three-dimensional autonomous obstacle avoidance algorithm

Research ArticleThree-Dimensional Autonomous Obstacle AvoidanceAlgorithm for UAV Based on Circular Arc Trajectory

Jiandong Guo ,1 Chenyu Liang,2 Kang Wang,2 Biao Sang,2 and Yulin Wu2

1Key Laboratory of Unmanned Aerial Vehicle Technology of the Ministry of Industry and Information Technology,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China2College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Correspondence should be addressed to Jiandong Guo; [email protected]

Received 14 August 2020; Revised 22 February 2021; Accepted 3 April 2021; Published 22 April 2021

Academic Editor: Nicolas Avdelidis

Copyright © 2021 Jiandong Guo et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper proposes an innovative and efficient three-dimensional (3D) autonomous obstacle algorithm for unmanned aerialvehicles (UAVs) which works by generating circular arc trajectories to avoid obstacles. Firstly, information on irregular obstaclesis obtained by an onboard detection system; this information is then transformed into standard convex bodies, which are usedto generate circular arc avoidance trajectories, and the obstacle avoidance problem is turned into a trajectory tracking strategy.Then, on the basis of the geometric relationship between a UAV and obstacle modeling, the working mechanism of theavoidance algorithm is developed. The rules of obstacle detection, avoidance direction, and the criterion of avoidance success aredefined for different obstacle types. Finally, numerical simulations of different obstacle scenarios show that the proposedalgorithm can avoid static and dynamic obstacles effectively and can implement obstacle avoidance missions for UAVs well.

1. Introduction

UAVs are widely used in military and civilian fields becauseof their outstanding advantages, such as flexibility, lightweight, strong mobility, and good concealment [1]. Nowa-days, the growth and applications of UAV technologies notonly change the development direction of many industriesbut also bring huge market and economic benefits [2]. How-ever, with the complication of flight missions and usage sce-narios, higher requirements are placed on the autonomousflight capabilities and intelligence of UAVs, and autonomousobstacle avoidance technology for UAVs has graduallybecome one of the most important technologies [3].

The real-time autonomous obstacle avoidance problemstudied in this article refers to the avoidance of various colli-sions during flight through the target path by avoidanceactions, which are calculated according to the obstacle infor-mation based on known data or data coming from anonboard detection system in real time, as shown in

Figure 1. Meanwhile, the difficulty of this problem lies inthe irregularity, dynamics, and complexity of obstacles andthree-dimensional space.

Sense and avoid (S&A) is a major pattern for obstaclethreat avoidance. The aircraft’s obstacle avoidance methodscan usually be divided into following two categories:

(1) The method of resolving the new trajectory based onpath planning: the main idea of this method is totransform the obstacle avoidance problem into a pathplanning problem [4, 5]. With the advances ofresearch in this field, many significantly improvedpath planning algorithms have been proposed,including the Voronoi diagram (VD) [6] based ongraph theory, artificial potential field (APF) [7, 8]based on field theory, the RRT [9] algorithm basedon sampling theory, the A ∗ [10] algorithm basedon heuristic information, and other algorithms basedon swarm intelligence optimization theories [11–13].

HindawiInternational Journal of Aerospace EngineeringVolume 2021, Article ID 8819618, 13 pageshttps://doi.org/10.1155/2021/8819618

https://orcid.org/0000-0002-4733-2550

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https://doi.org/10.1155/2021/8819618

While these algorithms have advantages, they alsohave certain limitations. VD has fast speed in itssearching trajectory with high safety, but it is difficultto apply this method to a complex or high-dimensional dynamic environment. APF is simplein principle and has high computing efficiency, butit can easily fall into the local optimum with hightime cost. The RRT algorithm does not require pre-processing of the state space and has a wide searchrange in the task space with high coverage and fastconvergence, but the searching path is often not opti-mal. The A ∗ algorithm is simple and efficient, but itcan easily fall into an infinite loop and has many ver-tices in the trajectory

