UAV Rendezvous: From Concept to Flight Test

Daniel B. Wilson, Ali Haydar Goktogan and Salah SukkariehThe Australian Centre for Field Robotics (ACFR)

The University of Sydney, Australia[d.wilson, a.goktogan, s.sukkarieh] at acfr.usyd.edu.au

AbstractThe algorithms onboard Unmanned Aerial Vehi-cles are increasing in complexity and thus require awell established concept to flight test developmentprocess to accelerate deployment and avoid lossof aircraft. We present a modular multi-UAV al-gorithm development framework which combinesdesign, simulation, performance evaluation and de-ployment in a single, high level graphical environ-ment. The framework is then utilised to develop aheuristic direct search algorithm for rendezvous toleader-follower formation. Fixed-wing simulationand quadrotor flight test results validate the ren-dezvous algorithm.

1 IntroductionDriven by technological advances, Unmanned Aerial Vehi-cles (UAV) are increasing in complexity, particularly in termsof the algorithms being implemented. With increased com-plexity comes a higher probability of unforeseen problems,errors and uncertain system performance. Ideally, all algo-rithm testing would occur during flight testing since this en-vironment is most representative of the actual UAV deploy-ment. Such an approach is highly time consuming and willinevitably lead to loss of aircraft. Instead, a majority of prob-lems should be identified and system performance evaluatedin a laboratory environment where rapid testing and iterationcan occur. Consequently, a robust and well established sim-ulation to flight testing framework is critically important forUAV algorithm development.

To this end, we have created a modular development frame-work which enables rapid, iterative algorithm development bycombining algorithm design, simulation, performance evalu-ation and implementation in a single high level graphical en-vironment. This approach avoids time consuming and errorprone conversion between development environments and al-lows iterative development to occur offline. The frameworkwas developed using Matlab’s Simulink [MATLAB, 2011]because it provides a level of abstraction higher than tradi-tional programming languages such as C++ and Java. It also

Figure 1: A screenshot from the multi-UAV simulation visu-alisation.

facilitates automatic C++ code generation for deployment ona UAV. The hierarchical and modular nature of the graphicalenvironment, coupled with standard interfaces, enables seam-less integration at a central location. This is particularly use-ful in a research environment where collaboration is key andparticipation is dynamic.

As a minimum, a UAV simulation consists of an aircraftmodel and a control scheme to generate control inputs toachieve mission goals [Jung and Tsiotras, 2007]. Our systemextends this by simulating guidance, navigation and control(GNC) algorithms, modelling sensor noise, bias and latencyas well as modelling actuator and environmental characteris-tics. Visualisation was used to provide the user with intuitivefeedback as shown in Fig. 1. The modular architecture, com-bined with standardised interfaces allows interchangeable ve-hicle dynamic models, GNC algorithms and sensor models.Configuration files are used to modify specific vehicle aero-dynamic, geometric and propulsive coefficients, as well aslevels of sensor uncertainty and severity of environmental dis-turbances. In this way, numerous UAV system configurationsand algorithms can be quickly benchmarked against one an-other using quantitative performance data.

To demonstrate the rapid development process, rendezvousto leader-follower formation is considered. As a nonholo-

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

nomic multi-UAV problem, fixed-wing rendezvous is com-plex by nature, so a high level development process is es-sential. The problem can be formulated as an optimisation,where the objective is to select a point on the leader’s path thatminimises the error between the leader and follower arrivaltimes to a satisfactory threshold. These minima correspond topoints where rendezvous is feasible. Given the unconstrainedleader’s paths, there are potentially many feasible rendezvouspoints. We wish to identify the earliest occurrence of theseminima. The vehicles are nonholonomic and the leader’spath is unconstrained so the derivative of the arrival time er-ror function in intractable to calculate. Therefore, traditionalconvex optimisation techniques such as gradient descent can-not be employed. Instead, we utilise a heuristic direct searchmethod which is considered to be derivative free [Lewis et al.,2000]. Once the rendezvous point has been identified, the cor-responding minimum length path is generated for the followerto navigate. Fixed-wing simulation results show the develop-ment process identifying an algorithm shortcoming which isthen resolved before flight testing occurs. Flight tests usingtwo quadrotors to emulate fixed-wings then demonstrate therendezvous algorithm being successfully deployed on UAVsusing the same development framework. The modularity andflexibility of the framework is evident by the seamless transi-tion from simulation to flight test and fixed-wing to quadrotor.

