Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/220758180

DynamicModelingandHardware-In-The-LoopSimulationfortheCable-DrivenParallelRobotIPAnema.

ConferencePaper·January2010

Source:DBLP

CITATIONS

5

READS

36

3authors:

Someoftheauthorsofthispublicationarealsoworkingontheserelatedprojects:

SimulationofMachineToolsViewproject

Cable-drivenParallelRobotsViewproject

PhilippMiermeister

FraunhoferInstituteforManufacturingEngin…

18PUBLICATIONS103CITATIONS

SEEPROFILE

AndreasPott

FraunhoferInstituteforManufacturingEngin…

99PUBLICATIONS555CITATIONS

SEEPROFILE

AlexanderWilhelmVerl

UniversitätStuttgart

304PUBLICATIONS1,974CITATIONS

SEEPROFILE

AllcontentfollowingthispagewasuploadedbyAndreasPotton13October2017.

Theuserhasrequestedenhancementofthedownloadedfile.

Dynamic Modeling and Hardware-in-the-loop Simulation for thecable-driven parallel cable robot IPAnemaPhilipp Miermeister, Andreas Pott, Alexander VerlFraunhofer IPA; Nobelstrasse 12, D-70569 Stuttgart, Germany

AbstractIn this paper, the mechatronic model of the cable-driven parallel robot IPAnema is presented. The dynamic equationsare established including the dynamic behavior of the mobile platform, the pulley kinematics of the winches, and a cablemodel based on linear springs. The model of the actuation systems consists of the electro-dynamic behavior of the powertrain as well as the dynamics of the servo controller. The presented model is feasible for real-time simulation, controllerdesign, as well as case studies for high-dynamic or large-scale robots. Simulation results and experimental measurementswith the cable-driven parallel robot IPAnema are presented and compared.

1 Introduction

A cable-driven parallel robots consists of a rigid machineframe, a mobile platform, and a number of winches thatcontrol the length of their respective cables by coiling themonto a drum. Coordinated motion of the winches allow tomove the mobile platform on arbitrary trajectories in spaceto fulfill robot tasks such as handling, assembly, and takingmeasurements. Compared to industrial robots cable robotsare able to generate high velocities and accelerations due tovery small inertia. On the other hand, large workspace andhigh payloads are possible due to the efficient force trans-mission through the cables. Simulation allows to studysuch extreme scenarios quickly and in a cost-efficient way.Therefore, a mechatronic model of cable robots is desirableto plan and virtually prototype large-scale or high-dynamicrobots. Further applications are design and optimization offorce control as well as motion planning.

In the last decade, a lot of research has been carried out tostudy both theory (see e.g. [1, 6, 7, 14]) and implementa-tion [9, 11] of cable robots. A dynamic model and fuzzycontrol for a cable robot with six cables was presented asmodel for radio telescopes [15]. A dynamic model usingtechniques from multi-body system dynamics of the ca-ble robot Segesta was introduced [2, 4]. The dynamicsof under-constrained cable robots was used for simulationand control [8, 10]. The work presented in this paper re-lated especially to the cable robot IPAnema, where detailson the system architecture and application can be found in[12].

2 Dynamic model of cable-drivenparallel robots

Figure 1: Experimental setup of the cable robot IPAnemawith eight cables

The mechatronic system of the cable robot IPAnema is di-vided into a mechanical part including the platform with ncables and winches on the one side and the electrical parton the other side as illustrated in Figure 2. The electricalpart consists of n servo motors and position controllers.The governing numerical control is not further modeled.Its generated position signal θi with i = 1, ..., n is usedas reference signal for the cascaded controller. The dy-namic behavior of the individual subsystems is describedby ordinary differential equations (ODEs) of first or secondorder. For simulation and numerical integration the equiva-lent state space representation is obtained by transformingthe high order ODEs into first order ODE-systems. Theoverall system structure with its forward dynamics, inversekinematics, and the modeled subsystems with their associ-ated input and output quantities is shown in Figure 2.On the electrical side the servo motors are described bytheir electrodynamics equations with the supply voltage

