Cooperative Multi-UAV Collision Avoidance Based

applied sciences Article

Cooperative Multi-UAV Collision Avoidance Based on Distributed Dynamic Optimization and Causal Analysis Mingrui Lao 1,2 and Jun Tang 1,3, * 1 2 3

*

Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China; [email protected] The School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China Department of Telecommunication and System Engineering, Universitat Autònoma de Barcelona, Sabadell 08201, Spain Correspondence: [email protected]; Tel.: +34-688-113-447

Academic Editor: Josep M. Guerrero Received: 1 December 2016; Accepted: 12 January 2017; Published: 17 January 2017

Abstract: A critical requirement for unmanned aerial vehicles (UAV) is the collision avoidance (CA) capability to meet safety and flexibility issues in an environment of increasing air traffic densities. This paper proposes two efficient algorithms: conflict detection (CD) algorithm and conflict resolution (CR) algorithm. These two algorithms are the key components of the cooperative multi-UAV CA system. The CD sub-module analyzes the spatial-temporal information of four dimensional (4D) trajectory to detect potential collisions. The CR sub-module calculates the minimum deviation of the planned trajectory by an objective function integrated with track adjustment, distance, and time costs, taking into account the vehicle performance, state and separation constraints. Additionally, we extend the CR sub-module with causal analysis to generate all possible solution states in order to select the optimal strategy for a multi-threat scenario, considering the potential interactions among neighboring UAVs with a global scope of a cluster. Quantitative simulation experiments are conducted to validate the feasibility and scalability of the proposed CA system, as well as to test its efficiency with variable parameters. Keywords: collision avoidance; UAV; 4D trajectory; distributed dynamic optimization; casual analysis

1. Introduction Recently, the unmanned aerial vehicle (UAV) has received a wide range of urban, civilian and warfare applications [1]. It offers several extraordinary features, especially the acceptance of long-endurance and high-risk missions that could not be reasonably performed by manned aircraft. For any assignment, a common problem is that the UAVs may encounter each other. Consequently, an effective collision avoidance (CA) system is a prerequisite for free flight. There are several existing widely used or adequately evaluated CA systems for conventional aviation, and these can be applied on UAVs, such as the efficient Medium Term CA approach based on four-dimensional (4D) trajectories (trajectories defined in the three spatial dimensions together with a time-stamp) to resolve conflicts in a terminal maneuvering area (TMA) [2], the Traffic Alert and Collision Avoidance System (TCAS) equipped to issue advisories on how to maneuver vertically to prevent collisions [3], and the Airborne Separation Assurance System (ASAS) that enables the flight crew to maintain separation of an aircraft from one or more other aircraft and provides flight information concerning the surrounding traffic [4]. There are also several auxiliary systems that could provide the aircraft (or UAVs) with precise information about the state of the nearby traffic, such as the Automatic Dependent Surveillance Broadcast (ADS-B) system [5–7]. Appl. Sci. 2017, 7, 83; doi:10.3390/app7010083

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In addition, an extensive and meticulous survey of various methodologies ranging from abstract concepts to prototype systems for avoiding collisions between UAVs has been summarized in [4]. Typical techniques applied to escort UAV safety include the Monte Carlo approach [8], geometric optimization model [9], symbiotic simulation [10], probabilistic approach [11], consensus [12], evolutionary algorithm [13,14], Kalman filter [15], Markov decision process [16], Dubins curve based algorithm [17], Predictive Control [18], reachable sets based methods [19], and so on. Each method has its own advantages and characteristics, and no matter which is employed, it aims to guarantee minimum separation between UAVs. However, some of the studies only focus on the two-UAV scenarios (not multiple vehicles). Furthermore, most of these methodologies could not support exploring the emergent dynamics between the generated trajectories and the surrounding traffic. Thus, there is a need to check the detailed states of the CA process with a global view to achieve the optimal strategy, while it is essential to understand the cause–effect relationship of each CA action and how the effects of a maneuver impact on the neighboring aircraft. Note that tight couplings between aircraft trajectories in dense scenarios (i.e., flocks applications) can deal with the propagation of non-controllable upstream and downstream maneuvers between trajectories. The overextended UAV usage of flock applications would lead to a higher number of threats, which could raise the risk of potential collisions. For simplicity, the CA problem is currently being discussed on UAVs (without pilot intervention) that are flying in a segregated airspace. In this paper, it is assumed that a group of cooperative UAVs, which are stabilized by the autopilot, are flying to their own destination and having to avoid collisions with other UAVs in an efficient real-time communication. Each vehicle is equipped with a trajectory control unit which relies on the CA algorithm that is used as a predictive control considering real-time data-link communication with surrounding traffic. In this research, we propose two efficient algorithms: conflict detection (CD) and conflict resolution (CR), which, as two sub-modules, constitute a novel CA system for multi-UAV. The main contributions of this paper are as follows:

•

•

•

This paper presents an innovative strategy, distributed dynamic optimization approach (DDOA), to provide alternative trajectories for each UAV, by adding some essential constraints (i.e., performance, cost and distance) to make the problem treatable while the feasible trajectory generation for multi-UAV is a non-deterministic polynomial (NP) problem. The novel causal analysis is developed to choose a preferred resolution trajectory, performing an analysis of scenario state space in order to explore the dynamic evolution and then determine all reachable states. By decomposing the complex scenario into several common clusters, the solution space is greatly reduced. Quantitative measurement experiments are carried out to validate the feasibility and scalability of the CA system for the free flight of multi-UAV. In addition, the average computation time does not grow exponentially as the airspace density increases.

To prevent mid-air collisions between UAVs, the proposed CA system has been developed to serve as the last-resort safety net, which is an on-board CDR system providing resolution advisories. This paper is organized as follows: Section 2 illustrates the CA system functional architecture; Section 3 presents the core algorithm of the CD and CR sub-modules; Section 4 achieves the simulation results using the proposed system; finally, conclusions and future work are summarized in Section 5. 2. The Proposed CA System Architecture The CA system should be supported by vigorous algorithms to increase the airspace capacity. Figure 1 illustrates the detailed fundamental processes of the complete CA system, in which the input is the 4D (three dimensions (3D) position + time) trajectory information belonging to each UAV; a high speed processor equipped with CD algorithm deals with the trajectories and obtains relevant information to predict whether a collision is going to occur in the future. If a potential collision is detected, DDOA computes the feasible solutions and causal analysis selects the optimal

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Appl. 2016, 6,xFOR PEER

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one. The control command is sent to the involved UAVs to resolve current threats and the states Appl. 2016, 3 of 14 one. The 6,xFOR controlPEER command is sent to the involved UAVs to resolve current threats and the states improve online. improve online. one. The control command is sent to the involved UAVs to resolve current threats and the states improve online.

