Schematic representation 3D left and 2D right of the robot and the impact surface on the virtual cartesian coordinate system 3.1 Analysis in the time domain Figures 4 to 7 depict some o
Trang 2where, X : Acceleration related target dynamics d
X : Velocity related target dynamics d
t
M : Inertia related impedance parameter in the virtual system
B t: Damping related impedance parameter in the virtual system
6 Experiment with the prototype of a MFR
Fig 14 shows the prototype of a MFR for handling building materials In this figure, the
basic system consists of a 6DOF manipulator and a mobile platform with caterpillar tread;
the portion that excludes building material is an additional module (robot controller,
vacuum suction device, F/T sensor and controller etc.) for handling building materials
The development of a MFR applied to the construction area is not achieved by actual system
production alone Studies on system operation technology are also necessary for the
developed system to be fully effective in operation The construction material installation
method suitable for a robot which was developed in this paper is shown in Fig 15 Each
process can be outlined as follows:
1) First, construction materials piled on the ground are fixed to a robot with an adsorption
device The type of loading for materials carried from the ground is determined by the
most efficient adsorption posture within the operation range of a manipulator
2) An operator rapidly moves the robot to an installation site through a wireless controller
Here, a mobile platform whose velocity can be controlled by the input of a control sig
nal is principally used The posture of construction materials is adjusted by the motion
of a manipulator if necessary
3) Construction materials carried to the vicinity of an installation position are installed thr
ough interaction with materials already installed by an operator That is, compliance oc
curs upon contact, so that press pits for materials and systems are completed safely
4) After the operation is completed, the robot is returned to the site of construction materi
als loading through a wireless controller for the next operation
Fig 14 The prototype of a MFR for handling building materials
Fig 15 The building materials installation method
A simulation for handling building materials is implemented to evaluate the performance of the prototype of MFR for construction works The test is implemented indoors with an operation environment similar to that of an actual construction site An experimental system
to implement press pits after inserting building materials into the correct position was designed as in Fig 16
Fig 16 An experimental system
Trang 3Inserting building materials between the supporting board and the L-board is substituted
for actual installation operation As the gap is narrower than the thickness of building
materials, they are moved horizontally and vertically with the supporting board connected
to ‘spring A’ being pressed in order to complete the installation operation If the supporting
board is pressed, it means that compliance occurred; if the length of compression exceeds a
certain range, the result is contact force which causes the robot to move in the opposite
direction In this experiment, building materials were limited to 60 N, considering the
specifications of the manipulator, and manufactured into models of curtain wall or panel
Fig 17 shows a simulation for handling building materials through an experimental system
Once building materials are completely fixed to a robot through a vacuum suction device at
a loading site, the robot is moved relatively rapidly to the vicinity of the installation position
through a wireless controller Precise positioning is performed by human-robot cooperative
control In handling building materials, an operator is encouraged to collect information on
the operation in real time in order to cope with changing environments Here, the speed or
efficiency of operation is proportional to an operator's workmanship
Fig 18 shows the result of a mock-up test of a building material handling work using an
experimental system A comparison was made between the contact force (F e) with
environments and an operator's force (F h), measured by sensors during the handling of
building materials F h and F e refer to the mean value of forces measured in the x, y, and z
directions by a force/torque sensor during operation time T h and T e, respectively, as shown
in the following (10)
(a) Adsorption of a building material (b) Transportation through a wireless controller
(c) Positioning through human-robot cooperation (d) Installing (coupling) of a building material
Fig 17 An experimental system
Fig 18 F e and F h in simulation
Each section can be described as follows:
1) Section A – A building material is carried to an installation position by the operators' fo
rce (F h) As seen in the graph, about 50 N of building materials are carried by about 70
N of external force supplied by an operator The force augmentation ratio (α) is about 7,
which is necessary to access the supporting board of the experimental system
2) Section B - Contact with the environment (experimental system) begins to occur, genera
ting a maximum of 70 N of contact force (F e) Even at the moment of contact, the operator's force is maintained to press the supporting board of the experimental system 3) Section C - Not the operator's force but rather his or her torque is transmitted to improv
e posture About 2 N of compliance force is generated by the correlation between the external force provided and the impedance parameters of the experimental system This value is used to press a spring connected to a supporting board into a position with a certain value
4) Section D – A building material is carried horizontally to be inserted between the supporting board and the L-board
5) Section E – A building material is inserted; about 7 N of external force is provided by a
n operator to make press pits, generating about 25 N of contact force
6) Section F - Inserted horizontally, a building material is then inserted vertically
Trang 4Inserting building materials between the supporting board and the L-board is substituted
for actual installation operation As the gap is narrower than the thickness of building
materials, they are moved horizontally and vertically with the supporting board connected
to ‘spring A’ being pressed in order to complete the installation operation If the supporting
board is pressed, it means that compliance occurred; if the length of compression exceeds a
certain range, the result is contact force which causes the robot to move in the opposite
direction In this experiment, building materials were limited to 60 N, considering the
specifications of the manipulator, and manufactured into models of curtain wall or panel
Fig 17 shows a simulation for handling building materials through an experimental system
Once building materials are completely fixed to a robot through a vacuum suction device at
a loading site, the robot is moved relatively rapidly to the vicinity of the installation position
through a wireless controller Precise positioning is performed by human-robot cooperative
control In handling building materials, an operator is encouraged to collect information on
the operation in real time in order to cope with changing environments Here, the speed or
efficiency of operation is proportional to an operator's workmanship
Fig 18 shows the result of a mock-up test of a building material handling work using an
experimental system A comparison was made between the contact force (F e) with
environments and an operator's force (F h), measured by sensors during the handling of
building materials F h and F e refer to the mean value of forces measured in the x, y, and z
directions by a force/torque sensor during operation time T h and T e, respectively, as shown
in the following (10)
(a) Adsorption of a building material (b) Transportation through a wireless controller
(c) Positioning through human-robot cooperation (d) Installing (coupling) of a building material
Fig 17 An experimental system
