PARAMETRIC MULTIBODY MODELING OF … · Stefano Baglioni University of Perugia Dep. of Industrial...

1 Copyright © 2013 by ASME

Proceedings of the ASME 2013 International Mechanical Engineering Congress & Exposition IMECE2013

November 13-21, 2013, San Diego, California, USA

IMECE201364815

PARAMETRIC MULTIBODY MODELING OF ANTROPOMORPHIC ROBOT TO PREDICT JOINT COMPLIANCE INFLUENCE ON END EFFECTOR POSITIONING

Stefano Baglioni University of Perugia

Dep. of Industrial Engineering Via G. Duranti 1

06125 Perugia, Italy

Filippo Cianetti University of Perugia



Claudio Braccesi University of Perugia



Luca Landi University of Perugia



ABSTRACT Nowadays, in the field of robotic, one of the most important

objectives is to reduce robot error positioning and improve its

dynamic behaviour. One of the main source of error in end

effector positioning is due to the joint compliance: robot joint

components under operating conditions can be deformed as a

function of their stiffness/damping properties. Generally, for

industrial robots, harmonic drive gearings are used, their

principal characteristics are high transmission ratio and law

weight, on the other hand, to realize high transmission ratio,

harmonic drive gearings work on inner gear elastic

deformation, conferring to the robot joints an excessive

compliance that, in some robot applications, cannot be

neglected. In this research activity multibody modelling and

simulation approach has been used to analyse joint compliance

influence on robot position accuracy. The principal aim of this

work was the formulation of a modelling procedure that

starting from classical robots modelling approach (i.e. Denavit

Hartenberg) defines an universal database and a parametric

modelling procedure that allows the designer to use any

multibody commercial codes to analyse anthropomorphic

robots considering or not the compliance effect. All the

procedure was developed and managed into a numerical code

environment (Matlab/Simulink).

An example of commercial anthropomorphic robot was

considered by assuming its principal kinematic and dynamic

characteristics. Parametric models of the robot have been

developed in two different multibody modelling environments

(Simmechanics, Adams/View). Moreover the models structure

has been built in order to control the robot movements both in

motion (open loop) or in force (closed loop). In this case they

are interfaced with Simulink code in a so called co-simulation

approach that allows to developed a generic control system

and test it by using one or more models, less or more refined.

1. INTRODUCTION The objective of this study is the development of a procedure

able to carry out dynamic analysis for generic industrial

anthropomorphic robot manipulators in order to reduce end

effector error positioning and improve robot dynamic

behavior.

The mean by it has been realized is the multibody approach

which represents a very flexible and direct way to analyse

dynamic systems.

To reach this aim, the authors built a fully parametric robot

modeling procedure which, starting from the robot

characteristic properties evaluation, allows an easy multibody

modeling that, if opportunely expressed, can be used in any

multibody code available.

In detail, through a compiled procedure, an “universal”

database of all necessary parameters describing the robot has

been developed and made available for the multibody model

construction.

Thus, the first fundamental step of the developed procedure is

the robot geometry identification and representation in a

simulation environment. It has been done through a systematic

procedure of reference coordinates system definition,

according to the well known Denavit-Hartenberg convention,

subsequently reappraised by Veitschegger-Wu.

Another important step realized is the identification and

treatment of all technical information which defines the robot

dynamic behaviour. For example, in the subsequently analysed

test case these parameters have been identified both through

CAD 3D or by web catalogues examination.

http://en.wikipedia.org/wiki/Robot


Finally, once the robot multibody model has been generated

both kinematic and dynamic analysis can be carried out.

In addition, the developed procedure has been realized in order

to obtain more or less accurate robot representation. In this

way it is given to the user the possibility to focus the analysis

on determined components evaluating their properties or their

influence on the global robot dynamic behaviour.

A practical example is represented by the joint compliance

evaluation. Joints compliance influence on end effector error

positioning has been evaluated through dynamic analysis

comparison between a model made up of flexible joint and

another of rigid joint.

Furthermore, to test the control system behaviour, another

kind of analysis has been made available: the so called co-

simulation. Since Simulink is a suitable software for control

systems development, improvement and validation, a

procedure to accomplish dynamic simulation of the Simulink

control system coupled to the robot multibody model has been

developed.