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Figure 1. Functionalarchitecture architecture of of the the novel novel collision collision avoidance avoidance (CA) (CA) system. system. 1.Functional

Figure 1.FunctionalCA architecture of the novel collision avoidance (CA) system. The system consists consists of two two components: The core core of of the the operational operational CA system of components: • The CD module that analyzes the flight information depending on 4D trajectory has two The core of the operational CA system consists of two components: The CD module that analyzes the flight representation information depending 4Dinforming trajectory the has CR twomodule. different • different roles: generating the intuitionistic of threatson and • The CD module that analyzes the flight information depending on 4D trajectory has two roles:The generating the intuitionistic representation threats and informing CRstages: module. • CR module integrates CD and resolvesofthe detected conflicts inthe two DDOA different roles: generating the intuitionistic representation of threats and informing the CR module. aims to avoid collisions by generating alternative trajectories each UAV with a local optimization • The CR module integrates CD and resolves the detectedfor conflicts in two stages: DDOA aims to • The CR module integrates CD and resolves the detected conflicts in two stages: DDOA scope; causal analysis focuses on exploring the emergent the alternative avoid collisions by generating alternative trajectories for eachdynamics UAV with abetween local optimization scope; aims to avoid collisions by generating alternative trajectories for each UAV with a local optimization trajectories generated by DDOA and the rest involved trajectories. Based on the detected threats, the causal analysis focuses on exploring the emergent dynamics between the alternative trajectories scope; causal analysis focuses on exploring the emergent dynamics between the alternative CR should be informed with thethe geographical coordinates where theon collision would threats, occur, the generated by DDOA and rest involved trajectories. Based the detected thetime CR trajectories generated by DDOA and the rest involved trajectories. Based on the detected threats, the whenshould the collision wouldwith occur, the involved UAVs. Though CRcollision is a combinatorial problem in be informed theand geographical coordinates where the would occur, the time CR should be informed with the geographical coordinates where the collision would occur, the time exponential growth with the increasing number of UAVs, in our research several strategies such as when the collision would occur, and the involved UAVs. Though CR is a combinatorial problem in when the collision would occur, and the involved UAVs. Though CR is a combinatorial problem in setting constraints are needed narrow the solution spaceinprogressively to get the final optimal exponential growth with thetoincreasing number of UAVs, our research several strategies such as exponential growth with the increasing number of UAVs, in our research several strategies such as solution. Figure 2 conceptually The DDOA several setting constraints are neededillustrates to narrowthe thesolution solution procedure. space progressively to getgenerates the final optimal setting constraints are needed to narrow the solution space progressively to get the final optimal locally-optimal CA trajectories considering different constraints, e.g., the two UAVsgenerates should meet the solution. Figure 2 conceptually illustrates the solution procedure. The DDOA several solution. Figure 2 conceptually illustrates the solution procedure. The DDOA generates several performance requirements, satisfy considering the state equation, keep a e.g., safe the distance, etc. should This causal locally-optimal CA trajectories differentand constraints, two UAVs meet locally-optimal CA trajectories considering different constraints, e.g., the two UAVs should meet the analysis allows takingrequirements, into consideration possible solutions that ensure the completeness of the performance satisfy all thethe state equation, and keep a safe distance, etc. This causal performance requirements, satisfy the state equation, and keep a safe distance, etc. This causal the solution theninto reduces the spaceallonce again based on some constraints (e.g., analysisspace, allowsand taking consideration the possible solutions that specific ensure the completeness analysis allows taking into consideration all the possible solutions that ensure the completeness of the least cost). of the solution space, and then reduces the space once again based on some specific constraints the solution space, and then reduces the space once again based on some specific constraints (e.g., (e.g., the least cost). the least cost). Causal analysis with constraints Causal analysis with constraints Causal analysis

Optimal Solution Optimal Solution

DDOA Causal analysis with constraints DDOA with DDOA constraints DDOA

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Figure 2.Step‐by‐step optimal process.

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Figure 2. Step-by-step optimal Figure 2.Step‐by‐step optimal process. The hardware architecture of the novel CA system consists of the following major components: CA processor—performs airspace surveillance, intruder tracking, own UAV state tracking, conflict The hardware hardware architecture architecture of of the the novel CA CA system system consists consists of of the the following following major major components: components: The detection and conflict resolution, and novel it uses discrete status inputs of involved UAVs to control the CA processor—performs processor—performs airspace airspace surveillance, surveillance, intruder tracking, own UAV state tracking, tracking, conflict conflict CA intruder tracking, logic parameters that determine the protection volume around own ownUAV UAV;state State transmitter—is detection and conflict resolution, and it uses discrete status inputs of involved UAVs to control the detection and conflict resolution, and it usesbetween discrete UAVs status inputs involved UAVs to control the CA CA used to provide air-to-air data exchange so thatofcoordinated, complementary CA logic parameters that determine the protection volume around own UAV; State transmitter—is logic parameters determine protection volume around own UAV; State transmitter—is to trajectories can bethat issued when the required; Control unit—guarantees the multiple cooperativeused UAVs used to provide air-to-air data exchange between UAVs so that coordinated, complementary CA provide air-to-air data exchange between UAVs so that following the generated optimal trajectory to resolve thecoordinated, conflicts. complementary CA trajectories trajectories can be issued when required; Control unit—guarantees the multiple cooperative UAVs following the generated optimal trajectory to resolve the conflicts. 3. Core Algorithm Analysis

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3. Core Algorithm Analysis

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can be issued when required; Control unit—guarantees the multiple cooperative UAVs following the generated optimal trajectory to resolve the conflicts. 3. Core Algorithm Analysis 3.1. Representation of 4D Trajectory and Conflict Detection The continuous trajectory of UAV can be modeled as a sequence of discrete points (waypoints) expediently for computer processes. There is a direction between every two adjacent waypoints due to the velocity vector. The position of 3D and corresponding time—called spatial-temporal information—makes up the 4D trajectory of each UAV. For U AVi (i = 1, 2, ..., n), its dynamic characteristics can be described in a Cartesian coordinate system [20]. The region formed by x and y axes indicates the horizontal plane, and z stands for the altitude. 

 xti   pit =  yit , vit = zit dϕit dt

= ωti ,



dpit dt

   vix,t vit cos ϕit cos θti     =  viy,t  =  vit cos ϕit sin θti  vit sin ϕit viz,t

0 < θti < 2π,

− π2 ≤ ϕit ≤

(1)