Fig 18 F e and F h in simulation
Each section can be described as follows:
1) Section A – A building material is carried to an installation position by the operators' fo
rce (F h) As seen in the graph, about 50 N of building materials are carried by about 70
N of external force supplied by an operator The force augmentation ratio (α) is about 7,
which is necessary to access the supporting board of the experimental system
2) Section B - Contact with the environment (experimental system) begins to occur, genera
ting a maximum of 70 N of contact force (F e) Even at the moment of contact, the operator's force is maintained to press the supporting board of the experimental system 3) Section C - Not the operator's force but rather his or her torque is transmitted to improv
e posture About 2 N of compliance force is generated by the correlation between the external force provided and the impedance parameters of the experimental system This value is used to press a spring connected to a supporting board into a position with a certain value
4) Section D – A building material is carried horizontally to be inserted between the supporting board and the L-board
5) Section E – A building material is inserted; about 7 N of external force is provided by a
n operator to make press pits, generating about 25 N of contact force
6) Section F - Inserted horizontally, a building material is then inserted vertically
Trang 5A total of about 17 seconds is spent on the test, with an average 7 N or less required of an
operator
7 Conclusions and future works
The prototype of MFR for handling building materials presented in this study combines a
manipulator and a mobile platform standardized in modular form to compose its basic
system Also, the hardware and software necessary for each area of application were
composed of additional modules and combined with the robot’s basic system The
suggested MFR can execute particular operations in various areas such as construction,
national defense and rescue by changing these additional modules One of the advantages of
the proposed MFR can be handled building materials through human-robot cooperation
For this cooperation, the robot controller (HRI device) and end-effector (vacuum suction
device) are combined in the basic system Also, human-robot cooperative control is done
through target dynamics modeling of human, robot, environment and control of impedance
and external force inputted from the power/torque sensor attached to the additional
module In addition, a wireless control and emergency control function were added through
other extra equipment
Applying the suggested MFR to construction works can be used as one of solutions to the
problem of unbalanced supply of manpower, a problem raised in construction industry
Also, construction safety will be assured because when a construction material is
implemented by press fit with a material already installed, compliance occurs within the
elastic range of the material and it is installed without damaging either object
The expected results applying to advantages and disadvantages of both existing curtain wall
installation robot (ASCI) and MFR are compared with and analyzed in Table 4 As seen from
the table, the proposed robot will be expected that it will be safer and more efficient than the
existing one
cooperation Number of
Be compatible in various work through a change of a basic system and additional modules Safety Damage to construction materials and robot system by malfunction and system through force reflection Protection construction materials
Table 4 Comparison and analysis of the ASCI and MFR in a construction site
A manipulator and a mobile platform, the basic system of the MFR, are combined to suit
various working conditions and construction materials as module type Therefore it is
possible to install a variety of construction materials in various construction sites Actual
size of MFR for construction works is developing through the experiment result executed in our laboratory
To apply a MFR at real construction sites, we must execute additional work required for application Firstly, according to analysis of job definition and working condition, it is deduced that the conceptual design of a construction robot for installing bulk building materials Secondly, practical arts (including robotized construction process) for applying to real construction sites should be proposed Finally, after field test at a real construction site, productivity and safety of the developed system are compared with the existing construction equipment
In next study, we will apply a MFR to a real construction site to install bulk glass ceiling that
is installed 15m above the ground Also, in realizing the potential of the suggested MFR, additional modules which consider the abilities and specifications required by national defense and rescue operations will be developed in the future
Bernold, L.E (1987) Automation and robotics in construction: A challenge and change for
an industry in transition International Journal of Project Management: The Journal of the International Project Management Association, Vol 5, No 3, page numbers (155–
160), ISSN 0263-7863 Choi, H.S., Han, C.S., Lee, K.Y & Lee, S.H (2005) Development of hybrid robot for
construction works with pneumatic actuator Automation in Construction, Vol 14,
No 4, (November 2004) page numbers (452–459), ISSN 0926-5805 Cusack, M (1994) Automation and robotics the interdependence of design and construction
systems Industrial Robot, Vol 21, No 4, page numbers (10–14), ISSN 0143-991X
Fukuda, T., Fujisawa, Y., Arai, F., Muro, H., Hoshino, K., Miyazaki, K., Ohtsubo, K &
Uehara, K (1991) A New Robotic Manipulator in Construction Based on
Man-Robot Cooperation Work Proceedings of the 8th International Symposium on Automation and Robotics in Construction, pp 239-245, Stuttgart, Germany, June 1991,
IAARC, Eindhoven Fukuda, T., Fujisawa, Y., Kosuge, K., Arai, F., Muro, H., Hoshino, K., Miyazaki, K., Ohtsubo,
K & Uehara, K (1991) Manipulator for Man-Robot Cooperation International Conference on Industrial Electronics, Control and Instrumentation, pp 996-1001, Kobe,
Japan, October 1991, IEEE, CA Gambao, E., Balaguer, C & Gebhart, F (2000) Robot assembly system for computer-
integrated construction Automation in Construction, Vol 9, No 5-6, (June 2000) page
numbers (479–487), ISSN 0926-5805
Trang 6A total of about 17 seconds is spent on the test, with an average 7 N or less required of an
operator
7 Conclusions and future works
The prototype of MFR for handling building materials presented in this study combines a
manipulator and a mobile platform standardized in modular form to compose its basic
system Also, the hardware and software necessary for each area of application were
composed of additional modules and combined with the robot’s basic system The
suggested MFR can execute particular operations in various areas such as construction,
national defense and rescue by changing these additional modules One of the advantages of
the proposed MFR can be handled building materials through human-robot cooperation
For this cooperation, the robot controller (HRI device) and end-effector (vacuum suction
device) are combined in the basic system Also, human-robot cooperative control is done
through target dynamics modeling of human, robot, environment and control of impedance
and external force inputted from the power/torque sensor attached to the additional
module In addition, a wireless control and emergency control function were added through
other extra equipment
Applying the suggested MFR to construction works can be used as one of solutions to the
problem of unbalanced supply of manpower, a problem raised in construction industry
Also, construction safety will be assured because when a construction material is
implemented by press fit with a material already installed, compliance occurs within the
elastic range of the material and it is installed without damaging either object
The expected results applying to advantages and disadvantages of both existing curtain wall
installation robot (ASCI) and MFR are compared with and analyzed in Table 4 As seen from