The paper is organised as follows. First, the rendezvousproblem is formulated and the algorithmic solution explained.The algorithm development framework which is used to de-sign, simulate, evaluate and flight test the rendezvous algo-rithm is then described. Simulation and flight test results thendemonstrate the successful implementation of the develop-ment process. Finally, conclusions and suggestions for futurework are offered.

2 Related WorkPrevious works related to this work fall into two categories,robot rendezvous and UAV simulation. [Croft et al., 1998]develop an optimal rendezvous point selection algorithm forrobot interception with a moving target. The algorithm as-sumes that the robot travel time, as a function of rendezvouscompletion time, can be approximated by a polynomial andis therefore differentiable. This assumption is not valid inour work since the calculation of the derivative is intractable.Evolutionary optimisation techniques have been employedfor path planning applications, but they take a long time toescape local minima [Jia, 2004]. Techniques exist to con-strain the execution time to around 5 seconds with a desktopcomputer [Nikolos et al., 2003], though this is not suitablefor real-time implementations. [Park et al., 2004] solve asimilar rendezvous problem by choosing a fixed rendezvouspoint and then minimising the arrival time error by increasingthe length of the follower’s path. We propose a more optimalsolution by only considering minimum-length paths and us-ing the leader’s complete path as the rendezvous point search

space.UAV algorithm development environments of varying rel-

evance have been proposed in the past. A single UAV simula-tion framework was developed in [Jung and Tsiotras, 2007],although their focus was on aircraft stability derivative identi-fication, they provide useful details about their simulation ar-chitecture. [Saunders and Beard, 2010] created a Hardware-in-the-loop (HIL) simulation for vision algorithm prototyp-ing. The algorithms were written in C/C++ and simulatedusing a Matlab wrapper. This methodology avoids conver-sion from simulation to autopilot firmware but is more timeconsuming and less flexible than developing in the simulationenvironment directly, which is what is done in our work. Amulti-UAV simulation for cooperative control algorithm de-velopment was described in [Rasmussen et al., 2005]. Thiswork provides a nice environment for early algorithm proto-typing and simulation but does not facilitate automatic codegeneration for deployment.

3 RendezvousThe problem being considered in this work is fixed-wingUAV rendezvous to leader-follower formation. We first for-mulate the problem and outline the constraints and assump-tions. A minimum-length path planning method to guidethe follower to rendezvous is then presented. We then pro-pose a rendezvous point selection algorithm that utilises theminimum-length path planning method. Finally, a method forhandling algorithm divergence is presented.

Figure 2: The rendezvous problem formulation.

3.1 Problem FormulationWe consider the rendezvous to leader-follower formationproblem in the Cartesian plane as shown in Fig. 2. A

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

leader with initial state [xl(0), yl(0), ψl(0)]T denoted ql(0)and fixed velocity vl, is following a predefined path γl. A fol-lower with initial state qf (0) and fixed velocity, vf , aims toplan and follow a path γf to rendezvous with the leader. Thefollower goal configuration qg ∈ γl, is a distance d behind theleader as described by Eq 1. It is assumed that γl is knownby the follower apriori and the leader is uncooperative in thesense that it will not deviate from γl to aid in rendezvous.

qg = ql

(Tr −

d

vl

)(1)

The terminal leader-follower constraint dictates that at therendezvous time, Tr, the follower must approach (xg, yg) inthe same direction as the leader, so qg includes a specific ψg .The follower must also approach from behind the leader sothat d > 0 and the velocity of the leader and follower at qgmust be equal. For rendezvous to be deemed successful, thetwo aircraft must arrive at the rendezvous configuration si-multaneously, i.e. the arrival time error, Te must be zero. Inpractice, |Te| shall be below a threshold, ε, of problem spe-cific rendezvous accuracy.