The swarm intelligence algorithm is used to simulate theevolutionary strategy of a population in the natural environ-ment or the characteristics of survival of a biological group,and uses multiple individuals in the group to perform an iter-ative search in the task space to find the optimal solution,such as the genetic algorithm (GA) [11, 14], the ant colonyalgorithm (ACO) [12, 15], and the differential evolution algo-rithm (DE) [13, 16]. Additionally, this kind of method haslow computational complexity, flexible application, strongsearch ability, and good robustness; however, it requires hugecomputing resources and high-quality equipment.

Refs. [5, 17] present comparative cases of these path plan-ning algorithms for different scenarios and obstacle layoutsin terms of time consuming and optimal solutions, and thesimulation results show that the designed path planningalgorithms often conflict with each other in terms of optimal-ity and convergence.

(2) The second method of resolving the guidance lawbased on geometrical relationships: this method cal-culates the guidance law of obstacle avoidance actionaccording to the relative distance [18], speed [18, 19],angle [20], and other key information [21] betweenthe aircraft and collisions. Compared to the obstacleavoidance methods for path planning mentionedabove, the key factor for this type of method is the

modification of the UAV’s trajectory in real time toavoid collisions along its path with the help of feed-back datum from onboard sensors taken from theenvironment, which often is divided into two steps,namely, detection and avoidance. The drone’s explo-ration capabilities depend on the onboard sensors,which are commonly divided into cooperative andnoncooperative groups. Cooperative technologiesare those that can receive data from the obstacleswhich can then broadcast its information. Amongthe leading cooperative technologies are Traffic Alertand Collision Avoidance System (TCAS) [22] andAutomatic Dependent Surveillance Broadcast(ADS-B) [23]. The relative distance, bearing, altitude,latitude, longitude, etc. can be obtained from thethreat. However, these technologies have not yetshown enough maturity for utilization in everydrone. Noncooperative technologies depend on mea-suring instruments, such as infrared cameras [21],photoelectric radars [18], laser rangefinders [24],and acoustooptic processors [25]. Each sensor hasdifferent limitations, and no single sensor can pro-vide all the necessary information for obstacles. Theoptical and acoustic sensors are most suitable forangular measurements, while radar and laser are bestfor ranging. Therefore, research has been devoted tothe field of sensing and detection, includingimproved sensor sensitivity [26, 27].

Many obstacle avoidance algorithms have been proposedaccording to the geometrical relationships between aircraftsand collisions. Sasongko et al. [19] proposed a method whichcalculated a set of avoidance waypoints to avoid collisionsbased on an obstacle model and an aircraft’s speed vector.Zheng et al. [18] established fuzzy rules to obtain avoidancemaneuver options according to the aircraft’s forward speedand the distance between the vehicle and obstacles. Al-Kaffet al. [21] proposed an avoidance method through trackingalong the safe flight boundary consisting of a set of obstaclefeature points, which were obtained by determining the coor-dinate relationship between the aircraft and obstacles in realtime. Overall, these obstacle avoidance methods based ongeometrical relationships are easy to implement and test,but they are difficult to apply in actual complex flightenvironments.

This work is aimed at solving the problem of real-timeautonomous obstacle avoidance for UAVs in three-dimensional space, and an innovative obstacle avoidancealgorithm based on a circular arc trajectory is proposedaccording to the geometric relationship between UAVs andobstacles through obstacle modeling. This paper is organizedas follows: Section II describes the obstacle avoidance prob-lem and obstacle modeling. Section III analyzes the workingmechanism of the novel algorithm, which we have namedthe Circular arc Trajectory Geometric Avoidance (CTGA)algorithm. Section IV presents the simulation results forstatic simple, complex, and dynamic obstacles, respectively,and analyzed the control accuracy and performance. SectionV gives the conclusions and future work.