Robot electrics Robot mechanics

Numericalcontrol

Positioncontrol

Velocitycontrol

ddt

Currentcontrol

id,ref,i=0

Electrodynamics

Amperemeter

Winchmechanics

Positionencoder

Cables Platform

InverseKinematics

Environment

θi

θref,iiq,ref,i udq,i TSM,i

idq,i

θeff,i

θDrum,i

fi

f

x

x, x, x

fP, τ P

qAT

Figure 2: Mechatronic model of a cable-driven parallel robot

udq,i as input quantities and the measured motor currentsidq,i together with torque TSM,i as output quantities. Themeasured motor currents are fed back to the inner currentcontrol of the cascaded control. The current controller re-alizes a field orientated control, which separately controlsthe currents respective the d- and q-axis using id,ref,i, iq,ref,ias reference input. id,ref,i is set to zero, while iq,ref,i is pro-vided by the upstream velocity control with θref,i as refer-ence and d

dtθeff,i as actual motor velocity. The generatedmotor torque TSM,i acts on the drum inside the winch to-gether with the cable force fi and therefore both are con-sidered as input quantities for the winch mechanics. Thedrum angle θDrum,i, the effective rotor angle θeff,i, and therotary velocity θeff,i are considered as output quantitiesof the winch subsystem, whereas the rotor angle θeff,i isneeded for the outer position and velocity control loop.Describing the platform pose by generalized coordinatesx allows to determine the cable lengths q and the struc-ture matrix AT [14] by inverse kinematics. The platformmotion is determined by the cable forces f as well as bythe applied force fP and torque τ P, which act on the toolcenter point.

3 Modelling of robot mechanicsFor parallel kinematics the computational effort for solv-ing the forward kinematics is significant and the solutionis not unique. Here, the proposed simulation model usesinverse kinematics and forward dynamics, which are fastand easy to solve and can be done in real-time. To avoidforward kinematics the generalized coordinates of the plat-form pose are chosen as x =

[rT ΘT

]T, where r is

the position vector with respect to the inertial frame K0

and Θ =[pw pT

Q]T

with pQ =[px py pz

]Tis

the platform rotation described by quaternions in order toavoid singularities and to provide numerical stability. Itshould be noted, that quaternions have to fulfill the nor-

malization constraint Θ2 − 1 = 0 if used to parameterizerotations. By introduction of the skew-symmetric matrix

pQ =

0 −pz pypz 0 −pz−py px 0

, (1)

the associated rotation matrixR is derived from the quater-nions as shown in [13]

R = E + 2pwpQ + 2pTQpQ. (2)

To describe the platform kinematics, the local vector bi andthe cable vector li are introduced, whereas bi describes thecable attachment points of the mobile platform and l is de-termined by the vector loop as shown in Figure 3 with theclosure-constraint

li(x) = ai − r −Rbi. (3)

a = (0)rC +R0C

((C)r1 (x) +RCM(x)(M)rP2 (x)

)(4)

ey

rC

r,R

rM

rBC

l

b

A

qP

qG

B

KP ex

ey

ez

α2

α4

α3

rP2

KM

ex

ez

α1

KC

ex

ey

ez

r1

K0 ex

ey

ez

Figure 3: Advanced kinematic loop including a winch pul-ley

Vector rC refers to the fixed pivot point C, vector r1 de-scribes the center point of the pulley respective KC, andvector rP2 describes the cable contact point A respectiveKM. R0C and RCM denote the transformation from KCinto K0 and from KM into KC, respectively. The mobileplatform is described as a free floating rigid body withoutconstraints, for which the stationary state follows from theforce equilibrium

[u1 · · · unb1×u1 · · · bn×un

]︸ ︷︷ ︸

AT

f1...fn

︸ ︷︷ ︸

f

+

[fPτ P

]︸ ︷︷ ︸

w

= 0. (5)

Using the Newton-Euler formulation for the platform dy-namics yields a differential algebraic equation system(DAE) with six second-order differential equations, one al-gebraic equation, and seven unknowns[

mPE 00 IP

]T x−

[Dlin 00 Drot

]T x

+

[0

IPP Θ + ωIPω

]︸ ︷︷ ︸

gC

= w +ATf (6)

Θ2 − 1 = 0 (7)

Thereby mP and IP describe the platform mass and tensorof inertia, while the damping matrices Dlin and Drot re-gard the friction of the environmental medium and cableattachment points. Matrix E is the identity matrix and Tis defined as

