peloni, alessandro and barbera, daniele and laurenzi...

Peloni, Alessandro and Barbera, Daniele and Laurenzi, Susanna and

Circi, Christian (2015) Dynamic and structural performances of a new

sailcraft concept for interplanetary missions. The Scientific World

Journal, 2015. ISSN 2356-6140 , http://dx.doi.org/10.1155/2015/714371

This version is available at https://strathprints.strath.ac.uk/54145/

Strathprints is designed to allow users to access the research output of the University of

Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights

for the papers on this site are retained by the individual authors and/or other copyright owners.

Please check the manuscript for details of any other licences that may have been applied. You

may not engage in further distribution of the material for any profitmaking activities or any

commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the

content of this paper for research or private study, educational, or not-for-profit purposes without

prior permission or charge.

Any correspondence concerning this service should be sent to the Strathprints administrator:

[email protected]

The Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research

outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the

management and persistent access to Strathclyde's intellectual output.

http://strathprints.strath.ac.uk/

mailto:[email protected]

http://strathprints.strath.ac.uk/

Research Article

Dynamic and Structural Performances of a New SailcraftConcept for Interplanetary Missions

Alessandro Peloni,1 Daniele Barbera,2 Susanna Laurenzi,3 and Christian Circi3

1School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK2Faculty of Engineering, University of Strathclyde, Glasgow G1 1XW, UK3Department of Astronautic, Electrical and Energy Engineering, Sapienza University of Rome, Via Salaria 851, 00138 Rome, Italy

Correspondence should be addressed to Christian Circi; [email protected]

Received 6 February 2015; Accepted 11 June 2015

Academic Editor: Manuel Lozano

Copyright © 2015 Alessandro Peloni et al. his is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Typical square solar-sail design is characterised by a central hub with four-quadrant sails, conferring to the spacecrat the classicalX-coniguration. One of the critical aspects related to this architecture is due to the large deformations of both membrane andbooms, which leads to a reduction of the performance of the sailcrat in terms of thrust eiciency. As a consequence, stifer sailarchitecture would be desirable, taking into account that the rigidity of the system strongly afects the orbital dynamics. In thispaper, we propose a new solar-sail architecture, which is more rigid than the classical X-coniguration. Among the main pros andcons that the proposed coniguration presents, this paper aims to show the general concept, investigating the performances fromthe perspectives of both structural response and attitude control. Membrane deformations, structural ofset, and sail vibrationfrequencies are determined through inite element method, adopting a variable pretensioning scheme. In order to evaluate themanoeuvring performances of this new solar-sail concept, a 35-degree manoeuvre is studied using a feedforward and feedbackcontroller.

1. Introduction

Solar sailing is a promising technology, which allows plan-ning missions otherwise impracticable using traditionalpropulsion systems. herefore, the solar-sailing conceptopens up new avenues for scientiic discoveries in manyields of astronautic science, from materials engineering tolight dynamics [1–5]. Due to the continuous and propellant-free thrust, solar sails are mainly studied for orbits withhigh ΔV requirements, such as Earth Pole-sitter orbits [6–8], orbits at the Earth-Moon libration points [9, 10], or newkinds of orbits around the Earth, as the Taranis orbits [11,12]. Attitude control and optimal steering laws to improvesailcrat performances have recently been studied in severalworks as well [13–17].

Sailcrats have a very large and complex structure, typi-cally formed by four petal membranes, which are tensionedto form the square shape using deployable ultrathin com-posite booms [18–22]. Alternative methods for deploying

and tensioning the membrane were also investigated andtested, such as in the case of IKAROS, the irst-launchedsolar-sail demonstrator [23]. In that case, the four trapezoidalmembranes are linked together using spaced strips, whichfacilitate the folding of the membrane.he solar sail was thendeployed and kept extended in a lat shape by the centrifugalforce due to the spin of the sailcrat itself. In all mentionedcases, even in the IKAROS demonstrator that did not usebooms, the solar sail is visually and physically divided intofour membranes and a central hub, which gives the typicalX-coniguration to the spacecrat.

his work proposes a new approach to the solar-saildesign with a diferent kind of coniguration, in which theclassical central bus is divided into four hubs displacedat the corners of the square sail. With this coniguration,the sail tensioning can be controlled more easily and thetensioning motors, if any, can be directly placed on thehubs. he membrane tensioning is an important topic, dueto the formation of wrinkles or bubbles born from the

Hindawi Publishing CorporationΤe Scientific World JournalVolume 2015, Article ID 714371, 14 pageshttp://dx.doi.org/10.1155/2015/714371

http://dx.doi.org/10.1155/2015/714371

2 he Scientiic World Journal

2

43

1

2

43

1

Opening sequence

Sail membrane

Stowed sailcrat Deployed sailcrat

Figure 1: Sailcrat opening sequence.

tensioning or thermal load. his feature is crucial for themasking, shadowing, and thermal issue that may alict sailperformances. From an attitude control point of view, thisconiguration allows the attitude control thrusters, if any, tobe directly mounted on the hubs rather than on the top ofa lexible boom. herefore, the thruster is more likely to bein the nominal position. his feature and the stifer natureof the architecture itself entail the sail being latter than inthe X-coniguration. Moreover, this type of architecture canbe considered as the unit part of a bigger modular solar sail.On the other hand, the dislocated nature of this conigurationincreases the moments of inertia of the sailcrat, with apossible decrease of the attitude control eiciency.

his paper investigates the structural and the dynamicsperformances of the proposednovel coniguration of the solarsail. To compare both the structural and the attitude controlperformances of this new architecture with those available inliterature, a 40m side sail has been considered for the study.

he paper is organised as follows: the new sail conig-uration is presented in Section 2; a inite element model isreported in Section 3 for the evaluation of maximum out-of-plane displacement, vibration frequencies, and calculationof the ofset between the centre of mass and the centre ofpressure. he ofset value is used in Section 4 to investigatethe solar-sail attitude control performances for a 35-degreedeep space manoeuvre.

2. Solar-Sail Concept Configuration

he solar-sail geometry proposed in this study is a classicalsquare, with the booms on the perimeter of the membraneand themass of the satellite divided into four parts, collocatedon the square’s corners and joined at the booms’ end. heopening sequence from the closed-shape launch conigura-tion to the deployed one (Figure 1) is helped by the strainenergy stored in the booms. he deployment velocity is afunction of the booms’ shapes and the parameters of thedeployment mechanism [24, 25].