Tl = t(ql(0), qg) +d

vl(2)

Tf = t(qf (0), qg) (3)

|Te| = |Tf − Tl| < ε (4)

t( . , . ) is the flight time between two configurations and Tland Tf are the global leader and follower rendezvous point ar-rival times respectively. The objective is to find qg which min-imises the global time-to-rendezvous Tr and satisfies Eq 4.

Each UAV is modelled as a Dubins vehicle [Dubins, 1957],with fixed forward speed and constant altitude.

x(t) = v sinψ(t)y(t) = v cosψ(t)

ψ(t) = u(t)(5)

The turn radius R(t) in γf shall satisfy the turn radius con-straint Eq. 6 for a maximum bank angle, φmax.

ρmin =v2f

g tanφmax

R(t) ≥ ρmin, ∀t ∈ [0, Tr]

(6)

The rendezvous point selection algorithm must only knowthe time taken for the follower to fly to the goal point, so morecomplicated path planning strategies and velocity profiles canbe incorporated without any change in the rendezvous pointselection algorithm. To guide the follower along the path,ψf (t) shall be controlled by adjusting the bank angle φf (t)using the relationship in Eq 7.

φf (t) = tan−1

(vf ψ(t)

g

)(7)

3.2 Generating Minimum-Length PathsThe Minimum Principle [McGee et al., 2005], dictates thatthe time-optimal path consists of intervals of maximum rateturns and straight lines. This idea was originally proposed byDubins [Dubins, 1957] who proved that in the absence of ob-stacles, a curvature constrained shortest path from a startingstate q0, to an end state q1, consists of, at most, three seg-ments. Each of these segments must be either a straight lineor an arc with radius ρmin. The resulting Dubins path typesconsist of right turns R, left turns L and straight segments S.

The minimum-length path was calculated by constructingtwo circles of radius ρmin at q0 and q1 to represent initial andfinal left and right turns of maximum rate as shown in Fig. 3.The tangents between each of these four circles were thencalculated to yield sixteen possible paths. Eight paths wereeliminated by checking the traversability of the path at thestart of the tangent. A further four were eliminated using thesame method at the end of the tangent. The shortest of thefinal four paths was selected as the minimum-length path. Adetailed explanation of this method can be found in [Hota andGhose, 2009]

−250 −200 −150 −100 −50 0 50 100−200

−150

−100

−50

0

50

100

x

y

q0

q1

Minimum−length path

ρmin

α

θ

δ

θ

Figure 3: A minimum-length path connecting q0 and q1 witha minimum turn radius.

This path planning strategy is applicable to a problemwith the specific constraints and assumptions outlined in Sec-tion 3.1 and can be changed to suit different vehicle kinemat-ics and problem constraints.

3.3 Rendezvous Point SelectionFor rendezvous to be feasible, the leader and follower mustarrive at the selected rendezvous point simultaneously. It fol-lows then that the rendezvous point selection problem can be

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

formulated as an minimisation of |Te| to a satisfactory thresh-old as shown in Eq 4. A further constraint dictates that inthe presence of multiple feasible rendezvous points, the ear-liest point is selected to ensure Tr is optimal. Tr is chosenas the search space because it is one dimensional and ql canbe expressed as a function of Tr. The nonholonomic vehicleand terminal rendezvous constraints in this problem make Teas a function of qg non-differentiable and discontinuous withoften many local minima. Therefore, traditional optimisationtechniques such as gradient descent cannot be employed. Ide-ally, one would search over some interval of Tr, find the setof qg that satisfies Eq 4 and then choose qg that correspondsto the smallest Tr. This approach would be highly inefficientand an appropriate search space is difficult to define. Instead,we propose an iterative direct search method with a problemspecific heuristic. This heuristic dictates that the search shallbegin at Tr = Tinit which is the minimum time taken for thefollower to fly to any points on γl. Additionally, the searchshall propagate Tr in the positive direction. This exploits twofundamental properties of the problem,