T =

[E 00 P

](8)

where matrix

P = 2[−pQ pwE + pQ

]∈ R3×4 (9)

describes the relation between quaternions and the rotaryvelocity ω = P Θ [13]. Deriving Eq. (7) twice with re-spect to time yields an ODE-system of the form mPE 0

0 IPP0 Θ

︸ ︷︷ ︸

M

x =

Dlin 00 DrotP

0 Θ

x+

[w +ATf − gC

0

]︸ ︷︷ ︸

k

. (10)

Solving of the linear second-order equation Mx = k andsubsequent integration of x involves drift effects caused bydifferentiation of Eq. (7) which can be dealt with by pro-jecting the predicted solutions ΘP and ΘP onto the con-straint manifold, respectively. Projection of ΘP is equal to

the normalization of quaternions

Θ =ΘP

‖ΘP‖2(11)

while projection of ΘP is expressed by

Θ = ΘP −ΘΘP

Θ2Θ. (12)

The cables are modeled as parallel spring damper systemwith a variable spring rate ci and damping rate di, due tothe changing effective cable length qeff,i. Cables absorbonly tractive forces yielding a piecewise function that reads

fi =

{ci(qeff,i)∆qi + di(qeff,i)∆qi for fi > 00 for fi 6 0 .

(13)

rθDrum

h

d cA

qD

rP1

cB

s(θ) rP2

qP

A

l∆qB(x)

Figure 4: Winch Kinematics

The effective initial cable length qeff,0,i = qN,i(x0) is cal-culated by the nominal cable length qN,i(x) = ‖l(x)‖2 +qP,i(x) + qG,i whereas qP,i describes the cable length rest-ing on the pulley and qG,i(θDrum,i) = cA + cB + si(θDrum,i)describes the cable length inside the winch as shown inFig. 4. With the unwound cable length qD,i = riθDrum,ithe effective cable length reads qeff,i = qeff,0,i + qD,i andthe difference between the nominal cable length and theunwound cable length can be written as

∆qi(x, θDrum,i) = qN,i(x)− qN,i,0 − qD,i . (14)

Deriving Eq. (14) with respect to time for i = 1, ..., nyields

∆q = ATx− qD . (15)

The winch dynamics is primarily determined by the winchmechanic’s moment of inertia JW,i and the frictionaltorque TF,i(fi), which itself depends on the cable force fi.

With the cable force on the one side and the motor torqueon the other side, the drum acceleration follows with

θeff,i =rDrum,ifi + TRot,i + TF,i(fi)

JW,i. (16)

4 Modeling of Robot ElectricsThe robot’s electrical system includes the drives with em-bedded position controllers for the servo motors, the am-plifiers, and the servo motors. The amplifiers use pulse-width modulation to provide the motors with the neces-sary rotating three-phase voltage. For the simulation modelthe amplifiers are assumed as ideal devices and have notbeen modeled while the permanent magnet synchronousmotors (PMSM) are modeled as simplified motors withoutdamping windings, iron loss, and with symmetrical star-connected motor windings.

Controller

Figure 5: PMSM with inverter

To realize field orientated control, the electrodynamics dif-ferential equations are transformed from the stator’s threephase system into a two phase rotor fix frame using Clarke-and-Park-transformation [5]. Introducing the winding re-sistance R12,i and the flux linkage ψdq,i, the voltage dif-ferential equation respective the dq-frame reads

ψdq,i = udq,i −R12,iidq,i − θeff,iTI,iψdq,i , (17)

where udq,i describes the input voltage controlled by theupstream cascaded control and the matrix TI,i is defined as

TI,i =

[0 −11 0

]. Motor current

idq,i = L12,i−1 (ψdq,i −ψR,dq,i

)(18)

is used for the inner current control loop. L12,i describesthe winding inductance and ψR,dq,i the rotor flux linkagecaused by the permanent magnets. Considering the polepair number ZP,i, the motor torque is obtained by

TRot,i =3

2ZP,i

(TI,iψdq,i

)idq,i. (19)

The position control calculates the reference value for thedownstream velocity control by the set point θi and the ef-fective angle θeff,i using the controller amplification kθ,i

θref,i = kθ,i (θi − θeff,i) . (20)

For the velocity control loop a proportional integral con-troller with an amplification of kθ,i and a time constantkT θ,i is used. Calculation of the control deviation