Finally, the afore explained procedure has been validate

analysing a specific robot test case in two different multibody

environments (Adams and Simmechanics) and comparing the

results.

2. DIRECT KINEMTATIC: DENAVIT-HARTENBERG VERSUS VEITSCHEGGER-WU CONVENTION The robot direct kinematic analysis allow the knowledge of

the movement of each element constituting a robot structure

while it is solving an assigned operation.

An anthropomorphic robot can be schematized through a

number i of arms connected each other through joints in which

an in-built fixed reference coordinate system is placed.

In this way it is possible to represent any robot in a generic

pose that generally corresponds to the so called “zero state” or

“reference position” of the robot.

Practically, the robot geometry, defined by the position and

orientation of each coordinates system, can be described by a

series of homogenous transformation between triads.

Generally those coordinate system can be arbitrary placed, but

a systematic procedure of their definition is provided by the

Denavit-Hartenberg convention [1].

With reference to Figure 1, assuming the i-th axis as the

motion axis of the joint which connect the (i-1)-th Arm to the

i-th Arm, according to Denavit-Hartenberg convention it is

possible to define the i-th triad as follows:

Align zi with the axis of motion (rotary or sliding) of (i+1)-th

joint.

Locate the origin Oi of the i-th triad at the intersection of zi

and the common normal between zi and zi-1 axis, and Oi’ on

the intersection between the normal common and zi-1 axis

Establish xi axis along the common normal between zi and zi-

1 axis assuming positive the direction from joint i to (i+1)-th

joint.

Assign yi to complete the right-handed coordinate system.

Once the coordinate systems in-built to the arms has been

placed it is possible to define the i-th homogenous

transformation through the four parameters of Denavit-

Hartenberg which define position and orientation of the i-th

triad relative to (i-1)-th triad.

ai distance between Oi and Oi’,

di displacement of Oi' along zi-1,

αi angle, about xi, axis between zi-1 axis and zi axis,

considering positive counterclockwise rotations,

θi angle, about zi-1, axis between xi-1 axis and xi axis,

considering positive counterclockwise rotations,

About those parameters, ai and αi are always constant and

dependent from consecutive joint geometry defined by the

presence of i-th arm; instead one between di and θi is a

variable as a function of the kind of joint to be represented

(translational di or rotational θi ) while the other is a constant.

Now it is possible to express the homogenous transformation

which connects the (i-1)-th triad to the i-th triad as product of

transformation matrices as in equation 1. Where c and s refer

to the trigonometric functions sine and cosine.

The aforementioned robot kinematic identification has been

subsequently modified by Veitschegger-Wu [2] through the

introduction of an additional kinematic parameter βi in order to

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allow the evaluation of small position errors even in case of

two parallel consecutive joint axes [3].

According to Figure 2, it is possible to notice how the new

introduced parameter describes a rotation of the (i+1)th- joint

motion axis about yi axis.

Analytically the new transformation is obtained

postmultiplying the Ai Denavit-Hartenberg matrix by a matrix

which describes the additional matrix rotation Rot(y, βi) ,

shown in equation 3, in this way small position and orientation

variations can be always described through small variations of

the five kinematic parameters: ai , αi , di , θi e βi (Equation 2).

In equation 2 it is assumed:

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Figure 2: Veitschegger-Wu kinematic parameters [2]. Figure 1: Denavit-Hartenberg kinematic parameters [4].

Figure 3: 3D kinematic Veitschegger-Wu representation of a

6 DOF anthropomorphic robot arm.

Figure 4: 3D representation of anthropomorphic robot arm

with geometry correction.


In the developed multibody modeling procedure this

additional parameter βi allow to realize, for the degrees of

freedom of each joint, the axis misalignment from the ideal

axis. Thus it is possible to simulate the small errors that can be

done in the robot assembly process or due to the deterioration

of the joint component during the robot life. Anyway, for βi

equal to 0 Rot(y, βi) becomes an identity matrix and the

Veitschegger-Wu convention degenerate into Denavit-

Hartenberg convention.

3. ROBOT GEOMETRY IDENTIFICATION The explained Denavit-Hartenberg or Veitschegger-Wu

convention provides a “minimal” representation of the robot

focused on motion axis identification. Substantially it

summarize the robot kinematic behavior adequate only for

kinematic analysis solution.

