6 Dof Conference
Transcript of 6 Dof Conference
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Modelling and stable walkinganalysis of 6 degrees of freedombiped robot
Presented byGeo Jose, A P Sudheer
Mechatronics/Robotics laboratory
Dept. of Mechanical EnggNational institute of technology, Calicut
E-mail: [email protected]
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Introduction
Assistance Replacement
Automation Complete replacement
Humanoids/Bipeds Non-anthropomorphic robots
Redesign of human environment
Biped compensated by larger
foot size
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Dynamically unstable
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Objective
Dynamic stability analysis of a 6 dof biped
walking on a flat terrain based on ZMP
criterion
Design a foot which satisfies the locomotion
requirements
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Methodology
Kinematic modelling Denavit-Hartenberg method
Inverse kinematics Iterative method(Levenberg-Marquardt method)
Dynamic modelling Newton-Euler algorithm
Stability analysis Both in sagital and frontal plane based on ZMP
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Biped model
Y0,Y
01
Z0, Z01
X0,X
01
l3
l5l1
l0
l2 l4
Z2
X1
Z1
X2 X
3
Z3
Z4
Z6
X4
Z5?1
?2
?3
?4
?5
?6
X5,X
6
Y0,Y
01
Z0, Z01
X0,X
01
Y0,Y
01
Z0, Z01
X0,X
01
l3
l5l1
l0
l2 l4
Z2
X1
Z1
X2 X
3
Z3
Z4
Z6
X4
Z5?1
?2
?3
?4
?5
?6
X5,X
6
l3
l5l1
l0
l2 l4
l1
l0
l2l2 l4l4
Z2
X1
Z1
X2 X
3
Z3
Z4
Z6
X4
Z5?1
?2
?3
?4
?5
?6
X5,X
6X
5,X
6
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D-H modelling
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Biped mass and dimensions
Mass M0 M1 M2 M3
Kg 0.068 0.115 0.115 0.080
Link length l0 l1 l2 l3
Meter 0.032 0.070 0.075 0.109
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D-H table
Link (radians) a(meter) d(meter) (radians)
1 1 0.070 0 -/2
2 2 0.075 0 0
3 3 0 -0.109 0
4 4 0.075 0 0
5 5 0.070 0 /2
6 6 0.032 0 0
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Ai= i-1Ti=
Ai=
Where, i =1, 2,,6
pose of end-effector with respect to base frame=0T6
Where, 0T6 =0T1*
1T2*.*5T6
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Trajectory planning
Cartesian space trajectory planning
Cycloid function is used
Step length of 0.2mis taken
20 break points are taken on the trajectory
Pose corresponding to each of these points is
computed. (4x4 transformation matrix)
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Inverse kinematics
0T6= (4x4 pose matrix)
6 equations and 6 unknowns;
Non-linear simultaneous equations involvingtrigonometric functions makes the solution setmore complex
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Inverse kinematic solution
Algebraic, geometric and iterative methods
Non-traditional search techniques such as
Artificial Neural Networks(ANN), SimulatedAnnealing(SA)
Levenberg-Marquardt algorithm is used to
obtain solutions
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Dynamicanalysis
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During single support phase stance foot is
assumed to remain in flat contact on the ground
Impact is assumed to be perfectly inelastic
All links are assumed to be slender with CoM
(Centre of mass) and centeroid coinciding
Force on swing leg is zero
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Assumptions
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Stability criteria-ZMP The zero moment point is the point through which a
ground reaction force would need to pass in order tosatisfy dynamic equilibrium of the robot for a given
motion Biped is stable if ZMP is within the support polygon
created by the feet
Then the ankles can transmit the resulting moment
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ZMP cont...
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ZMP cont...
=0
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Walking simulation
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RESULTS
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Results......
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ZMP
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Conclusion For a step length of 20cms ZMP will stay well
with in a square foot having side 6cms
Design torques for controller design for the
proposed gait is computed
Since infinite set of gaits are possible; Some
optimisation technique is to be used to get an
optimum foot size for a particular step length
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References
J. Angeles, Fundamentals of robotic mechanical systems:
theory, methods, and algorithms. Springer Verlag, 2007.
M. Raibert et al., Legged robots that balance. MIT press
Cambridge, MA, 1986. F. Silva, T. Machado et al., Energy analysis during biped
walking, Proceedings of 1999 IEEE International Conference
on Robotics and Automation, vol. 1, IEEE, pp. 5964, 2002.
Z. Tang, C. Zhou, and Z. Sun., Trajectory planning for smoothtransition of a biped robot, Proceedings of ICRA03 IEEE
International Conference in Robotics and Automation, 2003,
vol. 2, IEEE, 2003, pp. 24552460.
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P. Vadakkepat and D. Goswami, Biped locomotion: stability,
analysis and control, Robotica, vol. 27, no. 1, pp. 355365,2009.
M. Vukobratovic and B. Borovac., Zero-moment point-thirty
five years of its life, International Journal of Humanoid
Robotics, vol. 1, no. 1, pp. 157173, 2004.
T. Zielinska, C. Chew, P. Kryczka, and T. Jargilo., Robot gait
synthesis using the scheme of human motions skills
development, Mechanism and Machine Theory, vol. 44, no.
3, pp. 541558, 2009.
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