∆θi = θref,i − θeff,i (21)

leads to the desired motor current

idq,ref,i =

[0

kθ,i

(∆θi + kT θ,i

−1∆θi

) ]. (22)

The reference value for the d-axis is set to zero, since amotor current along the d-axis has no influence on the mo-tor torque. As with the velocity, the current is controlledby a proportional integral controller with an amplificationof kdq,i, a time constant kTdq,i, and the control deviation

∆idq,i = idq,ref,i − idq,eff,i (23)

yielding the supply voltage

udq,i =

[kd,i (∆id,i) + k−1Td,i

∫∆id,i dt

kq,i (∆iq,i) + k−1Tq,i

∫∆iq,i dt

]. (24)

5 Implementation and Hardware-in-the-Loop Simulation

The cable-driven parallel robot IPAnema (Fig. 1) is cur-rently under investigation at the laboratories of FraunhoferIPA. This robot provides a six degrees-of-freedom end-effector with seven or eight cables and focuses on in-dustrial applications in the field of material handling aswell as fast pick-and-place applications. The winches areequipped with the permanent magnet synchronous mo-tors IndraDyn S by Bosch Rexroth, which contain multi-turn absolute encoders allowing to obtain the absolute ca-ble length at any time with a resolution of 50µm. Thecontrol system is based on the Windows PC-based real-time extension RTX and an adopted NC-controller by ISG(Stuttgart, Germany) as shown in Fig. 6. The robot can beprogrammed by G-Code (DIN 66025) similar to machinetools using the Win32 user interface of ISG-NC. On theindustrial PC the interpolation cycle time of the trajectorygenerator is 2 ms.To get an universal and highly configurable model of thecable robot which can be used for system investigationand hardware-in-the-loop simulation, the model is imple-mented by use of Simulink and Matlab, whereas each sub-system is modeled individually and connected as has beenindicated in Fig. 2.The simulation model basically consists of ordinary dif-ferential equations, which are implemented by equivalentblock diagrams. Simulink is used for model implementa-tion, while Matlab is used for data management and analy-sis. The assembly of a single controller, motor, winch andcable results in a chain of four submodels, which describes

Control PC

Win32 Environment

Shared Memory

RTX Environment

Process

Process Remote PC

3D Visualization

Cable robot

Drives

SER

CO

S B

usIn

terf

ace

NC Kernel

Simulation Scheduler

Simulation Model Thread

Simulation Data

NC- and System Data

HLI

ISG-NCUser

Interface

TCP/

IP

Inte

rfac

eGraphic User

Interface

SystemClock

Mutex

Simulink RealtimeWorkshop Simulink Model

Data Files

Figure 6: Integration of the simulation model with the cable robot’s numerical control hardware by use of Simulink’sRealt-Time Workshop and the real-time extension RTX

the transfer behavior of a single power train i with the setpoint θi as input quantity and the cable force fi as out-put quantity. To get an universal model of the cable robot,i.e. a model for an arbitrary number of cables and winchesall state variables and signals of the power train are ex-tended by n dimensions. The parametrization of the robotmodel is done by a XML-file which allows to save differ-ent robot configurations and load them on demand. At thebeginning of a simulation run, the XML-file of the desiredsimulation model is loaded utilizing the javax.xml.xpathand javax.xml.parsers class to load the data and assign-ing them to the related model variables inside the Matlabworkspace. Input data provided by the numerical controlare stored together with the simulation results inside theMatlab workspace using time series objects which providemethods for resampling, differentiation, filtering and otheroperations enabling efficient data management.The Real-Time Workshop of Simulink is used to generate source andheader files for real-time simulation. The files consist of Cor C++ code and provide public functions for accessing thesimulation model.Running the simulation model inside the real-time envi-ronment demands a time deterministic fixed step solver fornumerical integration, since variable step solver may vio-late the time slots given by the real-time environment. Herea fourth order Runge-Kutta (ODE 4) integrator with a stepwidth of 9 · 10−5 s is used, which allows real-time sim-ulation on the target device. Depending on the availablecomputational power, different integrators may be used.After code generation the model is integrated with the RTXextension and control hardware as shown in Fig. 6. RTX is