• regardless of the kinematic and rendezvous constraints,Tr must always be greater than the time taken for thefollower to fly from qf (0) to the closest point on γl• the first qg that satisfies Eq 4 when propagating Tr is the

optimal rendezvous point

Algorithm 1 Calculate rendezvous pointqinit = min(s(qf (0), γl))

Tinit =s(qf (0),γl)

vfTl1 = Tinitfor i = 1→ maxIterations doqgi = ql(Tli − d

vl)

γfi = minLengthPath(qf (0), qgi , ρmin)

Tfi =s(γfi )

vfTei = Tli − Tfiif |Tei | < ε thenTe = Teiqg = qgiend loop

else if divergence thenTe = max[Tei ≤ 0]qg = qgi−1

end loopelseTli+1

= Tli +Tei

2end if

end for

The algorithm is initialised by calculating the point, qinitwhich corresponds to the minimum Euclidean distance be-tween qf (0) and γl, where s( . , . ) is the length of the prob-lem specific, minimum length path. The follower’s expected

flight time to this point, Tinit is then calculated and becomesthe first point to be sampled in the search space. Tinit is cal-culated to avoid searching over the space where rendezvousis known to be impossible.

Next, the goal point qg1 ∈ γl corresponding to the initialsample point is determined. The follower’s minimum-lengthpath to qg1 is then constructed and the flight time to this point,Tf1 , calculated. The arrival time error, Te1 is then inspectedto determine whether Eq 4 is satisfied. If it is, qg1 is the ren-dezvous point, otherwise the next sample point is calculatedby adding half Te1 to the current sample point. If divergenceis detected or the maximum number of iterations have beenreached, the loop is stopped. A summary of the rendezvouspoint selection algorithm is provided in algorithm 1.

3.4 DivergenceDivergence checking was necessary to ensure algorithm sta-bility, particularly near discontinuities which are inherent tothe problem. This can occur for small changes in Tr whenR → S → L or L → S → R paths fail to exist [Xuan-Nam et al., 1994] and when step heading changes exist in γl.Divergence checking was performed by inspecting the evolu-tion of Tei to ensure it was decreasing. When it occurs, thealgorithm oscillates between two feasible paths where neithersatisfies Eq 4. When divergence is detected, the path corre-sponding to a max[Tei ≤ 0] is selected. This is because a pos-itive Te is impossible to eliminate since this corresponds tothe follower arriving at qg late, even with a minimum-lengthpath. It is, however, possible to eliminate a negative Te, wherethe follower arrives early, by increasing ρmin and hence Tf .This was done by exploiting the linear relationship betweenminimum path length and ρmin. First, a new path γfnew wascalculated between qf (0) and ql(tl) using ρ = ρmin + ε. Thenew minimum turn radius ρnew to achieve the desired pathlength s(γf ) − vf Te was calculated through interpolation.An algorithmic representation can be found in algorithm 2.Algorithm 1

Algorithm 2 Calculate ρnew to account for discontinuityif divergence thenγnew = minLengthPath(qf (0), qg, ρmin + ε)sdesired = s(γf )− Te

ρnew = ρmin + ε(sdesired−s(γf )s(γnew)−s(γf )

)

end if

4 Algorithm Development FrameworkTo transition the rendezvous algorithm from concept to flighttest in an error free and timely manner, an algorithm develop-ment framework was created. Matlab Simulink tools wereutilised to encapsulate UAV algorithm design, simulation,evaluation and deployment in a single high level graphicalenvironment as shown in Fig. 4. The framework comprised

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

three main component, modelling and simulation (M&S), al-gorithm deployment and visualisation. The M&S componentcreated a realistic virtual world for the algorithms to operatewithin and allowed quick evaluation. The algorithm deploy-ment component was designed such that custom algorithmscould be simulated within the virtual world and automaticallyconverted to C/C++ code without any change in the module.Visualisation was used to provide the user with an intuitiveunderstanding of the behaviour of the algorithm. A detaileddescription of each component is provided in this section.

