Drone Package Delivery: A Heuristic approach for UAVs path planning and tracking

In this paper we propose a new approach based on a heuristic search for UAVs path planning with terrestrial wireless network tracking. In a previous work we proposed and exact solution based on an integ er linear formulation of the problem. Unfortunately, the exact resolution is limited by the computation complexity. In this case, we propose in this paper a new approach based on a heuristic search. More precisely, a heuristic adaptive scheme based on Dijkstra algorithm is proposed to yield a simple but e ff ective and fast solution. In addition, the proposed solution can cover a larg e area and generate a set of optimum and near optimum pa ths according to the drone battery capacities. Finally, the simulation results show that the drone tracking is sustainable even in noisy wireless network environmen t.


Introduction
For decades, Unmanned Aerial Vehicles (UAVs) are widel y used in modern warf are for surv eillance, reconnaissance, sensing, battle damag e assessmen t and attacking.The benefit of UAVs incl ude red uced costs and no warfighte risk.In fact UAVs use is increased by time, especiall y under the concept of the netw orkcen tric oper ation environmen t and under the concept of rev olution in military affairs.Recen tl y, technol ogical adv ances in micro controllers, sensors, and batteries have drama ticall y increased their utility and versa tility and yet, a new horizon is open for civilian uses.This beg an with limited aerial pa trols of the nation's borders, observ ation and aerial mapping, disaster response incl uding search and support to rescuers, sports ev ent cov erag e and la w enf orcemen t.Although the mar ket is almost nonexisten t toda y, this is most likel y in the civil fie d tha t drones are expected to pla y the larg est role.Recen tl y, those f ying machines have also been destined to the commercial mar ket and have gained much atten tion.In fact , a forthcoming plans for commercial drone use have been recen tl y announced by a number of companies around the world such, Amazon, Wallmart , DHL, and Zookal which are investing in mini drones dev el opmen t for variety of tasks, incl uding freight and packag e deliv ery to consumers.The introd uction of drones in civil applica tions raises new challeng es to the governmen t authorities in charg e of fligh security and air traffic manag emen t which have to balance saf ety and public concerns ag ainst the poten tial economic benefit By virtue of their small size, mini drones are di fficul t to be detected and to be tracked.In this frame, the European Parliamen t adopted a resol ution on the use of drones, which requires Member States to implemen t various regula tions to ensure the saf ety of the airspace and to ensure the priv acy of citizens threa tened by the use of these f ying machines.Through this resol ution, it is considered tha t reg ardless of their sizes, the question of iden tifying is essen tial, and emphasized the need to provide appropria te sol utions in terms of locating and tracking.In other words, this new report aims to ensure the traceability of all UAVs, but also oper ators and owners as a sine qua non-conditions for any use.