Waypoint pathUAV trajectory

Figure 1: Obstacle avoidance problem.

2 International Journal of Aerospace Engineering

2. Mathematical Description of ObstacleAvoidance Problem

2.1. Modeling of Obstacles. When a UAV is performing aflight mission, there are many potential obstacles that mayexist on the flight path, such as buildings, mountains, andtrees. Most of these obstacles are often irregular and difficultto handle directly, and the obstacle data detected by onboardsensors is often incomplete. Paying too much attention to thedetails of obstacle shapes will greatly increase the difficultyand calculation of the obstacle avoidance algorithm designand reduce the obstacle avoidance efficiency. Therefore,when the detection system of the aircraft captures the colli-sion threat information, a series of sampling points areobtained. According to these sampling points, an obstaclecircle is fitted by some fitting algorithm, such as the leastsquare method, but it has a large calculation amount and isnot suitable for real-time obstacle avoidance for UAVs. Wecan compute the radius R and center ½ox, oy�T of an obstaclecircle using the following:

R = 12 max ∪

m−1

i=1∪m

j=i+1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixi − xj� �2 + yi − yj

� �2r

, ð1Þ

ox

oy

" #= 12

xi,idx − xj,idx

yi,idx − yj,idx

" #, ð2Þ

where ðxi, yiÞði = 1, 2,⋯,mÞ is the convex hull of those sam-pling points detected by the onboard system, idx is the indexof equation (1).

In this way, an obstacle circle is fitted which can cover thewhole or key parts of the obstacle, it not only simplifies thedescription of obstacle, but it also facilitates the design ofobstacle avoidance algorithm according to obstaclemodeling.

It is possible that in some cases, the UAV may encounterobstacle obstructions that are larger than the distancebetween the aircraft and an obstacle. In other cases, the detec-tion system may not be able to capture the whole size or keyparts of the obstacle, due to its detection limitation. To dealwith such situations, the UAV can continuously detect obsta-cle information during the avoidance process, and multipleobstacle circles are used to characterize the large obstacle.Examples showing the determination of an obstacle circlebased on detection sampling points can be seen in Figures 2and 3.

In three-dimensional space, it is reasonable that obstaclescan be modeled with one or more standard convex bodiesaccording to the obstacle detection system, such as a hemi-sphere, a cylinder, a cone, and a circular table. Their approx-imate expressions can be unified as follows [28]:

Γ = x − x0a

� �2p+ y − y0

b

� �2q+ z − z0

c

� �2r, ð3Þ

where ðx, y, zÞ is an arbitrary point on the obstacle model, ðx0, y0, z0Þ represents the coordinate of the center point ofthe obstacle model, the parameters a, b, c and p, q, r are con-

stants and determine the shape and size of the obstaclemodel. Figure 4 shows the various types of typical convexbodies obtained from different detection data combinations.Γ < 1, Γ = 1, and Γ > 1 express the inside, surface, and outsideof the obstacle model, respectively.

According to these obstacle models, when a UAVencounters obstacles in the preplanned flight path, simpleobstacles can be modeled by a single standard convex bodyand complex obstacles can be represented by a combinationof multiple convex bodies, as depicted in Figure 5. Hence, cir-cular arc trajectories can be designed, wherein the autono-mous obstacle avoidance problem is transformed into atrajectory tracking strategy.