a self-contained real-time subsystem running on Windowsplatforms while bypassing the Windows scheduler to pro-vide the desired determinism and hard real-time response.The communication of the real-time subsystem and theWindows operating system is established using pointers ona shared memory. While the user interface of the ISG-NC runs inside the Windows environment, the NC kernelis executed inside the RTX subsystem due to its real-timedemands. The NC kernel computes the desired motor po-sitions by inverse kinematics and subsequently transmitsthe values to the drives of the cable robot using a fibre op-tics bus as shown in Fig. 6. Furthermore, the bus is usedto receive actual values from the motors’ current sensors.The received values are stored inside the shared memorytogether with the reference positions using the high levelinterface (HLI) data structure. The model runs simultane-ously to the cable robot and access the HLI to obtain theactual desired motor positions for every time step. On theother side, the shared memory is used to transfer simula-tion results to the user interface inside the Windows envi-ronment. For better visualization, the user interface imple-ments a scope for data plotting and a TCP/IP interface, thatenables the connection to a 3-D visualization tool on thesame or a remote computer. Real-time simulation togetherwith the visualization tool provides a good impression ofthe platform behavior for a given trajectory as shown inFig. 7.

Figure 7: Real-time visualization of the platform trajec-tory of a cable robot with eight cables. The platform ori-entation is shown by the orientation vectors attached to thetrace line. The front area shows the platform behavior nearthe workspace boundary

To execute the simulation model inside the RTX real-timeenvironment, the source and header files generated by theReal-Time Workshop have to be integrated with an invok-ing real-time process. A simulation scheduler as indicatedin Fig. 6 is implemented to ensure synchronicity betweenthe simulation model and the real robot. The simulationscheduler represents the main thread and is started togetherwith the superordinate real-time process which itself isstarted by the Windows user interface on demand. Dur-ing the initialization phase, the scheduler thread allocatesthe necessary shared memory for data exchange and cre-ates mutex objects as well as a timer object. The mutexobjects are required for synchronized access of the sharedmemory and they can be globally accessed by the Win32process of the user interface as well as by the RTX pro-cess. After initialization, the scheduler enters the mainloop which contains routines for instruction and error han-dling and starts the timer object which controls the simu-lation speed by calling the simulation thread with a spec-ified rate. For real-time simulation, the specified rate hasto coincide with the integrator step size predefined by theSimulink model. The simulation thread contains the actualsimulation model and functions for instruction processing.Access to the included simulation model during runtime isbasically provided by the simulation model’s step functionand two public structures which contain the desired mo-tor angles θi and the simulation results for the quantitiesx, l respectively. The simulation step function computesa single integration time step using the public input struc-ture together with the local system states and stores the re-sult in the public output structure. From that,the simulationthread computes the next n integration steps by calling thesimulation step function n times for every thread call andstores the simulation results inside the shared memory. Anincreasing n allows to reduces overhead, but results in anincreasing zero-order hold behavior for the input values.

It is obvious, that the data exchange between the Windowsuser interface and the simulation thread has to be synchro-nized to avoid data corruption. Data capturing with a sam-

pling frequency of 100 1/s on the RTX side requires an ac-cess time less than 10 ms on the Windows side, which cannot be guaranteed due to the time-variant response behav-ior caused by the Win32 architecture. A buffer mechanismis necessary to regard the time-critical runtime behavior aswell as the large data volume which has to be transferredfrom the real-time environment to the Windows environ-ment within a short period of time. Therefore, a triplebuffer is set up inside the shared memory which can be si-multaneously accessed by the simulation thread as well asby the Win32 user interface. Buffer swapping and accessrights are managed by a mutex. While time critical func-tions, needed for the simulation model, are implementedinside the RTX environment, every other functionality isrealized inside the Win32 environment, which enables theuse of high-level programming languages such as C#. Tomake use of the advantages brought along by C# an theNET. framework without marshalling the entire real-timeapplication programming interface (RT-API), a dynamiclink library (DLL) is written. The DLL itself is using the Clanguage and serves as an interface between C# and the RT-API by performing low level tasks as shared memory ac-cess, synchronization, and process handling. Therefrom,the user interface communicates with the real-time envi-ronment by marshalling the functions that are provided bythe DLL.