Figure 1. Drone package delivery
It is obvious tha t pa th planning is one of the most crucial tasks for mission definitio and manag emen t of the aircr aft and it will also be an importan t requiremen t for UAVs tha t has autonomous fligh capabilities [1].Basicall y, an efficien t off-line pa th planning coul d help to ensure a permanen t localiza tion and tracking of the drone.Moreov er, the predetermined trajectory unable to avoid obstacles and ev entual collisions with other drones, and also to optimize certain functionalities in certain environmen t.How ev er, mission nature, battery capacity , drone char acteristics and hov ering capabilities strongl y inf uence the pa th planning str ategy [2].The oper ational problem tha t this work address is enabling the governmen t authorities in charg e of fligh saf ety to iden tify , locate and to track drones.Usuall y the area is larg e and the detection and localiza tion time to fin the UAV is the critical par ameter tha t shoul d be minimized.To this end and in order to make this possible, we presen t in this paper a newl y approach based on the expl oita tion of the available wireless netw ork cov erag e.This approach relies on a pow erful inter action, or collabor ation betw een the UAVs and the oper ators.Cooper ation in such environmen t implies tha t the drone periodicall y send its iden tific tion, localiza tion, speed and other inf orma tion to the remote oper ators through the available wireless netw orks.The sol ution we aim to presen t provide or inf orm of the optim um and the near optim um pa ths tha t the drone shoul d foll ow to ensure a reliable comm unica tion and high packet deliv ery rate depending on its battery autonom y.
In our previous work [3], we formula ted the problem as an Integ er Linear Problem.Moreov er, we expressed in an anal ytic manner the packet loss rate of tracking messag es depending on the UAV location and the wireless netw ork cov erag e.By sol ving the ILP problem using CPLEX, we were being able to anal yze how the radio cov erag e as well as the threshol d on the packet success rate, impact the number of possible sol utions and the trajectory of the UAV.Unf ortuna tel y, due to the computa tional complexity the proposed approach was not able to provide a pa th planning sol ution for a larg e area.In addition, the packet success rate was computed by considering onl y the radio channel and without any MAC layer oper ations.
Our curren t investig ations focus on the complexity issue raised for larg er area size.For the drone pa th planning, a heuristic adaptiv e scheme based on Dijkstr a al gorithm is presen ted to cope with the problem of scalability .The fligh pa th of drone is optimized in order to improv e its connectivity to the available terrestrial wireless netw ork and consequen tl y its localiza tion, iden tific tion and tracking.Moreov er, the sol ution is proposed to yiel d a sim ple but effectiv e and fast sol ution and tested under a more realistic scenario char acterized with a noisy environmen t.

State of the art
Path planning for kinema tic system issues has been widel y studied and has been addressed using di fferen t approaches and techniques.Thus, sev eral approaches exist for computing pa ths giv en some input variables of the environmen t.In gener al, the tw o most popular techniques are deterministic, heuristic-based al gorithms [4], [5], [6] and probabilistic, randomized al gorithms [7] and [8].The choice of the al gorithm to use depends on the type of problem to be sol ved.Although, the robotic bibliogr aph y on this subject is very rich, it's not the case for the UAV's one.
For the autonomous fligh of drones, pa th planning is one of the most crucial and importan t issues to sol ve.Now ada ys, the applica tion of UAV is extending from high-al titude fligh to very low-al titude, where the impact of the terr ain, the environmen t and the air traffic will be the key factors to be considered to avoid collisions [9].How ev er, we do not aim to provide an exha ustiv e list but we will be limited to provide the most relev ant work rela ted to the pa th planning reg arding to the nature of the objectiv es, problems formaliza tion and resol ving methods.
The author in [10 ] presen ted a framew ork to compute the minim um cost cooper ativ e route betw een a heterog eneous packag e deliv ery team composed of a truck and micro drones.They abstr acted the problem on a graph and formula te the issue as a discrete optimal pa th planning problem.In the same context of heterog eneous teams, the authors in [11 ] presen ted a pa th planning problem involving an UAV and a ground vehicle for intellig ence, surv eillance and reconnaissance missions.The addressed problem is similar to the ring-star problem and the hier archical ring netw ork problem.
On the other hand, the authors in [9] and [12 ] presen ted three dimensional pa th planning sol utions Drone Package Delivery: A Heuristic approach for UAVs path planning and tracking for unmanned aerial vehicles.The firs sol ution is based on interf ered f uid dynamic system, while the second approach uses linear progr amming where obstacle avoidance and targ et tracking are linearized to gener ate a linear progr amming model in a rela tiv e vel ocity space.Dealing with adv ersarial environmen ts, the authors in [13 ] and [14 ] presen ted sol utions for unmanned aerial vehicles pa th planning in uncertain an adv ersarial environmen t in sight to reach a giv en targ et, while maximizing the saf ety of the drone.They proposed a pa th planning al gorithm based on threa ts probability map which can be buil t from a priori surv eillance da ta and from a mechanism based on a predictiv e model control.
Another importan t work is [15 ], which contains concise summaries.It focused on dynamic problems and discussed a famil y of heuristic al gorithms for pa th planning in real-world scenarios such as A*, D*, ARA* and AD*.Finall y, it is worth men tioning the research done by [16 ] tha t can be considered one of the few papers dealing with pa th planning str ategies destined for a based UAVs netw ork.The authors compared deterministic and probabilistic pa th planning str ategies for autonomous drones to expl ore a giv en area with obstacles and to provide an overview imag e.The resul ts show ed tha t, al though the deterministic approach coul d provide a sol ution, it requires more knowledg e and time to gener ate a plan.How ev er, the probabilistic approaches are flexibl and adaptiv e.
To the best of our knowledg e, none of the abov e works have investig ated UAV pa th planning problem assuming tha t the UAV uses terrestrial wireless netw orks to transmit its positions.

