31 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

104 εμφανίσεις


Pekka Aarnio
, Kari Koskinen

and Sami Ylönen

*Information and Computer Systems in Automation, Helsinki University of Technology, Espoo, Finland

logy Laboratory, Helsinki
niversity of
echnology, Espoo, Finland

PL 5400, 02015 HUT, Finland

Phone Int +358 9 451 5240, Fax Int +358 9 451 5394, E

Work Partner robot is a combination of a hybrid locomotion robot plat
form, and a special two hand
manipulator mounted over the platform. A rigid body simulation model has been build of this whole system to
help in development process. The robot platform, called Hybtor, and the manipulator has to work in collaboration.
atic simulation model of the platform has been used for visual study of different locomotion styles and in
verification of the high level control software of the real physical platform prototype. Goals in dynamic model
simulations are to study locomotion s
tability and forces and torque in robot joints. A Virtual prototype model of
the two hand manipulator under design is used for kinematics analyses. Workspace considerations like collision
avoidance and reach are studied using different task scenarios in si


kinematic simulation, dynamic simulation, virtual prototyping, walking robot



In this paper we present how 3D graphical
simulation model of the Work Partner robot is build
and how it is used in the development process of

the robot platform and in studying the operation of
a humanoid type manipulator still under design.

The Work Partner robot is a special service
robot under development in Intelligent Machines
and Special Robotics Institute at Helsinki University
of Techn
ology (HUT). The Work Partner robot is a
combination of a hybrid locomotion robot platform
and a special two hand manipulator mounted over
the platform.

The robot platform, called Hybtor, has four legs
and wheels on its feet so that it can walk and step
er barriers on rough terrain or drive by wheels
accessing more speed on even ground. The power
for leg joint motion, as well as for the wheels, is got
from actuators with brushless EC
motors. A
combustion engine is used for battery charging in
order to obt
ain a continuous working capability of
several hours. The Hybtor construction is more
precisely presented in reference [Halme et al., 1999].

The manipulator under design will be mounted
over the front plane of the platform. It has a main
body with two degr
ees of freedom and two hands
with six degrees of freedom each and body with two
degrees of freedom. Manipulator will also have a
stereo camera head on it's shoulders. Virtual
prototype model has been made of this manipulator.

Real mobile robots are very

complex systems so
that simulations with virtual models can give only
some approximate results. That is why virtual
prototypes are not any substitute for the real
physical prototypes. Simulations can however
support the concurrent development and design
rocess of a mechatronic machine.

Some kind of simulation is used in all most every
research project of mobile robots. Most usual tool is
some general purpose simulation software or user
made standard programming language simulation
code. These provide a hi
gh degree of flexibility but
on the other hand require in depth knowledge of
both the software and the physics of the system to
be modelled. It is difficult to construct and manage
reliably large


because t
here is big error
making possibility and als
o changes are difficult to
make. Examples of the use of flexible general
purpose tools for simulation of
walking and mobile

are e.g
[Muller et al., 2000], [Buehler et al.,
1999], [Blazevic et al., 1999], [Rehbinder et al., 1999]

Another solution is
to use

simulation software packages

that been designed
for a certain area of engineering

(e.g. Adams,
impack, Envision).

With these tools geometry can
be modelled, kinematics and dynamics of the system
can be defined, simulation can be performe
d with 3D
visual animation and result data analysed.
advantages are that user don’t have to derive the
equations of motion. The kinematics and often also

modules are

available. These programs are

very interactive menu
driven so tha
t changes to

model and diff
erent parameters are easy to make
Because of the specialization they can have also
restrictions and undesired features when used for
simulation of a walking vehicle. A big problem with
commercial software is, that dynamical simulations
can not yet be performed in real
time [Granholm et
al., 2001].
Integrated simulation software tools and
visual 3D simulations of walking and mobile robots
have been done e.g. in
[Amar et al., 1995],
[Hartikainen, 1996], [Fraczek et al., 1999].

Our goal is
to use a simulation tool concurrently
with the real physical testings of the walking and
wheel driven mobile robot. We used a commercial
simulation software

packet, Envision TR/Delmian,
which we had available for other simulation projects.

This simulation
program is originally designed for
industrial robot simulations and off
programming and therefore many restrictions were
found. This program run on a standard PC
and no special simulation facilities had to be build.