π 2

The formula defines pit and vit , respectively, as the position and velocity of UAVi in 3D; let θti represent the course angle, the orientation of velocity vector vit in the x-y plane (measured from the x axis in counter-clockwise direction); let ϕit delegate the pitch angle, the orientation of velocity vector vit in the vertical plane (measured from the horizontal plane up as positive and down as negative); and ωti is the angular velocity. Considered simply, each UAV is supposed to keep its own velocity vi , i ∈ {1, 2, · · · , n} during regular flight. In the detection sub-module, the UAV that detects the conflict will read out the sensed data from sensor unit and check whether any intruder enters its safety zone. At each moment t, the relative distance between UAVi and nearby UAVj in the airspace can be simply calculated as: r ij Rt

=

j 2

j 2

j 2

( xti − xt ) + (yit − yt ) + (zit − zt )

(2)

In this research, the conflict detection logic can be defined as follows: if the current relative ij distance of the two UAVs is smaller than the Rcf ( Rt < Rc f ), and they have a trend to be closer, ij

i.e., when the value of Rt that is the relative distance between UAVi and nearby UAVj is getting smaller, the resolution maneuver fires regardless of whether the coming closest point of approach (CPA) [21] is in collision volume Rcl or not. Despite the fact that this way certainly may touch off several unnecessary resolution maneuvers, the collision risk is highly reduced since the situation in whichthe intruder suddenly changes its direction near the CPA is prevented. ij j Let pt = pit − pt be the distance vector in 3D space between UAVi and nearby UAVj at time t; ij

j

let vt = vit − vt be the relative velocity (closing speed) between the UAVs at time t. Distinctly, when ij

ij

the two UAVs are getting closer to each other (i.e., pt · vt > 0), a conflict is detected and it has to be ij

ij

resolved immediately; when the two UAVs are getting further apart (i.e., pt · vt < 0), there is no risk to deteriorate into a collision at all. 3.2. Conflict Resolution Algorithm This section focuses on the CR algorithm consisting of two subsections: DDOA and causal analysis. Different alternative trajectories for each involved UAV are generated by DDOA in a collision, and the globally optimal one is selected by causal analysis considering the follow-up effects.

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3.2.1. Distributed Dynamic Optimization Approach The UAVi trajectory is discrete and the sampling interval is ∆t. Therefore, in the m-th moment, the related position and pitch angle of UAVi are xi (m), yi (m), zi (m), ϕi (m), m ∈ N. The discrete kinematic model of UAVi is:     x i ( m + 1) xi (m) + vi cos( ϕi (m)) cos θi · ∆t  y (m + 1)   y (m) + v cos( ϕ (m)) sin θ · ∆t    i   i i i i (3)  =   z i ( m + 1)    zi (m) + vi (sin ϕi (m)) · ∆t ϕ i ( m + 1) ϕi (m) + ωti · ∆t In order to generate an amending trajectory for CA, it is better if each UAV could adjust its track as few times as possible, execute the trajectory as shorter as possible and reach the target point as soon as possible. Therefore, at time m, the objective function Oi (m) of UAVi comprises three aspects above: Oi (m) = w1 Ci (m) + w2 Di (m) + w3 Ti (m)

(4)

In this formula, w1 , w2 , w3 are the corresponding weight coefficients of the three indexes Ci (m), Di (m), Ti (m). Their values reflect different application contexts, e.g., w3 > w1 indicates that the controllers prefer shorter time to achieve the destination even if the fuel cost is higher. Before the computation, normalization processing is needed. The three indexes can be calculated using the following formulas. ( | ϕi (m) − ϕi (m − 1)| i f m ≥ 1 Ci (m) = (5) 0 if m = 0 where Ci (m) expresses the track adjustment cost of UAVi, which is defined as the change value of pitch angle. h i 2 2 2 1/2 Di (m) = k pi (m) − pid k2 = ( xi (m) − xid ) + (yi (m) − yid ) + (zi (m) − zid )

(6) T

where Di (m) indicates the distance from current location to its destination pid = ( xid , yid , zid ) . Ti (m) = m · ∆t + Di (m)/vi

(7)

where Ti (m) represents the total flight time of UAVi. Assume that there are N intervals from time m to the destination, thus the position and corresponding pitch angle sequences of UAVi in [m, m + N − 1] are respectively: ∆

Pi = [ pi (m), pi (m + 1), · · · , pi (m + r ), · · · , pi (m + N − 1)] T ∆

Ψi = [ ϕi (m), ϕi (m + 1), · · · , ϕi (m + r ), · · · , ϕi (m + N − 1)] T ∀r ∈ [0, N − 1]

(8)

The objective function for progressive optimization is: N −1

minOi (m + r ) = min(

∑

(w1 Di (m + r ) + w2 Ti (m + r ) + w3 Ci (m + r )))

(9)

r =0

Note that it should meet the following constraints in the optimization process: " q( ϕi (m + r )) =

1 −1

#

" Ci (m + r ) −

B −A

#

"

=

1 −1

#

"

( ϕi (m + r ) − ϕi (m + r − 1)) −

B −A

#

≤0

(10)