the table, the proposed robot will be expected that it will be safer and more efficient than the
existing one
cooperation Number of
Be compatible in various work through a change of a basic system
and additional modules Safety Damage to construction materials and robot system by malfunction and system through force reflection Protection construction materials
Table 4 Comparison and analysis of the ASCI and MFR in a construction site
A manipulator and a mobile platform, the basic system of the MFR, are combined to suit
various working conditions and construction materials as module type Therefore it is
possible to install a variety of construction materials in various construction sites Actual
size of MFR for construction works is developing through the experiment result executed in our laboratory
To apply a MFR at real construction sites, we must execute additional work required for application Firstly, according to analysis of job definition and working condition, it is deduced that the conceptual design of a construction robot for installing bulk building materials Secondly, practical arts (including robotized construction process) for applying to real construction sites should be proposed Finally, after field test at a real construction site, productivity and safety of the developed system are compared with the existing construction equipment
In next study, we will apply a MFR to a real construction site to install bulk glass ceiling that
is installed 15m above the ground Also, in realizing the potential of the suggested MFR, additional modules which consider the abilities and specifications required by national defense and rescue operations will be developed in the future
Bernold, L.E (1987) Automation and robotics in construction: A challenge and change for
an industry in transition International Journal of Project Management: The Journal of the International Project Management Association, Vol 5, No 3, page numbers (155–
160), ISSN 0263-7863 Choi, H.S., Han, C.S., Lee, K.Y & Lee, S.H (2005) Development of hybrid robot for
construction works with pneumatic actuator Automation in Construction, Vol 14,
No 4, (November 2004) page numbers (452–459), ISSN 0926-5805 Cusack, M (1994) Automation and robotics the interdependence of design and construction
systems Industrial Robot, Vol 21, No 4, page numbers (10–14), ISSN 0143-991X
Fukuda, T., Fujisawa, Y., Arai, F., Muro, H., Hoshino, K., Miyazaki, K., Ohtsubo, K &
Uehara, K (1991) A New Robotic Manipulator in Construction Based on
Man-Robot Cooperation Work Proceedings of the 8th International Symposium on Automation and Robotics in Construction, pp 239-245, Stuttgart, Germany, June 1991,
IAARC, Eindhoven Fukuda, T., Fujisawa, Y., Kosuge, K., Arai, F., Muro, H., Hoshino, K., Miyazaki, K., Ohtsubo,
K & Uehara, K (1991) Manipulator for Man-Robot Cooperation International Conference on Industrial Electronics, Control and Instrumentation, pp 996-1001, Kobe,
Japan, October 1991, IEEE, CA Gambao, E., Balaguer, C & Gebhart, F (2000) Robot assembly system for computer-
integrated construction Automation in Construction, Vol 9, No 5-6, (June 2000) page
numbers (479–487), ISSN 0926-5805
Trang 7Han, H (2005) Automated construction technologies: analyses and future development strategies,
Master’s thesis of science in architecture studies at the Massachusetts Institute of
Technology, MA
Hogan, N (1985) Impedance control: an approach to manipulation, Part I-III ASME Journal
of Dynamic Systems, Measurements and Control Vol 107, No 3, (September 1985)
page numbers (1-24), ISSN 0022-0434
Hollingum, J (1999) Robots in agriculture The Industrial Robot, Vol 26, No 6, (1999) page
numbers (438-445), ISSN 0143-991X
Isao, S., Hidetoshi, O., Nobuhiro, T & Hideo, T (1996) Development of automated exterior
curtain wall installation system Proceedings of International Symposium on
Automation and Robotics in Construction, pp 915-924, Tokyo, Japan, June 1996,
IAARC, Eindhoven
Kangari, R (1991) Advanced robotics in civil engineering and construction 91 ICAR Fifth
International Conference on Advanced Robotics, pp 375-378, ISBN 0-7803-0078-5, Pisa,
Italy, 19-22 Jun 1991, IEEE, CA
Kazerooni, H (1989) Human/robot interaction via the transfer of power and information
signals – part I & II: Dynamics and control analysis IEEE Proc of IEEE International
Conference on Robotics and Automation, pp 1632-1647, AZ, USA, May 1989, IEEE, CA
Kazerooni, H & Mahoney, S.L (1991) Dynamics and control of robotic systems worn by
humans, ASME Journal of Dynamic Systems, Measurement and Control, Vol 133, No
3, (September 1991) page numbers (379-387), ISSN 0022-0434
Kochan, A (2000) Robots for automating construction—An abundance of research
Industrial Robot, Vol 27, No 2, page numbers (111–113), ISSN 0143-991X
Kosuge K., Fujisawa, Y & Fukuda, T (1993) Mechanical system control with
man-machine-environment interactions Proc of IEEE International Conference on Robotics and
Automation, pp 239-244, Atlanta, USA, May 1993, IEEE, CA
Lee, S.H Adams, T.M & Ryoo B.Y (1997) A fuzzy navigation system for mobile
construction robot Automation in Construction, Vol 6, No 2, (May 1997) page
numbers (97-107), ISSN 0926-5805
Lee, S.Y., Lee, K.Y, Lee, S.H, Kim, J.W & Han, C.S (2007) Human-Robot Cooperation
Control for Installing Heavy Construction Materials Autonomous Robots, Vol 22,
No 3, (April 2007) page numbers (305-319), ISSN 0929-5593
LeMaster, E.A & Rock, S.M (2003) A local-area GPS pseudolitebased navigation system for
mars rovers Autonomous Robots, Vol 14, No 2-3, (March 2003) page numbers
(209-224), ISSN 0929-5593
Miller, J.S (1968) The Myotron – A Servo-controlled exoskeleton for the measurement of muscular
kinetics Cornell Aeronautical Laboratory Report VO-2401-E-1
Masatoshi, H., Yukio, H., Hisashi, M., Kinya, T., Sigeyuki, K., Kohtarou, M., Tomoyuki, T &
Takumi, O (1996) Development of interior finishing unit assembly system with
robot: WASCOR IV research project report Automation in Construction, Vol 5, No
1, (1996) page numbers (31–38), ISSN 0926-5805
Mosher, R.S (1967) Handyman to Hardiman Automotive Engineering Congress SME670088
Poppy, W (1994) Driving force and status of automation and robotics in construction in
Europe Automation in Construction, Vol 2, No 4, page numbers (281–289), ISSN
0926-5805
Roozbeh K (1985) Advanced Robotics in Civil Engineering and Construction Proc of IEEE
International Conference on Robotics and Automation, pp 375-378, Tokyo, Japan,
September 1985, IEEE, CA Santos, P.G., Estremera, J., Jimenez, M.A., Garcia, E & Armada, M (2003) Manipulators
helps out with plaster panels in construction The Industrial Robot, Vol 30, No 6,
(2003) page numbers (508–514), ISSN 0143-991X
Skibniewski, M.J (1988) Robotics in civil engineering, Van Nostrand–Reinhold, ISBN
0442319258, New York Skibniewski, M.J & Wooldridge, S.C (1992) Robotic materials handling for automated
building construction technology Automation in Construction, Vol 1, No 3, (1992)
page numbers (251– 266), ISSN 0926-5805
Warszawski, A (1985) Economic implications of robotics in building Building and
Environment, Vol 20, No 2, page numbers (73~81), ISSN 0360-1323
Wen, X., Romano, V.F & Rovetta, A (1991) Remote control and robotics in construction
engineering 91 ICAR Fifth International Conference on Advanced Robotics, ISBN 0-7803-0078-5, Pisa, Italy, 19-22 Jun 1991, IEEE, CA
Whitcomb, L.L (2000) Underwater robotics: Out of the research laboratory and into the
field Proceedings of IEEE International Conference on Robotics and Automation, pp
709-716, ISBN 0-7803-5886-4, San Francisco, USA, April 2000, IEEE, CA
Wong, B & Spetsakis, M (2000) Scene reconstruction and robot navigation using dynamic
fields Autonomous Robots, Vol 8, No 1, (January 2000) page numbers (71-86), ISSN
0929-5593
Trang 8Han, H (2005) Automated construction technologies: analyses and future development strategies,
Master’s thesis of science in architecture studies at the Massachusetts Institute of
Technology, MA
Hogan, N (1985) Impedance control: an approach to manipulation, Part I-III ASME Journal
