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    Proceedings of the ISRM 2009, 1. IFToMM International Symposium on Robotics and Mechatronics, September 21-23, 2009, Hanoi, Vietnam

    Simulators and Demonstrators - Efficient Tools in the

    Development Process of Mechatronic Systems

    Manfred Hiller, Thorsten Brandt, Tobias Bruckmann, Wildan LaloUniversity of Duisburg-Essen, Faculty of Engineering, Chair of Mechatronics

    Lotharstr. 1, D-47057 Duisburg, Germany

    I. Introduction

    The design process of robotic systems, andeven more general - of mechatronic systems - ischaracterized by a combination of various disci-plines. These disciplines include mechanical en-gineering, electrical and electronic engineering,computer science, as well as, information tech-nology, and others, depending on the particulartechnical realization. This means, that mecha-tronics is mainly driven by its technical appli-cations, and, therefore, from this point of view,robotic systems represent a major field of appli-cation within the world of mechatronics. Thesame is even truer for automotive systems, sincetoday in the automotive industry, the multidisci-plinary mechatronic approach is regarded to beone of the megatrends in the development pro-cess of automotive systems and components.

    Looking back at the long history of the deve-lopment of automotive systems, the last decadesresemble a technical revolution: passive andactive safety systems such as airbags or beltpretensioners, aiming at crashworthiness, aremeanwhile in serial production. Beyond that,driver assistance systems, directly supportingthe driver in order to avoid critical situations,more and more find their way into modern vehi-cles. This trend mainly originates from the rapiddevelopment of electronic devices such as elec-tronic control units (ECU), sensors, and actua-tors including the necessary software. In par-allel to various developments in the automotivesector, also the field of modern robotics is per-manently profiting from a rapid progress in elec-tronics, microtechnology, and in particular sen-sor technology.

    This contribution, which represents also anoverview over the research of the last twodecades at the Chair of Mechatronics at theUniversity of Duisburg-Essen, exemplifies sev-eral common aspects in the design process ofdifferent kinds of robotic systems, like large-scale redundant manipulators, mobile robots or

    tendon-based parallel structures. Some of them

    - like the concrete pump with its demonstratoras an example for a large-scale manipulator orthe wire-driven manipulator SEGESTA - are pre-sented in this paper in more detail than others.

    II. The Mechatronic Design Process and its

    Modifications

    Within the last decades, mechatronic sys-tems became part of many engineering products.

    Therefore, numerous design examples of suchsystems are meanwhile available. The accord-ing experience of engineers with the design ofmechatronic systems was systematically sum-marized in a reference process, which is for ex-ample documented by the society of German en-gineers (Verein Deutscher Ingenieure - VDI) inthe development guideline VDI2206 [1].

    The so-called V-model, shown in Fig. 1, was

    originally used to describe the development ofpure software products and was extended tocover the development of mechatronic systems:First of all, the requirements for the producthave to be defined clearly before the engineers

    begin with the design of the mechatronic pro-duct. When the overall design of the mecha-tronic product is defined, the domain specific de-sign phase starts. Therein mechanical, electricaland software issues of the product are addressedindividually. The last phase, called system inte-gration, is visualized by the right branch of the

    V-model. In this phase, the product design is va-lidated against its requirements. This validationprocess is repeated iteratively until the degree ofmaturity of the design is high enough to releasethe product. However, for particular classes ofmechatronic systems, the development processsuffers from the fact that the predefined require-ments of the mechatronic product can only be

    validated very lately by use of cost intensive pro-totypes. Examples for such systems are verycost expensive machines such as constructionmachines and systems, which contain the hu-man in the control loop.

    This paper shows different approaches how to

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    Syste

    mDesign

    Syste

    mInte

    gratio

    n

    Domain specific Design

    Modelling and Modell Analysis

    Mechanical Engineering

    Electrical Engineering

    Information Engineering

    Validation of Characteristics

    Requirements Product

    Prototype

    ScaledPrototype

    Simulator

    Fig. 1: Modified mechatronic design process.

    deal with this kind of systems. For very largescale - and therefore cost intensive - systemsdownscaled mechatronic demonstrators (scaledprototypes) are proposed while for the develop-ment of human-centered mechatronic systemssimulators seem to provide an appropriate tool.

    The modification of the development processis also visualized in Fig. 1. For most mecha-tronic products prototypes are used to validatethe design. However, depending on the particu-lar product also scaled prototypes or simulatorscan be used. The decision for one of the threedepends on the type of mechatronic systems andits degree of maturity. Hence, it is also possibleto use combinations of simulators, scaled pro-totypes and prototypes in different design itera-tions. For example the human machine interfacecan be designed very early by use of a simulator,

    while other details of the mechatronic systemscan be validated by use of mechatronic proto-types.

    All approaches, including scaled demonstra-tors and simulators, are widely applied in sev-eral research projects at the Chair of Mecha-tronics at the University of Duisburg-Essen.Most of these projects focus on robotic or au-tomotive applications. Here it is challengingthat both fields develop in opposing directions.In the past, ground vehicles were exclusivelyhuman controlled, while nowadays driver anddriver assistance systems guide the individual

    vehicle more and more commonly; meanwhile

    first research vehicles even drive completely au-tonomously. The development of modern roboticsystems started at the other end of the spectrum.First assembly robots for example were onceprogrammed and then operated for a long time

    without further human interference. Nowadays,

    first assembly robots share their workspace withhuman co-workers. If the human worker ap-proaches the end-effector, the robot reduces its

    working speed. This is one example where the workspace of the robot has to be monitored ina similar fashion by the robot control system asthe traffic space of a road vehicle has to be ob-served by a driver assistance system.