6 System Validation

The complexity of the model, caused by the number ofcoupled equations and the possible high system dimensionmakes it difficult to find errors during the implementationprocess. The overall model is based on physical equationswhich allows to check the model implementation for con-sistency by using the principle of conservation of energy.In contrast to the n-dimensional state space vectors andequations of the motors, winches, and cables of a robotwith n cables, the system energy can be represented by ascalar value summarizing the energy of the individual unitsas indicated in Fig. 8. The system input energy is definedby the motor’s input energy WSM,in, that is transferred bythe winches and cables to the platform considering energydissipation.

Motors Winches Cables Platform

SM,inW

R12WL12V WinchK Winch,dampWCableWCableV PV PK P,dampW

Figure 8: Energy flow of the individual subsystems

WR12,i, WWinch,damp,i, WCable,i, andWP,damp refer to the dis-sipated system energy caused by the winding resistance,winch friction as well as cable and platform damping, re-spectively.

10−5 10−4

10−8

10−6

10−4

Step size [s]

Rel

ativ

ede

viat

ion

(T=3

0s)

Figure 9: System energy balance for simulation runs(T=30 s)respective an increasing integration step size

Furthermore, the subsystems store energy in terms of po-tential and kinetic energy. VL12,i, VCable,i and VP regardthe potential energy of the winding inductance, cables, andplatform while KWinch,i and KP regard the kinetic energyof the winch mechanics and platform, respectively. Fromthat the energy balance of the whole system is computedwith

WBalance = WSM,in −n∑i=1

(WR12,i + VL12,i)

−n∑i=1

(KWinch,i +WWinch,damp,i)−n∑i=1

(WCable,i + VCable,i)

− VP −KP −WP,damp!= 0. (25)

Moving the platform along the circular trajectory indicatedby Fig. 10 and using Eq. (25) to compute the energy bal-ance after 30 s simulation time yields a small error whichis caused by numerical integration and depends linearly onthe integration step size as shown in Fig. 9.Further validation of the robot model is done by compari-son of the actual platform trajectory with a simulated tra-jectory using a Leica laser tracker system for position de-termination with a sample rate of 1 ms. Figure 10 showsthe measured and simulated circular trajectory respectivethe xy- and xz-plane with a maximum diameter of 600 mmand a velocity of 0.9 m/s, while Figure 11 shows the plat-form movement in direction of the x-axis with respect totime. The maximum positional deviation of the simulatedtrajectory respective the measured trajectory amounts to 5mm for the movement in the xy-plane and 9 mm for thexz-plane. Additionally, the motors’ internal current sen-sors are used to obtain the motor torques for comparisonagainst the simulated torques with a sample rate of 1 ms asshown in Fig. 11 for four winches.The quantitative difference of simulation and measurementmay result from uncertainties respective the initial condi-tions, model parametrization, and neglected structural ele-ments. Regarding to the initial conditions, the initial cabletension of an individual cable can not be measured and mydiverge from the cable tension used in the model. Further-more the initial pose of the platform may diverge from the

pose in the model, since only one reference point of theplatform is measured by the laser tracker. Subsidence ofthe cables an winch mechanics cause further uncertainties.Regarding the dynamic behavior of the mobile platform,the not modeled compliance of the robot frame cause os-cillations that are superimposed with the platform motion.The robot frame is not modeled since it is considered asauxiliary structure, which can be replaced by arbitrary mo-tor foundations. Concrete walls for example would be anideal foundation without a significant momentum. Newforce sensors that will be applied between the cables andwinches will lead to improved initial conditions and addi-tional measurements for system validation.

7 ConclusionsIn this paper a mechatronic model of the cable robotIPAnema was presented. The model consists of the me-chanical submodels for platform dynamics, cable behav-ior, and winch dynamics. The characteristics of the mo-tors and controllers were introduced. The resulting sys-tem model was generated using Matlab-Simulink and im-plemented into the real-time controller environment of thecable robot IPAnema. The coupling with the industrialcontrol system of the robot is presented. By consideringthe energy balance of the simulation model the model wasfound to be valid. Furthermore, the comparison betweensimulated motion and measurements with the IPAnema us-ing a Laser Tracker show good agreement. Thus, the modelwill be used in the future to plan and validate new geome-tries especially for large-scale robots as well as to designand optimize the force control.