2.2. Obstacle Avoidance Problem Description. In this article,both the surface and the inside of an obstacle model areregarded as no-fly zones or threat zones, i.e., Γ > 1. The prob-lem of autonomous obstacle avoidance for a UAV can bedescribed as how to keep the UAV always outside the no-fly zone or threat zone during the flight mission. Assume thatthe mission space is S; Sobs represents the threatened area ofthe obstacle, i.e., Γ ≤ 1, and Sfree represents the flyable safetyarea, i.e., Γ > 1. The relationship between the zones is shownas follows:

S = Sobs ∪ Sfree,Sobs ∩ Sfree =∅:

(ð4Þ

When the UAV detects an obstacle obstructing the targetflight path, it must be able to adjust the flight path to avoidthe obstacle. The CTGA algorithm can generate the circularavoidance trajectory in real time, and tracks the trajectoryto achieve safe flight. So the flight path for the UAV in thespace can be expressed as follows:

P = Ptarget + ∪n

i=1Piavoid, Pi

avoid = Γ > 1f g, ð5Þ

where Ptarget is the target flight path, Piavoid is the circular

avoidance trajectory for the obstacle at stage i, and n is thenumber of obstacles.

3. Circular Arc Trajectory Geometric Avoidance(CTGA) Algorithm

3.1. CTGA Principle and Procedure. The main idea of theCTGA algorithm is transforming the obstacle avoidanceproblem into path planning and path following, and it isbased on the geometric relationship between the aircraftand the obstacle. The algorithm assumes that the positionand velocity of the obstacles are given and accessible to theaircraft, then it designs a circular arc avoidance trajectoryaccording to the obstacle model (simple or complex, staticor dynamic). Therefore, the UAV avoids the obstacle bytracking the circular arc avoidance trajectory.

As illustrated in Figure 6, first, consider that a UAV is fly-ing while tracking a predefined flight path; then, the UAVdetects the collision threat based on the information of the

3International Journal of Aerospace Engineering

–400 –200 0 200 400 600 800 1000 1200 1400

X (m)

–200

0

200

400

600

800

1000

1200

1400

Y (m

)

Sampling pointsObstacleObstacle circle

(a) Simple obstacle

–200 0 200 400 600 800 1000 1200 1400 1600

X (m)

0

200

400

600

800

1000

1200

1400

1600

Y (m

)

(b) Complex obstacle

Figure 3: Obstacle circle fitting.

Figure 2: Obstacle detection.


detected parts at point T1, and an obstacle model enclosingthe whole or main part of the obstacle can be constructed,with the hemisphere model being an example for this case.Therefore, a circular arc avoidance template trajectory as areference path is generated in real time according to theobstacle model, whose radius corresponds to the obstaclemodel at the current altitude of the aircraft, and constantlychanges with the aircraft altitude; the real-time avoidancetrajectory can be expressed as follows:

x tð Þ − oxð Þ2 + y tð Þ − oy� �2 = R tð Þ2, R tð Þ∞H tð Þ,

z tð Þ = h1 + d cos λ tan γ,

(

ð6Þ

whereH represents the real-time altitude of the UAV, γ is theflight path angle, d is the distance from the UAV to WP1under horizontal projection, and λ is the angle between thesegment made by the UAV’s center and WP1, and the targetpath under horizontal projection.

Furthermore, in order to ensure that the generated circu-lar arc trajectory can bypass the obstacles with a feasible pathfor the aircraft, a safe distance Rsafe is added to the radius,which should be determined by the flight performance ofthe drones, so the radius of the circular arc trajectory is ðRðtÞ + RsafeÞ. In addition, limited by the minimum turningradius Rmin of the aircraft, the radius of the circular arc trajec-tory is as follows:

R tð Þ =max Rmin, R tð Þ + Rsafeð Þ, ð7Þ

where the expression of Rmin is as follows:

Rmin =V2

n

g tan ϕmaxð Þ : ð8Þ

Here, the value of the minimum turning radius is determinedby the ground speed and the maximum roll angle of theUAV.

Immediately, the guidance system of the UAV begins anavoidance maneuver with the minimum turn radius possibleof reaching the template trajectory tangentially at point T2 (itshould be pointed out that in order to reduce the risksinvolved with using the minimum turning radius duringthe maneuver avoidance flight, the strategy of the turn shouldbe considered in advance, so that the turning radius can beslightly increased in actual flight), and tracks the circulararc template trajectory. Finally, when the UAV avoids thecollision successfully at point T3, it will return to its originalnavigation course immediately.