    As both fields approach each other accord-ing to the degree of human machine interaction,there is a high potential to transfer methods fromone field of research to the other. This transferis an additional benefit on top of the applicationof common mechatronic design methods in thedevelopment of automotive, as well as, in the de-

    velopment of robotic systems.

    In this paper several examples of highly com-plex mechatronic systems are given. One exam-ple is the large quadruped walking machine AL-DURO shown in Fig. 2(a). For security reasons itis very difficult to test new walking patterns withthe full scale prototype, which has a weight ofabout 1.6 tons. Therefore, higher control func-tions are mainly tested on the scaled prototype

    ADONIS. As this prototype focuses on control

    functions, the actuation type could be changed

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    3.5m

    0.5m

    60m 1.5m

    Fig. 2: Prototype and scaled mechatronic prototype of (a) a walking machine and (b) a concrete pump.

    from hydraulic to electric actors. Another exam-ple, which is discussed in this paper is the devel-opment of a new control strategy for a large scaleconcrete pump shown in Fig. 2(b). The new in-

    teraction strategy is developed and tested basedon a simulator and on the scaled mercatronics-Demonstrator, which is shown on the right handside in Fig. 2(b). The final functionality of thesystem is studied in field tests with a full scaleconcrete pump. This example, presented later inmore detail shows how the different validationconcepts of simulator, demonstrator and proto-type nicely fit into the overall development pro-cess of complex mechatronic systems. All of thegiven examples are the result of a mechatronicdesign process accompanied by a sophisticated

    tool chain, which leads from algorithm design upto the implementation on real-time hardware.

    III. Methodologies

    A. Mechatronic Design and Rapid Mechatronic

    Prototyping

    As already shown in the previous section,mechatronic systems typically are characterized

    by a high degree of complexity due to the strongcrosscoupling of the involved different engineer-ing disciplines. This complexity originates fromthe large number of couplings on various levels

    of the contributing elements and components,

    coming from different disciplines. The difficultyfor the design engineer in his daily work is, thatthese couplings have to be considered in an earlyphase of the design process. In this contribution,

    only mechatronic real-time systems and multi-body dynamics will be regarded in more detail.

    B. Development of Mechatronic Real-Time Sys-tems

    The term real-time is often used to describethe capability of a program to run fast in inter-active speed, i.e. synchronous to the real time onaverage. In a technical sense it is not enough tohave a fast program additionally it has to ful-fill defined requirements depending on the def-

    inition of real-time. To compose a real-timesystem, besides the program also the underly-ing hard- and software needs to be real-time ca-pable. A popular definition for a real-time sys-tem was given by Donald Gillies: A real-timesystem is one in which the correctness of thecomputations not only depends upon the logi-cal correctness of the computation but also uponthe time at which the result is produced. If thetiming constraints of the system are not met,system failure is said to have occurred. POSIXStandard 1003.1 defines real-time for oper-ating systems as: Realtime in operating sys-

    tems: the ability of the operating system to pro-

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    vide a required level of service in a bounded re-sponse time. Another approach separates be-tween soft and hard real-time systems. Here,hard real-time means the type of real-time sys-

    tem in the sense used above, while soft real-timeapplies for systems which have reduced con-straints on lateness but still must operate veryquickly. Generally, a delay in a hard real-timesystem causes damage immediately while in softreal-time applications the damage accumulates

    with the delay. Note, that real-time says nothingabout computational power or speed as long asdata processing can always be done within thegiven time (this may be up to some seconds, min-utes or even more), hard real-time requirementsare fulfilled. In this paper, real-time systemsare used to control mechanical systems. Sincegenerally precise and fast motion is demanded,there are hard real-time requirements, especially

    with respect to reliability and safety considera-tions.

    B.1 The Mechatronic Tool Chain

    Usually, the modeling of a mechatronic sys-tem starts with deriving a mathematical descrip-tion. Generally, the resulting formulas can be

    very complicated and thus, their hand-tailoredmanipulation may result in errors. Therefore,Computer Algebra Systems (CAS) should be pre-

    ferred. Additionally, they offer automatic codegeneration for popular programming languageslike MATLAB R, C, or Fortran. This allows to portthe mathematical model directly to the develop-ment environment to design and test the con-troller algorithms during the simulation stage.Referring to VDI2206 (Fig. 1 of the previous sec-tion), offline simulation merges into HIL simula-tion and finally prototype integration and test-ing. Here, the availability of an integrated toolchain requires the availability of real-time sys-tems. Usually, first control programs are tested

    within simulation. Later on, rapid prototyp-ing realtime systems allow the comfortable test-ing of the implemented algorithms which are fi-nally migrated to target hardware like automo-tive ECUs or industrial robot control systems(which are again real-time systems). There is a

    wide variety of real-time operating systems avail-able on the market. Many of them are optimizedfor highest real-time performance (dSPACE, Vx-

    Works, LynxOS, QNX, . . . ), but for these de-mands, normally hand-tailored written code isnecessary. Nevertheless, automatic code gen-eration by graphical development environments

    generates partially very efficient code compared

    to the hand-written code of a fair program-mer. Since the mechatronic development pro-cess should focus modeling and control due totime and cost constraints, coding should not re-

    quire advanced programmers. The same ideaholds for the mechatronic student education.

    Thus, high-level languages and graphical devel-opment are very popular within the mechatronictool chain.