4.1 Modelling and SimulationFlight Dynamic ModelThe flight dynamic model (FDM) implements a nonlinear6DOF fixed-wing aircraft model with equations that can befound in [Jung and Tsiotras, 2007]. The inputs to the FDM,[δf δe δa δr δt]

T , are deflections of the flaps, elevator,ailerons, rudder and throttle respectively as well as the wind,[wN wE wD]T . At each time step, the FDM utilises the in-puts to propagate the previous vehicle state to the true currentstate which is given by,

x = [PT V T aT ωT QT Va] (8)

where P = [X Y Z]T and V = [vN vE vD]T are the po-sition and velocity in the navigation frame, a = [ax ay az]

T

is the acceleration in the body frame, ωBIB = [p q r]T is theangular velocity in the body frame, Q = [q0 q1 q2 q3]T is theattitude quaternion and Va is the airspeed.

SensorsThe GPS measurements were modelled with position and ve-locity Gauss-Markov noise correlation and transport delay.The IMU model included white noise, bias, cross-coupling,mounting pose and the gravity vector from the 1984 WorldGeodetic System (WGS84 geoid model) [NIMA, 1984]. Themagnetometer was modelled by rotating the 2010 WorldMagnetic Model (WMM2010) [NOAA, 2012] magnetic vec-tor to the body frame and adding white noise. Static pres-sure was calculated using the International Standard Atmo-sphere (ISA) [Government, 1976] model, given the heightabout mean sea level (MSL) and white noise. Dynamic pres-sure utilised Eq 9, given the ISA air density, ρisa, Va and whitenoise.

pdyn =1

2ρisaV

2a (9)

ActuatorsThe actuators were modelled with saturation limits and ratesaturation limits. Time lag was modelled with first order dy-namics. This block also converted from raw servo commandsto control surface deflections.

4.2 Algorithm DeploymentThe algorithm deployment module contained all algorithmsto be simulated and then automatically converted to C/C++code for deployment. This approach avoids a time consumingand error prone conversion from the graphical environment toembedded C++ code and ensures that the deployed algorithmis functionally equivalent to the simulated algorithm. In addi-tion to the rendezvous algorithm, this module contained GNCalgorithms to generate appropriate aircraft inputs, given highlevel mission objectives and noisy sensor measurements.

Vehicle state estimates were obtained from noisy sensordata using an extended Kalman Filter (EKF) in a loosely cou-pled GPS/INS arrangement. The 13 dimensional state vectoris given by,

x = [PT V T QT ωTb ] (10)

where ωb = [pb qb rb]T is the IMU gyro bias which in-

cludes both the scale factor error and time-varying bias in asingle term. The inertial navigation process model is given inEq 13, where the inputs are the IMU measurements a and ω.na and nω are the accelerometer and gyro measurement noiseterms.

a = a− na (11)

ω = ωbib − ωb − nω (12)

x =

P

V

Qωb

=

VCnb a− (2ωnie + ωnen)× V + g

12 ΩωQnωb

(13)

A full derivation of the INS mechanisation equations canbe found in [Rogers, 2007]. The rotation matrix, Cnb , is usedto transform between the body frame and navigation frameand is given below,

Cnb = 2

0.5− q22 − q2

3 q1q2 − q0q3 q1q3 + q0q2

q1q2 + q0q3 0.5− q21 − q2

3 q2q3 − q0q1

q1q3 − q0q2 q2q3 + q0q1 0.5− q21 − q2

2

(14)Ωω is a skew matrix composed of bias corrected gyro mea-

surements,

Ωω =

0 −ωp −ωq −ωrωp 0 ωr −ωqωq −ωr 0 ωpωr ωq −ωp 0

(15)