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 xi (m  r )  [ xi (m  r  1)  vi cos(i (m  r  1)) cos i  t ] 6 of 14  y (m  r )  [ y (m  r  1)  v cos( (m  r  1))sin   t ] i i i i i 0 ei ( pi (m  r ))   (11)  zi (m  r )  [ zi (m  r  1)  vi (sin i (m  r  1))  t ]      xi (m + r ) − [ xi (m + r − 1(m )+  rv)i cos i ((mϕi (rm) + r − 1)) cos θi · ∆t]  i  y (m +r ) − [y (m + r − 1 ) + v cos ( ϕi (m + r − 1)) sin θi · ∆t]   i i i (11) ei ( pi (m + r )) =  =0  di ( piz(im (m + )− [zi (rm))+rd− 1) + vi (sin + r− r ),r p r ) ϕi (pmj (m r ) 1))·0∆t] (12) j (m  0  pi (m 2 ϕi ( m + r ) − ϕi ( m + r ) In the above formulas, q(i (m  r ))  0 explains that the value change of UAVi pitch angle di ( pi (m + r ), p j (m + r )) = d0 − k pi (m + r ) − p j (m + r )k2 ≤ 0 (12) should be in the variation range of (A,B); ei ( pi (m  r ))  0 shows that the calculation of UAVi In the above formulas, q( ϕi (m + r )) ≤ 0 explains that the value change of UAVi pitch angle position and pitch angle at time m + r is based on the corresponding information at m + r − 1; should be in the variation range of (A,B); ei ( pi (m + r )) = 0 shows that the calculation of UAVi di ( pi (m  r ), p j (m  r ))  0 illustrates that the distance between UAVi and UAVj must not be shorter position and pitch angle at time m + r is based on the corresponding information at m + r − 1; the minimum d0. dthan ( p ( m + r ), p j (m +safe r )) distance ≤ 0 illustrates that the distance between UAVi and UAVj must not be shorter i i Integrating the objective function with constraints, the next waypoint ( pi (m  1), i (m  1)) can than the minimum safe distance d0 . be calculated based the current statewith the optimization ( pi (constraints, m), i (m)) . Repeating Integrating the on objective function the next waypoint ( pi (m +procedure, 1), ϕi (m + the 1)) can be calculated based on the current state ( p ( m ) , ϕ ( m )) . Repeating the optimization procedure, complete amending trajectory made up of a series of discrete waypoints is generated. i i the complete trajectory made up of a series of discrete waypoints is generated. Besides, amending the algorithm for generating CA waypoints is robust enough to resolve successive Besides, the algorithm for generating waypoints is robust enough in to resolve threats. threats. For example, if UAV1 encountersCA UAV2 and UAV3 seperately a short successive interval, the two For example, if UAV1 encounters UAV2 and UAV3 seperately in a short interval, the two threats threats could be resolved via a compositive CA trajectory withonly a distance constraint between could resolved via a compositive CA trajectory withonly a distance constraintminimum between UAV1 and UAV1 be and UAV3 added to the optimization calculation.This section calculates deviation UAV3 to the optimization section calculates minimum deviation of the planned of the added planned trajectory by an calculation.This objective function integrated with track adjustment, distance, and trajectory by an objective function integrated with track adjustment, distance, and time costs, taking time costs, taking into account the vehicle performance, state and separation constraints. into account the vehicle performance, state and separation constraints. 3.2.2. Causal Analysis 3.2.2. Causal Analysis The size (computational complexity) of the conflict resolution problem is typically very large, The size (computational complexity) of the resolution problem is typically large, which represents a real challenge to deal with theconflict exponential growth of the state space invery a realistic which represents a real challenge to deal with the exponential growth of the state space in a realistic environment containing dozens of UAVs. A highly efficient technique to reduce the problem size is environment containing dozens A highly efficient to reduce the problem sizeon is clustering [22]. The scenario can of beUAVs. decomposed into severaltechnique sets of independent clusters based clustering [22]. between The scenario can trajectories be decomposed into several setsThe of independent clusters based on the interaction planned for a period of time. partition principle is mainly in the interaction between planned trajectories for a period of time. The partition principle is mainly in view of the distances between the neighboring UAVs. These independent clusters can be processed view of theto distances between the neighboring UAVs. 3These clusters can be processed in in parallel significantly improve efficiency. Figure is theindependent concept illustration. parallel to significantly improve efficiency. Figure 3 is the concept illustration. Appl. Sci. 2017, 7, 83

U

UA V3

Tr 3

Cluster B UA T V1 r2 Tr 1 Tr1 1

r 11 1T UAV Tr1 UAV1

Cluster A Tr11

Tr1

UAV2

V2 A

T r2

Cluster C Solution for original situation Without clusters Solution for cluster B

UAV2 Tr2

Solution for cluster C

Tr21

UAV3 Tr3

Tr31

Solution for cluster A

Figure 3. Concept illustration of clustering. Figure 3. Concept illustration of clustering.

The is decomposed into several clustersclusters with treatable sizes withsizes few trajectories. The original originalproblem problem is decomposed into several with treatable with few Thus, the overall solution is a combination of conflict-free solutions obtained by a causal trajectories. Thus, the overall solution is a combination of conflict-free solutions obtained by analysis a causal for thesefor regional clusters.clusters. The core idea ofidea the of causal analysis is to explore the state space of the analysis these regional The core the causal analysis is to explore the state space of CA scenario to achieve the optimal resolution. It utilizes the alternative trajectories and relevant cost the CA scenario to achieve the optimal resolution. It utilizes the alternative trajectories and relevant

cost generated by the DDOA, which includes the track adjustment, distance, and time costs.

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generated DDOA, which includes the track adjustment, and time costs.amendment Therefore, Therefore, by forthe n UAVs involved in the same scenario, the total distance, cost of the trajectories Therefore, for n UAVs involved in the same scenario, the total cost of the trajectories amendment for n UAVs involved in the same scenario, the total cost of the trajectories amendment can be defined as: can be defined as: can be defined as: n Nn−N1 1

n N 1 Cost   C(im (m rr)) + D mm+r )r) T m  r) CostCost =∑ CC Di i(((m +ii ((T i (m+ ∑    r)  D  r)  T mi (mr )+ r ) i i 1 r  0 i

(13) (13) (13)

i =1 ir= 1 0r  0

The process state could be described by a specific four-tuple: The process state could be described by a specific four-tuple: four-tuple:

  •  •  •   •

conflict , cost ,(active UAV ),(resolution trajectories) (14) , cost(,(active active U UAV ))} conflict (14) f lict, cost, AV),( ), (resolution resolution trajectories trajectories (14) {con An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple. An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple. An instance state a = {2,1,(1,2,3),(11,111,31,32)} is used to explain the tuple. Conflict: indicates the threat that will be resolved (conflict 2 is active in state a). Conflict: indicates the threat that will be resolved (conflict 2 is active in state a). Conflict: indicates threat that willfor bethe resolved (conflict 2 is active in state a). Accumulated cost:the Cost summation respective resolution trajectories (cost = 1 in state a). Accumulated cost: Cost summation for the respective resolution trajectories (cost = 1 in state a). Accumulated Cost summation for the respective (cost =among 1 in state a). Active UAVs:cost: is a processed tuple and represents allresolution the UAVstrajectories in this scenario, them Active UAVs: is a processed tuple and represents all the UAVs in this scenario, among them the active one would be underlined (UAV1 and UAV3 are active to have conflict 2 in state a). Active UAVs: is a processed tuple and represents all the UAVs in this scenario, among them the the active one would be underlined (UAV1 and UAV3 are active to have conflict 2 in state a). Activeone resolution toand store solution trajectories and the2 active active would betrajectories: underlined used (UAV1 UAV3 are active to have conflict in stateresolution a). Active resolution trajectories: used to store solution trajectories and the active resolution trajectories are represented with underlines to resolve the active collision (111, 31 or 32 can be Active resolution trajectories: to store solutionthe trajectories and the active trajectories are represented withused underlines to resolve active collision (111, 31 orresolution 32 can be used to resolve conflict 2 in state a). Here the number is composed with the aircraft trajectories are represented underlines to resolve the active (111, 31 or can be used to resolve conflict 2 with in state a). Here the number is collision composed with the32aircraft identification i and amending strategy descend/climb (1/2). used to resolve conflict 2 in state a). Here the number is composed with the aircraft identification identification i and amending strategy descend/climb (1/2). iThe andcausal amending strategycan descend/climb (1/2). exploration be summarized with the following steps in Figure 4: The causal exploration can be summarized with the following steps in Figure 4: The causal exploration can be summarized with the following steps in Figure 4: yes yes

DDOA

Generate Active DDOA Generate solution Active conflict solution trajectory conflict trajectory

Produce Produce Process Process state state

Create a Create a branch branch

Update Update cost and cost and active active conflict conflict

Active Active conflict conflict

no no

Select Select optimal optimal solution solution

Figure 4. Causal exploration flow chart. Figure 4. Causal Causal exploration flow chart.

