small-group simulation. transition forwarders to provide connections to the mobiledrone, allowing them to achieve better AMTs than LCRT.Moreover, EGMP uses transition forwarders without changingthe multicast structure and these transition forwarders cantransmit to the mobile drone in time, contributing to EGMP’shigher AMT than T-LCRT. This improvement is achieved byasking the mobile drone to travel around 20 meters further.
B. Evaluation of Large-Group Mobile Multicast
Network Traffic Load (Mbit/s) A v e r age M u l t i c a s t D e l a y ( s ) LCRTT-LCRTEGMPETTA
Fig. 6. Comparison of AMDs in the large-group simulation. .128 0.192 0.256 0.32 0.384 0.448 0.512 0.576 0.64 0.704 0.768 0.832 0.896 0.96
Network Traffic Load (Mbit/s) A v e r age M u l t i c a s t T h r oughpu t ( % ) LCRTT-LCRTEGMPETTA
Fig. 7. Comparison of AMTs in the large-group simulation.
The large-group simulation has the 165 drones distributed sothat each transmission range has 10 drones. Three mobiledrones exist: the first one moves 587 meters at a speed of10m/s, the second one moves 346 meters at a speed of 25m/s,and the third one moves 608 meters at a speed of 20m/s. Weevaluate the four multicasting algorithms when the networktraffic load varies from 128Kbit/s to 960Kbit/s. Based onFig. 6, the four protocols yield similar relative results for AMDin the large-group simulation as was observed in the small-group simulation. Similar reasons for the results in Fig. 4 canexplain the results plotted in Fig. 6.In Fig. 7, ETTA achieves higher AMT performance than otherprotocols. As compared to the AMT from the small-groupsimulation (in Fig. 5), although the relative results are similar,ETTA outperforms other protocols by a wider margin in thelarge-group simulation. ETTA achieves good AMT ( orabove) when the network traffic load is ≤ or more traffic withguaranteed AMT than EGMP and T-LCRT. This is because inthe large-group simulations, EGMP and T-LCRT require morecomplicated procedures or take more time to find transitionforwarders. More transition forwarders issue extra data trafficto the system as well. This improvement is achieved by askinga mobile drone to travel around 87 meters further on average.V. C ONCLUSION
In this paper, we studied drone multicasting in order to enablehigh-performance group communications between drones. Ourdevelopment focused on how to seamlessly transit mobiledrones in a resource-efficient manner, given the resource lim-itations experienced by drones and their wireless connections.A new algorithm, ETTA, was proposed that takes advan-tage of the obstacle-free aerial communication environmentto establish straight-line trajectories for mobile drones. Assuch straight-line trajectories may not always be seamless,we theoretically presented the trajectory adjustment conditionby which the ETTA algorithm can determine the seamless-ness of a straight-line trajectory. To replace an interrupted straight-line trajectory, we proposed new schemes to form adistance-controlled trajectory with forwarders already on themulticasting tree. As such, the ETTA algorithm allows fastdrone transitions while controlling traffic overheads issuedto the network. Our simulation results proved that ETTAdelivers multicast data with acceptable performance when themulticasting system carries more traffic than comparedmobile multicasting protocols.Rmore traffic than comparedmobile multicasting protocols.R