of Dynamic Systems, Measurements and Control Vol 107, No 3, (September 1985)
page numbers (1-24), ISSN 0022-0434
Hollingum, J (1999) Robots in agriculture The Industrial Robot, Vol 26, No 6, (1999) page
numbers (438-445), ISSN 0143-991X
Isao, S., Hidetoshi, O., Nobuhiro, T & Hideo, T (1996) Development of automated exterior
curtain wall installation system Proceedings of International Symposium on
Automation and Robotics in Construction, pp 915-924, Tokyo, Japan, June 1996,
IAARC, Eindhoven
Kangari, R (1991) Advanced robotics in civil engineering and construction 91 ICAR Fifth
International Conference on Advanced Robotics, pp 375-378, ISBN 0-7803-0078-5, Pisa,
Italy, 19-22 Jun 1991, IEEE, CA
Kazerooni, H (1989) Human/robot interaction via the transfer of power and information
signals – part I & II: Dynamics and control analysis IEEE Proc of IEEE International
Conference on Robotics and Automation, pp 1632-1647, AZ, USA, May 1989, IEEE, CA
Kazerooni, H & Mahoney, S.L (1991) Dynamics and control of robotic systems worn by
humans, ASME Journal of Dynamic Systems, Measurement and Control, Vol 133, No
3, (September 1991) page numbers (379-387), ISSN 0022-0434
Kochan, A (2000) Robots for automating construction—An abundance of research
Industrial Robot, Vol 27, No 2, page numbers (111–113), ISSN 0143-991X
Kosuge K., Fujisawa, Y & Fukuda, T (1993) Mechanical system control with
man-machine-environment interactions Proc of IEEE International Conference on Robotics and
Automation, pp 239-244, Atlanta, USA, May 1993, IEEE, CA
Lee, S.H Adams, T.M & Ryoo B.Y (1997) A fuzzy navigation system for mobile
construction robot Automation in Construction, Vol 6, No 2, (May 1997) page
numbers (97-107), ISSN 0926-5805
Lee, S.Y., Lee, K.Y, Lee, S.H, Kim, J.W & Han, C.S (2007) Human-Robot Cooperation
Control for Installing Heavy Construction Materials Autonomous Robots, Vol 22,
No 3, (April 2007) page numbers (305-319), ISSN 0929-5593
LeMaster, E.A & Rock, S.M (2003) A local-area GPS pseudolitebased navigation system for
mars rovers Autonomous Robots, Vol 14, No 2-3, (March 2003) page numbers
(209-224), ISSN 0929-5593
Miller, J.S (1968) The Myotron – A Servo-controlled exoskeleton for the measurement of muscular
kinetics Cornell Aeronautical Laboratory Report VO-2401-E-1
Masatoshi, H., Yukio, H., Hisashi, M., Kinya, T., Sigeyuki, K., Kohtarou, M., Tomoyuki, T &
Takumi, O (1996) Development of interior finishing unit assembly system with
robot: WASCOR IV research project report Automation in Construction, Vol 5, No
1, (1996) page numbers (31–38), ISSN 0926-5805
Mosher, R.S (1967) Handyman to Hardiman Automotive Engineering Congress SME670088
Poppy, W (1994) Driving force and status of automation and robotics in construction in
Europe Automation in Construction, Vol 2, No 4, page numbers (281–289), ISSN
0926-5805
Roozbeh K (1985) Advanced Robotics in Civil Engineering and Construction Proc of IEEE
International Conference on Robotics and Automation, pp 375-378, Tokyo, Japan,
September 1985, IEEE, CA Santos, P.G., Estremera, J., Jimenez, M.A., Garcia, E & Armada, M (2003) Manipulators
helps out with plaster panels in construction The Industrial Robot, Vol 30, No 6,
(2003) page numbers (508–514), ISSN 0143-991X
Skibniewski, M.J (1988) Robotics in civil engineering, Van Nostrand–Reinhold, ISBN
0442319258, New York Skibniewski, M.J & Wooldridge, S.C (1992) Robotic materials handling for automated
building construction technology Automation in Construction, Vol 1, No 3, (1992)
page numbers (251– 266), ISSN 0926-5805
Warszawski, A (1985) Economic implications of robotics in building Building and
Environment, Vol 20, No 2, page numbers (73~81), ISSN 0360-1323
Wen, X., Romano, V.F & Rovetta, A (1991) Remote control and robotics in construction
engineering 91 ICAR Fifth International Conference on Advanced Robotics, ISBN 0-7803-0078-5, Pisa, Italy, 19-22 Jun 1991, IEEE, CA
Whitcomb, L.L (2000) Underwater robotics: Out of the research laboratory and into the
field Proceedings of IEEE International Conference on Robotics and Automation, pp
709-716, ISBN 0-7803-5886-4, San Francisco, USA, April 2000, IEEE, CA
Wong, B & Spetsakis, M (2000) Scene reconstruction and robot navigation using dynamic
fields Autonomous Robots, Vol 8, No 1, (January 2000) page numbers (71-86), ISSN
0929-5593
Trang 10Miguel F M Lima, J A Tenreiro Machado and António Ferrolho
x
A Sensor Classification Strategy
for Robotic Manipulators
Portugal, {lima, antferrolho}@mail.estv.ipv.pt
Portugal, jtm@isep.ipp.pt
1 Introduction
In practice the robotic manipulators present some degree of unwanted vibrations The
advent of lightweight arm manipulators, mainly in the aerospace industry, where weight is
an important issue, leads to the problem of intense vibrations On the other hand, robots
interacting with the environment often generate impacts that propagate through the
mechanical structure and produce also vibrations
In order to analyze these phenomena a robot signal acquisition system was developed The
manipulator motion produces vibrations, either from the structural modes or from
end-effector impacts The instrumentation system acquires signals from several sensors that
capture the joint positions, mass accelerations, forces and moments, and electrical currents
in the motors Afterwards, an analysis package, running off-line, reads the data recorded by
the acquisition system and extracts the signal characteristics
Due to the multiplicity of sensors, the data obtained can be redundant because the same
type of information may be seen by two or more sensors Because of the price of the sensors,
this aspect can be considered in order to reduce the cost of the system On the other hand,
the placement of the sensors is an important issue in order to obtain the suitable signals of
the vibration phenomenon Moreover, the study of these issues can help in the design
optimization of the acquisition system In this line of thought a sensor classification scheme
is presented
Several authors have addressed the subject of the sensor classification scheme White
(White, 1987) presents a flexible and comprehensive categorizing scheme that is useful for
describing and comparing sensors The author organizes the sensors according to several
aspects: measurands, technological aspects, detection means, conversion phenomena, sensor
materials and fields of application Michahelles and Schiele (Michahelles & Schiele, 2003)
systematize the use of sensor technology They identified several dimensions of sensing that
represent the sensing goals for physical interaction A conceptual framework is introduced
that allows categorizing existing sensors and evaluates their utility in various applications
This framework not only guides application designers for choosing meaningful sensor
17
Trang 11subsets, but also can inspire new systems and leads to the evaluation of existing
applications
Today’s technology offers a wide variety of sensors In order to use all the data from the
diversity of sensors a framework of integration is needed Sensor fusion, fuzzy logic, and
neural networks are often mentioned when dealing with problem of combing information
from several sensors to get a more general picture of a given situation The study of data
fusion has been receiving considerable attention (Esteban et al., 2005; Luo & Kay, 1990) A
survey of the state of the art in sensor fusion for robotics can be found in (Hackett & Shah,
1990) Henderson and Shilcrat (Henderson & Shilcrat, 1984) introduced the concept of logic
sensor that defines an abstract specification of the sensors to integrate in a multisensor
system
The recent developments of micro electro mechanical sensors (MEMS) with unwired
communication capabilities allow a sensor network with interesting capacity This
technology was applied in several applications (Arampatzis & Manesis, 2005), including
robotics Cheekiralla and Engels (Cheekiralla & Engels, 2005) propose a classification of the
unwired sensor networks according to its functionalities and properties
This paper presents a development of a sensor classification scheme based on the frequency
spectrum of the signals and on a statistical metrics