    B.2 Real-Time Soft- and Hardware

    The very first digital real-time controllers weredesigned using microcontroller hardware. Mean-

    while, microcontrollers have become a both eco-nomic and flexible base for real-time control.

    They offer a respectable computation power, as

    well as a number of input/output (I/O) optionslike digital, analog, serial and bus communi-cation. Many of them can be programmed inC/C++ or even by graphical environments likeMATLAB/Simulink R or LabVIEW. On the otherhand, in the meantime PCs are very popular asthe hardware base for real-time systems due totheir low costs and their wide availability. PCsalways need an operating system to run userprograms. The first operating systems (e.g. DOS)

    were designed for only one user and one ap-plication running at the same time. Thus, thetime behavior was deterministic for a spe-

    cific system and program, one could tell howlong the run of an algorithm would take. Inthe meantime, operating systems have becomemuch more powerful in terms of usability andcomfort for the price of a high system load.Popular operating systems like MS-Windows orLinux focus on graphical user interfaces, mul-timedia and entertainment. Multi-User operat-ing systems can interact with many users at thesame time while multi-tasking makes it possi-

    ble to run several programs at the same time.Therefore, the programs have to share the pro-

    cessor time. This is done by so-called sched-ulers. Simple schedulers use time slices to runthe programs in turn. Priorities can make pro-grams run preferred to others. Since one cannot predict the number and priority of runningprocesses and other users, the prediction of thecomputation time for a program within such asystem is nearly impossible. Thus, standard op-erating systems like MS Windows XP/Vista orLinux cannot be used for hard real-time pur-poses. Nevertheless, it is possible to modifythese operating systems - mainly by specifyingthe scheduler and introducing additional soft-

    ware layers between hardware and the original

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    operating system. Popular real-time Linux ex-tensions like RT-Linux or RTAI follow this con-cept. Just like Linux itself, these extensions arepartly released under the GPL, i.e. they are us-

    able at no fee. Additionally, in the meantime,popular commercial real-time operating systemslike xPC are basing on PC technology. These al-low besides traditional implementation in lan-guages like C or Fortran a comfortable im-plementation of the control system in graphicaldevelopment environments. Besides graphicalimplementation, also graphical user interfaces(GUI) are a comfortable and intuitively usablechoice to control and supervise a mechatroniccontrol system.

    C. Multibody Dynamics

    Multibody systems with a complex topologicalstructure, i.e. with a strong coupling betweenthe individual bodies via joints are characterized

    by the occurrence of a large number of closedkinematical loops. Thus, those systems havea large number of joint coordinates, many con-straints, but typically only few degrees of free-dom (d.o.f.). Examples are machines, robots,manipulation systems, walking machines, andall kinds of vehicles. It has been shown in the

    past, that the key for a compact formulationof the equations of motion is given by an ef-ficient derivation of the kinematic equations ofthe system. This geometry-based approach pro-

    vides also a large potential for minimizing thecomputational amount and permits the directinterpretability of the numerical results, due tothe geometrical/physical character of the chosenparameters. Furthermore, it facilitates the cou-pling of the mechanical (multibody) subsystems

    with other subsystems in the overall mecha-tronic system.

    A meanwhile successfully applied approach isbased on three concepts: the characteristic pairof joints and the concept of kinematical trans-former together with block diagrams for an effi-cient and, if possible, recursive analysis of kine-matical loops; and in addition the concept ofkinematical differentials for an efficient evalua-tion of the partial derivatives, i.e. Jacobians andsecond derivatives [2], [3], [4], [5]. Based ondAlemberts Principle, the equations of motion inminimum coordinates q may be written as:

    M(q)q + b(q, q) = Q(q, q) (1)

    with the notations and dimensions:

    n : number of degrees of freedoms (d.o.f.),q : (n 1)-vector of generalized coordinates,

    M : (n n)-mass matrix,b : (n 1)-vector of generalized centrifugaland gyroscopic forces,

    Q : (n 1)-vector of generalized applied forces.

    With help of the method of kinematical differen-tials developed by Kecskemethy, the elements ofthe equations of motion can be calculated using

    the pseudo velocities r(j)i ,

    (j)i and the pseudo ac-

    celerations ri, i [4]. The elements gets the form

    Mj,k =

    nB

    i=1 mir

    (j)i

    r(k)i +

    (j)i Si

    (k)i ,(2)

    bj =

    nBi=1

    mir

    (j)i

    ri+

    (j)i

    Si i + i Sii

    , (3)

    Qj =

    nBi=1

    r(j)i fS

    ei +

    (j)i S

    ei

    . (4)

    The vectors, which are bookmarked with thesymbol , are called pseudo velocities andpseudo accelerations, respectively. They result

    from the analysis of the global kinematics withthe pseudo input velocities

    q(j)i =

    1 for i = j0 for i = j

    , i, j = 1, . . . , n , (5)

    and are defined by

    r(j)i = ri

    q = q(j) = riqj ,

    ri = ri

    q =

    q = 0=

    fj=1

    fk=1

    2ri

    qjqkqj qk ,

    (j)i = i

    q = q(j) = iqj ,

    i = i

    q = q = 0 =f

    j=1

    fk=1

    2i

    qjqkqj qk .

    (6)

    IV. Applications

    In the following sections, different examplesof mechatronic systems studied at the Chair of

    Mechatronics are given. Therein, methods such

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    as Multibody Systems Dynamics build the nec-essary basis for the creation of model-based con-trol algorithms and assistance systems. In par-ticular, the methods explained above are ap-

    plied to a full scale concrete pump and its down-scaled demonstator. Furthermore, the develop-ment of an assistance system for a drilling boomin coal mining is shown. Besides that, the ap-plication of scaled demonstrators is illustratedin the development of control algorithms for thelarge scale walking machine ALDURO and itsdown-scaled demonstrator ADONIS, but this ex-ample will only be briefly discussed. The sectioncloses with the scalable wire robot SEGESTA.