The gyro bias is modelled as a random walk where nωbis

a zero-mean Gaussian random variable. GPS, barometer andmagnetometer measurements are used to observe the system.The EKF measurement model is given below,

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

Roll

Pitch

Yaw

Lat

Lon

Alt

Vn

Ve

Vd

ax

ay

az

p

q

r

psta

pdyn

OAT

Hx

Hy

Hz

Va

Visualisation

z

1

Stop Simulationif hits ground

STOPSimulation Pace

1 sec/sec

SetPace

Sensor Models

AngAccel

Sensors

IAds_out

IMagnet_out

IImu_out

IGps_out

Reset

0

Guidance, Navigation & Control

IAds_in

IMagnet_in

IImu_in

IGps_in

IServos_out

Air_data

Euler

Sensors

Air_data

Euler

Sensors

Flight Dynamic Model

Controls

Winds

RST

States

Sensors

VelW

Mach

Ang Acc

Euler

AeroCoeff

PropCoeff

EngCoeff

Mass

ECEF

MSL

AGL

REarth

AConGnd

Create Wind

wind_out

Aircraft states

0.4008

0.04439

0.4254

−0.5911

2.639

97.84

21.92

9.816

0.6305

0.233

−0.3132

−10.9

−0.335

0.06021

0.1113

9.99e+004

349.6

287.4

2.659e+004

−2.442e+004

−4.467e+004

24.03

0.02347

0.06677

Actuators

IServos_in Actuators

Euler

AirData

Figure 4: Simulink model for one complete UAV simulation.

y =

PgpsVgpspbaroHmag

=

Pk−N + Cnbk−Nrgps + nPgps

Vk−N + Cnbk−Nωk−N × rgps + nVgps

pisa + npsta

(Cnb )THwmm + nH

(16)where Pk−N and Vk−N are position and velocity vectors in

the navigation frame, delayed by N samples due to GPS la-tency. rgps is the position vector connecting the GPS antennato the IMU, ωk−N is the time delayed gyro measurement andCnbk−N

is the time delayed rotation matrix. pisa is the ISApressure at the current MSL altitude and Hwmm is the mag-netic vector as per the WMM2010. nPgps , nVgps , npsta and nHare the measurement noise terms for the GPS position, GPSvelocity, static pressure and magnetometer respectively [Shin,2005].

Given the estimated state of the vehicle, guidance algo-rithms generated low level commands to achieve high levelmission goals. For rendezvous to leader-follower forma-tion, the leader guidance simply follows a predefined path,whereas the follower implements the rendezvous-point selec-tion algorithm to generate and follow a kinematically feasiblepath to rendezvous.

Low level control algorithms generated input to the

ailerons, elevator, rudder and throttle to achieve the bankangle, altitude, airspeed and vertical velocity targets set bythe guidance. This was done with proportional-integral-derivative (PID) controllers and feedforward to account foraircraft aerodynamic and geometric properties.

4.3 VisualisationVisualisation utilised Flightgear v2.6, which is an open-source flight simulator developed and maintained by Curt Ol-son [Olson, 2012]. Two instances of Flightgear ran on a re-mote computer. The FlightGear interface transmitted positionand attitude information for each UAV to the remote com-puter via UDP. Multiplayer mode was enabled to allow bothaircraft to be visible in a single window as shown in Fig. 1.In the future, visual feedback from the visualisation could beused to simulate vision sensors.

5 ExperimentsThe successful and rapid transition of the rendezvous algo-rithm from concept to flight has been demonstrated in sim-ulation and flight tests. We have performed a set of vir-tual simulations of two simulated fixed wing UAVs perform-ing rendezvous using the algorithm development framework.The same framework was further demonstrated where twoquadrotors performed the same mission in a real flight test.

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

Table 1: Initial conditions and rendezvous errors for simula-tion and flight tests.

