6 Dof Conference

8/7/2019 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

4/22/2011 Dept. of Mechanical Engg, NITC 2

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

Dept. of Mechanical Engg, NITC 6


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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

Solution set is infinite4/22/2011 Dept. of Mechanical Engg, NITC 11


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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


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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