As an explanatory case, Figure 5 illustrates the whole feasible solutions of a case scenario, and As an explanatory case, 5 illustrates thethe whole feasible solutions of a of case scenario, and As explanatory case,Figure Figure illustrates whole feasible solutions a case Figure 6an shows its reachability tree. 5Using the causal exploration algorithm, there are scenario, six final Figure 6 shows its reachability tree. Using the causal exploration algorithm, there are six final and Figure 6 shows reachability tree.Evidently, Using thestate causal algorithm, there final process states as theits feasible solutions. d isexploration preferred to be utilized thanare thesixothers process states as the feasible solutions. Evidently, state d is preferred to be utilized than the others process states as the feasible due to the minimum cost. solutions. Evidently, state d is preferred to be utilized than the others due due tominimum the minimum to the cost.cost. Tr2 Tr2 1 C= =1 Tr11 C Tr11 Tr2 Tr2

Tr3 Tr3

Tr2 Tr2

Tr1 Tr1

(a) (a)

(f) Total Cost=1.5 (f) Total Cost=1.5 Tr31 C= 1 Tr31 C= 1

(g) (g) (c) (c) Tr3 Tr3

Total Cost=1.5 Total Cost=1.5

Tr2 Tr2 1 C= =1 Tr11 C Tr11

Tr1 Tr1

C= 1 C= 1(d)

C=1C.5=1.5

Tr1 Tr1

Tr3 Tr3

Tr3 Tr3

Tr11

Tr21 Tr21 Tr22 Tr22

Tr2 Tr2 1 C= =1 Tr11 C

(b) (b) Tr3 Tr3

.5 .5 =1 1 C C=

Tr12 Tr12

Tr2 Tr2 1.5 C= .5 1 Tr111C= Tr111

Tr3 Tr3

(d)

Total Cost=1 Total Cost=1

(e) Total Cost=1.5 (e) Total Cost=1.5

Figure 5. The feasible solutions. Figure 5. The feasible solutions.

Total Cost=2 Total Cost=2

Tr32 Tr32

C=1.5 C=1.5 (h) Total Cost=2.5 (h) Total Cost=2.5

Appl. Sci. 2017, 7, 83 Appl. 2016, 6, 83

8 of 14 8 of 14 (a) {1,0,(1,2,3),(11,12,21,22)}

(b) (c) {2,1,(1,2,3),(11,111,31,32)} {0,1.5,(1,2,3),12}

(d) {0,1,(1,2,3),21}

(e) {0,1.5,(1,2,3),22}

(f) (g) (h) {0,1.5,(1,2,3),111}{0,2,(1,2,3),(11,31)}{0,2.5,(1,2,3),(11,32)}

Figure Figure 6. 6. The CA reachability reachability tree. tree.

4. Simulation and Results 4. this section, section, we we carry carry out out simulation simulation experiments to evaluate the efficacy of of the the proposed proposed In this the CA CA system. system. The computational results represent collision-free maneuvers maneuvers for for algorithms for the multiple UAVs UAVsthat thatare aremodeled modeledwith withdetailed detaileddynamics. dynamics. multiple 4.1. 4.1. A Case Scenario To our simulation experiments areare performed on Toverify verifythe thefeasibility feasibilityofofthe theproposed proposedalgorithms, algorithms, our simulation experiments performed aonmanually generated scenario of five (with (with the corresponding trajectories Tr1, Tr2,Tr1, Tr3,Tr2, Tr4 and a manually generated scenario ofUAVs five UAVs the corresponding trajectories Tr3, Tr5), illustrated in Figurein 7. Figure This scenario the following characteristics: Tr4 and Tr5), illustrated 7. This includes scenario includes the following characteristics:

(1) It fairly complex complex scenario scenario with with multiple multiple UAVs. UAVs. Indeed, three trajectories, trajectories, (1) It is is aa fairly Indeed, among among the the first first three Tr1 imposes sequent threats to both Tr2 and Tr3; moreover, an encounter emerges between Tr4 Tr1 imposes sequent threats to both Tr2 and Tr3; moreover, an encounter emerges between Tr4 and Tr5, which further increases the complexity of the scenario. and Tr5, which further increases the complexity of the scenario. (2) It domino effect) between neighboring threats. For (2) It involves involves the theinterrelationship interrelationship(also (alsocalled called domino effect) between neighboring threats. instance, a new secondary threat between UAV3 and UAV5 may emerge in the process of For instance, a new secondary threat between UAV3 and UAV5 may emerge in the process resolving their respective previous threat. of resolving their respective previous threat. (3) It resolvessuccessive successivethreats threats a compositive CA trajectory, i.e.,is UAV1 is todetected to (3) It resolves via via a compositive CA trajectory, i.e., UAV1 detected encounter encounter UAV2 and UAV3 separately in a short continuous time period and the two UAV2 and UAV3 separately in a short continuous time period and the two successive conflicts successive conflictsoverall can berather considered overall rather than one by one. can be considered than one by one. Appl. 2016, 6, 83above In the

9 of 14 scenario, each UAV is assumed to be heading towards its own target position along the straight line. Simulations start with the initial information about the position and velocity of the UAVs in a scenario. For the local area, the UAV states have been treated as broadcast information with efficient real-time communication. The assumptions and the parameter setup values are given in Table 1. The proposed algorithms are coded in C++ and the simulation is performed on an EliteBook laptop with a processor Intel i5 of 2.6 GHz and 4 GB of RAM.