Table 1 shows the main sailcrat’s characteristics, accord-ing to [26], while Figure 2 shows the solar-sail reference frametaken into account. he sail mass in Table 1 is computed by

considering the same ilm as in [26], in which the 1200m2

sail has a mass of 6 kg. he boom mass is calculated in thesame way. he origin of the body reference frame is set on

the geometric centre, roll axis (�) is perpendicular to the sail

plane, and pitch (�) and yaw (�) axes are the transverse axes

Table 1: Sailcrat properties.

Sail side [m] 40

Sail area [m2] 1600

Sail mass [kg] 8

Boom mass [kg] 10

Control mass (each) [kg] 1

Satellite mass (each) [kg] 33

Sailcrat total mass [kg] 153�� (roll) [kg⋅m2] 1.1 × 105�� (pitch) [kg⋅m2] 5.6 × 104�� (yaw) [kg⋅m2] 5.6 × 104

1

2

3

4

Orbital light path

k

i

j�

R0

RG

CP ≡ O

CM ≡ G

Figure 2: Solar sail in interplanetary trajectory.

parallel to the booms.� is the cone angle between the Sun-linedirection and the roll axis, R� is the position vector of centreof mass with respect to the Sun, and R0 is the position vectorof the origin of body reference frame with respect to the Sun.he primary attitude control system is based on centre-of-mass (CM)/centre-of-pressure (CP) ofset due to the shit of 4ballast masses along the sailcrat’s perimeter.he steady-stateofset between the centre ofmass and the centre of pressure ofthe proposed coniguration, due to themembrane tensioning,is smaller than the one used in literature for the classical X-shaped solar sail [27–29], as will be discussed in Section 3.3.Because sliding masses do not afect rotations along roll axis,a Pulsed-Plasma-hrusters (PPTs) system is introduced aswell. In the scheme presented there are two pairs of PPTsmounted on two opposite satellites, but four pairs of thrusterscan be utilized for redundancy or if greater torque on rollaxis is required. It is important to underline that thrusters aremounted on a satellite at the corners of the square sail, insteadof at the end of the booms as in X-coniguration.hismeans agreater ease of assembly and amajor stability of the structure.he total satellitemass considered is about 150 kg [26] and thefour dislocated satellite buses have equal masses.

he Scientiic World Journal 3

3. Structural Analysis

In this study, we performed nonlinear static analysis, basedon Finite Element Method (FEM), adopting the commercialcode ABAQUS.he aims of this investigation were the deter-mination of the membrane out-of-plane delections causedby the solar pressure, the natural modes of the structures, andthe disturbing momentum due to ofset between the CP andthe origin of the body reference frame, varying the tensionapplied to the corner of the solar sail. Particular attentionwas paid when calculating the ofset value, which will beused in the dynamics analysis to evaluate the manoeuvringperformances of the novel square coniguration.

he solar sail is a large thin membrane structure withthe bending stifness negligible compared to the in-planestifness; thus themembrane cannot carry compressive stress.he lat square shape is controlled by the use of tensioningloads applied at the membrane corners. When the tensionedmembrane is exposed to the solar pressure, out-of-planelarge deformations occur and wrinkles can be formed withthe origin sets in the corner membrane. he numericalsimulation of the wrinkles’ formation is still an open issue,since the wrinkles alter the membrane shape and thus theinal performances of the solar sail. Authors investigatednumerically the wrinkles’ amplitude tension load depen-dency, considering the membrane truncated at the corners inorder to avoid stress concentrations in those locations [30].However, the analysis of the wrinkles’ behaviour is not thefocus of this current study and will be analysed in a separatework.

In this study, we investigate the structural response of alat, square, thin-ilm membrane tensioned at the corners.Considering the FEMmodel, the easiest way of pretensioningthe membrane is to apply a tension load on the nodespositioned at the four corners. However, this approach canproduce diiculties on the convergence of the numericalsolution as consequence of the singularities which arisewhen a single force is applied to a single node of the FEMmodel. To avoid these singularities, Sleight and Muheim [31]proposed the use of a virtual tension obtained by applyinga ictitious thermal load on the sail tensioning cable. hissolution, which is a pure mathematical expedient, createsa deined displacement of the corners that correspond to atensioning load. Furthermore, the extreme dimensions of thesolar sails can add convergence problems of the nonlinearanalysis. To overcome these problems, the authors in [31] usedthe cables, modelled as truss elements, when applying theictitious negative temperatures and producing a membranetensioning.

Similarly, in our FEM model, we applied a negativetemperature to the cable nodes to induce the shrinkage ofthe wires which connect the membrane and the booms. hisshrinkage strains the membrane with well-known tensioningload. In addition, the prestresses produced in the membranehelp the stabilisation of the analysis and the convergence ofthe solution [32].

he structural simulation was composed of three steps.he irst one was a linear displacement-temperature coupledstep, during which a negative temperature diference was

imposed on the Kevlar cables in order to prestress the mem-brane. he second step consisted of a nonlinear quasi-staticanalysis, where the load was applied linearly. In this step, thevolume-proportional damping factor was considered to helpthe convergence of the quasi-static problem. he third stepregarded the determination of the natural modes using theSubspace algorithm [33].

At the end of each simulation, the nodal translations androtations were processed by a Matlab script to calculate thecentre of pressure, which was then used to determine theofset between the centre ofmass (CM) and centre of pressure(CP).

he considerations concerning the determination of theCP position started from the following equation:

d� = 1�� ∫ (� ⋅ ��)��, (1)

where �� is the projected area of the element, � is the solarradiation unit vector, �� is the normal to the element, and ��is the position vector of the area element ��. he normal tothe surface element, ��, varies as a consequence of the nodalrotation; hence an opportune rotationmatrix was required tobe calculated.

In our system, (1) can be rewritten in discretised form as

d� = �∑�=1(� ⋅ ��) ��, (2)

where � is the nodal in-plane translation. he use of tri-angular membrane elements avoids out-of-plane rotationsand, as a consequence, the normal vector of the element isconstant because of rigid deformation. he ofset calculationwas performed applying a solar radiation pressure (SRP) forcewith an angle of 35 degrees between the normal vector to thesolar-sail plane and the unit vector of the solar radiation.