    A. A Large-Scale Redundant Manipulator and its

    Demonstrator

    A.1 Automation in Construction Machines

    While mechatronic developments were driven very early and intensively in automotive,aerospace and automated production applica-tions, other industrial branches remained nearlyuntouched by this upcoming discipline. Thereasons were multifaceted, but the developmentcosts per piece (due to the smaller lots), robust-ness problems and safety aspects may have beenreasons that mechatronic solutions were not in-tegrated at this early stage. An example of these

    branches where mechatronics did not succeedat that time is the construction machines in-dustry (cranes, excavators, mining etc.). Sincethe Chair of Mechatronics in Duisburg is lo-cated in the Ruhr area, where many produc-ing companies are settled especially for heavyindustries, transport of goods and coal mining

    there was always a close contact to the re-gional companies [6], [7], [8]. While the veryfirst steps were quite difficult, due to the men-tioned problems, the rapid develoment in themechatronic field and the rising competition onthe market also driven by global competitors

    led to more attendance towards the potentialof mechatronic methods and the integration ofavailable mechatronic components also in thisspecial field. Thus, projects like the automationof concrete pumps (Fig. 3) or drilling booms formining applications (Fig. 4) led to new challengesfor mechatronic methods and solutions.

    A.1.a Controllers, Sensors, Actuators, Bus Sys-tems. Mechatronic solutions generally re-quire sensors to measure physical quantities,a CPU to run controller programs, actuators totake influence onto a system or process and fi-

    nally, a communication system to exchange in-

    formation between the devices. To integratethe advantages of mechatronic functionalitiesinto the product and, in the meantime, alsoto save costs these devices have been devel-

    oped rapidly mainly by the automotive indus-try. Therefore, cheap and robust mechatroniccomponents are widely available on the mar-ket. This development made it also possible under both cost and safety considerations tointegrate mechatronic solutions into industriesproducing small batches especially into con-struction machines. Thus, embedded IndustialPCs (IPC) have become very popular as well assmart actuators and communication busses likethe Controller Area Network (CAN), which wasinitially developed by the automotive industry.

    A.1.b Cartesian Control. Just like other in-dustrial sectors, the market for construction andmining is driven by the need of cost reduc-tion. Here, one of the main factors is avail-ability, i.e. non-productive times due to main-tenance and repair must be short. On the otherhand, these machines are generally operated byhuman workers. This causes a considerablenumber of breakdowns due to misuse or hu-man weakness (lack of concentration, tiredness,mental state) and raises the demand for user as-sistance systems. One of the most important

    steps is to give the user an intuitive input de-vice at hand. Generally, the large and complexmechanisms used in construction machine de-sign lead to complicated, non-linear connections

    between actor and endeffector movements, re-quiring a trained expert for manual control ofthe machine. Here, cartesian control, which is

    well-established in industrial robotics, is a help-ful tool to assist human operators and to reduceinefficient usage or even misusage.

    A.2 Assistance Systems for a Large-Scale Kine-

    matically Redundant Concrete Pump

    The solution of inverse kinematics plays animportant role for the design of human-centredmechatronic systems such as kinematically re-dundant robots. In this section, an overviewof an operating concept of kinematically redun-dant robots is presented. It is based on the so-called affine manipulability, which describes aconfiguration-dependent measure based on theoperability of the robot. By formulating the in-

    verse kinematics as a linear program (LP) themaximization of the manipulability measure andthus of the operability is achieved. The ma-

    nipulability measure can then be communicated

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    Fig. 3: Concrete pump c by Schwing GmbH, Herne, Germany.

    Fig. 4: Drilling boom c by Deilmann-Haniel Mining Systems GmbH, Dortmund, Germany.

    to the operator haptically via a force-feedback joystick or visually by an appropriate human-machine-interface. Furthermore, technical lim-its such as end-stops and maximal joint veloc-ities can be considered explicitly by linear in-equalities. This section closes with an exampleof the LP inverse kinematics applied on the re-dundant 5-arm mercatronics-Manipulator anda discussion of the behaviour of the affine ma-nipulability in different situations.

    A.3 Inverse Kinematics

    A.3.a Affine Manipulability. In the followingthe idea of affine manipulability is explained,

    which is used in the formulation of the lin-ear programming program. For a kinemati-cally redundant manipulator according to Fig. 5the end-effector moves from w0 to a similar,i.e. affine pose (position/orientation) wfeasible ,

    which is possibly not the desired pose wdesired

    given by the operator. Therebyw Rm describes

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    w0

    wfeasible

    wdesired

    Fig. 5: Affine manipulability: the desired position and/or orientation wdesired is transformed to a similar(affine) position and/or orientation wfeasible which can be realised by the manipulator [9].

    the m-dimensional vector of position and/or ori-entation of the end-effector. The relationship be-tween wfeasible and wdesired is then defined by

    wfeasible w0 = p (wdesired w0) (7)

    where p is the affine manipulability or the ma-nipulability indicator. Thereby it is reasonableto limit p in the range of 0 p 1, in order toprevent the end-effector of moving in oppositeor beyond the desired direction. For this rea-son it is obvious that the desired pose, or the

    best approach to it, is reached if p = 1 and thuswfeasible = wdesired.