Table 1.The assumptions of parameters and unmanned aerial vehicle (UAV) properties

Rcf (km) 1.2

Rcl (m) 100

Velocity (m/s) 30

Δt (s) 1

A (rad) −1.047

B (rad) 1.047

w1  w2  w3 Figure Five-UAV scenario with the generated generated optimal optimal resolution. resolution. Figure 7. 7. the Five-UAV the In this causal analysis, cost ofscenario variouswith feasible CA trajectories assists the decision making of solution selection. After executing the proposed CA system, the optimal strategy, that Tr1 The entirety of the reachable states of this multi‐UAV scenario are displayed in Figure 8. From synthetically amends upward UAV5 climbs, to is implemented. In the above scenario, eachand UAV is assumed be heading towards its own target position along the proposed multi‐threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends the straight line. Simulations start with the initial information about the position and velocity of the (Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with UAVs in a scenario. For the local area, the UAV states have been treated as broadcast information Tr3 if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA with efficient real-time communication. The assumptions and the parameter setup values are given in trajectory (Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the new encounter (see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends downward (Tr41) or UAV5 turns upward (Tr51). In state d, there would be no domino effect between the neighboring UAVs (see state h and state i), while a new threat would appear between the descending UAV3 and climbing UAV5 (see state k) and have to be resolved through the

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Table 1. The proposed algorithms are coded in C++ and the simulation is performed on an EliteBook laptop with a processor Intel i5 of 2.6 GHz and 4 GB of RAM. Table 1. The assumptions of parameters and unmanned aerial vehicle (UAV) properties. Rcf (km)

Rcl (m)

1.2

100

Velocity (m/s)

∆t (s)

30 1 w1 = w2 = w3

A (rad)

B (rad)

−1.047

1.047

In this causal analysis, the cost of various feasible CA trajectories assists the decision making of Figure 7. Five-UAV scenario with generated optimal strategy, resolution.that Tr1 synthetically solution selection. After executing the proposed CAthe system, the optimal amends upward and UAV5 climbs, is implemented. The entirety of the reachable states of this multi‐UAV scenario are displayed in Figure 8. From The entirety of the reachable states of this multi-UAV scenario are displayed in Figure 8. the proposed multi‐threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends From the proposed multi-threat resolution point of view, solo UAV1 climbs (Tr11) or UAV2 descends (Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with (Tr21) to resolve the first threat (see state a). However there would generate a secondary threat with Tr3 Tr3 if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA if trajectory Tr11 is applied (see state b). Then UAV1 could climb again and a composite CA trajectory trajectory (Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the (Tr111) is generated (see state d). Meanwhile, UAV3 could descend (Tr31) to resolve the new encounter new encounter (see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends (see state e). For resolving the threat between UAV4 and UAV5, UAV4 amends downward (Tr41) or downward (Tr41) or UAV5 turns upward (Tr51). In state d, there would be no domino effect UAV5 turns upward (Tr51). In state d, there would be no domino effect between the neighboring between the neighboring UAVs (see state h and state i), while a new threat would appear between UAVs (see state h and state i), while a new threat would appear between the descending UAV3 and the descending UAV3 and climbing UAV5 (see state k) and have to be resolved through the climbing UAV5 (see state k) and have to be resolved through the following heading change (see state p following heading change (see state p and state q). and state q).

Figure 8. The reachability tree of this multi-UAV multi-UAV scenario. scenario.

On the the other other branch, branch, the the first first threat threat is is resolved resolved by by the the amendment amendment of (see state state c), c), and and two two On of Tr2 Tr2 (see options are considered to solve the encounter between UAV1 and UAV3 (see state f and state g). In options are considered to solve the encounter between UAV1 and UAV3 (see state f and state g). In state state the collision between and UAV5 be avoided directly without domino effect (seel f, the f, collision between UAV4UAV4 and UAV5 could could be avoided directly without domino effect (see state state l and state m). However in state g, a new threat (see state n) would appear between the and state m). However in state g, a new threat (see state n) would appear between the descending descending UAV3 and climbing UAV5be and it could resolved by one of the involved UAV3 and climbing UAV5 and it could resolved bybe one of the involved trajectories (see trajectories state r and (see state r and state s). state s). Since the the cost costcriterion criterionisistaken taken into consideration in the decision-making process, is clear Since into consideration in the decision-making process, it is it clear that that state i (UAV1 climbs twice for the sequent threats with UAV2 and UAV3, and UAV5 amends state i (UAV1 climbs twice for the sequent threats with UAV2 and UAV3, and UAV5 amends upward upward to avoid thewith collision with UAV4) is the bestfeasible one ofscenarios. the feasible amended to avoid the collision UAV4) is the best one of the Thescenarios. amendedThe trajectories of trajectories of UAV1 and UAV5are represented in Figure 7. UAV1 and UAV5are represented in Figure 7.

Table 2. UAV1 and UAV5 modified trajectories.

Time

ID

Appl. Sci. 2017, 7, 83

Amended Trajectory X (m) Y (m) Z (m)

Time

ID

Amended Trajectory X (m) Y (m) Z (m)

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17:17:48 UAV 1 370.43 510.68 669.57 UAV 1 593.19 733.44 721.53 17:18:10 17:17:50 UAV 1 387.85 528.10 686.68 UAV 5 628.79 779.87 572.48 Table 2 summarizes406.44 the amended of UAV1 and UAV5 (for the sake of simplicity, 17:17:52 564.10 waypoints 701.14 UAV 1 UAV 1 614.07 754.32 716.18 17:18:12 the data are recorded every two seconds). UAV1 starts to change its headings at 17:17:48 and returns 17:17:54 UAV 1 425.92 566.17 713.00 UAV 5 614.12 754.47 578.76 to the original trajectories at 17:18:18, while UAV5 starts at 17:18:04 and ends at 17:18:24. 17:17:56 UAV 1 446.44 586.69 720.60 UAV 1 633.94 774.19 705.67 17:18:14 17:17:58 UAV 1 467.54 UAV 5 599.14 728.52 580.34 Table597.79 2. UAV1 723.66 and UAV5 modified trajectories. 17:18:00 UAV 1 17:18:02ID UAV 1 Time

488.67 628.92 721.03 Amended Trajectory 509.24 649.50 713.75

X (m)

UAV 1 529.85 17:17:48 U AV1 370.43 17:18:04 668.57 UAV 5387.85 17:17:50 U AV1 550.95 17:17:52 U AV1UAV 1 406.44 17:18:06 17:17:54 U AV1 425.92 UAV 5 656.73

Y (m)

Z (m)

17:18:16 Time

UAV 1 UAV ID5

651.64 791.89 689.14 584.16Amended 702.58 Trajectory 578.76 X (m)

Y (m)

Z (m)

670.10 510.68 848.77 528.10

720.90 669.57 532.96 686.68

17:18:18

691.20 564.10 566.17 828.26

723.99 701.14 713.00 551.38

17:18:20 17:18:12 17:18:22

UAV 1 667.72 807.97 669.57 U AV1 593.19 733.44 721.53 UAV 5 569.50 U AV5 628.79 677.18 779.87572.48572.48 UAV 5 555.03 U AV1 614.07 652.12 754.32564.58716.18 U AV5 614.12 754.47 541.56 628.78 551.38578.76 UAV 5