Bearing these ideas in mind, this paper is organized as follows Section 2 describes briefly
the robotic system enhanced with the instrumentation setup Section 3 presents the
experimental results Finally, section 4 draws the main conclusions and points out future
work
2 Experimental platform
The developed experimental platform has two main parts: the hardware and the software
components (Lima et al., 2005) The hardware architecture is shown in Fig 1 Essentially it is
made up of a robot manipulator, a personal computer (PC), and an interface electronic
system
The interface box is inserted between the robot arm and the robot controller, in order to
acquire the internal robot signals; nevertheless, the interface captures also external signals,
such as those arising from accelerometers and force/torque sensors The modules are made
up of electronic cards specifically designed for this work The function of the modules is to
adapt the signals and to isolate galvanically the robot’s electronic equipment from the rest of
the hardware required by the experiments
The software package runs in a Pentium 4, 3.0 GHz PC and, from the user’s point of view,
consists of two applications: the acquisition application and the analysis package The
acquisition application is a real time program for acquiring and recording the robot signals
After the real time acquisition, the analysis package processes the data off-line in two
phases, namely, pre-processing and processing The preprocessing phase consists of the
signal selection in time, and their synchronization and truncation The processing stage
implements several algorithms for signal processing such as the auto and cross correlation,
and Fourier transform (FT)
Interface Box
From Position Sensors
PCI Bus
Card 4 DSP Force/Torque
Card 3 Encoder Counter
Card 1
RS 232 Serial Port
External Axis
Flexible Beam Accelerometers
Force/Torque Sensor
Power Supply
r r r r r Low Pass Filter
& Level Adjust
To Motors
Robot Controller r
Card 2 D/A
Motor Driver
r r r r Hall-Effect Current Sensor
Buffer Circuit
From Accelerometers Power & Signal Connector
Adapter Circuit PC
Fig 1 Block diagram of the hardware architecture
3 Experimental results
According to the platform described in Section 2 a set of experiments is developed Based on the signals captured from the robot this section presents several results obtained both in the time and frequency domains
In the experiments a flexible link is used that consists of a long and round flexible steel rod clamped to the end-effector of the manipulator In order to analyze the impact phenomena
in different situations two types of beams are used Their physical properties are shown in Table 1 The robot motion is programmed in a way such that the rods move against a rigid surface Figure 2 depicts the robot with the flexible link and the impact surface
During the motion of the manipulator the clamped rod is moved by the robot against a rigid surface An impact occurs and several signals are recorded with a sampling frequency of
f s = 500 Hz The signals come from several sensors, such as accelerometers, force and torque sensor, position encoders, and current sensors
In order to have a wide set of signals captured during the impact of the rods against the vertical screen thirteen trajectories were defined Those trajectories are based on several points selected systematically in the workspace of the robot, located on a virtual Cartesian coordinate system (see Fig 3) This coordinate system is completely independent from that used on the measurement system For each trajectory the motion of the robot begins in one
of these points, moves against the surface and returns to the initial point A parabolic profile was used for the trajectories
Trang 12subsets, but also can inspire new systems and leads to the evaluation of existing
applications
Today’s technology offers a wide variety of sensors In order to use all the data from the
diversity of sensors a framework of integration is needed Sensor fusion, fuzzy logic, and
neural networks are often mentioned when dealing with problem of combing information
from several sensors to get a more general picture of a given situation The study of data
fusion has been receiving considerable attention (Esteban et al., 2005; Luo & Kay, 1990) A
survey of the state of the art in sensor fusion for robotics can be found in (Hackett & Shah,
1990) Henderson and Shilcrat (Henderson & Shilcrat, 1984) introduced the concept of logic
sensor that defines an abstract specification of the sensors to integrate in a multisensor
system
The recent developments of micro electro mechanical sensors (MEMS) with unwired
communication capabilities allow a sensor network with interesting capacity This
technology was applied in several applications (Arampatzis & Manesis, 2005), including
robotics Cheekiralla and Engels (Cheekiralla & Engels, 2005) propose a classification of the
unwired sensor networks according to its functionalities and properties
This paper presents a development of a sensor classification scheme based on the frequency
spectrum of the signals and on a statistical metrics
Bearing these ideas in mind, this paper is organized as follows Section 2 describes briefly
the robotic system enhanced with the instrumentation setup Section 3 presents the
experimental results Finally, section 4 draws the main conclusions and points out future
work
2 Experimental platform
The developed experimental platform has two main parts: the hardware and the software
components (Lima et al., 2005) The hardware architecture is shown in Fig 1 Essentially it is
made up of a robot manipulator, a personal computer (PC), and an interface electronic
system
The interface box is inserted between the robot arm and the robot controller, in order to
acquire the internal robot signals; nevertheless, the interface captures also external signals,
such as those arising from accelerometers and force/torque sensors The modules are made
up of electronic cards specifically designed for this work The function of the modules is to
adapt the signals and to isolate galvanically the robot’s electronic equipment from the rest of
the hardware required by the experiments
The software package runs in a Pentium 4, 3.0 GHz PC and, from the user’s point of view,
consists of two applications: the acquisition application and the analysis package The
acquisition application is a real time program for acquiring and recording the robot signals
After the real time acquisition, the analysis package processes the data off-line in two
phases, namely, pre-processing and processing The preprocessing phase consists of the
signal selection in time, and their synchronization and truncation The processing stage
implements several algorithms for signal processing such as the auto and cross correlation,
and Fourier transform (FT)
Interface Box
From Position Sensors
PCI Bus
Card 4 DSP Force/Torque
Card 3 Encoder Counter
Card 1
RS 232 Serial Port
External Axis
Flexible Beam Accelerometers
Force/Torque Sensor
Power Supply
r r r r r Low Pass Filter
& Level Adjust
To Motors
Robot Controller r
Card 2 D/A
Motor Driver
r r r r Hall-Effect Current Sensor
Buffer Circuit
From Accelerometers Power & Signal Connector
Adapter Circuit PC
Fig 1 Block diagram of the hardware architecture
3 Experimental results
According to the platform described in Section 2 a set of experiments is developed Based on the signals captured from the robot this section presents several results obtained both in the time and frequency domains
In the experiments a flexible link is used that consists of a long and round flexible steel rod clamped to the end-effector of the manipulator In order to analyze the impact phenomena
in different situations two types of beams are used Their physical properties are shown in Table 1 The robot motion is programmed in a way such that the rods move against a rigid surface Figure 2 depicts the robot with the flexible link and the impact surface
During the motion of the manipulator the clamped rod is moved by the robot against a rigid surface An impact occurs and several signals are recorded with a sampling frequency of