The CTGA algorithm includes three major processes:obstacle detection, avoidance direction selection, and

Figure 5: Illustration of UAV avoiding obstacles.

Hemsiphere (p = q = r = 1; a = b = c)

10

5

0

z

0

y x0

10

–10 –10

10

Cylinder (p = q = r = 1; r>1; a = b)

10

5

0

z

y x0 010

2010

20

Cone (p = q = r = 1; r<1; a = c)

10

5

020

10 1020

0 0

z

y x

Circular table (p = q = r = 1; r<1; a = b)

10

5

020

1020

100 0

z

y x10

0

x0

–10 –10

10

10

5

0

z

y x0 01010

20

Cone (p = q = r = 1; r<1; a = c)

0 1020

Circular table (p = q = r = 1; r<1;

10

5

020

10z

Figure 4: Typical convex body obstacle model.


avoidance success criteria determination. The detailed obsta-cle avoidance process, in conjunction to following the prede-fined waypoint path, is described in Figure 7.

3.2. Obstacle Detection and Avoidance Determination. Defin-ing a detection radius Rdet is important to allow an aircraftenough time and distance to maneuver away from the obsta-cles without colliding, which is determined by the vehicleonboard sensor.

The UAV detects a static obstacle during the flight, where

PO�! is the position vector of the UAV and the obstacle, and Δ

is the angle of the speed vector V!

n and PO�!, as shown inFigure 8. When the distance between the UAV and the obsta-cle is less than or equal to the detection radius

PO�!��

�� ≤ Rdet + Robs: ð9Þ

If the UAV is considered to be within the range of the

WP2

WP1

T3

T2

T1

Λ

𝛾

(a) 3D obstacle avoidance problem

T3

T2

T1

WP2

WP1

Λ

𝜆

(b) 2D obstacle avoidance problem

Figure 6: UAV obstacle avoidance with CTGA.

• Set waypoint path• Obstacle data

Obstacle detected ?

Avoidancesuccess ?

• Build obstacle model• Generate circular arc trajectory

Y

Y

Y

N

N

N

Track waypoint path

Track ends ?

End flight

Avoidance procedure

• Judge avoidance direction• Track template trajectory

Figure 7: UAV guidance procedure.

Vn

Rdet

P

O

Robs

Rdet

Δ

Figure 8: Obstacle detection and avoidance.


obstacle, then further checks should be made, and the judg-ment condition that the UAV needs to enter the avoidancestate is as follows:

φ t, Vn, Δð Þ =1, PO�!

�� sin Δ < Robs,

0, PO�!��

�� sin Δ ≥ Robs,

8><>: ð10Þ

where Robs is the radius of the corresponding obstacle modelat the current altitude of the UAV. When equation (10) isequal to 1, the UAV should avoid the obstacle immediately.

However, equations (9) and (10) cannot be applied todynamic obstacles. For dynamic obstacles, we need to be ableto predict whether the aircraft will collide after flying for acertain time Δt at the current speed after the obstacles aredetected. The rule for determining whether dynamic obsta-cles need to be avoided is as follows:

POt�!��

�� = Rdet + Robs, at time t,

PO�!t+Δt

�� < Robs, ∃Δt > 0:

8><>: ð11Þ

To some extent, the performance of the onboard sensordetermines the obstacle avoidance capability of the vehicle,which is also the prerequisite and basis for obstacle avoid-ance. Therefore, the UAV is equipped with a suitable sensingdetection system, one that is compatible with the perfor-mance of the UAV, the specific flying environment, and thecharacteristics of the obstacle.