A general idea of virtual
prototyping is to
support development of complex systems. Our main
goal in simulations is to study operation and control
of the robot system using computerized model. Two
kinds of models have been built of the robot
platform: kinematic and dynamic. Kinemat
ic model
has been used for visual study of different
locomotion styles. Kinematic model has also been
used for debugging of the control software of the
real physical Hybtor prototype. High level control
software has been connected to the kinematic
on model through a special connection so
that different control commands can be verified first
against the model.

Dynamic model makes it possible to analyse
support forces and torque at different joints.
Unstable behaviour can be clearly seen from
on animations. From simulation data critical
actuator motor current values has been noticed,
which helps in real prototype testing. Platform
simulations are presented in chapter 2.

One goal of the simulations is to visualize and
demonstrate not only locomo
tion patterns of the
platform but also different working scenarios of the
whole combination of platform and manipulator. The
Work Partner is going to be an autonomously
moving robot, which helps a human host in different
tasks in outside environments. Some

tasks have to
be done using the special two hand manipulator
mounted on the front of the robot platform. The
Hybtor platform is responsible of carrying the
manipulator near the objects so that it can reach
them with one or two hands. The workpieces might

be down on the ground so that the reachable area,
manipulator working area, is also dependent of the
platform altitude. The manipulator and platform has
to work in co
operation. Some possible work
scenarios have been simulated and reach ability and
ion issues analysed. Preliminary manipulator
simulations are presented in chapter 5.


Simulation model of the Hybtor platform
and the two hand manipulator.



The structure of the Hybtor consists of an
rticulated main body and legs with three revolute
joints between links, which are the hip joint, the
thigh joint and the knee joint. The fourth revolute
joint is for the wheel. The hip joint and link can be
used for robot inclination. Total number of
endent degrees of freedom is thirteen.

The Hybtor platform is modelled as a robot
device consisting of rigid body links without any
flexibility. The moving links are connected to each
other with ideal revolute joints. One joint
corresponds to one degree of

freedom. Two kinds of

models has been build: a kinematic model and a
dynamic model.

Model building using Envision is started with
the 3D graphic modelling of the device parts. Earlier
made CAD drawings of the parts of Hybtor were
imported to the modelling

tool and link base
coordinates and auxiliary coordinates were defined
according to Denavit
Hartenberg convention.
Graphical model of Hybtor is presented in Fig.1


Kinematic model

The real mechanical structure has EC
powered linear actuators connecte
d to both links
over the revolute joint. The actuator operates like a
mechanical muscle pushing and pulling the links
apart so that the angle between the links changes.
This kinematic loop in each actuator system is not
modelled, because of the almost line
correspondence between the actuator length and
revolute joint angle during normal configurations.

Direct kinematic joint motion can be simulated
directly after interactive definition of the kinematic
types of each link and the constraint definition of

the kinematic loop in the articulated main body
system, which consists of four dependent revolute
joints. Trajectory following simulations of each leg
ankle point needs solution of a inverse kinematics
problem. This kind of inverse kinematics algorithm
or the legs had to be defined and coded by the
user. However after this time consuming process of
building inverse kinematics library module it was
easy to test the algorithm by simulations of the
build model.


Dynamic model

The dynamic model is obtained
from the
kinematic model by adding dynamics properties to
the robot model such as mass, inertia moments, joint
friction as well as by extending the virtual
environment with gravitation field and ground
contact model. Dynamic model is used in torque
s and stability analysis. Unfortunately
dynamic simulations with ground contact modelling
can not be run in real

The forward dynamic calculations are based
upon a recursive form of Hamilton’s equations of
motion. In this formulation, the state varia
bles are
the base location, devices total momentum and joint
dof positions and generalized momenta. The
Hamiltonian equations consists of 2n first order
differential equations replace the n second order
equations in Lagrange formulations. The

of the recursive form algorithm is O(n),

where n is the number of the links.


ground contact model

The Envision software packet does not have any

special module for ground contacts. A ground
contact model has been defined and embedded as
an extra modu
le to the program.