Instead, in case of dynamic analysis through multibody

modeling the minimal kinematic representation is not

sufficient as it not always provide complete information on the

effective joint positions as required by this approach.

As example, in case of two consecutive joints with orthogonal

motion axis the cited convention detects only the shorter

distance between the two motion axis, i.e. it doesn’t provide

information on the effective robot joint spatial configuration.

As we will show, for anthropomorphic robot manipulator that

happens during the transition from the elbow triad to the first

spherical wrist triad.

To leap over this problem additional information are required

to complete a correct robot multibody modeling. Thus, in the

modeling procedure developed by the authors other five

parameters aGCi , αGCi , dGCi , θGCi e βGCi , with the same

meaning of ai , αi , di , θi e βi , have been introduced. They

describe a new homogenous transformation, called 1i

iGCA

(similar to equation 2) from the i-th coordinate system

detected by Veitschegger-Wu convention to another coordinate

system opportunely oriented and located in the exact place

where the “real” joint is designed. Those parameters which

allow to identify the effective robot joint spatial configuration

have been called “Geometry Correction Parameters”.

The overall homogenous transformation which starting from

the (i-1)th- triad brings to the coordinate system placed on the

effective i-th joint position is analytically described by

equation 4.

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Comparing Figure 3 and Figure 4 it is possible to better

understand the differences between the “Veitschegger-Wu”

convention, useful for kinematic analysis, and the developed

procedure with geometry correction useful for dynamic

analysis in multibody simulations.

In these schematizations the arms are represented by black

lines while the joints are represented by triads where the red

line represents the x axis, the green line represents the y axis

and the blue represents the z axis (motion axis).

In detail it is possible to notice the different position of the

fourth coordinate system which represents the first triad of the

wrist. According to Veitschegger-Wu convention it is placed at

the minimum distance along the normal common between the

motion axis of the third and fourth joint. Instead, after

adopting the geometry corrections, it is placed in the effective

spatial location of the robot wrist.

The identification of the correct geometry is crucial for the

robot modeling and dynamic simulation in multibody

environment so as to analyze the effective robot element

behaviors such as flexible joint.

4. MULTIBODY MODELING According to aforesaid to accomplish dynamic analysis of an

anthropomorphic robot manipulator the tool chosen by the

authors is the multibody modelling environment.

The authors’ ideas is to realize a procedure that starting from

an universal database definition allow to obtain parametric

robot models in any multibody code.

The developed procedure, in which the user has to provide the

necessary inputs as ascii universal files, is explained in the

following steps.

Preliminarily, in Matlab environment, the inputs defining the

robot characteristics are processed to make available a

common database, also this constituted by ascii universal files,

where the adopted multibody code can find all the needed

information.

Then, the multibody modelling begins with the definition of a

base reference coordinate system (absolute reference) and the

set-up of the working environment (units, gravity,…).

Subsequently, the robot structure is developed iteratively

implementing the aforementioned Veitschegger-Wu plus

“Geometry Corrections” convention so as to identify the robot

characteristic points which define the geometry: arms, joints

and degrees of freedom.

Figure 5: ith- Robot stage for iterative multibody modelling.


Substantially, through this iterative procedure, in order to

obtain a multibody model of a given n-DOF (degrees of

freedom) anthropomorphic manipulator, the whole robot

structure has been conceived as a sequence of n fundamental

stage each one representing the principal robot elements: i-th

arm (body plus joint), i-th actuator (which provides the

specific motion law (angular displacement or torque)) and i-th

sensor monitoring the variables of interest.

In Figure 5, for the developed iterative multibody modelling

procedure, a flowchart representing the i-th stage of a generic

robot model is shown.

The generated robot multibody model is of parametric kind

since the element properties are described by variables whose

values are defined in the universal database.

In so doing, for the user is easy and quick to realize robot

models with different characteristics (geometry, constraints,

mass and inertia properties, motion laws,…). As we will see,

for the different multibody environments this step is assisted

by specific tools developed by authors.

Another fundamental aspect to mention is: this procedure

allows to generate different kind of models in order to realize

more or less accurate representations of the robot test case.

Thus, the feasible robot multibody models differ each other

about the robot modeling complexity level defined by the user:

starting from a simplified representation of the robot with rigid

ideal joint and motion controlled in open loop (useful to

evaluate geometry and kinematic behavior) up to robot model

with joint compliance and motion controlled in closed loop

(useful to verify motor and control system performance or the

robot dynamic behavior) [5].