Problem statement and system description
In this paper , we are considering a packag e deliv ery service using UAVs.Basicall y, a UAV has to deliv er a packag e from a depot or warehouse to a predetermined destina tion or consumer .The main objectiv e of this paper is to provide an off-line pa th planning tha t aims to minimize the deliv ery dela y with respect to the UAV's resid ual energy constr ain t while ensuring an optim um tracking of the UAV's at the oper ator side.
In this frame, the system is modeled as 2D area A without any obstacle.The projection of the f ying area is represen ted by a rectangular with length of x max and a wid th of y max .We suppose tha t the drone D rone keeps the same al titude h from the starting poin t O to the destina tion D. A set of wireless receiv ers or Base Stations BS = {BS 1 , BS 2 , ....BS n } is depl oyed randoml y at di fferen t al titudes in order to provide a wireless access infr astructure.In addition, we assume a partiall y noisy environmen t with the existence of a certain number of noise nodes

.N N n } depl oyed within
A and uses the wireless infr astructure as an access netw ork.We also consider tha t the drone has a limited fligh autonom y Υ and is equipped with a wireless interf ace in order to comm unica te with the other Base Stations.The la tter has a short sensing rang e compared to the size of the region of interest.Moreov er, we consider tha t A is discretized into C hexag onal cells of the same dimension.This implies discrete position for the UAV, which then is supposed to be located in the cen ter of the considered cell.The transition cost betw een tw o neighbor cells depicts certain reliability of comm unica tion, i.e. a certain probability tha t the comm unica tion is not interrupted and has a specifie Reception Packet Rate RP R. In this paper , the OMNeT++ 4.61 sim ula tor and the INET framew ork were used to gener ate both the signalto-in terf erence-pl us-noise ratio SIN R maps and the Receiv ed Packet Rate for all possible transitions in A.
Our goal is to determine a pa th or a set of pa ths tha t maximize the drone localiza tion and tracking using a wireless netw ork, such as cell ular or IEEE 802.11x technol ogies.For this purpose, we assume tha t after each period T , the drone gener ates a messag e of size d bits containing its iden tific tion, position and speed.The on-board wireless interf ace tries to send each gener ated messag e to the remote UAV monitoring and controlling system via the set BS while the jamming nodes attem pt to overload the netw ork by sending messag es in a contin uous and unpredictable manner to the BS.For tha t reason, a messag e can be corrupted or ev en lost due to possible interf erence and collisions.The opportunity to transmit also depends on the radio cov erag e, the capacity of the rela ted wireless technol ogy and the drone 's location.

