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Design of a controller for Design of a controller for sitting of infantssitting of infants
Semester ProjectSemester ProjectJuly 5, 2007July 5, 2007
Supervised by:Supervised by:Ludovic RighettiLudovic RighettiProf. Auke J. IjspeertProf. Auke J. Ijspeert
Presented by:Presented by:Neha P. GargNeha P. Garg
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Content
Introduction & Motivation
Observations
Hand Made trajectory
Analysis of trajectory
Dynamical System
Further Work
Conclusions
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
3
RobotCub Project
Aim: study cognitive abilities of a child
How: by building a 2 year old infant-like
humanoid robot ICUB
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Need for Locomotion
Cognitive Development
Explore Environment
Locomotion
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Real Infants
Two main phases of sitting
Bringing of one leg forward
Movement of arm to sit on hip
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Demonstration
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Video of hand-made trajectory
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Main Characteristics
Torso Movement Leg Movement First Phase Complete
Second Phase Start Arm Movement Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Critical Phase
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The Trajectory
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Robustness
Checked in only critical period
Variation of the points specified for DOFs that effect critical period
Trajectory is quiet robust
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Robustness
Right Arm
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Point 6
Point 7
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Robustness
Torso
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Point 6
Point 7
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Robustness
Right Leg
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Point 3
Point 4
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Center of Mass
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
Can information about projection of CM during sitting can be used to classify transitions as good or bad?
Defining stability measure as integration of distance of center of mass from support polygon with time during sitting
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Center of Mass
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Torso Speed
Can we predict sitting/falling before critical period ?
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Observations from analysis
Clear division of sitting in two phases
Robot unstable in the second phase
Robustness more important than stability
Some amount of instability required for sitting
Torso speed cannot be used to predict sitting/falling
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Two Main Tasks
Switching from crawling to sitting
Designing mathematical equations for sitting trajectories
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Switching from crawling to sitting
When an external signal S is given, robot should switch from crawling to sitting
This can be done by:
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
),()1(
),()1(
crawlingFor
2
1
cycxfScy
cycxfScx
dd
dd
),(
),(
sittingFor
4
3
sysxfSsy
sysxfSsx
dd
dd
ddd sxcxx
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Switching from crawling to sitting
This may cause abrupt shift from crawling to sitting
Switching should occur only when while crawling hip and shoulder joints are moving in the same direction as they will move after shifting
For this we replace S by
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
icyDie
SS
1
1.'
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Switching from crawling to sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Dynamical System for Sitting
For all of the trajectories except Left Leg (Abduc /Adduc and Rotation) the following equation can be used:
Where parameter P decides when the system should start and when the system starts it goes towards
can also be changed if required
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
))0(.( dddddd
dd
yxxPy
yPx
dx0
dx0
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Dynamical System for Sitting
For example: for torso pitch
P = 1
=
Where S1 becomes 1 when second phase starts
And is calculated as:
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
dx0 )12.(11 valvalSval
)2.01*(1000
)2.01*(1000
11
P
P
e
eS
)_0_()_0_(100)3__()3__(1001
1
1
11
kneeleftxkneeleftxkneeleftxkneeleftxlegleftxlegleftxee
P
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Dynamical System for Sitting
For example: for left knee
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
10 valx d
)2_08.02_(1001
1torsoxtorsox
eP
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Dynamical System for Sitting
For Left Leg (Abduc/Adduc and Rotation), the movement has to be synchronized with left knee
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
2__,3__1
11
1
))0()0((
__100
)2_08.02_(100
__21
legleftlegleftbecande
K
eTwhere
xxxxcxcKTx
kneeleftykneelefty
torsoxtorsox
ddkneeleftkneeleftdd
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Dynamical System for Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Dynamical System for Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Dynamical System for Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Dynamical System for Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Dynamical System for Sitting
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Demonstration
Crawling and Sitting using Dynamical System
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Further Work
Addition of sensory feedback while sitting Robot Falling
Collection of biological data to know whether the movements while sitting are controlled by brain or spinal cord
Development of controller for transition from sitting to crawling
Increase in the limit up to which hip joint can be extended
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Conclusions
Main characteristics of sitting behavior of infants and the period of instability have been identified
A controller for sitting of the robot in the same way as infants has been implemented
Sensory feedback can be easily integrated by modifying values of parameter (P) according to sensory input
Robot can be switched from crawling to sitting by providing an external signal
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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Thanks a lot!
Questions?
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions
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References[1] G. Sandini, G. Metta, and D. Vernon, “Robotcub: an open framework for
research in embodied cognition,” 2004, paper presented at the IEEE RAS/RJS International Conference on Humanoid Robotics, Santa Monica, CA.
[2] L. Righetti and A.J. Ijspeert. “Design methodologies for central pattern generators: an application to crawling humanoids”, Proceedings of Robotics: Science and Systems 2006, Philadelphia, USA
[3] Michel, O. “Webots:Professional Mobile Robot Simulation.”Int. J. of Advances Robotic Systems, 2004, pages:39-42,vol.1
[4] G. Metta, G. Sandini, D. Vernon, D. Caldwell, N. Tsagarakis, R. Beira, J. Santos-Victor, A. Ijspeert, L. Righetti, G. Cappiello, G. Stellin, F. and Becchi. “The RobotCub project - an open framework for research in embodied cognition”, Humanoids Workshop, Proceedings of the IEEE -RAS International Conference on Humanoid Robots, December 2005
[5] MATLAB Function pchip: Fritsch, F. N. and R. E. Carlson, "Monotone Piecewise Cubic Interpolation," SIAM J. Numerical Analysis, Vol. 17, 1980, pp.238-246
• Introduction & Motivation
• Observations
• Hand Made Trajectory
• Analysis of trajectory
• Dynamical System
• Further Work
• Conclusions