Anyway, it will be always given the possibility to generate

models with a desired complexity level considering only some

of the aforementioned robot element behavior.

Future development will increase the model complexity level

introducing the possibility of adding more robot component

behaviors such as friction in joints, servo motor rotational

inertia influence on robot dynamic performance, joint

clearances, flexible components,…

Then, in order to validate the developed procedure, multibody

models of a test case anthropomorphic robot have been

realized in two commercial multibody codes: Simmechanics

[6] and MSC. Adams [7].

Adams is a reliable tool that is widely accepted in industry, it

offers a 3D based graphical interface and a simple command

language supporting the user in modelling, set-up simulations

and postprocessing. Moreover it is able to interfaces to several

other commercial tools and software. On other hand

Simmechanics, being a Matlab toolbox, is suitable for very

fast model set-up and debugging. Both software allow a

control system validation through Simulink Co-simulation.

This step will be deeply analysed in further paragraph.

In Adams environment the parametric multibody model

construction has been done using a command language

iterative procedure (macro files) coupled to the generation of a

dedicated toolbar useful for modifying generated models or for

the desired complexity level set-up.

An overview of the implemented toolbar capabilities is shown

in Figure 6.

While, in Simmechanics environment the parametric

multibody modelling take place interactively: the user must

build the robot structure adopting the subsystems, each one

with the desired complexity level, developed by the authors.

Finally, in both case, before running dynamic simulation, it is

necessary to choose the solver and to set its properties. Solver

choice and properties settings can widely vary according to the

simulation type, results accuracy and simulation length.

Anyway, since the solver setting is not the main target of this

work, it is just important to mention that both multibody code

are able to solve the dynamic equation through a wide range of

integrators that can lead to full agreement results.

Figure 6: Snap-shot of “Robotic” utilities ADAMS toolbox (developed by the authors).


5. COMPLIANCE DUE TO JOINT ELASTICITY One of the main source of error in end effort positioning is due

to the joint compliance based on the following assumption:

“joint components under operating conditions can be

elastically deformed as a function of their stiffness/damping

properties”.

Generally for industrial robots harmonic drive gearings are

used, their principal characteristics are high transmission ratio

and law weight. On other hand to realize high transmission

ratio an harmonic drive gearing works on inner gear elastic

deformation, by the way its stiffness along motion direction is

not satisfactory and it confers an excessive compliance to the

robot joints that in some applications cannot be neglected.

According to aforesaid, joint elasticity is predominant if

compared to arms deflection under load, thus the robot

structure can be seen as a number n of rigid arms connected

each other through elastic joints [8,9,10].

A complete review compliance approach state of art is

presented in [11].

In this study case only revolute joint and related compliance,

along motion direction, has been considered.

To model the compliance, that is a deflection or a rotational

error respect to the desired imposed motion, it is necessary to

define a kinematic chain that allow to split the imposed

relative rotation from that the robot arm shows due to joint

flexibility.

So, the joint compliance has been conceived as the

composition of a so called rigid joint, which allow to define

the desired motion law by imposing a motion (open loop) or

by applying a controlled torque (closed loop), and of a so

called elastic joint added to introduce the joint compliance

behaviour.

In detail the i-th kinematic chain related to the i-th joint,

between (i-1)-th and i-th arm, is composed by a revolute joint

between (i-1)-th arm and a i-th dummy part (rigid joint), a

revolute joint between the i-th dummy part and the i-th arm

(elastic joint) and a i-th torsional spring damper force in

parallel with the elastic joint (Figure 7).

In this study we considered and modelled only torsional spring

damper in order to evaluate compliances simply along motion

direction. Further development will consider the

implementation of a six components spring damper so as to

evaluate objects deformations along all space directions.

In Figure 7 and Figure 8 the multibody modeling of a joint

with compliance respectively through a flowchart for

Simmechanics and through graphic representation for Adams

environment is represented.

Figure 7: Compliance modelling in Simmechanics environment.

Figure 8: Compliance modelling in Adams environment.


It is important to highlight that the introduced dummy part has

been defined with mass and inertia properties that can be

considered negligible if compared with the other robot model

components.