    A.3.b Formulating the Inverse Kinematics as aLinear Program. According to [10] the linearprogram LP which solves the inverse kinematicsof (redundant) manipulators can be formulatedas follows:

    maxqi+1

    ,,p{p} (8)

    subject to

    M + JTTCP 0JTCP 0 wi wi+1

    qi+1p

    =

    M qi + qref + fT

    JTCP qi

    (9)

    and the explicitely formulated constraints 0 p 1, +, qmin qi+1 qmaxand, if applicable, further (technical) constraintson velocity and acceleration level can be added.

    Thereby, q, q0 Rn describe the n-dimensional vector of the joint coordinates of the manipula-

    tor in the actual and previous time step. is

    the vector of Lagrange-multipliers which resultfrom the formulation of the Lagrange function[10]. M, Rnn are diagonal, positive definite

    weighting matrices. According to [11] the vec-tor f can be interpreted as artificial, generalizedforce. The weighting matrices M, and vector fare measures which can influence the null spacemotion of the manipulator such that for examplecollision avoidance with the help of potential the-ory can be applied [12]. qref, R

    n is a reference vector in joint space and can be, for instance,defined by the midpoint between the joint lim-its. Therefore, joint positions are favoured whichare preferably far away from the joint limits suchthat the manipulability is increased.

    In the following the linear program LP isapplied on the kinematically redundant 5-armmercatronics-Manipulator is introduced.

    A.4 Themercatronics-Manipulator: A Kinemati-

    cally Redundant, Down-Scaled Demonstrator

    In cooperation with a spin-off (mercatronicsGmbH [13]) of the Chair of Mechatronics in Duis-

    burg an electrically driven, six degree-of-freedommanipulator was constructed (Fig. 6). It is ascaled demonstrator with the structure of typicalmobile concrete pumps. At the same time of con-struction the computer-aided modeling and sim-ulation of this manipulator was realized, in orderto configure the sizes of the DC motors and tosupport model-based control design. The topo-logical structure of the manipulator is given inFig. 6(b). The manipulator consists of five arms,

    which are connected by revolute joints with hor-izontally, parallelly arranged rotation axes (arms1, 3, 4 and 5) and a prismatic joint (arm 2). Fur-

    thermore, there is a revolute joint in the base,

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    arm 1

    arm 2arm 3

    arm 4

    arm 5

    (a)

    (b)

    (c)(d)

    rigid body

    revolute joint

    prismatic joint

    socket

    Fig. 6: Development process from (a) real system (by courtesy of Schwing GmbH) via (b) topologicalstructure to (c) virtual scaled simulation and (d) scaled demonstrator.

    whose vertical axis allows a three dimensionalmotion of the robot. The manipulator has a max-imum range of about 1.5m.

    A.4.a Modelling the Kinematical TransmissionMechanism. Real concrete pumps are driven bylinear hydraulic actuators as they provide highefficiency and power density. For this reasoncomplex kinematical transmission mechanisms

    are required in order to transform the linear mo-tion to rotational motion. Fig. 7 shows a typ-ical kinematic transmission chain. In order tokeep the features of the translational-rotationaltransmission of the real system, it is necessaryto simulate this transmission behaviour on thescaled demonstrator as well. As the booms ofthe demonstrator are driven by DC-motors via

    worm gears (rotational-rotational transmission),a virtual simulation of the real transmission isrequired. The topology of the kinematical struc-ture of the linear-rotational transmission as de-picted in Fig. 7 is shown in Fig. 8. Note the

    two kinematical loops L1 and L2 which have to

    be calculated in order to determine the nonlin-ear transmission between (angle between twoneighbouring arms) and s (cylinder stroke). Thesolvability of this special mechanism depends onthe choice of the input coordinate. This can beclarified with the help of so-called kinematicaltransformers [15]. As can be seen in Fig. 9, us-ing as input and s = s() as output coordinate,such that

    s = s() (10)

    the mechanism can be solved analytically, i.e.without the use of numerical approximation pro-cedures such as the Newton-Raphson method.

    The block diagram actually explains how to solvethe mechanism: first, solve loop L1 (numberof degrees of freedom fL1 = 1) with input tocalculate the joint coordinates 1, 2 and 3,then solve loop L2 (number of degrees of freedomfL2 = 1) with inputs 1 and 2 to determine 4,5 and s, whereby solving each loop separately is

    done with the characteristic pair of joints geo-

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    leverhydraulic cylinder

    booms

    couple

    Fig. 7: Typical structure of linear-rotational kinematic transmission chain (Stephensons mechanism)[14].

    L1

    L2

    1

    2

    3

    4

    5

    s

    boom i

    boom i + 1

    cylinder

    couple

    lever

    elementary joint

    virtual body

    rigid body

    closed kinematical loop

    Fig. 8: Topology of the kinematical structure of the linear-rotational kinematic transmission chain.

    L1 L2

    fL1 = 1 fL2 = 2

    1

    2

    3 4 5

    s

    Fig. 9: Kinematical transformers of the mechanism with as input coordinate.

    metrical methods [16]. On the other hand, hav-ing s as input and as output such that

    = (s) (11)

    it is necessary to choose an initial guess value of1 and then iterate with respect to 1 until

    |2,L2 2,L1 | , (12)

    where is sufficiently small (Fig. 10). Fig. 11exemplifies some transmission behaviours of the

    linkage mechanisms.

    A.4.b Inverse Kinematics of the mercatronics-Manipulator. In a first approach the descrip-tion of the end-effector pose is described in cylin-drical coordinates , r and z as can be seenin Fig. 12(a). Therefore, the rotation of the

    base about the vertical axis can be formulatedindependently from the inverse kinematics, suchthat the inverse kinematics can be reduced to aproblem of a planar manipulator in the rz-planeas depicted in Fig. 12(b).