Problem formulation
In order to describe the proposed ma thema tical model tha t represen ts the optim um pa th planning problem, it is useful to introd uce the foll owing nota tions and definitions First , we model the problem with the help of a directed and val ued graph G consisting of n hexag onal cells, where the val ua tion of an arc is comprised betw een 0 and 1, indica ting the reception packet rate (RP R) on tha t arc.
Finall y, we defin c ij the cost of using the arc going from cell c i to cell c j .The f ow going tha t way is denoted by a binary variable, noted as x ij , where 1, if the drone mov es from cell i to cell j 0, otherwise.
(1) The cost of a pa th represen ts its reliability and it is set to the prod uct of the RP R of each cell forming the resul ted pa th: As, the RP R ij is comprised betw een ]0, 1], this means more we add a new cell to the pa th more the pa th cost is low.Thus, the firs tw o objectiv es for our drone pa th planning problem are reported as foll ows: where, as define ear lier , c ij is the cost of the arc going from cell c i to cell c j .In this paper , we consider c ij as the amoun t of energy consumed by the drone on tha t arc, The objectiv e functions ( 3) and ( 4) represen t respectiv el y the minimiza tion of the energy consumed by the drone and the maximiza tion of the tracking probability betw een the start poin t O and the destina tion D. Basicall y, we shoul d fin the shortest possible pa th, in terms of consumed energy , tha t passes through the cells with highest Receiv ed Packet Rate, see Fig 2.
In addition to the last tw o objectiv es, we also add a third objectiv e tha t aims to minimize the tracking time loss of the drone, by avoiding passing through sev eral adjacen t cells with low RP R. For exam ple, as ill ustr ated in Fig 3, if we have to choose betw een the pa th a (0.9, 0.9, 0.9, 0.1, 0.1, 0.1) and the pa th b (0.9, 0.1, 0.9, 0.1, 0.9, 0.1) with the same length and the same averag e packet deliv ery ratio, than we have to privileg e the sol ution b rather than a.The privileg e of the sol ution b is motiv ated by the fact tha t we have few er adjacen t cells with low packet deliv ery probability .The main benefi of this choice is to have the comm unica tion rupture spaced out on the time rather than having a long time with no comm unica tions.
To this end, we need to anal yze the cells da ta in terms of RP R val ues and their positions in the pa th by crea ting series of averag es of di fferen t subsets of the full pa th.Basicall y, giv en K a pa th and the subset size equals to 2, the firs elemen t is obtained by taking the averag e of the tw o initial adjacen t cells of the selected pa th.Thereafter , the subset is modifie by shifting it forw ard, excl uding the firs cell and incl uding the next cell in K.This crea tes a new subset of numbers K.This kind of ma thema tical transf orma tion is also used in the signal processing in order to mitig ate the higher frequencies and to retain onl y the low frequencies or the contrary.
The principle of averag es on a shifted window is interesting in the case when we use prediction Since the geometric averag e is less sensitiv e than the arithmetic averag e to the highest or lowest val ues of a series, we propose the foll owing cost function: Thus, by appl ying the formulas 5 on the previous pa ths a = {0.9,0.9, 0.9, 0.1, 0.1, 0.1} and b = {0.9,0.1, 0.9, 0.1, 0.9, 0.1} we will get: a = {0.9,0.9, 0.5, 0.1, 0.1} and f (a) = 0.33, and b = {0.5, 0.5, 0.5, 0.5, 0.5} and f (b) = 0.5.Since we need to maximize the function f , the pa th b will be selected.
Finall y, in addition to the last objectiv es, we add a new constr ain t rela ted to the UAV's maximal fligh distance: where δ is the maxim um energy tha t the UAV coul d have.As introd uced in our problem formula tion section, our objectiv es are firs to minimize the traveling distance and to maximize the tracking probability betw een the start poin t the destina tion poin t.The firs objectiv e correspond to the classical Dijkstr a al gorithm.On the other hand, for the second objectiv e we are dealing with probabilities.We have to fin the shortest pa th where the prod uct of the probabilities RP R i of the visited cells tha t constitute a giv en pa th is maximized.More over, each time a cell is added to a pa th, the prod uct of the probabilities decreases.In this case, our al gorithm firs starts by initializing the cost of the origin cell c o to 1.The cost of the remaining cells is set to 0. Starting from the origin poin t, we buil t step by step a set of P mar ked cells.For each mar ked cell c i , the cost is equal to the prod uct of the Receiv ed Packet Rate probabilities of all predecessors cells.At each step, we select an unmar ked vertex c j whose cost is the highest among all vertexes not mar ked, then we mar k c j and we upda te from c j the estima ted costs of unmar ked successors of c j .We repea t un til exha ustion unmar ked vertexes.