3.1. Finite Element Model. he geometry of the solar sail wasschematised in three main parts: the solar-sail membranegiven by a square plate with 40m of edge; the boomsrepresented by four large wires; the tensioning cables givenby four small wires. Booms were localised at 0.25m from themembrane edges, and the tensioning cables were positionedat the corners. he membrane latness of the classical X-coniguration is usually increased by dividing the entire sailinto several strips.his helps the deployment and also reducesthe stresses along the booms [34]. On the other hand, bothpackaging and jointing of themembrane are challenging tasksand require particular attention. he solar-sail architecturepresented in this work does not require the strip strategydescribed above.

he material properties adopted in this work were takenfrom literature [31, 35] and are summarised in Table 2.

he inite element model was obtained by discretisingthe geometry with diferent element types. In particular, thesail membrane was modelled using membrane triangularelements (M3D3) with constant thickness, whereas the linearbeam elements (B31) with circular cross section were used forthe booms [25, 34, 36]. he tensioning cables were modelled


Table 2: Materials properties.

Components Material Radius [m] hickness [m] Modulus [N/m2] Poisson’s ratio Density [kg/m3]

Boom Composite 0.15 0.0004 124 × 109 0.30 1908

Tensioning cable Kevlar 0.0005 N/A 62 × 109 0.36 1440

Membrane CP1 N/A 3.5 × 10−6 2.17 × 109 0.34 1434

using thermally coupled truss elements (T3D2T) as requiredby the displacement-temperature coupled step.

Tensioning force was calculated using a Matlab script,which implements (3) considering the Kevlar cable as anisotropic material:

� = � ⋅ �kevlar ⋅ �cable ⋅CTEkevlar, (3)

where�cable is the cross-section area of the cable,�kevlar is theKevlar Young modulus, CTEkevlar is the thermal expansioncoeicient, and � is the imposed temperature.

Assuming that the sail membrane is perfectly relective,the total pressure load due to SRP is 2� = 9.12 × 10−6 N/m2.he pressure was applied in the normal directionwith respectto the sail membrane. he boundary conditions were appliedon the nodes at the corners of the square membrane, wherea beam element and a truss element interlock. In particular,multipoint constraints (MPC) were used to connect theabovementioned nodes to a master node. In this case, theMPC type is a beam providing a rigid link between themaster node and the slave ones. he master nodes may havediferent degrees of freedom, which can vary during thesimulation. In our analysis, all master nodes were pinnedduring the pretensioning step, whereas the translation alongthe perpendicular direction with respect to the membraneplane and the relative rotation were constrained during theSRP loading step.

Before starting the simulations, a mesh convergenceanalysis was accomplished in order to investigate the meshinluence on both analysis and inal results. In particular, westudied the efects of the number of the membrane elements,considering the maximum displacement, which occurs overthe sail during the solar-pressure action as a triggeringparameter. As discussed above, a pretension load is requiredto achieve enough stifness, since the membrane bendingrigidity is negligible. he minimum pretensioning load wascalculated by a trial-and-error technique, establishing that0.6N for each tensioning cable is the minimum load neces-sary to stabilise the membrane in lat coniguration. Figure 3shows the trend of maximum displacement of the membraneas function of the number of elements. he graph shows thatover 13,000 elements the value of maximum displacementis constant; thus we adopted this number of membraneelements for the analysis.

3.2. Numerical Results. In this section, we present the resultsof the maximum out-of-plane deformation and the irstthree vibration frequencies due to solar radiation pressure,considering several tensioning cases. In Table 3 the results

Table 3: Pretensioning scheme results.

Boundary cabletemperature [∘C]

Efective tensioningload [N]

Maximumout-of-plane

displacement [m]−25 0.6 0.1004−50 1.12 0.09938−100 2.3 0.09734−400 9 0.08520−800 18 0.07005

0.1

0.101

0.102

0.103

0.104

0.105

0.106

0.107

0.108

0.109

0 2 4 6 8 10 12 14 16 18 20

Max

imu

m d

isp

lace

men

t (m

)

Element number ×103

Figure 3: Mesh sensitivity analysis.

of the structural analysis for the maximum out-of-planedisplacements achieved varying the tensioning force at thecorners of the membrane are reported. As discussed inSection 3, the tensioning force on the membrane corners wasobtained by inducing the shrinkage of the cables. his wasachieved by imposing a negative temperature as boundarycondition at the nodes of the truss elements. However, itis worth to note that the temperature boundary conditionsreported in Table 3 are a ictitious thermal load, which is anumerical expedient to generate an efective tension appliedto the membrane corners (see (3)).

As shown in Table 3, the irst tension load at whichthe analysis converges is given by 0.6N. As expected, theinal out-of-plane displacement decreases with an increaseof the pretensioning load. Figure 4 shows the out-of-plane


X

Y

ZX

Y

Z

+8.359e − 09

−8.367e − 03

−3.347e − 02

−4.184e − 02

−5.020e − 02

−6.694e − 02

−7.530e − 02

−8.367e − 02

−9.204e − 02

−1.004e − 01

+1.346e − 07

−5.840e − 03

−1.168e − 02

−1.752e − 02

−2.336e − 02

−2.920e − 02

−3.504e − 02

−4.088e − 02

−4.672e − 02

−5.256e − 02

−5.840e − 02

−6.424e − 02

−7.008e − 02

−1.673e − 02

−2.510e − 02

−5.857e − 02

U,U

3

U,U

3Figure 4: Out-plane displacement for 0.6N and 18N tensioning load [m].

Table 4: Vibration frequency.

Tensioning case 0.6N Tensioning case 18N

Mode number Frequency [Hz] Mode number Frequency [Hz]

1 3.01406� − 02 1 3.40415� − 022 3.04789� − 02 2 3.61394� − 023 3.11011� − 02 3 3.73543� − 024 3.77720� − 02 4 3.79401� − 02

displacements obtained with the minimum tensioning force(on the let) and the maximum tensioning force (on theright), in the case of a maximum thrust during a 35-degreemanoeuvre. he two displacement distributions are similar,but the maximum displacement value is largely reduced incase of tensioning at 18N. he load required to tensionthe sail membrane properly is an important design keyfactor, because it afects the wrinkles’ formation on the sailmembrane [30], and it is limited by structural stability of thebooms.

he last part of the FEM analysis investigates the naturalvibration modes of the solar-sail membrane for the diferentpretensioning cases.he results are reported inTable 4, whereit can be observed that the vibration modes shit to higherfrequencies with the increasing of the pretensioning load.hese results can be related to the membrane stress state,which is directly inluenced by the intensity of the tensioningload. An increase of such loads corresponds to an increase ofthe vibration frequency. he total displacements associatedwith the irst four modes of the 0.6N and 18N tensioningcases are shown in Figures 5 and 6, respectively. Comparingthe images in Figures 5 and 6, it can be observed that theshapes of the modes encountered in the 0.6N tensioning

case are diferent from those of the 18N tensioning one.his diference may be explained by the loose state of themembrane in case of tension at 0.6N. Further, the 0.6Ntension load is the lowest value of the tension force toreach the numerical convergence of the solution in the staticanalysis, but this value may add some uncertainties to thedynamic analysis. In fact, we noted that, in the case ofpretensioning at 0.6N, the irst four modes of the solar-sail membrane presented shapes similar to ones reportedin Figure 6, which are the typical shape modes of a squaremembrane.