The i-th torsional spring-damper force is defined by the

following equation:

iiiii bKT (5)

in which Ki is the stiffness, bi is the damping, i and i

respectively represent the relative rotation and angular

velocity.

6. CONTROL SYSTEM DEVELOPMENT: “CO-SIMULATION” Since Simulink is a suitable software for control systems

development, improvement and validation, a procedure which

allows to set up a dynamic analysis of the Simulink control

system coupled to the multibody model has been developed.

This kind of simulation is the so called co-simulation [12].

The co-simulation consist of a dynamical simulation where the

equation describing the control system are solved by the

Simulink integrator while the motion equation of the robot are

solved by the adopted multibody integrator.

This is possible when the user opportunely defines the

necessary input and output variables for both control system

and multibody model. Moreover the user has to properly set-

up the communication parameters by which the two software

exchange the information relative to the input/output variables.

Substantially the target of a co-simulation is to make a

connection so that any change in one of the models affects the

behaviour of the other.

In detail, in case of Simmechanics multibody model there are

not particular devices to be taken in to account since both

Simulink and Simmechanics are both Matlab toolboxes. In this

case the co-simulation can be done directly connecting the

Simmechanics multibody model of the robot to the Simulink

model of the control system.

Instead, in case of Simulink-Adams dynamic co-simulation an

Adams dedicated procedure has been developed by the

authors. This procedure brings the user to create a Simulink

block representing the multibody model which can be

connected to the Simulink model of the control system.

In Figure 9 a flowchart representing the co-simulation in

Simulink environment is shown. From the figure it is possible

to see the connection between the multibody and the control

system and the typical variables in the running of a control

system modelling. In detail from the multibody model are

carried-out the variables describing the robot motion in the

joint space ( i rotation, i angular velocity and i

angular

acceleration) while the input variables are the motion low that

can be given as T torque, I current intensity, i rotation.

Anyway, if previously defined, the two software can exchange

information about any kind of variable.

7. ROBOT TEST CASE DESCRIPTION In this paragraph, the main properties of the robot test case,

selected to validate the developed multibody modelling

procedure, are presented.

The analysed robot is a 6 DOF anthropomorphic robot

manipulator made-up of six arm and six revolute joints

connected to the servo motors through harmonic drive

gearings.

In Figure 10 the robot in the zero position posture is

represented as its top, lateral, front and isometric view.

Figure 9: Control system development. Co-simulation.


In Table 1 and Table 2 respectively the five Veitschegger-Wu

parameters which define the robot kinematic and the five

“Geometry Correction” parameters which define the exact

geometry position of each joint are shown.

In Tables 3, Table 4 and Table 5 the main parameters which

describe the robot mass and inertia properties are shown. For

each i-th Am those parameters have been evaluated referring

to the i-th triad defined by the i-th homogeneous

transformation according to Veitschegger-Wu convention.

After harmonic drive catalogue investigation, for each joint,

the value of the stiffness K has been identified. Then the

damping constants have been evaluated in order to obtain a

mechanical system with an adequate level of damping. In

Table 7 the elastic properties of stiffens K and damping

constant b for each joint connecting the (i-1)-th Arm to the ith-

Arm, are presented

Finally, in order to make the robot end effector able to follow

the desired trajectory, called “Greca”, the imposed “Motion

Laws” have been defined as function of joint rotation θ(t).

This trajectory, shown in Figure 11, is a typical path for

anthropomorphic robot manipulators assigned to milling or

painting manufacturing.

The Motion Laws are given to the multibody software as an

input function described by spline (Akima method).

The desired 3D end effector trajectory presented in Figure 11

is obtained with the less complex model of the robot: motion

controlled through joint angular rotation i.e. no control system

influence and rigid joint i.e. no compliance introduced.

In the following paragraph the effect of the joint compliance

and of the control system will be analyzed to determine the

robot dynamic performance and to validate the developed

multibody modeling procedure.