3.3. Avoidance Direction Selection. The guidance system gen-erates the circular arc avoidance trajectory in real time afterdetecting the obstacle threat, and it will reduce the avoidanceroute by choosing a reasonable avoidance direction. If theaircraft’s velocity vector points to the right of the obstaclecenter, then it will fly along the circular arc template trajec-tory in a counterclockwise direction. Otherwise, it flies clock-wise. The direction angle Δ can be obtained as follows:

Δ = ψobs − χ, ∈ −π, π½ �, ð12Þ

where ψobs is the angle from the connection of the UAV andobstacle center to the geography north, and χ is the courseangle of the aircraft. If Δ > 0, the UAV tracks a circular arcavoidance trajectory in a clockwise direction; otherwise, ittracks counterclockwise.

However, in the case of situations with complex or largeobstacles which cannot be captured completely at the firsttime, we can use multiple standard convex bodies to modelthe complex obstacle. The circular arc avoidance trajectoriesare composed of different convex bodies; at the same time,the judging of the direction is always in process during theobstacle avoidance flights. As shown in Figure 9, when theUAV detects the obstacle again, the avoidance direction isaffected by the previous obstacle. So the above rules do notapply to complex obstacle avoidance. In this case, we only

need to judge the first obstacle avoidance direction as thedirection in all complex obstacle avoidance processes.

3.4. Avoidance Success Criteria Determination. Avoidancesuccess can be defined as keeping the UAV always outsidethe collision threat during the avoidance flight. The UAV fol-lows the circular arc template trajectory until it is able to con-tinue towards the original path in a straight line and withoutpassing through the obstacle. We can compute the angle Λ(see in Figure 6) to determine whether avoidance is success-

ful, which is the angle between position vector PO�! and thevector of the current position of the UAV to the next way-point. If Λ > 90°, the UAV avoids the obstacle successfully;otherwise, the UAV continues to track the template avoid-ance trajectory.

Similarly, a complex obstacle consists of n convex bodies.If i < n, the criteria requires that the angle Λ > 90° or the dis-tance between the UAV and the next obstacle is less than orequal to the detection radius. If i = n, the criteria onlyrequires that Λ > 90°.

4. Simulation Results and Analysis

4.1. Simulation Assumptions. In order to verify the effective-ness of the proposed three-dimensional autonomous obstacleavoidance algorithm, the novel algorithm is performed inMatlab/Simulink. Here are some of the assumptions:

(1) In this section, we use a high-order, nonlinearnumerical model of the Cessna 172 fixed-wing air-craft to test the effectiveness of the algorithm, whichis constructed in Simulink. The overall aerodynamicparameters for the aircraft model are described in[29], and some flight performance constraints of theaircraft are defined in this paper. The maximum rollangle is ϕmax = ±30°, and the maximum pitch angleis θmax = ±20°. Suppose the initial position of theUAV in the inertial coordinate systems is (0, 0,-200)m and the cruising speed is Vn = 50m/s. Unlessotherwise specified, the predefined state of the UAVin all simulation tests is the same

Robs,1

O1

P

P

O2

Robs,2

Δ > 0

Δ ≤ 0

𝛹obs𝜒

Figure 9: Avoidance direction selection.


(2) This article mainly proposes an autonomous obstacleavoidance algorithm, and it does not require specificonboard sensors. Therefore, any sensor that can beinstalled on a UAV, which can acquire accurate infor-mation such as the position and speed data of obsta-cles is applicable. Meanwhile, it does not consideruncertain factors that affect the measurement accu-racy of sensors or change the flight environment, suchas wind speed and electromagnetic interference. In thesimulation tests, the parameters such as the positionand velocity of the obstacles are assumed and prede-fined, and the process of sense and detection is ignored

(3) The flight speed of the UAV model in this paper islimited to 40-80m/s, and the overall maneuverabilityof the UAV is also limited, as well as its maximumattitude. Therefore, there is a certain restriction onthe moving speed for the dynamic obstacles

4.2. Obstacle Avoidance Simulations. The CTGA algorithm1is carried out in some cases when the UAV goes throughpotential collisions in the predefined flight path with simple,complex, and dynamic obstacles, respectively. In all simula-tion tests, the aircraft is operated to follow a waypoint flightpath, and the coordinates of the predefined waypoint pathare (0, 0, -200)m to (4000, 2000, -300)m in a north-east-Down coordinate, with the safe distance set at Rsafe = 100m.