3.3. Determination of the Structural Ofset. he disturbingofset was determined using a Matlab script for each ten-sioning case. In this calculation, the model was simpliiedassuming that the booms could withstand the axial loads dueto the sail tensioning and that the wrinkles of the membranewere negligible. his approach allowed us to investigate themaximum tensioning load required to reduce as much aspossible the ofset. he ofset position on the sail plane(�, �) is greatly inluenced by the SRP modelling. he solarvector is given by two components, one along the negative� direction and one along the negative � direction. Becauseof the symmetry of the structures, the same conclusion can

be obtained considering � direction instead of � direction.Results of these calculations are reported in Table 5, where itcan be noted that an increased load grants an ofset reductiondue to the increasing of the in-plane membrane stifness. Inparticular, the solar-sail coniguration proposed in this workhas a smaller ofset than the one for the classical X-shapeconiguration reported in literature [26].

he percentage change of the ofsets extrapolated fromthe FEM analysis was taken into account for the attitude

6 he Scientiic World Journal1

st

2n

d

3rd 4th

Mag

nit

ud

e,U

X

Y

ZX

Y

Z

X

Y

Z X

Y

Z

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

+8.333e − 02 +8.333e − 02

+8.333e − 02+8.333e − 02

Figure 5: First four vibration modes for 0.6N loading case.

Table 5: Ofset calculation results.

Force [N] Ofset [m] Ofset [%]

0.6 0.0051 0.0128

1.12 0.005 0.0125

2.3 0.0049 0.0123

9 0.0041 0.0103

18 0.0034 0.0085

dynamics analysis. In particular, the dynamics analysis con-sidered only the worst case ofset scenario, which is theminimum applicable tensioning force (0.6N) and is the0.0128% of the sail edge size. he new sail concept is stiferand guarantees a smaller ofset than the X-shape one, whichis 0.25% of the sail edge size [26].

4. Dynamics Sailcraft Performances

Due to dislocatedmass, the proposed sailcrat’s conigurationis characterised by moments of inertia greater than theclassical one. herefore the study of the performances foran attitude manoeuvre is essential to understand whetherthis architecture can be a valid light coniguration. A 35-degree manoeuvre is taken into account to compare theseperformances with literature data. Note that, due to slowdynamics, classical interplanetary missions require small-amplitude manoeuvres per day [37, 38], while a fast manoeu-vre is required only for “nonclassical” interplanetarymissions

[39, 40]. A body reference frame {�, �, �, �} is consideredfor modelling sailcrat attitude dynamics, as described inSection 2.

he primary attitude dynamics control is performed withfour ballast masses (��), of which masses 1 and 3 shit only


st

2n

d

3rd 4th

X

Y

ZX

Y

Z

X

Y

Z X

Y

Z

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

Mag

nit

ud

e,U

+1.000e + 00

+9.167e − 01

+8.333e − 01

+7.500e − 01

+6.667e − 01

+5.833e − 01

+5.000e − 01

+4.167e − 01

+3.333e − 01

+2.500e − 01

+1.667e − 01

+0.000e + 00

+8.333e − 02 +8.333e − 02

+8.333e − 02+8.333e − 02

Figure 6: First four vibration modes for 18N loading case.

along �-axis and masses 2 and 4 shit only along �-axis(Figure 7). he coordinates of the masses are reported in (4),where � is the sail side length and �� ∈ [−�/2, �/2]

r1 = [[[[0�2�1]]]],

r2 = [[[[[0�2�2

]]]]],

r3 = [[[0−�2�3]]] ,

r4 = [[[[0�4−�2

]]]].

(4)

he sailcrat attitude dynamics is as follows [41]:�h0�� +�OG× a0 = T0, (5)


L

Roll control thrust k

r1

r2

r3

r4

ji

CP ≡ O

CM ≡ G

Figure 7: Solar-sail coniguration scheme.

where h0 is the angular momentum of the system referred tothe origin of body reference �,� is the total sailcrat mass,a0 is the absolute acceleration of point �, T0 is the torquereferred to �, and OG is the position vector of the centre ofmass from the reference point �, as shown in

OG = �� 4∑�=1r� = �� [[[

0�2 + �4�1 + �3]]] . (6)

he total angularmomentum is given by the angularmomen-tum of the bus, booms, and membrane (h0,sail) and theangular momentum of masses for attitude control (h0,�). Inparticular h0,sail is

h0,sail = [[[�� 0 0

0 �� 0

0 0 ��]]] ⋅[[[��]]] = J0,sail ⋅� (7)

and h0,� is

h0,� = 4∑�=1J�,� ⋅�, (8)

where J�,� is the matrix of inertia due to �th control mass. he�-termwhich appears in (7)-(8) is the angular velocity vectorof the spacecrat expressed as

� = �� + �� + ��. (9)

he absolute acceleration of the reference point� is expressedby the absolute acceleration of the CM as

a0 = a� − �2OG��2 = F� + FSRP� − �2OG��2 , (10)

where F� is the gravitational force vector and, consideringthe simpliied solar-sail force model [18], the solar radiation

pressure force vector is FSRP = −2�� cos2��, where � is thevalue of SRP at 1 AU (� = 4.56 × 10−6 N/m2), � is the sailarea, � = 0.85 is the solar-sail eiciency factor, and � is theangle between Sun-line direction and roll axis, as describedin Section 2. he torque relative to the origin � is given bythe gravitational force and SRP force, as shown in

T0 = T� +Tof

≅ �∑�=1�� (OG+GP�)

⋅ (−�R��3

�−�∇[R��3

�]�=��

⋅GP�)+ �× FSRP,(11)

where � is the Sun gravitational constant, GP� is the distancebetween CM and the �th point of the sailcrat, and � is thedisturbance ofset vector. Since ballast masses 1, 3 and 2, 4 arecoupled, (5) can be rewritten through the following scalar:

4�� (�1 �1 + �2 �2) �� + [�� +�� (�2 + 2�21 + 2�22)] ��+ [�� − �� + 2�� (�22 − �21)] �� − �2

�� [2�2 (2 �1+ 2��2 + 4�� 2 − 2�2

��1 + 2��2) − 2�1 (2 �2− 2��1 − 4�� 1 + 2��1 − 2�2

��2)] = − 3��3

�[��

− �� + 2�� (�22 − �21)] �12�13 + �� − ��,4��1 �1�� +[�� +�� (�22 + 2�2

1)] �� +[�� − ��

+�� (�22 + 2�21)]�� − �2

�� [2�SRP�� 1+ 2�1 (2��1 + 4�� 1 − 2��2 − 4�� 2 + 2��2+ 2��1)] = − 3��3

�[�� − �� +�� (�22 + 2�2

1)]

⋅ �11�13 + �� − ��,4��2 �2�� +[�� +�� (�22 + 2�2

2)] �� +[�� − ��

−�� (�22 + 2�22)]�� − �2

�� [−2�SRP�� 2− 2�2 (2��1 + 4�� 1 − 2��2 − 4�� 2 + 2��2+ 2��1)] = 3��3

�[�� − �� −�� (�22 + 2�2

2)]

⋅ �11�12 + �� − ��,

(12)

where (��, ��, ��) are SRP force components in body ref-

erence frame and (�11, �12, �13) are the components of ��


expressed in body reference as �� = �11 � + �12� + �13�and depend on the set of rotations chosen for the attituderepresentation. Let us call (�, �, �), respectively, the roll,pitch, and yaw angles of the spacecrat relative to the orbitalreference frame, obtained by a rotational sequence of �3(�) −�2(�) −�1(�) from the orbital to the body reference frame.hekinematics equations are

� = 1�� (��1 + ��2) ,� = 1�� (−��1 + ��2) ,� = 1�� (��1 + ��2 + ��3) ,

(13)

where

�1 = �� + �� −(�� + ��) ��2

�,

�2 = �� + �� −(−�� + ��) ��2

�,

�3 = �� − �� −�� 2

�,

�� = �SRP� (� ⋅ �)

(14)

is the force per unit mass in the orbital angular momentum

direction (�). In order to achieve the desired manoeu-vre, a combination of feedforward and feedback control,as described in [42, 43], is used. In Sections 4.1 and 4.2feedforward and feedback methods are briely presented.

4.1.he Feedforward Controller. Feedforward control is basedon a parameterisation of a desired manoeuvre, expressed asa nth-order polynomial in the generic angle �. he orderof polynomial depends on the boundary conditions and itshould not be too big to reduce wandering phenomena. Aseventh-order polynomial has been considered in this studyas follows:

� (�) = �� (��7 +��6 +��5 +��4 +��3 +��2 +��+�) , (15)

where �� is the desired angle of manoeuvre and � =�/�MAN is the nondimensional time. �MAN is the inaltime ater the manoeuvre. In order to ind the coeicients(�, �, �,�, �, �, �,�) in (15), the boundary conditions for�(�) are listed in Table 6.

Table 6: Feedforward boundary conditions.

� �� (�)�� =0 �� (�)�� =�MAN

0 0 ��1 0 0

2 0 0

3 0 0

According to the boundary conditions in Table 6, theparameterisedmanoeuvre angle is expressed by the followingseventh-order polynomial:

� (�) = �� (−20( ��MAN

)7 + 70( ��MAN

)6

− 84( ��MAN

)5 + 35( ��MAN

)4) . (16)

In order to design simply the feedforward controller, thefollowing assumptions are made [42]:

(i) Inertia matrix is diagonal and constant, not afectedby the position of control masses.

(ii) SRP force is the only force acting on the sailcrat.

(iii) he centre of mass lies on sail plane (�, �).With the hypothesis above, Euler equation is simply given by

J ⋅ �+�× J ⋅� = T� +Tofset, (17)

where T� is the control torque:

T� = [��,�, − �SRP 2�� , �SRP 2�� ]� . (18)

Using (17)-(18) and deining � as the angle between Euler axisand pitch axis, the feedforward control law formasses is givenby

� (�) = �2�� − �� (�) sin�2�SRP�� ,

� (�) = �2�� + ��

� (�) cos�2�SRP�� . (19)

To comply with geometrical boundaries, the dynamical scal-ing of the manoeuvre time �∗MAN is used [44]:�∗MAN = � ⋅ �MAN, (20)

where

� = max(√ sgn (�∗) (�∗ − (�/2��) ��)�max − (�/2��) �� sgn (�∗) ,√ sgn (�∗) (�∗ − (�/2��) ��)�max − (�/2��) �� sgn (�∗)) .

(21)


CM CP

1

2

3

4To the Sun

Yaw manoeuvrek

j

i

(a)

CM

CP

1

2

3

4To the Sun

Pitch manoeuvrek

j

i

(b)

Figure 8: Schematisation of yaw (a) and pitch (b) manoeuvre.

�∗ and �∗ are the maximum shit of control masses requiredalong the �-axis and �-axis, respectively.4.2. he Feedback Controller. he pitch/yaw feedback controlis based on the error between the desired manoeuvre and theone carried out by the sailcrat. he feedback control logicis in Proportional-Integral-Derivative (PID) form as below[26]:

� = −�� −�� −�� ∫ � d�, (22)

where � is the error between desired angle and real oneand ��, ��, and �� are the derivative, proportional, andintegral gain, respectively. his control can be decoupled ineach axis and gains can be determined as Single-Input-Single-Output (SISO) problem. Of course, whenever tuning a gain,the system response changes and the best gains are iterativelyset.

A rate limiter and a saturation limit are added to sim-ple PID controller, because of mechanical and geometricalboundaries. hese boundaries are

�max = �2 ,�max = �max

TC, (23)

where TC = 560 s is the actuator time constant taken intoaccount, according to the value in [26]. he roll feedbackcontrol is performed with on-of controllers that work whenthe tolerance on roll angle is exceeded.he controller chosenis a set of 4 PPTs positioned coupled on 2 opposite satellitesand the average thrust of each PPT chosen is 150 �N [45]. Forthis study, a required roll angle of 0 degrees with a toleranceof ±0.1 degrees is set, so that the thrusters switch on when theroll angle exceeds this value.