    A.4.c Horizontal Pull-In of the End-Effector.

    The horizontal pull-in starts from the configura-

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    L1 L2

    fL1 = 1 fL2 = 2

    q = 1

    22

    3 4 5

    s

    Fig. 10: Kinematical transformers of the mechanism with s as input coordinate.

    Fig. 11: Typical nonlinear transmission behavior between stroke and angle.

    r

    r

    z

    z

    q1

    q2

    q3 q4

    q5

    Fig. 12: Description of the end-effector (a) in cylindrical coordinates , r and z and (b) projected intothe rz-plane.

    tion given in Fig. 13(a). In Fig. 13(b) the motionto the final configuration is shown. It can beseen that arm 2 reaches its joint limit, such that

    the motion of the end-effector cannot be contin-ued. This situation also signalizes the affine ma-nipulability in Fig. 14(a), which decreases from

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    Fig. 13: (a) Starting configuration and (b) final configuration of the horizontal pull-in.

    Fig. 14: (a) Affine manipulability, (b) joint position and velocity.

    one to zero. Accordingly the joint velocities alsotend to zero as depicted in Fig. 14(b).

    A.4.d Horizontal Pull-Out of the End-Effector. The initial configuration is given in Fig. 15(a),the motion to the final configuration is shownin Fig. 15(b). In Fig. 16(a) the development ofthe manipulability is depicted. It can be seenthat near the singular configuration the value ofthe manipulability decreases to zero and there-fore signalizes the end of the desired motion.

    B. The Large-Scale Walking Machine ALDURO

    and its Demonstrator ADONIS

    Walking robots as industrial applications area very recent development. Research on walk-ing robots, however, has been carried out for thelast five decades, but few have left the labora-tories. Some of the reasons are insufficient re-liability, high costs and hesitant markets. Thefirst sectors to invest in walking robots were themilitary, along with the nuclear and space in-dustries. They all have to address the problemof locomotion in unstructured terrains hostile toman. The most evident advantage of legged ma-

    chines against wheel driven vehicles is their abil-

    ity to move in unstructured terrain. Possible ar-eas of application for legged working platformstherefore are outdoor tasks such as forestry orconstruction in mountainous terrain. Smallerrobots can be used for inspection of inaccessi-

    ble, hazardous or contaminated areas. Whilethe focus of interest in the past was more onthe side of six-legged systems, today four-leggedand also biped robots are under development.

    As an example, the design and realization of thelarge-scale four-legged walking machine ALDUROis an ongoing project at the Chair of Mechatron-

    ics at the University of Duisburg-Essen sincemore than 10 years [17], [18], [19], [20]. Dueto its size and the herewith associated techni-cal problems, meanwhile the down-scaled andsimplified smaller system ADONIS has been built,and is mainly used for testing purposes, like con-trol and walking strategies as shown by Heckhoffand Kara (Fig. 2) [21], [22].

    C. SEGESTA - A Prototype of a Parallel Wire Robot

    Compared to serial manipulators, parallelkinematic structures offer advantages in terms

    of force-to-weight ratio and positioning accuracy.

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    Fig. 15: (a) Initial configuration and (b) final configuration.

    Fig. 16: (a) affine manipulability, (b) joint position and velocity.

    Since all actuators are placed on the base ofthe manipulator, they do not need to support ordrive the mass of the other actuators. Therefore,

    by using light-weight manipulators with smallactuators, realized as parallel kinematic struc-tures, one is able to generate high-dynamic mo-tion. While in the classical concept of Stewartplatforms the linear actuators are spindles or hy-draulic/pneumatic cylinders, one is able to gen-erate even higher accelerations by replacing the

    spindles or cylinders by wires which are actu-ated by electric motors on the base of the manip-ulator. The system is called a tendon-based par-allel manipulator or wire robot. Since wires cantransmit only tension, kinematically they have to

    be regarded as unilateral constraints. Due to thecomplexity of its mechanical properties, together

    with the high requirements regarding actuation,sensing, and control, this is a typical example ofa mechatronic system.

    C.1 Kinematics

    For wire robots, different classifications basedon the difference between the number of wiresm and the number d.o.f. n have been proposedin the past. This difference is called the redun-dancy r = m n (see [23], [24] [25] and [26]).

    C.1.a Inverse Kinematics. Inverse kinemat-ics denotes the problem of calculating the joint

    variables for a given end-effector pose. For wirerobots, the joint variables are the lengths of the

    wires, comparable to the strokes of linear ac-tuators. Therefore, the kinematical descriptionof a wire robot is comparable to the kinematicstructure of a Stewart-Gough platform, presum-ing the wires are always tensed and can thus betreated as line segments representing bilateralconstraints. Modeling a wire robot as a platform,

    which is connected to m points on the base by m bilateral constraints, it is reasonable to denotethe platform pose x =

    BrT

    and the

    base points Bbi, i = 1 i m, referenced in the

    inertial frame 6-B . Also the platform connection

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    bi

    li r

    p

    6-P

    6-B

    Fig. 17: Kinematics of a wire robot.

    points pi are referenced in the platform-fixed co-

    ordinate frame 6-P . The orientation of the plat-form in the base frame is represented by the ro-tation matrix BRP. Note that throughout thischapter roll-pitch-yaw angles are used. Assum-

    ing the wires are led by point-shaped guidances(e.g. small ceramic eyes) from the winches to theplatform, the base vectors Bbi are constant. Thesimple vector chain shown in Fig. 17 delivers

    Bli =Bbi

    Br BRPPpi

    Bpi

    , 1 i m (13)

    immediately. Hence, the length of the ith wirecan be calculated by

    li = Bbi Bpi2 , 1 i m (14).