Sim 1 Sim 2 Flight 1 Flight 2d 30m 30m 0.7m 0.7mvcmd 25ms−1 25ms−1 0.8ms−1 1.2ms−1

altcmd 100m 100m 1.5m 1.5mρmin 80m 80m 1.0m 1.5mreplan off on off onderror 15.73m 4.12m 0.83m 0.07mψerror 3.74 2.36 5.92 5.02

The simplicity with which the algorithm was implemented onfundamentally different platforms is a testament to the mod-ularity and flexibility of the development framework.

In each test, leader and follower path guidance wasachieved using a nonlinear guidance logic as proposedby [Park et al., 2004]. This algorithm commands a lateralacceleration, ascmd

using Eq 17.

ascmd= 2

v2

L1sin η (17)

where L1 is the distance to a lookahead point on the refer-ence path, v is the aircraft’s velocity and η is the differencebetween the line-of-sight (LOS) angle ψLOS to the lookaheadpoint and the aircraft’s heading. L1 is used to tune the al-gorithm, where smaller values result in tighter tracking ofthe path and larger values result in less aggressive, smoothertracking. The lookahead point was calculated geometricallyby finding the intersections of the path and a circle with radiusL1 about the UAV’s position. The commanded lateral accel-eration was converted to a bank angle, φfcmd , using Eq 18.

φfcmd =ascmd

vf(18)

5.1 Simulation

Simulations of the rendezvous algorithm were performed us-ing fixed-wing UAVs. Results from an initial test are shownin Fig. 5(a). Here, the flight path plot shows poor trackingof the reference path which lead to a longer flight time thananticipated and a rendezvous separation error of 15.73m. Re-vision of the rendezvous algorithm incorporated replanningto account for the poor guidance. Figure 5(b) shows resultswhere the modified algorithm was able to account for theseguidance inaccuracies and result in a much more accurate fi-nal rendezvous separation, in the order of four times better.The early identification of this problem highlighted a funda-mental advantage of the development framework because theproblem was able to be resolved in a laboratory environmentwithout wasting time in the field or risking aircraft. A sum-mary of simulation results and initial conditions can be foundin Table 1.

5.2 Flight TestsRendezvous flight tests occurred in the multi-vehicle testbed at the Center for Advanced Aerospace Technolo-gies (CATEC). Two Ascending Technologies Hummingbirdquadrotors [Ascending, 2012] flew within a 15x15x5m arenawhile the position and orientation was observed by a VICONmotion capture system [Vicon, 2012]. Numerical differentia-tion was used to estimate the linear velocity.

Given the Vicon state estimate for each quadrotor, theguidance module calculated bank angle, altitude and veloc-ity commands at 100Hz for the leader to follow its predefinedpath and the follower to navigate the calculated path to ren-dezvous. An additional fixed-wing emulation layer was im-plemented after the guidance module to account for the kine-matic differences between fixed-wing aircraft and quadrotors.The conversion is given in Eq 19 where z is the commandedaltitude, vcmd is the velocity, ψ(t) is the inertial heading andθ(t) is the heading. Two Zigbee transceivers transmittedthe resulting attitude and thrust commands to the quadrotorswhere onboard stabilisation systems handled the low levelcontrol.

zvcmdψ(t)θ(t)

=

altcmdvcmd∫ψ(t) dt∫ψ(t) dt

(19)

Where,

ψ(t) =g tanφ(t)

vf(20)

In each experiment, a leader flew a 6x6m square path with1.5m radius circular corners of radius 1.5m at a fixed altitudeof 1.5m as shown in Fig. 6(b). A follower was randomly po-sitioned within the arena, initially with zero velocity and afixed altitude of 1m to avoid collisions with the leader. Wheninitiated by an operator, the follower flew forward until itsvelocity was equal to that of the leader. At this point, therendezvous algorithm was enabled to continuously replan fol-lower reference paths.