A simple way of modeling contact between rigid
body robot foot and the hard ground plane is to
imagine that there are stiff springs between the foot
and the ground plane. These spring model methods
belong to the family of penalty or regu
methods. Different kinds of contact models and their

adequation to different types of simulations are
evaluated by [Mirtich, 1999]

Spring model can be used, if great accuracy of
the contact forces is not needed. These contact
forces should keep the

robot vehicle on the ground
plane and not allow the foot to penetrate inside the
ground too much. One spring normal to the ground
plane corresponds to supporting or reaction force of

the ground. In walking robot applications also
frictional forces should
be modeled so that two
tangential springs are also included. These springs
have to be quite stiff in order motion to look natural.
To avoid great vibrations damping elements are also

The contact plane normal direction supporting
force is modeled w
ith a spring and a damper. The
normal force

acting on the wheel towards the
wheel center point, ankle point of the foot, can be
calculated following way, when there is a ground
contact (
<= 0




be a dist
ance vector between the wheel
and the ground plane,

is a the normal component
of the foot velocity and


are the spring and
damping coefficients.

Friction force during wheel brake mode

The plane tangential friction force between the
wheel and

the ground is calculated using one
version of penalty methods called sliding shoe
method, developed by Muller [Muller et al.,
1999]. Spring and damper is connected between a
foot and a virtual shoe element. The shoe block is
allowed to slide but
it will always stay on the
ground plane. This model compares the force
tangential to the ground plane with the maximum
static friction force, that depends on the force
normal to the ground plane. The foot starts sliding if
the tangential force exceeds the
static friction force.

When the foot contacts the ground, the virtual
shoe is positioned to the contact point of the foot


). When the foot motion has a tangential
velocity component
, restricting frictional force

is generated. The maximum sta
tic friction is


The tangential frictional forces are calculated in
the same manner as the normal force. Let

be a
tangential component of a position vector from the
virtual sliding shoe to the foot cont
act point:

<= 0



is a the plain tangential component of
the foot velocity and


are the spring and
damping coefficients in tangential direction. The
shoe position is updated for the n
ext time step
calculations. If the frictional force was less than the
maximum value, the shoe position

is not chanced,
but if it is greater than or equal to the maximum
value, shoe is pulled in direction opposite the
friction force from the foot positio

This movement of the shoe effectively means as
if it would be towed after the foot restricting the
motion of the leg.
[Muller et al., 2000]

Sliding shoe method was used to model friction
forces of the Hybtor foot wheels in brake mode.

model during wheel driving

Sliding shoe method is however not applicable
for wheel contact, when the wheel is rolling,
because the shoe would be driven over by the
wheel and at the next time step force direction and
magnitude would be incorrect. Another mo
del for
wheel driven situations was developed based on the

tire model described in [Rahnejat, 1998]. In this
model the force of friction

is a function of the
sliding velocity of the wheel.


be the contact patch longitudinal speed
component relat
ive to the road surface This velocity
is obtained as



is the actual longitudinal velocity of
the vehicle and


are the actual angular
velocity and the radius of the wheel. Then the total
sliding speed


is the sum



is the lateral slip speed component.

Now the
friction force
dependence of a tangential
total sliding velocity of a wheel is calculated as

( |v|



(| v| >a

, where

is a threshold
parameters and

are some constants. The
maximum value of this force is computed as the
vertical supporting force multiplied by the friction
coefficient. The a
pplied force restricting the motion
of the leg is calculated by low pass filtering of the
force vectors of few time steps in order to avoid
vibrations during simulation.

When using this filtering method however a foot
will creep slowly down a ramp even if
static friction
should hold it in place.



The platform of the Work Partner robot is
responsible of locomotion in different kinds of
terrain. It has to carry the manipulator near the
objects to be manipulated. It has four legs w
ith three

degrees of freedom and wheels on it's legs and an
articulated main body. Simulation model has been
made of this Hybtor platform. The Hybtor platform
is modelled as a robot device consisting of rigid
body links without any flexibility. The moving

are connected to each other with ideal revolute
joints. One joint corresponds to one degree of
freedom. Both kinematic and dynamic 3D models
have been built and used in simulations.


Kinematic simulations

Kinematic simulations are done for locomoti
visualization and monitoring purposes in control
software testing.

Movement of the legs and main body joint of the

platform model can be commanded directly giving
target joint angle values. Configuration of the robot
model changes at desired speed. Inv
erse kinematic
algorithm designed first on paper has been verified
for correctness by embedding the algorithm code as
a module to the simulation software. Using this
inverse kinematics module the centre point of the
robot wheels can be commanded to move al
certain trajectory paths. Now locomotion patterns
can be simulated and analysed visually. These
simulations reveal when joint angle limits are
exceeded and when collisions happen between
wheels or a wheel and the main body.