f s = 500 Hz The signals come from several sensors, such as accelerometers, force and torque sensor, position encoders, and current sensors
In order to have a wide set of signals captured during the impact of the rods against the vertical screen thirteen trajectories were defined Those trajectories are based on several points selected systematically in the workspace of the robot, located on a virtual Cartesian coordinate system (see Fig 3) This coordinate system is completely independent from that used on the measurement system For each trajectory the motion of the robot begins in one
of these points, moves against the surface and returns to the initial point A parabolic profile was used for the trajectories
Trang 13Fig 2 Steel rod impact against a rigid surface
Table 1 Physical properties of the flexible beams
Fig 3 Schematic representation 3D (left) and 2D (right) of the robot and the impact surface
on the virtual cartesian coordinate system
3.1 Analysis in the time domain
Figures 4 to 7 depict some of the signals corresponding to the cases: (i) without impact, (ii)
the impact of the rod on a gross screen and (iii) the impact of the rod on a thin screen using
either the thin or the gross rod
In this chapter only the most relevant signals are depicted, namely the forces and moments
at the gripper sensor, the electrical currents of the robot’s axes motors, and the rod
accelerations The signals present clearly a strong variation at the instant of the impact that
occurs, approximately, at t = 3 s Consequently, the effect of the impact forces (Fig 4 left)
Fig 4 Forces { F x , F y , F z } at the gripper sensor: thin rod (left); gross rod (right)
Fig 5 Moments { M x , M y , M z } at the gripper sensor: thin rod (left); gross rod (right) Figure 7 presents the accelerations at the rod free-end (accelerometer 1), where the impact occurs, and at the rod clamped-end (accelerometer 2) The amplitudes of the accelerometers signals are higher near the rod impact side Furthermore, the values of the accelerations obtained for the thin rod (Fig 7 left) are higher than those for the gross rod (Fig 7 right), because the thin rod is more flexible
3.2 Analysis in the frequency domain
Figures 8 and 9 show, as examples, the amplitude of the Fast Fourier Transform (FFT), of two signals captured during the same impact trajectory These figures illustrate the different
Trang 14Fig 2 Steel rod impact against a rigid surface
Table 1 Physical properties of the flexible beams
Fig 3 Schematic representation 3D (left) and 2D (right) of the robot and the impact surface
on the virtual cartesian coordinate system
3.1 Analysis in the time domain
Figures 4 to 7 depict some of the signals corresponding to the cases: (i) without impact, (ii)
the impact of the rod on a gross screen and (iii) the impact of the rod on a thin screen using
either the thin or the gross rod
In this chapter only the most relevant signals are depicted, namely the forces and moments
at the gripper sensor, the electrical currents of the robot’s axes motors, and the rod
accelerations The signals present clearly a strong variation at the instant of the impact that
occurs, approximately, at t = 3 s Consequently, the effect of the impact forces (Fig 4 left)
Fig 4 Forces { F x , F y , F z } at the gripper sensor: thin rod (left); gross rod (right)
Fig 5 Moments { M x , M y , M z } at the gripper sensor: thin rod (left); gross rod (right) Figure 7 presents the accelerations at the rod free-end (accelerometer 1), where the impact occurs, and at the rod clamped-end (accelerometer 2) The amplitudes of the accelerometers signals are higher near the rod impact side Furthermore, the values of the accelerations obtained for the thin rod (Fig 7 left) are higher than those for the gross rod (Fig 7 right), because the thin rod is more flexible
3.2 Analysis in the frequency domain
Figures 8 and 9 show, as examples, the amplitude of the Fast Fourier Transform (FFT), of two signals captured during the same impact trajectory These figures illustrate the different
Trang 15behaviors of the spectrum, depending on the signal in study All the signals of the
trajectories set referred previously were studied, but only the most relevant are depicted
Fig 6 Electrical currents { I1, I2, I3, I4, I5 } of the robot’s axes motors: thin rod (left); gross rod
(right)
Fig 7 Rod accelerations { A1, A2 }: thin rod (left); gross rod (right)
In order to examine the behavior of the FT signal, in a systematic way, a trendline was
superimposed over the spectrum over, at least, one decade The trendline is based on the
power law approximation (Lima et al., 2006)
f(t) cm
where F is the FT of the signal,cis a constant that depends on the amplitude, ω is the
frequency, andmis the slope
For each type of signal, the frequency interval was defined approximately in the middle range of the frequency content of the signal
Figure 8 shows the FFT amplitude of the electrical current of the axis 3 motor that occurs in the case of impact with the thin rod A trendline was calculated, and superimposed to the
signal (case ii), with slope m = −1.31 The others current signals were studied, revealing also
an identical behavior in terms of its spectrum spread, both under impact and no impact conditions, either for the thin rod or the gross rod The spectrum was approximated by trendlines in a frequency range larger than one decade
According to the robot manufacturer specifications (Robotec, 1996) the loop control of the
robot has a cycle time of t c = 10 ms This fact is observed approximately at the fundamental
(f c = 100 Hz) and multiple harmonics in all spectra of motor currents
The FFT amplitudes of the axes positions signals were studied (Lima et al., 2007), revealing also a behavior similar to the electrical current in terms of the spectrum spread for the tested conditions (impact, no impact, thin rod and gross rod)
Figure 9 shows the FFT amplitude of the F z force (case i) due to the impact with the thin rod
This spectrum is not so well defined in a large frequency range Nevertheless, the spectrum was approximated by a trendline in a frequency range of approximately one decade in order
to get a systematic method of comparison The trendline has a slope of m = −0.13
The torques and accelerations signals were studied also for the distinct test conditions, namely: impact, no impact, thin rod and gross rod Their FFT amplitudes revealed also an identical behavior in terms of its spectrum spread for the tested conditions
Whereas the trendlines used for the electrical currents and position signals FT seem appropriate, the same technique used for the forces/moments and acceleration signals is questionable However, in spite of this, trendlines were used for all FT signals in order to obtain comparable units In fact, the purpose of this research is to establish a relationship between signals of the same system based on the spectrum behavior
Fig 8 Spectrum of the axis 3 motor current I3 for the thin rod
Trang 16behaviors of the spectrum, depending on the signal in study All the signals of the
trajectories set referred previously were studied, but only the most relevant are depicted
Fig 6 Electrical currents { I1, I2, I3, I4, I5 } of the robot’s axes motors: thin rod (left); gross rod
(right)
Fig 7 Rod accelerations { A1, A2 }: thin rod (left); gross rod (right)
In order to examine the behavior of the FT signal, in a systematic way, a trendline was
superimposed over the spectrum over, at least, one decade The trendline is based on the
power law approximation (Lima et al., 2006)
f(t) cm
where F is the FT of the signal,cis a constant that depends on the amplitude, ω is the
frequency, andmis the slope
For each type of signal, the frequency interval was defined approximately in the middle range of the frequency content of the signal
Figure 8 shows the FFT amplitude of the electrical current of the axis 3 motor that occurs in the case of impact with the thin rod A trendline was calculated, and superimposed to the
signal (case ii), with slope m = −1.31 The others current signals were studied, revealing also