4.3. Numerical Results. Numerical simulations are carriedout in order to verify the performances of the proposed con-iguration. As reported in previous sections, a feedforwardcontroller was used to generate the desired manoeuvre overtime and a feedback controller with PID logic was set tocontrol the nonmodelled trends in feedforward controller.he characteristics of the sailcrat are those reported inTable 1, while velocities and accelerations of masses in (12)are considered null [26, 28]. he attitude is represented bythe rotational matrix which transforms body into orbitalreference frame:

[[[[��]]]]

= [[[[−�� −�� − �� −�� − �� −�� + �� −�� + ��

]]]][[[[��]]]].

(24)

In order to evaluate the performances of the proposedconiguration, a 35-degree manoeuvre in a circular planarEarth-like orbit is considered. In Figure 8(a) a 35-degree yawmanoeuvre with disturbance ofset on �-axis is schematicallyrepresented; in Figure 8(b) a 35-degree pitchmanoeuvre withdisturbance ofset on �-axis is schematically represented.

First, a 35-degree yaw manoeuvre without ofset (CP ≡�) is performed. Time histories of Euler angles and controlmasses over time are shown in Figures 9 and 10.

he manoeuvre is completed in less than 3 hours androll and pitch angles do not change from initial conditions.Figure 10 shows that the feedforward control ensures thesuccess of the manoeuvre, though the real position of thesliding masses difers slightly from the predicted one, as canbe seen around 2.5 hours, due to the nonmodelled forces in


0 1 2 3 4 5 6

Time (hour)

0 1 2 3 4 5 6

Time (hour)

0 1 2 3 4 5 6

Time (hour)

−0.2

−0.5

Real �

Predicted �

�(d

eg.)

Real �

Predicted �

�(d

eg.)

0

0.2

0

0.5

02040

Real �

Predicted �

�(d

eg.)

Figure 9: Euler angles over time for a 35-degree yaw manoeuvrewithout ofset.

0 1 2 3 4 5 6

0

10

20

Time (hour)

0

10

20

0 1 2 3 4 5 6

Time (hour)

Real position

Predicted position

Real position

Predicted position

−20

−10

−20

−10

y(m

)z

(m)

Figure 10: Positions of sliding masses over time for a 35-degree yawmanoeuvre without ofset.

the feedforward controller. However, no evident diferencesbetween real angles and predicted ones are visible by Figure 9.

he analysis with ofset takes into account only themaximum ofset calculated in Section 3.3, in order to havea worst-case analysis. Figures 11 and 12 show a 35-degreeyaw manoeuvre with 0.005m ofset (red curve) and with theliterature one of 0.1m (black curve).

Similar to the case without ofset, roll and pitch anglesdo not change from initial conditions and real and predictedangles overlap. he manoeuvre with the ofset presented in

0

0.2

0

0.5

02040

−0.2

−0.5

�(d

eg.)

�(d

eg.)

�(d

eg.)

0 1 2 3 4 5 6

Time (hour)

Real �, � = 0.1m

Predicted �, � = 0.1m

Real �, � = 0.005m


0 1 2 3 4 5 6

Time (hour)

Real �, � = 0.1m


0 1 2 3 4 5 6

Time (hour)

Real �, � = 0.1m


Real �, � = 0.005m


Real �, � = 0.005m


Figure 11: Euler angles over time for a 35-degree yaw manoeuvrewith disturbance ofset on �-axis.

0

10

20

0

10

20

0 1 2 3 4 5 6

Time (hour)

0 1 2 3 4 5 6

Time (hour)

−20

−10

−20

−10

y(m

)z

(m)

Real position, � = 0.1m

Predicted position, � = 0.1m







Figure 12: Positions of sliding masses over time for a 35-degree yawmanoeuvre with disturbance ofset on �-axis.

this paper is performed in less than 3 hours, as well as inthe case without ofset. On the other hand, the case with theliterature ofset performs the manoeuvre in more than 3.5hours.he reason for this gap can be found in the diferencesbetween the steady-state positions of control masses. he


00.10.2

0

20

40

0

0.5

0 1 2 3 4 5 6

Time (hour)

0 1 2 3 4 5 6

Time (hour)

0 1 2 3 4 5 6

Time (hour)

−0.2−0.1

−0.5

Real �

Predicted �

�(d

eg.)

Real �

Predicted �

�(d

eg.)

Real �

Predicted �

�(d

eg.)

Figure 13: Euler angles over time for a 35-degree pitch manoeuvrewith 0.005m ofset on �-axis.steady-state position of each sliding mass can be simplyobtained by (19), as shown in

�ss (�) = �2�� ,

�ss (�) = �2�� .

(25)

As shown in Figure 12 and in (25), the steady-state positionof the sliding masses on �-axis is �ss = 7.65 m with theliterature ofset of 0.1m; on the other hand, for an ofset valueof 0.005m, the steady-state position of the control masses on�-axis is only �ss = 0.38m.

As shown fromFigures 9 to 12, no roll control is necessaryduring a 35-degree yaw manoeuvre with ofset on �-axis,because the roll angle is null during the entire manoeuvre.Figures 13 and 14 show that for a 35-degree pitch manoeuvrewith a disturbance ofset on the same axis a roll control isnecessary.

Figure 13 shows that in a pitch manoeuvre the roll angledecreases slowly, so that only ater about 5 hours does theroll controller act, due to the threshold set to 0.1 degrees.For missions that require diferent attitude accuracy, thisthreshold can be set to diferent values. Excluding the timehistory of roll angle, the manoeuvre is completed as well as inthe previous examples.

Comparing these manoeuvres with those in literature,a 35-degree yaw manoeuvre presented in [26] and a 30-degree pitchmanoeuvre presented in [28] are both completedin about 2 hours. he manoeuvre presented in [42] for aperfectly relecting solar sail is much faster than the one

0

2Roll control torque

0

20Positions of sliding masses

0

20

Ro

ll t

hru

ster

on

-of

0 1 2 3 4 5 6

Time (hour)

Real position

Predicted position

0 1 2 3 4 5 6

Time (hour)

−20

−2

0 1 2 3 4 5 6

Time (hour)

Real position

Predicted position

−20

y(m

)z

(m)

Figure 14: Attitude controls over time for a 35-degree pitchmanoeuvre with 0.005m ofset on �-axis.

presented here, due to the higher moments of inertia of theproposed architecture. As mentioned above, high momentsof inertia are a disadvantage for an attitude manoeuvre andone of the aims of this study is to ensure the manoeuvrabilityof this coniguration. However, in interplanetary trajectoriesa fast manoeuvre is not always required and the conigurationpresented has performances compatible with the most chal-lenging interplanetary missions.