Path computation
In addition to the abov e al gorithm, we also deriv ed a set of near optimal pa ths.In fact , the sol ution was extended to compromise localiza tion da ta deliv ery rates and distance betw een the starting poin t and the destina tion with the respect of the drone autonom y.To this end, if the length of the optimal pa th is grea ter than the drone autonom y or sim pl y, the oper ator woul d to have mul tiple choice of short pa ths, then we re-execute the function abov e un til we get the desired sol ution and for each execution we set the RP R of the cells of the obtained pa th to , where is a small non-n ull val ue.This all ows us to gener ate a new pa th totall y di fferen t from the previous one.All these pa ths can then be compared using the cost abov e function f for a better drone tracking resul t. for each cell c i ∈ G do 3: end for 6: for each cell c j ∈ neighbors(c i ) do end while

Energy Consumption Model
In this section we estima te the energy consumed by each drone according to its char acteristics.
The main challeng e for the construction of rotarywing drones is to maximize its autonom y for a giv en mass, while providing the pow er needed for propulsion and for the embedded instrumen ts.It is theref ore importan t to carefull y manag e the available energy and the pa th planning with each other to have the best overall.In fact , recen t progress achiev ed on Lithium battery type all owed the electric fligh to achiev e a reall y interesting autonom y for entertainmen t or local missions, but still far from being effectiv e for long er trips and missions.In this paper , we consider a quad-copter which is a drone with four rotors at the ends of a cross.The four rotors provide the vertical force (Thrust) tha t all ows the unit to rise.In fligh , the quad-copter may ev olve foll owing its roll, pitch and ya w axes and also in transla tion in all directions, fi 4. Basicall y, the dynamic model of quad-rotor can be seen as a system where the spa tial ev olution 's are the outputs and the voltag e of each engine are the inputs, fi 5. Motion is achiev ed by changing the rota tion speed of one rotor or more.Thus, to control the roll of the UAV, it is su fficien t to act on the rota tional speeds of the motors 2 and 4. In the same way, the pitch of the UAV is controllable by acting on the motors 1 and 3.
Furthermore, main taining a stable fligh requires an equilibrium and a balance of all forces acting upon a drone.Weight , lift , thrust and drag are the acting forces on a drone.These Forces are vector quan tities having both a magnitude and a direction and consequen tl y, the motion of the drone through the air depends on the rela tiv e magnitude and direction of these forces.A gener al deriv ation of the thrust force equa tion shows tha t the amoun t of thrust gener ated depends on the mass f ow through the rotors and the chang e in rota tion speeds of the four propellers.
In fact , sev eral methods exist in the liter ature all owing to have an order of magnitude of the pow er of a propeller , such as the blade elemen t theory (BET) and the Froude theory .Even if these methods can provide a more precise resul t, they are based on a certain number of coefficien ts which cannot be computed onl y after empirical tests, like Thrust Coefficien t, Torque Coefficien t, Power Coefficien t, etc...In addition, the obtained coefficien ts are specifi to the tested propeller at a specifie rota tion speed and cannot be used for other types of propellers.Basic drone manoeuvres incl ude take-o ff, hov ering, changing al titudes, and landing.This manoeuvre requires differen t rotors and propeller rota tion speeds.To our knowledg e, the best method to approxima te drone pow er consum ption is to use formulas tha t connect pow er to rotor rota tion speed, propeller diameter and pitch like the one proposed by Abbott , Young, Boucher , and Aguerre.
As ill ustr ated in figur 4, Ω 1 , Ω 2 , Ω 3 , Ω 4 are the rota tion speed of the propellers; T 1 , T 2 , T 3 , T 4 are the Forces gener ated by the propellers; and final y mg is the weight of the quadrotor; In the foll owing, the Boucher formula is used.In fact , the la test was used to compute the fligh autonom y and the pow er consum ption for a real quadcopter drone type of P hantom 3 Advanced.The resul ts were very close to the ones presen ted by the man uf acturer: To link the aerodynamic properties of the propeller to the pow er and the engine speed, we will need three formulas: • the pow er supplied by the propeller P p in watts; • the thrust of the propeller in Kg: • and the speed of air passing through the propeller of in Km/h: where Diam is the propeller diameter in meter , P itch in meter and N t is the number of thousands rev olutions per min ute (rpm).In addition to the last formulas, we also need to compute: • The pitch: • The pow er consumed by the propeller  • The drone fligh end urance can be expressed as in [17 ], and by ignoring the consumed pow er at the idle sta te we get: where R e and C e are the rotor efficiency and the controller efficiency , gener all y fixe at 75% and 98% respectiv el y, α is the attack angle of the propeller , B C the Capacity of the battery , P C is the Power consumed by the propeller .
Since the pow er is the rate of doing work, it is equiv alen t to the amoun t of energy consumed per unit time.If work is done quickl y, more pow er is used and if work is done slowl y, very little pow er is used.Thus, the energy consumed by the propellers to ensure the thrust forces required for the fligh can be expressed as: Finall y, using the last equa tion we can deriv e the energy c ij required for a drone to f y from cell i to cell j.