Kinematic model can be si
mulated in real
which is not possible in dynamic simulations. The
time property of the kinematic model enables it's
use in interactive debugging of the higher level
control software of the physical prototype. This is
more precisely explained in c
hapter 3.


Dynamic simulations

The dynamic model is obtained from the
kinematic model by adding dynamics properties to
the robot model such as mass, inertia moments, joint
friction as well as by extending the virtual
environment with gravitation field and
contact forces. This type of model is used in torque
analysis and stability analysis. During simulations
virtual model of the robot is moving over virtual test
field which simulates the real ground.

As a result of these simulations we get
recordings, which can be visually
analysed. For example unstable situations, when the
robot is falling, can be noticed. An important goal of
the walking robot control is to maintain stability


Simulation test where the
Work Partner
robot is climbing over an obstacle.


Simulated thigh and knee joint torque

of the front legs during climbing over an
obstacle. Leg 1 solid line and leg 2 dashed line.


Simulated ground contact support forces
during obstacle climbing.
Leg 1 solid line and leg 2
dashed line. Leg 3 dashdot and leg 4 dotted line.

during all kinds of locomotion. Robot platform, with
only four legs, can easily become unstable when
ne leg is lifted up. These unstable situations are
observed from the simulation animations. Stability is
easier to maintain when the weight load is evenly
distributed to as many legs as possible. This load
distribution can be revealed from the recorded for
time series of a dynamic simulation.

During simulation important data, like contact
forces and joint torque in all four legs, are saved to
files for post processing and analysis

One animation clip picture of Simulation test
where the Work Partner robot

is climbing over an
obstacle is shown in fig 2. Joint torque result values
of this test are represented in fig 3. The stepping leg
is lightened and a force action of 85N is commanded
to forwards direction. Driven wheel helps also
climbing. Left front leg
1 is taking the first force
controlled step over the obstacle during time 0
6seconds and the other front leg 2 takes a step
during 18
24 seconds. The time between 6 and 18
seconds is needed for weight shifting configuration
change using hip inclination and

support leg
movements. The effects of weight shifting can be
seen from the ground support force plotting in fig 4.

Joint torque data analysis shows, for example,
how much and for how long time periods the
actuator nominal torque is exceeded. Motor nomina
torque is allowed to be exceeded, but high currents
for a long time will heat up the motors and increase
the energy consumption [Ylönen, 2000]. Simulations
showed that during walking , a leg has to be moved
to a position, where quite high knee joint torq
ue is
needed. These simulation results anticipated what
happened later during real prototype tests: one
motor of a knee actuator was damaged after being
several minutes on that bad configuration.

Dynamic platform model is used to compare
different locomoti
on styles. The Hybtor model was
simulated at walking mode locomotion and hybrid
locomotion mode and the results were compared.
During walking mode the Hybtor model was
commanded to walk in a normal wave gait fashion
where leg in transfer phase was lifted a
bout ten
centimetres during 0.6 m length step. Simulations
revealed that the hip joints had to be inclined and
the load that way shifted in order to maintain
stability during walking. This weight shifting
necessity has been noticed also during physical
totype tests.

In hybrid locomotion mode simulation the
supporting legs generate propulsion force, as in
walking. The wheel of the leg in transferring phase
is not lifted up but instead force controlled so that
the wheel is in contact with the ground during

whole transfer phase. That wheel can rotate freely or

can be driven to help forward motion. This way the
stability of the robot body is maintained without
shifting the weight. Hybrid locomotion mode is more

precisely explained in reference [Halme et a
l., 2000].

The actuator motor currents of the real Hybtor
robot were measured during force controlled
obstacle overrun. Simulation of the same kind of test

using the same force control algorithm gave
comparable results. Results are shown in fig. 5,
the simulated time series is time shifted for
better match. This gives some verification of the
correctness of the dynamic model.

Comparisons have shown, that in hybrid
locomotion, the maximum joint torque and motor
current values were smaller and differen
ces between
legs were also smaller. This implies that weight load
is better balanced on all legs even without weight
shift, which was found necessary in walking
locomotion mode in order to keep balance. These
simulation results has been presented more
isely in paper [Aarnio et al., 2000].


Measured motor current values (solid) and
simulation results (dashed) during

force controlled
obstacle overrun. Plotting a: thigh joint and plotting
b: kn
ee joint.