5. Conclusions

In this work, a new solar-sailing architecture has beenproposed and structural and dynamics performances havebeen investigated. he structural analysis has shown that thenew solar sail is stifer than the central-hub sail. his char-acteristic produces smaller out-of-plane deformation and,as a consequence, a reduction of the disturbing centre-of-mass/centre-of-pressure ofset. Furthermore, the proposedconiguration can easilymanage this ofset with an opportunesail tensioning load. he applied tensioning load dependson the booms’ stifness and it can be foreseen that it afectsgreatly themembrane wrinkling and that it increases with theload. In the proposed coniguration, the tensioning motors,the sliding masses motors, and PPTs can ind a good locationin the corner hubs, whereas in the central-hub sail theyare positioned at the end of the booms. his can allow thedesigning of a real shape and vibration membrane control,reducing the ofset with respect to the ofset reported inliterature for the central-hub sail. Furthermore, the corner-tensioned coniguration produces more important efectssuch as the reduction of the masking, the shadowing, andthe local thermal problems that can be controlled during the


light. In addition, it is worth noting that in the classical X-coniguration the efective area for a 40m side sail is 1200m2

instead of 1600m2, due to the membrane deformation andthe fact that around the booms there is no membrane. Onthe contrary, in the proposed coniguration the dispositionof the booms along the perimeter and the deformation ofthe membrane allow one to consider a major efective area,closer to nominal value of 1600m2. Starting from theseresults, numerical simulations of the attitude manoeuvresdemonstrated that the proposed architecture gives good per-formances, despite the largemoments of inertia. It was shownthat a 35-degree manoeuvre can be completed in less than 3hours, according to the usual requirements for interplanetarymissions. he new solar-sail concept is proposed for aninterplanetary mission, but advantages of this conigurationare useful also for planetarymissions. In general, the principalconstraint that must be taken into account is the velocity ofchange attitude manoeuvres. In fact, for a planetary mission,around the nodal line a fast change on the sail attitude canbe necessary; this event can be critical for this conigurationand the performances must be evaluated case by case. Onthe contrary the higher moment of inertia can be favourablefor missions where the sail attitude must remain constant(but this is valid also for the interplanetary case). In all casesstudied, the disturbing torque, caused by structural ofset,determines the steady-state positions of the slidingmasses. Asa consequence, the small ofset value of this sail conigurationguarantees a great increase in manoeuvrability.

Conflict of Interests

he authors declare that there is no conlict of interestsregarding the publication of this paper.

References

[1] M. MacDonald and C. R. McInnes, “Solar sail science missionapplications and advancement,”Advances in Space Research, vol.48, no. 11, pp. 1702–1716, 2011.

[2] C. Circi, “Mars andmercurymissions using solar sails and solarelectric propulsion,” Journal of Guidance, Control, and Dynam-ics, vol. 27, no. 3, pp. 496–498, 2004.

[3] B. Dachwald and W. Seboldt, “Multiple near-Earth asteroidrendezvous and sample return using irst generation solarsailcrat,” Acta Astronautica, vol. 57, no. 11, pp. 864–875, 2005.

[4] G. Mengali, A. A. Quarta, C. Circi, and B. Dachwald, “Reinedsolar sail force model with mission application,” Journal ofGuidance, Control, and Dynamics, vol. 30, no. 2, pp. 512–520,2007.

[5] G. Aliasi, G. Mengali, and A. A. Quarta, “Passive controlfeasibility of collinear equilibrium points with solar balloons,”Journal of Guidance, Control, and Dynamics, vol. 35, no. 5, pp.1657–1661, 2012.

[6] M. Ceriotti and C. R. McInnes, “Systems design of a hybrid sailpole-sitter,”Advances in Space Research, vol. 48, no. 11, pp. 1754–1762, 2011.

[7] M. Ceriotti and C. R.McInnes, “Generation of optimal trajecto-ries for Earth hybrid pole sitters,” Journal of Guidance, Control,and Dynamics, vol. 34, no. 3, pp. 847–859, 2011.

[8] J. Heiligers, M. Ceriotti, C. R. McInnes, and J. D. Biggs, “Dis-placed geostationary orbit design using hybrid sail propulsion,”Journal of Guidance, Control, and Dynamics, vol. 34, no. 6, pp.1852–1866, 2011.

[9] J. Simo and C. R. McInnes, “Solar sail orbits at the Earth-Moonlibration points,” Communications in Nonlinear Science andNumerical Simulation, vol. 14, no. 12, pp. 4191–4196, 2009.

[10] J. Simo and C. R. McInnes, “Asymptotic analysis of displacedlunar orbits,” Journal of Guidance, Control, and Dynamics, vol.32, no. 5, pp. 1666–1670, 2009.

[11] P. Anderson and M. Macdonald, “Extension of highly ellipticalearth orbits using continuous low-thrust propulsion,” Journalof Guidance, Control, and Dynamics, vol. 36, no. 1, pp. 282–292,2013.

[12] P. Anderson and M. Macdonald, “Static, highly elliptical orbitsusing hybrid low-thrust propulsion,” Journal of Guidance, Con-trol, and Dynamics, vol. 36, no. 3, pp. 870–880, 2013.

[13] G. Mengali and A. A. Quarta, “Solar sail trajectories withpiecewise-constant steering laws,” Aerospace Science and Tech-nology, vol. 13, no. 8, pp. 431–441, 2009.

[14] B. Dachwald, “Optimization of very-low-thrust trajectoriesusing evolutionary neurocontrol,”Acta Astronautica, vol. 57, no.2–8, pp. 175–185, 2005.

[15] T. Ingrassia, V. Faccin, A. Bolle, C. Circi, and S. Sgubini, “Solarsail elastic displacement efects on interplanetary trajectories,”Acta Astronautica, vol. 82, no. 2, pp. 263–272, 2013.

[16] C. Circi, “hree-axis attitude control using combined gravity-gradient and solar pressure,” Proceedings of the Institution ofMechanical Engineers, Part G: Journal of Aerospace Engineering,vol. 221, no. 1, pp. 85–90, 2007.

[17] G. Mengali and A. A. Quarta, “Near-optimal solar-sail orbit-raising from low earth orbit,” Journal of Spacecrat and Rockets,vol. 42, no. 5, pp. 954–958, 2005.

[18] C. R. McInnes, Solar Sailing: Technology, Dynamics andMissionApplications, Springer Praxis Publishing, Chichester, UK, 2004.