Results from a flight test where replanning was not usedare shown in Fig. 6(a). Here, a final separation error of 0.83mwas observed. In contrast, Fig. 6(b) shows a test where thealgorithm was modified to include replanning. The final sep-aration error for this test was 0.07m, an improvement of al-most 12 times. Similarly to simulation, final heading errorswere comparable. This comparison is provided to highlightthe benefit of simulation and to demonstrate a situation wherea potential problem was identified and resolved before flighttesting occurred. A summary of the initial conditions and ren-dezvous accuracy is provided in Table 1.

The results presented in this section demonstrate a com-plex, multi-UAV algorithm being simulated and flight tested

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

0 100 200 300 400 500 600 700

−200

−100

0

100

200

300

y (m)

x (m

)

ql(0)

qf(0)

γl

γf

γfref

0 5 10 15 20 250

100

200

300

Dis

tanc

e (m

)

Separation

d

0 5 10 15 20 250

1

2

3

Hea

ding

(ra

d)

ψf(t)

ψg

0 5 10 15 20 2522

24

26

Vel

ocity

(m

/s)

Time (s)

vl(t)

vf(t)

(a) Simulation 1, replanning off.

0 100 200 300 400 500 600 700

−200

−100

0

100

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300

y (m)

x (m

)

ql(0)

qf(0)

γl

γf

γfref

0 5 10 15 20 250

200

400

600

Dis

tanc

e (m

)

Separation

d

0 5 10 15 20 25

−2

0

2

Hea

ding

(ra

d)

ψf(t)

ψg

0 5 10 15 20 2522

24

26

Vel

ocity

(m

/s)

Time (s)

vl(t)

vf(t)

(b) Simulation 2, replanning on.

Figure 5: Leader and follower fixed-wing simulation data from a rendezvous manoeuvre. Replanning in (a) has allowed theheading and separation error to be low at rendezvous, even with inaccurate velocity command tracking and guidance errors.

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

3 4 5 6 7 8 9 10 11 123

4

5

6

7

8

9

10

x (m

)

y (m)

ql(0)

qf(0)

γl

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γfref

0 2 4 6 8 10 120

5

10

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tanc

e (m

)

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d

0 2 4 6 8 10 12−5

0

5

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ding

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d)

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ψg

0 2 4 6 8 10 120.6

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/s)

vl(t)

vf(t)

vcmd

(a) Flight 1, replanning off.

0 2 4 6 8 100

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)

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6m

1.5m

(b) Flight 2, replanning on.

Figure 6: Leader and follower quadrotor flight test data from a rendezvous manoeuvre with and without replanning. The finalheading error is low without replanning but the final separation error is high as a consequence of inaccurate velocity commandtracking.

Proceedings of Australasian Conference on Robotics and Automation, 3-5 Dec 2012, Victoria University of Wellington, New Zealand.

using the same high level graphical framework. The frame-work was able to identify and resolve a potential problemin simulation, before flight testing occurred. Successful ren-dezvous to leader-follower configuration was demonstrated inboth simulation and flight tests from a variety of initial condi-tions. The very different path geometries and flight velocitiesbetween the simulation and flight test demonstrates the algo-rithm working successfully within a wide range of conditions.

6 Conclusions and Future WorkA modular development framework for rapid, iterative al-gorithm development has been created by combining sim-ulation, performance evaluation and implementation into asingle, graphical environment. The framework was demon-strated through the simulation and flight testing of a multi-UAV rendezvous algorithm. Advantages of the developmentprocess were immediately clear when the simulation was ableto identify and resolve a design problem, before flight testingoccurred.

Future work will utilise the framework to flight test the ren-dezvous algorithm on fixed-wing aircraft and develop newmulti-UAV cooperative algorithms. Computer vision basednavigation will also be incorporated to develop relative navi-gation algorithms.

AcknowledgmentsThe authors thank Miguel Angel Trujillo Soto for his assis-tance during the experimentation and CATEC for the use ofthe test bed facility. This work is supported by the AustralianResearch Council (ARC) Centre of Excellence programme.

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