The high
level control software of the robot
platform running in the main computer commands
the low level control modules of the legs and the
main body. This high level control is responsible of
synchronized contr
ol of all legs and body, when
robot altitude or attitude has to be changed or
during locomotion. These commands are send over
the CAN
bus connecting the main computer to leg

Control algorithm design and coding is an
iterative process, wh
ere several changes in software
have to be tested. This kind of first stage software
verification is easier and safer using virtual
simulation model of the robot platform than the real
mechatronic machine. The same commands that
would have been sent over C
bus to leg control
modules in normal operation, are sent over Ethernet
to special interface module connected to Envision
simulation software using so called Low Level
Telerobotics Interface (LLTI) [Deneb, 1995]. This
Simulator connection, presented in F
ig.6, can be
used in three different modes in monitoring and
testing of the real Hybtor platform and control

Virtual control mode

Hybtor monitor mode

Control monitor mode

Virtual kinematics 3D model of the Hybtor
platform changes it's configura
tion according to the
commands so that algorithm correctness can be
visually verified from the model behaviour.
Erroneous control doesn't do any harm to the virtual
model and after code debugging new tests can be
run again immediately. This is how the simu
lator has
been used for high
level control software testing in
virtual control mode.
This method revealed some
coordinate transformation errors in the control code.
Final testing of the software have to be carried out
using the real physical prototype.

ring physical prototype test runs simulation
model can be used for monitoring the control or the
actual robot behaviour. This allows the comparison
of the actual configuration and intended
configuration in
control monitor mode
. One
possibility of malfuncti
on is a broken part, e.g. a
joint angle encoder. The simulation model can be
used to monitor the feedback data from the real
robot so that erroneous feedback data can be
detected in this
hybtor monitor mode

by comparing
the configuration of the Hybtor and
it's model.
Occasional use of this monitoring hasn’t yet
revealed any control errors. If unexpected behaviour
is noticed by visual monitoring, analysis of the
control and feedback time series data logged by the
simulator monitor system can reveal the exact

point of the erroneous command.


Simulator connection to the main control of
the robot platform.



The Work Partner robot is intended as a working
assistant for different kinds of tasks. The ro
platform moves to the place where the job has to be
done. A robot manipulator mounted over the
platform can then manipulate these objects or
workpieces, if they are in the workspace of the
manipulator. The robot platform and manipulator
has to do the t
asks in co
operation. A special
humanoid type manipulator is under design. It has a
main body with two degrees of freedom mounted on
the front plane of the Hybtor platform. It has two
hands with 5
6 degrees of freedom and a stereo
camera head so that manip
ulation can be visually
controlled. The manipulator should be capable of
picking objects of weight up to 5 kg using special
grippers. This manipulator on the robot platform
with one cross section of the hand workspace is
presented on figure 7.

This manipul
ator has to be a quite general
purpose one, because the actual tasks in the future
are not known. One goal of these preliminary
simulations is to study some operation scenarios
and the possible workspace of the manipulator. The
robot platform has to carry
the manipulator near the
objects and change it’s altitude to enable the
manipulator to reach the objects. Workspace issues
like reach and collision avoidance, has to be known
in advance for different types of tasks. Some objects

can be lifted or otherwise
manipulated with one
hand, while some objects need to be grabbed with
both hands. This means that there are at least three
different workspaces:

Workspace of one hand only (left or right).

Workspace of one hand helped by the
manipulator body joints.

space for two hand manipulation.


Cross section of the workspace of one
manipulator hand

Some work scenarios have been simulated to
demonstrate these workspaces. These simulations
are used in finding the right position

for the
manipulator and for tool and workpiece palettes
over the platform. These scenario simulations help
to find the right collision free trajectories and to
avoid travel limits of the joint angles.

Task 1: Reaching an object on the ground using
the bo
dy and one hand and picking it up and
placing it to a basket over the platform. Platform
altitude has to be lowered.

Task 2: Picking up a long object using both

Task 3: Sweeping object with one hand to the
workspace of the other hand and picking
it up.

These kinds of scenario simulations will be used
to aid manipulator control software algorithm
design. The combined control of the platform and
manipulator with main body and two hands and
grippers doing some specific task will be highly
d so that possibility to test the control
first against the simulation model will be extremely



In this paper we present how a computerized
simulation model of the work partner robot has been
used during development process of the platfo
control and in design process of the manipulator to
be mounted in front of the platform.