4.2.1. Simple Obstacle Avoidance. For the first simulation,between the waypoints, the aircraft will face some simpleobstacles which need to be avoided. For a simple obstacle,we only use a single convex body to model. The flight trajec-

tory and flight status of the UAV during the entire avoidanceprocess are shown in Figure 10.

It can be seen from Figure 10 that the UAV detects theobstacle threat twice and avoids obstacles successfully duringthe whole flight. First, the UAV detects obstacle I at 8 s; theCTGA algorithm generates the circular arc template avoid-ance trajectory real time, and determines the avoidancedirection as counterclockwise according to the relationshipbetween the flight direction and the obstacle position. Then,the UAV avoids obstacle I successfully at 33 s, and immedi-ately returns to the predefined waypoint path with maximumroll angle and continues to complete the flight mission. Then,the UAV detects and avoids obstacle II at 49-78 s.Figure 10(c) shows that during the avoidance flight, theUAV has always been outside of the obstacles and has main-tained a safe distance of about 100m away from the surface ofthe obstacles. The simulation results fully confirm that thealgorithm can effectively avoid simple obstacles.

4.2.2. Complex Obstacle Avoidance. For complex obstacles inthe flight mission, as has been discussed previously, we canuse multiple standard convex bodies to model complexobstacles. The flight trajectory, Euler angle response, and rel-ative distance are depicted in Figure 11.

It can be seen from the figures that the algorithm per-forms a multistage procedure to generate three circular tra-jectories due to the obstacle size and detection systemlimitation, and the UAV tracks the avoidance trajectories toavoid the complex obstacle successfully. The UAV firstdetects obstacle I and performs avoidance maneuvers at13 s, and after passing the first avoidance process, the UAV

Input: waypoint path W = fwp1,⋯,wpng, UAV position P = ðpn, pe, pdÞ, obstacles information, center O, radius Robs, and speed v.1: if state = 1 then2: UAV tracks the waypoints path3: end if4: for i← 1 to n do5: O←O + vt

6: jPO�!j←ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðpn − onÞ2 + ðpe − oeÞ2

q

7: ψobs ← arctan ððoe − peÞ/ðon − pnÞÞ8: Δ← ψobs − χ

9: if jPO�!j ≤ Rdet & Rdet sin Δ < Robs then10: state = 211: if Δ > 0 then12: UAV tracks the circular path in clockwise13: else14: UAV tracks the circular path in clockwise15: end if16: Λ← arctan ððwpnext,e − peÞ/ðwpnext,n − pnÞÞ − ψobs17: if Λ > pi/2 or jPOi+1

��!j ≤ Rdet18: state← 119: i← i + 120: end if21: end if22: end for23: return UAV maneuver operations

Algorithm 1: The CTGA algorithm.


04000

Up

(m) 500

35003000

2500

North (m)

2000 20001500

East (m)

10001000500 0

0

Actual trajectoryWaypoint path

(a) UAV avoidance flight trajectory

0 8 20 33 40 49 60 70 78 90

Time (s)

–30–20

0

2030

Roll

(deg

)

0 20 40 60 80

Time (s)

0

2

4

Pitc

h (d

eg)

(b) Euler angle response

0 8 20 33 40 49 60 70 78 90

Time (s)

0100200

400

600

800

1000

1200

1400

Dist

(m)

Obstacle I Obstacle II

(c) The relative distance between the UAV and the surface of the obstacle

Figure 10: UAV flight status of simple obstacle avoidance simulation.