References[1] Bruckmann, T., Mikelsons, L., Brandt, T., Hiller, M.,

and Schramm, D. (2008a). Wire robots part i – kine-matics, analysis and design. Parallel Manipulators– New Developments, ARS Robotic Books, Vienna,Austria. I-Tech Education and Publishing.

[2] Bruckmann, T., Mikelsons, L., Brandt, T., Hiller, M.,and Schramm, D. (2008b). Wire robots part ii – dy-namics, control and application. Parallel Manipula-tors – New Developments, ARS Robotic Books, Vi-enna, Austria. I-Tech Education and Publishing.

[3] Bruckmann, T., Pott, A., and Hiller, M. (2006).Calculating force distributions for redundantly actu-ated tendon-based Stewart platforms. Advances inRobot Kinematics, pages 403–412, Ljubljana, Slove-nia. Springer-Verlag.

[4] Fang, S. (2005). Design, Modeling and Mo-tion Control of Tendon-Based Parallel Manipulators.Fortschritt-Berichte VDI, Reihe 8, Nr. 1076. VDIVerlag, Düsseldorf.

−0.4−0.2 0 0.2 0.4−0.4

−0.2

0

0.2

0.4

x-Axis [m]

y-A

xis

[m]

−0.4−0.2 0 0.2 0.4

−0.2

0

0.2

0.4

x-Axis [m]

z-A

xis

[m]

−0.4−0.2

00.20.4

x-A

xis

[m]

−0.4−0.2

00.20.4

y-A

xis

[m]

0 5 10 15 20 25 30−0.4−0.2

00.20.4

Simulation time [s]

z-A

xis

[m]

Figure 10: Comparison of the simulated (dotted line) and measured (solid line) platform motion in direction of the x-,y-and z-axis.

−4−2

02

Torq

ue[N

m]

0 5 10 15 20 25 30

−4−2

02

Simulation time [s]

Torq

ue[N

m]

0 5 10 15 20 25 30

Simulation time [s]

Figure 11: Comparison of the simulated (dotted line) and measured (solid line) torque of four individual servo motorswith respect to time.

[5] Fischer, R. (2003). Elektrische Maschinen, Springer-Verlag.

[6] Gosselin, C. (2008). On the determination of theforce distribution in overconstrained cable-drivenparallel mechanisms. Proceedings of the SecondInternational Workshop on Fundamental Issues andFuture Research Directions for Parallel Mechanismsand Manipulators, pages 9–17, Montpellier, France.

[7] Gouttefarde, M., Merlet, J.-P., and Daney, D. (2007).Wrench-feasible workspace of parallel cable-drivenmechanisms. IEEE International Conference onRobotics and Automation, pages 1492–1497, Roma,Italy.

[8] Heyden, T. (2006). Bahnregelung eines seilgeführtenHandhabungssystems mit kinematisch unbestimmterLastführung. Fortschritt-Berichte VDI, Reihe 8,Nr. 1100. VDI Verlag, Düsseldorf.

[9] Hiller, M., Fang, S., Mielczarek, S., Verhoeven, R.,and Franitza, D. (2005). Design, analysis and real-ization of tendon-based parallel manipulators. Mech-anism and Machine Theory, 40(4):429–445.

[10] Maier, T. (2004). Bahnsteuerung eines seilge-führten Handhabungssystems. Fortschritt-BerichteVDI, Reihe 8, Nr. 1047. VDI Verlag, Düsseldorf.

[11] Merlet, J.-P. and Daney, D. (2007). A new design forwire-driven parallel robot. 2nd Int. Congress, Designand Modelling of mechanical systems.

[12] Pott, A., Meyer, C., Verl, A. (2010). Large-ScaleAssembly of solar power plants with parallel cablerobots Proceedings of ISR/Robotik 2010, Munich,Germany.

[13] Schielen, W. (1986). Technische Dynamik. B. G.Teubner, Stuttgart.

[14] Verhoeven, R. (2004). Analysis of the Workspace ofTendon-based Stewart Platforms. PhD thesis, Uni-versity of Duisburg-Essen.

[15] Zi, B., Duan, B., Du, J., and Bao, H. (2008). Dynamicmodeling and active control of a cable-suspendedparallel robot. Mechatronics, 18(1):1 – 12.

View publication statsView publication stats