Dynamic simulations of the robot platform are
used to study stability issues during different
locomotion modes. One simulation result is an
approximate force and to
rque time series from which
critical configurations can be foreseen in order to
avoid motor over loading. Normal walking mode
locomotion and hybrid locomotion mode
simulations confirm some benefits of hybrid
locomotion mode: stability, better load balancin
and lower maximum torque values.

Platform kinematic model has been used in
verification of the high
level control software
algorithms. Simulator monitoring could help in
software debugging because every module doesn't
have to be ready during testing and
because we
don't have to worry about consequences of
erroneous control of the model. True benefits can be

known after systematic use of simulator monitoring
during real robot tests. Wave
LAN connection to
simulator not yet implemented will be needed for
ring moving robot tests in outside environment.

Kinematic model of the two hand manipulator
still under design has been build and used to study
positioning and workspace issues: reach and
collision avoidance. Some possible work scenarios
have been demonstr
ated by simulations. Combined
control of the whole Work Partner robot, platform
and two hand manipulator, will be quite complicated
task. We believe that studying the control of the
different work sequences first using simulations will
make the design proc
ess more concurrent and


[Aarnio et al., 2000] Aarnio P., Koskinen, K., Salmi,
S. Simulation of the Hybtor Robot. CLAWAR
2000 3

Int. conference on Climbing and
Walking Robots Madrid, Spain, 2
4. Oct 2000

[Amar et Al., 1995] Amar, F
.B.,Bidaud P. Dynamic
Analysis of Off
Road Vehicles. Proc. Of the
fourth Int. Conf. On Experimental Robotics.
ISER’95, Stanford, 1995.

[Blazevic et al., 1999] Blazevic, P. Iles, A.
Development of multi
legged walking robot with
articulated body.

conference on Climbing and Walking Robots
Portsmouth, England, 13
15 Sept 1999. pp 205

[Bueh1er et al., 1999] Buehler, M, et. al. Stable open
loop walking in quadruped robots with stick legs
Robotics and Automation, 1999. Proceedings
1999 IEEE International Conference on , Volume:
3 , 1999 Page(s): 2348
2353 vol.3

[Deneb, 1995] Telegrip. Motion Pipeline Reference
Manual. Deneb Robotics Inc. 1995

[Fraczek et al., 1999] Fraczek, J.; Morecki, A.

Modelling of contact in walking machin
Systems, Man, and Cybernetics, 1999. IEEE SMC

'99 Conference Proceedings. 1999 IEEE
International Conference on , Volume: 6 , 1999
Page(s): 948
952 vol.6

[Granholm et al., 2001] Granholm G., Säilä J. Real time
simulation in product development.

Lehtonen M. VTT Symposium 210.
prototyping, VTT Research Program 1998
Espoo 2001. pp 31

[Halme et al., 1999] Halme A., Leppänen I., Salmi S.
Development of WorkPartner

design of
actuating and motion control system

nternational conference on
Climbing and Walking Robots Portsmouth,
England, 13
15 Sept 1999.

[Halme et al., 2000] Halme A., Leppänen, Salmi S.
Hybrid locomotion of a wheel
legged machine.
CLAWAR 2000 3

Int. conference on Climbing
and Walking Robots Madri
d, Spain, 2
4. Oct

[Hartikainen, 1996] Hartikainen K. Motion planning
of a walking platform design to locomote on
natural terrain. HUT. Automation technology
lab. Series A Report 16, Nov. 1996.

[Mirtich, 1996] B. Mirtich. Impulse
based Dynamic
ion of Rigid Body Systems. Ph.D. thesis,
University of California, Berkeley, Dec. 1996.

[Muller et al., 2000] J.Muller, M. Schneider, and M.
Hiller. Modeling, Simulation and Model
Control of the Walking Machine ALDURO.
IEEE/ASME Trans. on Mechatroni
cs, vol. 5, NO.
2,June 2000. pp.142

[Rahnejat, 1998] Homer Rahnejat.
Dynamics. Vehicles , Machines, and
Mechanisms. Society of Automotive Engineers,
Inc. USA. 1998.

[Rehbinder et al., 1999] Rehbinder, H. Ridderström,
C. Attitude estimation f
or walking robots.


International conference on
Climbing and Walking Robots Portsmouth,
England, 13
15 Sept 1999. pp 649

[Ylönen, 2000] Sami Ylönen.
Control System of the
Electromechanical Leg of a Service Robot.
Master's Thesis, Automati
on Technology
Laboratory, Helsinki University of Technology.