04000

500

Up

(m)

3000

North (m)

2000

1000 20001500

East (m)100050000 –500



0 13 22 30 40 54 60 70 80 90

Time (s)

–30–20

0

2030

Roll

(deg

)

0 20 40 60 80

Time (s)

0

2

4

Pitc

h (d

eg)


0 13 22 30 40 54 60 70 80 90

Time (s)

0100

500

1000

1500

2000

Dist

(m)

Obstacle I

Obstacle II

Obstacle III

(c) The relative distance between the UAV and the surface of obstacle

Figure 11: UAV flight status of complex obstacle avoidance simulation.


detects and avoids obstacle II at 22 s. Similarly, obstacle III isdetected at 30 s; then, the UAV avoids the last obstacle andreturns back to the waypoint path. As shown inFigure 11(c), during the avoidance flight, the UAV has alwaysbeen outside of the obstacles and about 100m away from thesurface of obstacles, so it can be confirmed that the CTGAalgorithm can also effectively avoid complex obstaclesthrough a multiple obstacle model.

4.2.3. Dynamic Obstacle Avoidance. For the third simulation,in order to verify if the CTGA algorithm is also effective for adynamic obstacle with a certain speed, we use a movingobstacle in the flight space, with an initial position of theobstacle center point at 1500m and 300m, and a movingspeed of 20m/s in the east, 10m/s in the north, and stoppingafter 40 s. The real-time flight trajectory, Euler angleresponse, and relative distance between the UAV and themoving obstacle are shown in Figure 12.

It can be seen from the figures that the UAV detects thedynamic obstacle at 14 s, because the moving direction of

the dynamic obstacle is towards the UAV. The whole avoid-ance process lasts 37 s, and avoidance finally ends at 51 s. TheUAV has always been outside of the obstacles and about100m away from the surface of the obstacles, so it can beconfirmed that the CTGA algorithm can also effectivelyavoid dynamic obstacles.

In summary, the CTGA algorithm provides an efficientobstacle avoidance method for UAVs. It is not only simple andconvenient, but it can also avoid static and dynamic obstacles.

5. Conclusion

An innovative autonomous obstacle avoidance algorithm forUAVs in 3D space based on a circular arc trajectory has beenproposed and discussed.

(1) The method of the obstacle model is simple accord-ing to obstacle data by an onboard detection system,which uses one or more standard convex bodies toenclose the detected parts of an obstacle.

4000

3000

North (m)2000

1000Up

(m)

500

–500

East (m)

00

500 1000 01500 2000



0 14 20 40 51 60 80

Time (s)

–30–20

0

2030

Roll

(deg

)

0 20 40 60 80

Time (s)

0

2

4

Pitc

h (d

eg)


0 14 20 40 51 60 80

Time (s)

0100

500

1000

1500

2000

Dist

(m)

(c) The relative distance between the UAV and the surface of the obstacle

Figure 12: UAV flight status of the dynamic obstacle avoidance simulation.


Consequently, the circular arc avoidance trajectory isdesigned through the obstacle model. It not onlytransforms an obstacle avoidance problem into apath following problem, but it also simplifies thedesign of an obstacle avoidance algorithm

(2) The proposed CTGA algorithm can avoid static anddynamic obstacles by simply referring to the geomet-ric relationship between a UAV and an obstacle, evenwhen the obstacle geometry is not available and can-not be obtained directly; a multistaged circular trajec-tory correction procedure can be employed. Thisalgorithm not only satisfies the maneuverability con-straints of a UAV, but it also requires less calculation,which has led to a good applicability in practicalengineering

The presented work is focused on the design of an obsta-cle avoidance algorithm for a UAV, and it has been verified ina simulation environment. Our future work will do moreextensive and complex simulations to analyze the character-istics and performance of the proposed algorithm and applythe algorithm to actual flight tests.

Data Availability

The data used to support the findings of this study areincluded within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (grant number56XAA17075).

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