17:17:56 U AV1UAV 1 446.44 572.14 586.69 712.39 17:18:08 17:17:58 U AV1 467.54 597.79 643.26 804.93

720.60 725.25 723.66 564.58

17:18:24

U AV1 633.94 608.28 774.19532.96705.67 UAV 5 529.72

UAV 5

17:18:10

17:18:14

U AV5

599.14

728.52

17:18:00 U AV1 488.67 628.92 721.03 U AV1 651.64 791.89 17:18:16 17:18:02 U AV1 509.24 649.50 713.75 U AV5 584.16 702.58 Figure 9 depicts the relative distance of each pair of UAVs that are involved in a AV1 figure, 529.85 U AV1 region 667.72of each 807.97 threat. FromUthis we can670.10 see that 720.90 the minimum separation UAV 17:18:04 17:18:18 U AV5 848.77 effect 532.96 U AV5 569.50 677.18 intruded upon, thanks 668.57 to the favorable attained by the CA algorithm.

580.34 689.14 578.76 detected

is669.57 never 572.48

U AV1 550.95 691.20 723.99 of 17:18:20 AV5 that 555.03 652.12 564.58 Figure 10 illustrates the pitch angle profiles UAV1 andUUAV5 amending their headings U AV5 656.73 828.26 551.38 17:18:22 U AV5 541.56 628.78 for the avoidance of corresponding threats in this scenario. At 17:17:48, UAV1 follows the 551.38 control U AV1 572.14 712.39 725.25 17:18:24 U AV5 529.72 608.28 532.96 input that changes its pitch angle from 0 to 0.71 and climbs subsequently. At 17:17:58, UAV1 and 17:18:08 AV5 and 643.26 804.93 564.58 UAV2 reach UCPA UAV1 begins to return to its original path. However, UAV1 climbs again at 17:18:02 because of the encounter with UAV3. At 17:18:18, UAV1 recoveries its course when both the Figure 9 depicts the relative distance of each pair of UAVs that are involved a detected threat. involved threats are resolved. And meanwhile, the neighboring collision betweeninUAV4 and UAV5 is From avoided this figure, via thewe upward can seeamendment that the minimum of UAV5. separation Using this region CA of advisory, each UAV there is never is no intruded domino effect upon, between sub-scenarios. thanks tothe thetwo favorable effect attained by the CA algorithm. 17:18:06

Figure Figure 9. 9. Relative Relative distance. distance.

Figure 10 illustrates the pitch angle profiles of UAV1 and UAV5 that amending their headings for the avoidance of corresponding threats in this scenario. At 17:17:48, UAV1 follows the control input that changes its pitch angle from 0 to 0.71 and climbs subsequently. At 17:17:58, UAV1 and UAV2 reach CPA and UAV1 begins to return to its original path. However, UAV1 climbs again at 17:18:02 because of the encounter with UAV3. At 17:18:18, UAV1 recoveries its course when both the involved threats are resolved. And meanwhile, the neighboring collision between UAV4 and UAV5 is avoided via the upward amendment of UAV5. Using this CA advisory, there is no domino effect between the two sub-scenarios.

Appl. Sci. 2017, 7, 83 Appl. 2016, 6, 83

11 of 14 11 of 14

Figure Figure10. 10.Pitch Pitchangle angleprofile profileof ofboth bothUAVs. UAVs.

4.2. Further Investigation 4.2. Further Investigation In this section, we conduct additional experiments to test the scalability of the proposed In this section, we conduct additional experiments to test the scalability of the proposed algorithms. algorithms. In [23], scalability is defined as the ability of an algorithm, system, or model to deal In [23], scalability is defined as the ability of an algorithm, system, or model to deal with increasing with increasing numbers of missions at a reasonable cost, or its ability to be effectively enlarged to numbers of missions at a reasonable cost, or its ability to be effectively enlarged to commensurate commensurate that growth. that growth. In practical applications, we may encounter different settings of UAVs, which depend on In practical applications, we may encounter different settings of UAVs, which depend on different different values of densities, variable Rcf and sense range. For instance, with the increase of values of densities, variable Rcf and sense range. For instance, with the increase of applications such applications such as surveillance in which various UAVs owning different capabilities and as surveillance in which various UAVs owning different capabilities and properties would cooperate properties would cooperate and compete for a certain target, it is expected that the airspace traffic and compete for a certain target, it is expected that the airspace traffic density will grow considerably density will grow considerably in certain reduced areas during short time periods. Since the CA in certain reduced areas during short time periods. Since the CA system is applied independently to system is applied independently to each cluster, the increasing UAV number in the whole airspace each cluster, the increasing UAV number in the whole airspace may improve the encounter possibility, may improve the encounter possibility, thereby raising the number of clusters, rather than the thereby raising the number of clusters, rather than the number of UAVs involved in a specific cluster. number of UAVs involved in a specific cluster. To validate the scalability, we use the computation time as a parameter to record the performance To validate the scalability, we use the computation time as a parameter to record the of the proposed CA system in handling different-density scenarios. Based on the simulation results in performance of the proposed CA system in handling different-density scenarios. Based on the Table 3, the average computation time (over 100 runs of random flight tests) for low density (20 UAVs), simulation results in Table 3, the average computation time (over 100 runs of random flight tests) medium density (60 UAVs), and high density (100 UAVs) traffic do not grow exponentially as the for low density (20 UAVs), medium density (60 UAVs), and high density (100 UAVs) traffic do not airspace density increases, attributing the high scalability to the independent clusters, which can be grow exponentially as the airspace density increases, attributing the high scalability to the frequently processed. independent clusters, which can be frequently processed. Table 3. Time taken in different densities. Table 3.Time taken in different densities UAVNumber Number UAV 2020 6060 100 100

Computation Time (s) (s) Computation Time 0.92 0.92 5.28 5.28 17.62

17.62

In addition, addition, several with varying values of tuning parameters Rcf and In severalextensive extensivesimulations simulations with varying values of tuning parameters Rcfsense and range range (SR) are constructed to observe the performance in terms of The CA maneuvers sense (SR) are constructed to observe the performance in efficiency. terms of efficiency. The CA should be optimal UAVs at can theirarrive respective destination minimum possible time. maneuvers should so be that optimal socan thatarrive UAVs at their respectiveindestination in minimum e e Define ti time. as theDefine expectant flight (not toflight maketime any deviation of the planned trajectory) tri as possible the time expectant (not to make any deviation of the and planned ti as the realistic flight time (fully follow the CA maneuvers) of U AVi (i = 1, 2, .., n), and the efficiency is trajectory) and tir as the realistic flight time (fully follow the CA maneuvers) of UAVi(i  1, 2,.., n) , given as [24]: and the efficiency is given as [24]: 1 n te E f f iciency = ∑ e ri (15) 1n in=1ti ti Efficiency   r (15) n i 1 ti