Table 1: Robot Veitschegger-Wu parameters

Component α [°] a [m] θ [°] d [m] 𝛽 [°]

Arm 1 90 0.26 0 0.27 0

Arm 2 0 0.68 90 0.0 0

Arm 3 90 0.0 0 0.0 0

Arm 4 -90 0.0 0 0.67 0

Arm 5 90 0.0 0 0.0 0

Arm 6 0 0.0 0 0.155 0

Table 2: Robot “Geometry Corrections” parameters

Component α [°] a [m] θ [°] d [m] 𝛽 [°]

Arm 1 0 0 0 0.072 0

Arm 2 0 0 0 0.072 0

Arm 3 0 0 0 0.432 0

Arm 4 0 0 0 0 0

Arm 5 0 0 0 0.132 0

Arm 6 0 0 0 0 0

Table 3: Center of mass position

Component X [m] Y [m] Z [m]

Arm 1 -0.1504 -0.1227 -0.0175

Arm 2 -0.361 -0.0003 0.1595

Arm 3 0.0187 -0.006 -0.0276

Arm 4 0.0 0.164 -0.0042

Arm 5 -0.001 -0.0016 0.0539

Arm 6 -0.003 0.0 -0.022

Table 4: Robot Mass and Inertia

Component Mass [Kg]

Inertia Ixx [Kg·m2]

Inertia Iyy [Kg·m2]

Inertia Izz [Kg·m2]

Arm 1 75.4 1.92 2.63 2.9

Arm 2 38.3 1.6·10-1 2.15 2.15

Arm 3 40.5 1.36 1.31 3.9·10-1

Arm 4 10.9 1.14·10-1 3.38·10-2 1.12·10-1

Arm 5 5.53 4.02·10-2 2.25·10-2 2.87·10-2

Arm 6 1.02 4.5·10-4 4.5·10-4 5.3·10-4

Table 5: Robot Inertia

Component Inertia Ixy [Kg·m2]

Inertia Ixz [Kg·mm2]

Inertia Izy [Kg·m2]

Arm 1 9.21·10-1 -1.87·10-1 -1.60·10-1

Arm 2 -1.07·10-3 5.30·10-2 5.50·10-4

Arm 3 -3.04·10-3 2.19·10-2 2.19·10-2

Arm 4 2.26·10-5 -3.91·10-5 7.64·10-3

Arm 5 -1.10·10-5 -2.37·10-4 2.29·10-3

Arm 6 0.0 0.0 0.0

Table 6: Joint Stiffness and damping constant

Component K [N·m/rad] b [N·m·sec/rad]

Joint 1 1.8·105 1.3·103

Joint 2 6.7·104 5.5·102

Joint 3 1.8·105 4·102

Joint 4 6.7·104 1.1·102

Joint 5 3.1·104 3.9·101

Joint 6 3.1·104 4.3


8. ROBOT DYNAMIC BEHAVIOUR AND MULTIBODY MODELS VALIDATION In Figure 12 a comparison between the desired and effector

trajectory and the trajectories evaluated through multibody

dynamic simulation is presented. It refers to a robot model in

which the Motion Laws are given as rotation in the joint space

(open loop) and revolute joints are considered with

compliance.

In detail the upper part of the figure shows the whole 3D path

while the bottom part put in evidence a detail of the path in

Figure 11: Desired trajectory “Greca”.

Figure 10: Adams Model of tested anthropomorphic robot.


which the joint compliance effect is more evident. The blue

line is related to the desired trajectory, the red line is related to

Adams multibody simulation while the black line refers to the

Simmechanics simulation.

From the upper part of this figure it is possible to notice a shift

along z axis between the desired trajectory and the one done

by a robot with elastic joint as expected.

From the bottom part of the figure it is possible to see the

differences between desired and simulated trajectories on the

x-y plane, so as to better understand the compliance influence.

The small differences in end effector path between Adams and

Simmechanics analysis are due to different evaluation of the

angular velocity and acceleration laws. The two codes have

different kind of derivative operator.

To step over this problem, it is recommended to provide to

both multibody all three functions describing the motion law:

rotation, angular velocity and acceleration.

According to aforesaid it is possible to say the two software

provide an equal estimation of the joint compliance behavior.

This results comparison highlights the goodness of both

models realized to predict the joint compliance dynamic

behavior.

In Figure 13 it is possible to notice a detail of the same end

effector trajectory in case of models made-up with elastic joint

and motion controlled in closed loop (imposed torque). The

blue line is related to the desired trajectory, the red line is

related to Adams multibody simulation while the black line

refers to the Simmechanics simulation.

From this figure it is possible to notice that the implemented

control system increase the oscillations of the end effector

trajectory making both developed multibody simulation

macroscopically similar to the real dynamic robot behaviour

(experimental tests and numerical comparison with multibody

simulation are still in progress).