    C.2 Dynamics

    According to Fig. 18 a wire robot can be mod-elled as a multibody system with m unilateralconstraints (see section III-C). In contrast to thegenerally complicated forward kinematics [27]the dynamical equations of motion are compa-rably easy to formulate with respect to the base

    frame 6-B . The wrench wwire of the wires acting

    on the platform can be written as (see 19)

    wwire =

    fwire wireT

    =

    mi=1

    fi

    mi=1

    pi fi

    T.

    (15)

    Since the forces act along the wires

    fi = fi li

    li2= fi i, (1 i m) (16)

    holds. It follows

    wwire =

    1 . . . m

    p1 1 pm m

    f1...

    fm

    f = ATf

    (17)

    The Newton-Euler equations lead to

    mpr = fE + fwire (18)

    I +

    (I

    ) = wire + E , (19)

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    with

    Mp : mass matrix of platform,

    E : identity matrix,

    gC Rn1 : Cartesian space vector of Coriolis

    and centrifugal forcesand torques,

    gE Rn1 : vector of the generalized applied

    forces and torques, not includingthe resultants of wire tensions.

    Taking wire force limits fmin and fmax (see [27])into account, it follows

    ATf + w = 0 with (21)

    fmin f fmax (22)

    C.3 Wire Force Calculation

    In section IV-C.2 a description of the forceequilibrium was presented. Here methods forthe calculation of a feasible force distribution f,i.e. a force distribution f which satisfies eqn. 21and the constraints in eqn. 22 are presented.Details can be found in [27], [28]. Obviouslyeqn. 21 represents an underdetermined sys-tem of linear equations. Its solution space isr-dimensional. Hence isolating the force distri-

    bution f leads to

    f = A+Tw + H , (23)

    where A+T denotes the Moore-Penrose Pseudo-Inverse of AT. Note that H is the nullspace orkernel of AT defined as

    H :=

    h1 . . . hr

    , (24)

    where

    AThi = 0, 1 i r. (25)

    In other words, a linear combination of the

    columns of H describes force distributions cre-ating an inner tension in the system without ap-plying wrenches wwire onto the end effector. Incase of an homogenious problem, i.e. w = 0, itdescribes the possible solutions of eqn. 21 for f.

    Additionally eqn. 22 must be satisfied, i.e. theforce limits have to be considered. Thus plug-ging eqn. 23 into eqn. 22 leads to

    fmin + A+Tw H fmax + A

    +Tw. (26)

    Therefore the task of identifying a feasible forcedistribution is equivalent to the problem of iden-

    tifying R such that eqn. 26 holds. Thus,

    the boundaries of the wire forces form an m-dimensional hypercube C Rm. All force dis-tributions satisfying eqn. 23 obviously form anr-dimensional subspace S Rm spanned by

    the kernel of the structure matrix (see Fig. 20).Hence, if the intersection F of the hypercube Cand the subspace S is non-empty, feasible solu-tions f exist, i.e. F = C S = , where F is a r-dimensional manifold in the Rm. A more detailedintroduction is given in [29] and [30]. Notewor-thy, the r-dimensional solution space generallyallows to compute force distributions with differ-ent characteristics: While for fast motion, small-est possible forces are demanded, for applica-tions requiring a high stiffness, high forces areadvantageous [31], [25].

    C.4 Nonlinear Optimization

    In [24] it is proven that the optimization a costfunction using a p-norm (1 < p < ) leads toguaranteed continuous wire forces along a con-tinuous trajectory. The required formulation ofthe optimization problem is as follows:

    minimize fp =p

    m=1

    fp

    subject to fmin f fmin ATf + w = 0. (27)

    This approaches requires the usage of an opti-mizer to calculate the results as shown in [32],[33], [24], [34], [35]. Standard optimizer imple-mentations as LAPACK or the NAG R library re-quire iterative computations, which may not beused within a realtime control system due totheir normally non-predictable worst-case run-time.

    C.5 Barycentric Force Calculation

    In this section, a non-iterative algorithm isshown, which provides continuous force distri-

    butions furthermost from the force limits. Thealgorithm provides a force distribution, whichlies in the center of gravity (COG or barycenter) ofthe intersection manifold F. The structure ma-trix AT has the dimension n m. Hence, withinthe workspace, the kernel can be computed asH = (h1 . . . hr) Rmr. Here, the kernel isused to define a map from the Rr to S R,i.e. for all , eqn. 26 must hold, where isthe (convex) polyhedron-shaped preimage of themanifold F under the mapping : R R, A+Tw + H . In other words, since mapsthe Rr onto the solution subspace S, it maps the

    polyhedron Rr onto the solution manifold

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    S

    C

    Fig. 20: The subset S intersecting the hypercube C in the case of n = 1 and m = 3.

    R2

    R2

    S

    S

    F

    H

    Fig. 21: Visualisation of the map H in the case of m = 3 and n = 1.