an identical behavior in terms of its spectrum spread, both under impact and no impact conditions, either for the thin rod or the gross rod The spectrum was approximated by trendlines in a frequency range larger than one decade
According to the robot manufacturer specifications (Robotec, 1996) the loop control of the
robot has a cycle time of t c = 10 ms This fact is observed approximately at the fundamental
(f c = 100 Hz) and multiple harmonics in all spectra of motor currents
The FFT amplitudes of the axes positions signals were studied (Lima et al., 2007), revealing also a behavior similar to the electrical current in terms of the spectrum spread for the tested conditions (impact, no impact, thin rod and gross rod)
Figure 9 shows the FFT amplitude of the F z force (case i) due to the impact with the thin rod
This spectrum is not so well defined in a large frequency range Nevertheless, the spectrum was approximated by a trendline in a frequency range of approximately one decade in order
to get a systematic method of comparison The trendline has a slope of m = −0.13
The torques and accelerations signals were studied also for the distinct test conditions, namely: impact, no impact, thin rod and gross rod Their FFT amplitudes revealed also an identical behavior in terms of its spectrum spread for the tested conditions
Whereas the trendlines used for the electrical currents and position signals FT seem appropriate, the same technique used for the forces/moments and acceleration signals is questionable However, in spite of this, trendlines were used for all FT signals in order to obtain comparable units In fact, the purpose of this research is to establish a relationship between signals of the same system based on the spectrum behavior
Fig 8 Spectrum of the axis 3 motor current I3 for the thin rod
Trang 17Fig 9 Spectrum of the F z force for the thin rod
3.3 Analysis of the spectrum trendlines slopes
Based on the several values of the spectrum trendlines slopes several statistics can be
performed During each trajectory of the robot eighteen signals were captured For each
trajectory there are three cases: (i) without impact, (ii) the impact of the rod on a gross
screen, and (iii) the impact of the rod on a thin screen As referred before, thirteen
trajectories were defined Additionally, the same trajectories were executed with the thin rod
and with the gross rod These samples lead to a population of 1404 slope values
A box plot provides a visual summary of many important aspects of a data distribution It
indicates the median, upper and lower quartile, upper and lower adjacent values (whiskers),
and the outlier individual points Figure 10 shows a box plot of the spectrum trendlines
slopes for the three cases of the thin rod impact, namely: (i) without impact, (ii) the impact of
the rod on a gross screen, and (iii) the impact of the rod on a thin screen Moreover, Fig 11
depicts the respective interquartile range (IQR) versus the median The IQR is obtained by
subtracting the lower (first) quartile value from the upper (third) quartile value
Fig 10 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the thin rod
Fig 11 IQR versus median for all the cases (i, ii, iii) using the thin rod
The IQR is a robust way of describing the dispersion of the data From Fig 11 three groups
of signals can be defined The ellipses depicted in the chart represent these groups The
forces {F x , F y , F z } and the accelerations {A1, A2} signals are located close to each other
Positions {P1, P2, P3, P4, P5}, moments {M x , M y }, and I3 signals are located on the left side of
the Fig 11 Finally, the other electrical currents {I1, I2, I4, I5} are situated in the middle of the
chart and near each other It rests the M z signal that apparently is alone
Figures 12 and 13 show the same statistic analysis described previously, but now for the
gross rod In Fig 13 again three groups of signals can be defined One groups the {F x , F y , F z,
A1, A2} signals, and the second is formed of the {I1, I2, I4, I5} signals The third group consists
of the {P1, P2, P3, P4, P5, M x , M y , M z , I3} signals Comparing with the thin rod case, it can be
seen that now the M z signal joined the group of “torques and positions”
Finally, figures 14 to 15 depict the statistics of the overall spectrum trendlines slopes, considering the data for the thin and gross rods Three groups are observed again: the group
of “positions and torques”, the group of “currents” and the group of “forces and
accelerations” As can be seen the I3 signal continues to remain in the same group of
“positions and torques” A deeper insight into the nature of this feature must be envisaged
to understand the behavior of the I3 signal
Fig 12 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the gross rod
Trang 18Fig 9 Spectrum of the F z force for the thin rod
3.3 Analysis of the spectrum trendlines slopes
Based on the several values of the spectrum trendlines slopes several statistics can be
performed During each trajectory of the robot eighteen signals were captured For each
trajectory there are three cases: (i) without impact, (ii) the impact of the rod on a gross
screen, and (iii) the impact of the rod on a thin screen As referred before, thirteen
trajectories were defined Additionally, the same trajectories were executed with the thin rod
and with the gross rod These samples lead to a population of 1404 slope values
A box plot provides a visual summary of many important aspects of a data distribution It
indicates the median, upper and lower quartile, upper and lower adjacent values (whiskers),
and the outlier individual points Figure 10 shows a box plot of the spectrum trendlines
slopes for the three cases of the thin rod impact, namely: (i) without impact, (ii) the impact of
the rod on a gross screen, and (iii) the impact of the rod on a thin screen Moreover, Fig 11
depicts the respective interquartile range (IQR) versus the median The IQR is obtained by
subtracting the lower (first) quartile value from the upper (third) quartile value
Fig 10 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the thin rod
Fig 11 IQR versus median for all the cases (i, ii, iii) using the thin rod
The IQR is a robust way of describing the dispersion of the data From Fig 11 three groups
of signals can be defined The ellipses depicted in the chart represent these groups The
forces {F x , F y , F z } and the accelerations {A1, A2} signals are located close to each other
Positions {P1, P2, P3, P4, P5}, moments {M x , M y }, and I3 signals are located on the left side of
the Fig 11 Finally, the other electrical currents {I1, I2, I4, I5} are situated in the middle of the
chart and near each other It rests the M z signal that apparently is alone
Figures 12 and 13 show the same statistic analysis described previously, but now for the
gross rod In Fig 13 again three groups of signals can be defined One groups the {F x , F y , F z,
A1, A2} signals, and the second is formed of the {I1, I2, I4, I5} signals The third group consists
of the {P1, P2, P3, P4, P5, M x , M y , M z , I3} signals Comparing with the thin rod case, it can be
seen that now the M z signal joined the group of “torques and positions”
Finally, figures 14 to 15 depict the statistics of the overall spectrum trendlines slopes, considering the data for the thin and gross rods Three groups are observed again: the group
of “positions and torques”, the group of “currents” and the group of “forces and
accelerations” As can be seen the I3 signal continues to remain in the same group of
“positions and torques” A deeper insight into the nature of this feature must be envisaged
to understand the behavior of the I3 signal
Fig 12 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the gross rod
Trang 19Fig 13 IQR versus median for all the cases (i, ii, iii) using the gross rod
Fig 14 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the thin and
gross rods
Fig 15 IQR versus median for all the cases (i, ii, iii) using the thin and gross rods
3.4 Metrics in the time domain
Several indices can be used to evaluate the relashionship between the signal, including statistical, entropy and information theory approaches These metrics are based on a