Results
In this section, we ev al ua te our proposed al gorithm.Two main objectiv es were fixed firs , to ensure a maxim um tracking of the drone al ong with its fligh while the second one was to minimize the energy required to travel al ong the pa th in accordance with the drone fligh autonom y and the capacity of its battery .In addition to the last objectiv es we also consider a third objectiv e which is to minimize the number of adjacen t cells with low RP R.
In this case, we assess our proposed the al gorithm in case of di fferen t scenarios.We start , using the OMNET++ sim ula tor, by gener ating the RP R map for a giv en al titude and in the presence of a giv en number of nodes using the wireless netw ork.Basicall y, in order to increase the packet losses we can increase the al titude of   In the foll owing, we provide some resul ts according to the sim ula tion par ameters summarized in the table 1.
For an ideal environmen t with no interf erence and noise, the drone shall fligh closer from the BS sta tion to ensure a permanen t tracking and localiza tion.How ev er, this is not the case in reality .Thus, the figure 6, 7, 8, 9 and 10 ill ustr ates the receiv ed packet rate in a noisy environmen t.It shows clear ly tha t more noise nodes (red dots) are presen t more we have low RP R. We can also notice tha t for the receiv ed packet rate, the resul ts are better in the edg e of the area, this ev en for the same SIN R.This can be explained by the fact tha t these subareas are less subject to ph ysical radio errors beca use of the position of the receiv er who will experience few er ph ysical collisions and busy channel sta te.
Figures 11a and 11b represen t respectiv el y the shortest pa th with highest RP R at 60m of al titude with the presence of 20 and 50 noise nodes.We compared our al gorithm to the shortest pa th using the well-known Dijkstr a al gorithm since to the best of our knowledg e there is no other work similar to our work in the liter ature.We also ill ustr ate, in figure 11c , the set of pa ths tha t we gener ated by our al gorithm to compute the optimal pa th and optimizing our third objectiv e.
To understand the impact of increasing the interferences on the pa th length and RP R, we varied the number of the nodes sim ula ting the noisy environmen t.We set the drone al titude to 60m and we measure the length of the optimal pa ths and their respectiv e RP Rs.As we can observ e in figur 12 and 13 , if we increase the number of noise nodes, we grad uall y decrease the quality of the signal and subsequen tl y the RP R and the pa th length also decrease.In fact , in case of good radio cov erag e, the drone tends to be attr acted to the cells with higher SIN R, which represen t the BS locations.On the other hand, when we degr ade the SIN R, the drone tends to take the shortest pa th to its destina tion.
In order to ev al ua te the efficiency of our sol ution, we tested the proposed al gorithm for a thousand random destina tion poin ts in an environmen t with low signal   In figure 16 and 17 we ill ustr ate the impact of the drone speed on the packet receiv ed rate and the consumed energy .The resul ts were obtained using the Omnet++ sim ula tor.We vary the drone speed from 10 m/s to 18 m/s, which are the most common drone speeds, and we compare the sim ula tor resul ts to the theoretical ones.We can notice tha t the RP R remains almost the same for drone speed varying from 10 m/s to 13 m/s.How ev er, this rate decrease once the drones exceed the speed of 14 m/s.Almost 10% of the tracking capability is lost due to the drone's speed.In addition to the same pa yl oad, a drone will consume about a double in terms of energy when increasing the speed from 10 m/s to 18 m/s.This consum ption is due to the increased rota tional speed of the propellers.Finall y, the figur 18 summarizes and ill ustr ates clear ly the adv antag e of our proposal in terms of drone localiza tion and tracking.In fact for tw o drones starting from the same poin t and f ying to the same destina tion at the same al titude, the capacity of tracking the drone at the controller side is di fferen t.As we can see, the tracking capability of the drone foll owing the pa th gener ated by our al gorithm reaches 88%, while for the one foll owing the Dijkstr a shortest pa th the tracking capability is about 14%.