Anyway, it is possible to notice how both models are in full

agreement about the oscillation peak entity evaluation.

Still, it is possible to see the Simmechanics model presents a

slight anticipation of the trajectory oscillation behavior. This

phenomenon is due to the added Simmechanics block called

“Memory” recommended when the Simmechanics multibody

modeling contains closed loops (an example is the

implemented control system realized through a feedback

control on joint angular rotation).

This results comparison highlights the goodness of both

models realized to predict the joint compliance plus control

system dynamic behavior.

CONCLUSIONS In conclusion it is possible to assert that the following

objectives has been reached:

A fully parametric procedure to generate any robot geometry

in multibody simulation environment based on the

Veitschegger-Wu convention has been developed. All the

necessary inputs, needed to accomplish a multibody analysis

are provided by the user as simple file.dat.

The developed parametric multibody modeling procedure

Figure 13: Robot compliances dynamic analysis. One

corner detail of trajectories. Closed loop simulation.

Figure 12: Robot compliances dynamic analysis. Full and

one corner detail of trajectories. Open loop simulation.


allow to generate different multibody models in order to

realize more or less accurate representations of the robot.

They differ each other by the number and kind of robot

elements modeled (multibody model complexity level). The

definition of the complexity level is chosen by the user that

in this way can control the influence of each modeled

component in robot dynamic performance.

A dedicated procedure, called Co-simulation, which allows

to set-up dynamic analysis of a control system developed in

Simulink environment coupled to a generic multibody code

has been developed.

For each complexity level the models realized in the two

cited multibody environments bring to fully agreement

results so as to validate the multibody modeling procedure

developed by the authors.

Future development will increase the model complexity level

introducing the evaluation of different robot component

behavior such as friction in joints, servo motor rotational

inertia influence on robot dynamic performance, joint

clearances, flexible components,…

Then, the model made-up by the higher complexity level will

be compared to experimental results in order to validate the

multibody robot end effector trajectory prediction.

REFERENCES [1] Denavit J. and Hartenberg R.S., "A kinematic notation

for lawer-pair mechanism based on matrices", Trans.

ASME Ser. E, J. App1. Mech., Vol. 22, p. 215-221, 1955.

[2] Veitschegger W. K., Wu C., "Robot accuracy analysis

based on kinematics", IEEE Journal of Robotics and

Automation, Vol. 2, No. 3 p. 171-179, 1986.

[3] Hayati S.A., “Robot geometric link calibration” 22nd

IEEE Conf. on Decision and Control, pp1477-1483, Dec

1983.

[4] Siciliano B., Sciavicco L., Villani L., Oriolo G.,

"Robotics: Modeling, Planning and Control", Springer-

Verlag, 1st Edition, 2009.

[5] Corke P., "Robotics, Vision and Control – Fundamental

Algorithm in Matlab", Springer-Verlag, 2011.

[6] The Math Works Inc., “Simmechanics User’s Guide”,

July 2002.

[7] MSC Software, “Adams/View User’s Guide”, 2010.

[8] Abele E., Bauer J. et al., "Comparison and validation of

implementations of a flexible joint multibody dynamics

system model for an industrial robot", CIRP Journal of

Manufacturing Science and Technology, Vol.4, p.38-43,

2011.

[9] Zollo L., Siciliano B., et al., "Compliance control for an

anthropomorphic robot with elastic joints: theory and

experiments", Journal of Dynamic Systems,

Measurement and Control, Vol.127, p.321-328,

September 2005.

[10] Abele E., Rothenbücher S., Weigold M., "Cartesian

compliance model for industrial robots using virtual

joints", Production Engineering Research and

Development, Vol. 2, p. 339-343, 22 July 2008.

[11] Erkaya S., "Investigation of joint clearance effects on

welding robot manipulators", Robotics and Computer

Integrated Manufacturing, Vol.28, p. 449-457, February

2012.

[12] Cheraghpour F., Vaezi M. et al., "Dynamic modeling and

Kinematic Simulation of Stäubli TX40 Robot Using

MATLAB/ADAMS Co-Simulation", International

conference of mechatronics, April 2011, Istanbul,

Turkey.

PARAMETRIC MULTIBODY MODELING OF … · Stefano Baglioni University of Perugia Dep. of Industrial...

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