[19] L. Johnson, R. Young, E.Montgomery, andD. Alhorn, “Status ofsolar sail technologywithinNASA,”Advances in Space Research,vol. 48, no. 11, pp. 1687–1694, 2011.

[20] L. Johnson, M.Whorton, A. Heaton, R. Pinson, G. Laue, and C.Adams, “NanoSail-D: a solar sail demonstration mission,” ActaAstronautica, vol. 68, no. 5-6, pp. 571–575, 2011.

[21] V. Lappas, N. Adeli, L. Visagie et al., “CubeSail: a low cost Cube-Sat based solar sail demonstration mission,” Advances in SpaceResearch, vol. 48, no. 11, pp. 1890–1901, 2011.

[22] U. Geppert, B. Biering, F. Lura, J. Block, M. Straubel, andR. Reinhard, “he 3-step DLR–ESA gossamer road to solarsailing,” Advances in Space Research, vol. 48, no. 11, pp. 1695–1701, 2011.

[23] Y. Tsuda, O. Mori, R. Funase et al., “Achievement of IKAROS—Japanese deep space solar sail demonstration mission,” ActaAstronautica, vol. 82, no. 2, pp. 183–188, 2013.

[24] C. Sickinger, L.Herbeck, and E. Breitbach, “Structural engineer-ing on deployable CFRP booms for a solar propelled sailcrat,”Acta Astronautica, vol. 58, no. 4, pp. 185–196, 2006.

[25] A. Stabile and S. Laurenzi, “Coiling dynamic analysis of thin-walled composite deployable boom,” Composite Structures, vol.113, no. 1, pp. 429–436, 2014.

[26] B. Wie and D. Murphy, “Solar-sail attitude control design for asail light validation mission,” Journal of Spacecrat and Rockets,vol. 44, no. 4, pp. 809–821, 2007.


[27] B. Wie, D. Murphy, M. Paluszek, and S. homas, “Robust atti-tude control systems design for solar sail, part 1: propellantlessprimaryACS,” inProceedings of the AIAAGuidance, Navigation,and Control Conference and Exhibit, Providence, RI, USA, 2004.

[28] S. N. Adeli, V. J. Lappas, and B. Wie, “A scalable bus-basedattitude control system for Solar Sails,” Advances in SpaceResearch, vol. 48, no. 11, pp. 1836–1847, 2011.

[29] B.Wie, “Solar sail attitude control and dynamics, part 1,” Journalof Guidance, Control, and Dynamics, vol. 27, no. 4, pp. 526–535,2004.

[30] W. Wong and S. Pellegrino, “Wrinkled membranes III: numer-ical simulations,” Journal of Mechanics of Materials and Struc-tures, vol. 1, no. 1, pp. 63–95, 2006.

[31] D. W. Sleight and D. M. Muheim, “Parametric studies ofsquare solar sails using inite element analysis,” in Proceedingsof the 45th AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics & Materials Conference, AIAA-2004-1509, PalmSprings, Calif, USA, April 2004.

[32] S. C. Gajbhiye, S. H. Upadhayay, and S. P. Harsha, “Freevibration analysis of lat thin membrane,” International Journalof Engineering Science and Technology, vol. 4, no. 8, pp. 3942–3948, 2012.

[33] I. Abaqus, Abaqus Analysis User’s Manual, 2010.

[34] J. M. Fernandez, V. J. Lappas, and A. J. Daton-Lovett, “Com-pletely stripped solar sail concept using bi-stable reeled com-posite booms,” Acta Astronautica, vol. 69, no. 1-2, pp. 78–85,2011.

[35] D. W. Sleight, T. Mann, D. Lichodziejewski, and B. Derbes,“Structural analysis and test comparison of a 20-meter inlation-deployed solar sail,” in Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and MaterialsConference, pp. 1408–1423, May 2006.

[36] S. Laurenzi, D. Barbera, and M. Marchetti, “Buckling design ofboom structures by FEM analysis,” in Proceedings of the 63rdInternational Astronautical Congress (IAC ’12), pp. 6367–6371,Naples, Italy, October 2012.

[37] A. Bolle and C. Circi, “Solar sail attitude control through in-plane moving masses,” Proceedings of the Institution of Mechan-ical Engineers, Part G: Journal of Aerospace Engineering, vol. 222,no. 1, pp. 81–94, 2008.

[38] G. Colasurdo and L. Casalino, “Optimal control law forinterplanetary trajectories with nonideal solar sail,” Journal ofSpacecrat and Rockets, vol. 40, no. 2, pp. 260–265, 2003.

[39] G. Mengali, A. A. Quarta, D. Romagnoli, and C. Circi,“H2-reversal trajectory: a new mission application for high-performance solar sails,”Advances in Space Research, vol. 48, no.11, pp. 1763–1777, 2011.

[40] G. Vulpetti, “3D high-speed escape heliocentric trajectories byall-metallic-sail low-mass sailcrat,” Acta Astronautica, vol. 39,no. 1–4, pp. 161–170, 1996.

[41] B.Wie, “Solar sail attitude control and dynamics, part 2,” Journalof Guidance, Control, and Dynamics, vol. 27, no. 4, pp. 536–544,2004.

[42] D. Romagnoli and T. Oehlschlagel, “High performance twodegrees of freedom attitude control for solar sails,” Advances inSpace Research, vol. 48, no. 11, pp. 1869–1879, 2011.

[43] C. Scholz, D. Romagnoli, B. Dachwald, and S. heil, “Perfor-mance analysis of an attitude control system for solar sails usingsliding masses,” Advances in Space Research, vol. 48, no. 11, pp.1822–1835, 2011.

[44] B. Siciliano, L. Sciavicco, L. Villani, and G. Oriolo, Robotics—Modelling, Planning and Control, Advanced Textbooks in Con-trol and Signal Processing, Springer, London, UK, 2009.

[45] B. Wie, D. Murphy, M. Paluszek, and S. homas, “Robustattitude control systems design for solar sails, part 2: microppt-based secondary acs,” in Proceedings of the AIAA Guidance,Navigation, and Control Conference and Exhibit, Providence, RI,USA, 2004.

Submit your manuscripts at

http://www.hindawi.com

VLSI Design

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporation

http://www.hindawi.com Volume 2014Hindawi Publishing Corporation

http://www.hindawi.com

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientiic World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Active and Passive Electronic Components


Chemical EngineeringInternational Journal of

Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation


Advances in

OptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

RoboticsJournal of


peloni, alessandro and barbera, daniele and laurenzi...

Documents