Conclusion
In this paper , we propose a pa th planning al gorithm for UAV.Our approach doesn 't onl y gener ate one single  optimal sol ution but a number of other near optimal pa ths with a trade-o ff betw een length distance and probability of localiza tion determined by the drone fligh autonom y.Theref ore, we choose the best pa th suited to the need of localiza tion and tracking but also to the capability of the UAV in terms of energy autonom y.More precisel y, if iden tific tion, localiza tion and tracking are the main concerns than we can choose the long er pa th which insures a high comm unica tion probability and if the UAV energy autonom y is a priority than the we need to choose the suitable pa th length according to the battery duration.Torqua y, Dev on, UK.Website:

Figure 2 .Figure 3 .
Figure 2. Example of a path from the origin A to the destination I where the shortest path with high packet delivery rate is (A, B, E, H, J, I) Differen t shortest pa th al gorithms exist like A*, Dijkstr a, Bellman-F ord and others.Our proposal is based and adapted from Dijkstr a al gorithms.The la test is one of the most common and effectiv e al gorithms used to search the shortest pa th betw een tw o vertices are in a graph in terms of distance.For our case, we adapt the Dijkstr a al gorithm to fin the shortest pa th with high comm unica tion reliability and high packet reception.

Algorithm 1
Optimal Path al gorithm Input: G The graph G RP R The Receiv ed Packet Rate map c o The origin cell c d The destina tion cell 1: function Optimal Path(G , RP R , c o , c d ) 2:

2
Near Optimal Paths Input: G , RP R , c o , c d 1: Path = Optimal Path(G , RP R , c o , c d ) 2: if length(P ath) > δ then 3: for each cell c i ∈ P ath do Path(G , RP R , c o , c d ) 7: end if

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Drone Package Delivery: A Heuristic approach for UAVs path planning and tracking EAI Endorsed Transactions on Internet of Things 10 2016 -01 2017 | Volume 3 | Issue 9 | e1

Figure 9 .Figure 10 .
Figure 9. RPR with 40 noise nodes at h=60m set of near Optimal paths

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Drone Package Delivery: A Heuristic approach for UAVs path planning and tracking EAI Endorsed Transactions on Internet of Things 10 2016 -01 2017 | Volume 3 | Issue 9 | e1

Figure 18 .
Figure 18.Optimal path Vs Dijkstra shortest path tracking

Table 1 .
Simulation parameters GHz the drone or the number of nodes acting as noisy nodes.