Figure 11 depicts the simulation results of efficiency with variable parameters. We could conclude the following:

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Figure 11 depicts the simulation results of efficiency with variable parameters. We could conclude the following: Appl. 83 • 2016, The6,efficiency

of 14 is decreasing as the Rcf value increases, because extensive conflict volume12leads to more threats that would be detected by the CD algorithm, thus more waypoints have to be • The efficiency is decreasing as the Rcf value increases, because extensive conflict volume amended to avoid potential collisions resulting in the higher realistic flight time. leads to more threats that would be detected by the CD algorithm, thus more waypoints have to be • Compared to SR = 9 km, the efficiency is lower when SR is equal to three kilometers with the amended to avoid potential collisions resulting in the higher realistic flight time. same Rcf , because the restricting sensor range may ignore the neighboring threats that could • Compared to SR = 9 km, the efficiency is lower when SR is equal to three kilometers with be synthetically resolved, and lately detect the intruder UAV, causing the number of amended the same Rcf, because the restricting sensor range may ignore the neighboring threats that could be waypoints to be higher. synthetically resolved, and lately detect the intruder UAV, causing the number of amended • With the same parameters of Rcf and sense range, high efficiency is obtained if the complete CR waypoints to be higher. algorithm including the causal analysis is utilized rather than only the DDOA. With the positive • With the same parameters of Rcf and sense range, high efficiency is obtained if the impact of causal analysis, the average increment of efficiency is respectively 2.83% and 3.47% complete CR algorithm including the causal analysis is utilized rather than only the DDOA. With for SR = 9 km and SR = 3 km. Consequently, the causal analysis is effective for the selection of the positive impact of causal analysis, the average increment of efficiency is respectively 2.83% and 3.47% optimal resolution trajectory. for SR = 9 km and SR = 3 km. Consequently, the causal analysis is effective for the selection of optimal resolution trajectory.

Figure Figure11. 11.Variation Variationof ofefficiency efficiency with with RRcfcfand andsense senserange rangefor forthe thetraffic trafficdensity densityof of20 20UAVs. UAVs.

5. 5.Conclusions Conclusions This twotwo efficient algorithms: CD algorithm and CR algorithm, which This paper paperhas haspresented presented efficient algorithms: CD algorithm and CR algorithm, constitute a novel CA system for multiple cooperative UAVs aiming to detect and resolve threats by which constitute a novel CA system for multiple cooperative UAVs aiming to detect and resolve generating an optimalan trajectory an overall minimum cost in 3Dcost airspace. The CD module threats by generating optimal with trajectory with an overall minimum in 3D airspace. The CD analyzes the spatial-temporal information composing a set of discrete 4D trajectories generate the module analyzes the spatial-temporal information composing a set of discrete 4Dtotrajectories to intuitionistic representation of detected conflicts. The CR algorithm integrates with the CD portion generate the intuitionistic representation of detected conflicts. The CR algorithm integrates with the and solves the through causal The DDOA provides new CD portion and detected solves thethreats detected threatsDDOA throughand DDOA andanalysis. causal analysis. The DDOA provides feasible alternative trajectories for each UAV involved in an encounter with a local optimization new feasible alternative trajectories for each UAV involved in an encounter with a local optimization scope, scope, and and itit generates generates alternative alternative avoiding avoiding trajectories trajectories by by an an objective objective function function (integrating (integrating track track adjustment, cost, distance, and time) in consideration of several constraints (i.e., performance, adjustment, cost, distance, and time) in consideration of several constraints (i.e., performance,state, state, and distance). The causal analysis explores the emergent dynamics between the alternative and distance). The causal analysis explores the emergent dynamics between the alternative trajectories trajectories generated by DDOA and the surrounding It hasadvantages numerous advantages such the as generated by DDOA and the surrounding traffic. It hastraffic. numerous such as splitting splitting the scenario to separate clusters, reducing the size of solution space, and exploring the scenario to separate clusters, reducing the size of solution space, and exploring the global optimal global optimal Based on the quantitative simulation results, proposed CA validated system has solution. Basedsolution. on the quantitative simulation results, the proposed CAthe system has been to been validated to be feasible and effective in resolving conflicts for multiple UAVs and high be feasible and effective in resolving conflicts for multiple UAVs and has high scalability forhas different scalability for different trafficdecreases densities;asthe decreases as the value of volume traffic densities; the efficiency theefficiency value of conflict volume increases, andconflict increases as the increases, and increases as the sense range increases; the causal analysis is effective for the selection sense range increases; the causal analysis is effective for the selection of an optimal resolution trajectory. of an optimal resolution trajectory. Future research will be dedicated to: (1) using a heuristic-based algorithm to improve our proposed approach, which could tackle the collision avoidance problem of more UAVs in high-density scenarios, while it also may require more computation time; (2) making a comprehensive review of the existing best performing methods that consider UAV factors and

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Future research will be dedicated to: (1) using a heuristic-based algorithm to improve our proposed approach, which could tackle the collision avoidance problem of more UAVs in high-density scenarios, while it also may require more computation time; (2) making a comprehensive review of the existing best performing methods that consider UAV factors and integrating them to our system in order to improve its performance; (3) considering several disturbances (e.g., wind) to improve the current system logic in order to hold the complex field situations; (4) integrating UAVs into(manned) general aviation to operate in a non-segregated airspace. Acknowledgments: The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (71601181), the Military Scientific Research Project (162017160500A21XXX), and the State Key Laboratory of Management and Control for Complex Systems-Open Project (20160109). Author Contributions: Mingrui Lao and Jun Tang designed the distributed dynamic optimization approach and causal analysis, conducted the simulations of the core algorithms and co-wrote the initial manuscript. Besides, Jun Tang helped improve the system design and put forward several construction suggestions. The final manuscript was read and approved by all authors. Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations The following abbreviations are used in this manuscript: 3D 4D ADS-B ASAS CA CD CPA CR DDOA NP TCAS TMA UAV

Three dimensional Four dimensional Automatic Dependent Surveillance Broadcast Airborne Separation Assurance System Collision avoidance Conflict detection Closet point of approach Conflict resolution Distributed dynamic optimization approach Non-deterministic polynomial Traffic Alert and Collision Avoidance System Terminal Maneuvering Area Unmanned aerial vehicle

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