    F. Since there is no explicit expression for ,a convenient representation is sought. As men-tioned above is a polyhedron. Thus, its ver-

    tices determine completely. Component-wise

    evaluation of both sides of eqn. 26 gives 2m hy-perplanes in R. The vertices of are intersectionpoints of r hyperplanes. Hence, all those inter-

    section points are calculated and examined with

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    respect to their compatibility with all inequali-ties. Obviously a vertex of the polyhedron hasto satisfy all inequalities of eqn. 26. In orderto compute the center of gravity of the obtained

    polyhedron, is triangulated, i.e. splitted into r-simplexes. In the case of r = 2 this just meansdividing into triangles. Advanced techniques asshown in [36] are required in the case of higherdimensions. Triangulation delivers a list of nssimplexes Pk with each having r + 1 vertices vkj

    with k = 1 . . . ns and j = 1 . . . r +1. The volumes Vkof the simplexes can be determined by integra-tion [37]. Furthermore their COG sk are com-puted by the equation

    sk,i =

    r+1

    =1vk ,i

    r + 1 , 1 i r, 1 k ns (28)

    which is used to calculate the COG s of thepolyhedron via

    is =

    ns=1

    (s,i V)

    ns=1

    V

    . (29)

    Finally, the solution is transformed back usingthe mapping

    fs = A+Tw + H s (30)

    where fs is the center of gravity of the manifoldF.

    Fig. 22(a) and 22(b) show the difference in thegenerated force distributions: While both meth-ods generate valid force distributions betweenthe force limits, the average force tension levelsare very different.

    C.6 Realtime Control Concept and Code Genera-

    tion

    The proposed algorithms in sections IV-C.4

    and IV-C.5 were implemented using a dSPACEDS1005 (PowerPC 450 Mhz) realtime system. This system is very beneficial for rapid proto-typing of control systems. The developmentstrictly followed the mechatronics developmentguidelines presented in [1] (see Fig. 1). First,the required algorithms were programmed in thenumerical software package MATLAB/Simulink R

    for first performance tests and debugging pur-poses. The implementation was done in the MAT-LAB R M-Language. In this step, the verifica-tion of the computed force distributions was per-formed and the robustness of the algorithms was

    proved.

    Second, using the M-Language[38], the codeswere transferred into the control scheme imple-mented as a Simulink model. This was done

    via Embedded MATLAB blocks, using the same

    implementation. At this stage, a simulation ofthe overall system was possible, allowing for vir-tual prototypes and visualizations. Also appli-cation concepts can be evaluated based on thissimulation model. As an example, the usageof a wire robot as a wind tunnel suspensionsystem for ship hulls was studied, see Fig. 23.Finally, the Simulink model was compiled forthe dSPACE realtime system using the RealtimeWorkshop[39]. Using this toolchain, the samecode base is always reused, avoiding implemen-tation errors and redundant work. Noteworthy,the control scheme implemented for rapid pro-totyping can also be used to generate the codefor industrial realtime targets such as micro-controllers or industrial PCs (IPC) running real-time operating systems. A number of automa-tion manufacturers (e.g. Beckhoff TwinCATR orB&R Automation Studio R) announced or alreadyprovide the required interfaces for simulationenvironments like MATLAB/Simulink R to sup-port the automatic code generation. Since theseindustrial targets are embedded into the widerange of industrial control components like sen-sors, smart actuators and field busses, standard

    devices are easily adressable and controllable.

    V. Conclusions and Outlook

    In this paper, an overview over the researchin the field of robotic applications in mechatron-ics of the last 20 years at the Chair of Mecha-tronics at the University of Duisburg-Essen has

    been given. It was the aim of this paper to show,that there is a close connection between researchfields like multibody system dynamics or real-time and HIL-systems, on the one hand side,and mechatronic systems on the other. Mechan-

    ical, and in particular dynamical aspects playan important role in many systems, named to-day mechatronic systems. Since robotic, as wellas, automotive systems, per se represent typi-cal classes of mechatronic systems, it is not byaccident, that those systems have been in thefocus of interest at the Chair of Mechatronicsat the University of Duisburg-Essen over morethan two decades, where in the case of roboticsystems our emphasis has been mainly on non-classical robots, as demonstrated in this contri-

    bution by the technical examples. Of great im-portance is also the fact, that from a method-

    ological point of view, methods which have been

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    0 87.50

    Force[N]

    100

    200

    400

    600

    800

    12.5 25 37.5 50 62.5 75

    22(a) Barycentric Approach

    0 87.50

    Force[N]

    100

    100

    200

    300

    400

    500

    12.5 25 37.5 50 62.5 75

    22(b) Optimizer Approach

    Fig. 22: Force Distributions along example trajectory using different force calculation algorithms.

    Fig. 23: Wire Robot as a Wind Tunnel Suspension System.

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    mainly developed e.g. for the investigation ofautomotive systems could also be applied, af-ter some adaptations, to robotic systems, and

    vice versa. This is also true for the idea, to

    avoid expensive experiments, done e.g. with realsize automobiles or large-scale mobile robots like

    Alduro, by replacing those vehicles or robots by down-scaled systems, like Adonis, whose -much cheaper - experimental results could also

    be used for the verification and validation forthe real size system. In addition, we tried toshow, that due to the strong coupling betweenthe multibody part and the other involved dis-ciplines in the particular mechatronic system,and which has to be considered already from the

    very beginning of the mechatronic design pro-cess, difficulties may arise from the question,how this overall approach could be further im-proved and optimised. This is actually part of the

    work and research, done at the Chair of Mecha-tronics in Duisburg-Essen.

    VI. Acknowledgements

    The research presented here has been - andstill is - funded by the National German Re-search Council DFG (Deutsche Forschungsge-meinschaft), and in parallel also by further pub-lic institutions. A major part of the financial sup-port is permanently coming from German com-

    panies in the field of mechanical engineering andautomotive industry.

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