bidimensional probability density function associated with the two signals x1(t) and x2(t)
acquired in the same time interval and can be calculated according with the expression:
2 1 2 1
2 1 2
1
),(
),(,
dx dx x x
x x x
x P
(2)
where β is the bidimensional histogram
The marginal probability distributions of the signals x1(t) and x2(t) are denoted as P(x1) and
P(x2), respectively The expected values, E(x1) and E(x2), and the variances, V(x1) and V(x2), are then easily obtained
The correlation coefficient R (Orfanidis, 1996) is a statistical index that provides a measurement of the similarity between two signals x1(t) and x2(t) and is define as
)()(
)()()(,
2 1
2 1 2 1 2 1
x V x V
x E x E x x E x x
where E(x1x2) is the joint expected value
The mutual information (Shannon, 1948; Cover, 2006), or transinformation (Spataru, 1970) is the index that measures the dependence of two variables in the viewpoint of the information
theory The mutual information for the two signals x1(t) and x2(t) is:
)()(),(log,
2 1 2 1 2 2
x x P x
x P x
x
)()(),(log),(,
2 1 2 1 2 2 1 2
The entropy (Shannon, 1948) is a statistical measure of randomness This index applied to
the two signal x1(t) and x2(t) gives the join entropy (MacKay, 2003 ) between the two signal
defined as:
Figure 16 shows the squared correlation coefficient R2 between the signals captured during
the same impact trajectory, for an experiment in the case of (i) using the gross rod The results obtain with R2 are simetric relative to the diagonal formed by R2(x i ,x j ) for i = j, where
the metric is maximum, as expected To clearly visualize the results only one side is shown The correlation between the same families of signals is higher than the correlation between different families For example, the correlation between the currents and positions are low The same occurs between the currents and the forces, moments and accelerations It exists a
Trang 20Fig 13 IQR versus median for all the cases (i, ii, iii) using the gross rod
Fig 14 Statistics of spectrum trendlines slopes for all the cases (i, ii, iii) using the thin and
gross rods
Fig 15 IQR versus median for all the cases (i, ii, iii) using the thin and gross rods
3.4 Metrics in the time domain
Several indices can be used to evaluate the relashionship between the signal, including statistical, entropy and information theory approaches These metrics are based on a
bidimensional probability density function associated with the two signals x1(t) and x2(t)
acquired in the same time interval and can be calculated according with the expression:
2 1 2 1
2 1 2
1
),(
),(,
dx dx x x
x x x
x P
(2)
where β is the bidimensional histogram
The marginal probability distributions of the signals x1(t) and x2(t) are denoted as P(x1) and
P(x2), respectively The expected values, E(x1) and E(x2), and the variances, V(x1) and V(x2), are then easily obtained
The correlation coefficient R (Orfanidis, 1996) is a statistical index that provides a measurement of the similarity between two signals x1(t) and x2(t) and is define as
)()(
)()()(,
2 1
2 1 2 1 2 1
x V x V
x E x E x x E x x
where E(x1x2) is the joint expected value
The mutual information (Shannon, 1948; Cover, 2006), or transinformation (Spataru, 1970) is the index that measures the dependence of two variables in the viewpoint of the information
theory The mutual information for the two signals x1(t) and x2(t) is:
)()(),(log,
2 1 2 1 2 2
x x P x
x P x
x
)()(),(log),(,
2 1 2 1 2 2 1 2
The entropy (Shannon, 1948) is a statistical measure of randomness This index applied to
the two signal x1(t) and x2(t) gives the join entropy (MacKay, 2003 ) between the two signal
defined as:
Figure 16 shows the squared correlation coefficient R2 between the signals captured during
the same impact trajectory, for an experiment in the case of (i) using the gross rod The results obtain with R2 are simetric relative to the diagonal formed by R2(x i ,x j ) for i = j, where
the metric is maximum, as expected To clearly visualize the results only one side is shown The correlation between the same families of signals is higher than the correlation between different families For example, the correlation between the currents and positions are low The same occurs between the currents and the forces, moments and accelerations It exists a
Trang 21strong correlation between the positions and the forces, moments and accelerations that
depends, as expected, on the trajectory
Fig 16 Correlation between the signals for the case (i) using the gross rod
Fig 17 Average mutual information between the signals for the case (i) using the gross rod
Figure 17 shows the average mutual information between the signals for the same
experiment used previously for the correlation Again the results obtain with I av (x1, x2) are
simetric relative to the diagonal where the metric is maximum Due to the same reason
referred before only one side is shown The values presented are normalized The values of
the index I av (x1, x2) between the positions are high
Figure 18 shows a chart based on the entropy between the signals for the same experiment used previously for the other metrics In fact, the values shown are proportional to the
inverse of the index H(x1, x2) due to the normalization used Again, the values of this index between the positions are high
The metrics shown in figures 16–18 were obtained for an experiment corresponding to one trajectory In future this approach should be applied for all the thirteen trajectories referred before
Fig 18 Metric based on the entropy between the signals for the case (i) using the gross rod
The other methodology is based on several metrics used to evaluate the relashionship between the signals in the time domain, namely the correlation, the average mutual information and the entropy These indices revealed the hidden relationships between the signals
The results merit a deeper investigation as they give rise to new valuable concepts towards instrument control applications In this line of thought, in future, we plan to pursue several research directions to help us further understand the behavior of the signals
5 Acknowledgment
The authors would like to acknowledge the GECAD unit
Trang 22strong correlation between the positions and the forces, moments and accelerations that
depends, as expected, on the trajectory
Fig 16 Correlation between the signals for the case (i) using the gross rod
Fig 17 Average mutual information between the signals for the case (i) using the gross rod
Figure 17 shows the average mutual information between the signals for the same
experiment used previously for the correlation Again the results obtain with I av (x1, x2) are
simetric relative to the diagonal where the metric is maximum Due to the same reason
referred before only one side is shown The values presented are normalized The values of
the index I av (x1, x2) between the positions are high
Figure 18 shows a chart based on the entropy between the signals for the same experiment used previously for the other metrics In fact, the values shown are proportional to the
inverse of the index H(x1, x2) due to the normalization used Again, the values of this index between the positions are high
The metrics shown in figures 16–18 were obtained for an experiment corresponding to one trajectory In future this approach should be applied for all the thirteen trajectories referred before
Fig 18 Metric based on the entropy between the signals for the case (i) using the gross rod
The other methodology is based on several metrics used to evaluate the relashionship between the signals in the time domain, namely the correlation, the average mutual information and the entropy These indices revealed the hidden relationships between the signals
The results merit a deeper investigation as they give rise to new valuable concepts towards instrument control applications In this line of thought, in future, we plan to pursue several research directions to help us further understand the behavior of the signals
5 Acknowledgment
The authors would like to acknowledge the GECAD unit