ashish dutta

8/2/2019 Ashish Dutta

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Dr. Ashish Dutta

Associate Professor

Dept. of Mechanical Engineering

Indian Institute of Technology Kanpur, INDIA

Humanoid robot design with softsole and springs for applicationsin optimal multi agent systems


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Evolution of multi agent systems fromwheeled robots to legged robots, UAVs, etc

Optimal multi agent system using mobilerobots

Design of energy optimal humanoid robot

with soft sole and springs as agents.

Other related research on exoskeleton,

orhtosis, etc.


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The idea of Multi agents (swarm robots) hasbeen borrowed from nature, emulating antcolonies, bee hives, etc.

The basic idea is to be able to perform acooperative task that cannot be performedby one individual robot.


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Fig. Mobile robot as agent.Fig. Two or more agents

pushing an object.


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Mobile robots coordination, net working,path planning.

Mobile robots were not necessarilyoptimized.

Mobile robots do not require balance and

are generally stable.

Newer types of agents: UAV, underwater

agents, bio-agents, humanoids, etc.


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Fig. Upper torso Humanoid that does not require balance.


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Multi Humanoid : System of system


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Fig. Quadrupeds agent Fig. Four legged and biped cooperation


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Wang and Kumar (2002) used the potentialfield method to obtain object closure using alarge number of robots.

Sugar and Kumar (1998) proposeddecentralized control of cooperating mobilemanipulators.

goal

object

mobilerobots

2. Optimal multi agent systems usingmobile robots


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A large number of robots have been used

(e.g. 100 or more) and capture points notoptimal.

Leader follower or potential field

approaches have been used for the robotmotion.

The dragging of the object is not optimized.

Obstacle avoidance is not considered.


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Why use a large number of robots if the task can bedone by few robots? Reduce energy consumption and Networking issues? Vary number of robots if required.

a. Optimal captureof a moving object using the

minimumnumber of robots.

b. Optimallypushing the captured object to the goal

point.

New contributions of our research


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Problem formulation: Given an object with n points on itsboundary, it is required to find the optimal grasp pointsfor satisfying form closure.

C.G.

1

6

13

20

Mobile Robot

10000100001000000100000010000Binary String

1 : Robot present

0 : Robot absent

GA based optimization using an objective function with

constraints.


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1cw ccwk

cw ccw

M Mf

N N N

+ = +

Prismatic Object

C.G.

1

6

13

20

Maximize

Moment is calculated byassuming unit normal forceapplied by robots.

N : Total No. of Robots

Mcw : Sum of CW moments

Mccw: Sum of CCW moments

k : parameter for

controlling No. of agents.


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Visibility angle () should be null

( ) ( ){ }

{ }1 2 .....

i

n

=

= i+1 i i i-1

r - r , r - r

Visibility angle is the common angle between allfreedom angles()

This constraint takes care of translation inaccessibility.

3

freedom

angles

1

31

No angle left uncover

4

2

4

2

3

freedom

angles

1

3

1

4

4

small angle left uncovered


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There should be robots creating moments in both the direction about C.G.

Feasible solution Non-feasible solution

C.G.

CW

CCW

CCW

C.G.

CW

CW

CW

This constraint takes care of rotation inaccessibility.


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- o wo ro o approac es e same e ge.

- Robots envelop never intersect with eachother on the object boundary.

Huge negative penalty (say -1e20) is imposed ifany of the constraint is violated.

Non-feasible solution

Object


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Simulation is carried out in MATLABTM using

the Genetic Algorithm.

A Binary String is used as design variable.

Population Size 52, Mutation probability0.12, Crossover Probability 0.8

Constraint violation attracts huge negative

penalty (say -1020).

Avg. simulation time is around 300 second,with Intel-P4 Machine.


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Fig. Results of simulation


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Parameter k inoptimization function isvaried to get differentsolution with different no.of robots for same object.

Variation of number of robots with constant K


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1 2 3.( ..... )

.

nf

f

= + + + +

=

D F F F F

D F

Desired

direction of

motion (D)

Robots participating in

pushing

Robots not sharing any load

Maximize

Fi

.. (1)

Problem formulation forpushing


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Gordy GA code is used to optimize eq (1)

724

19

29

16

13

1

000000000000000100100001000010

Binary String


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D

F3 F2F1

F4

D

F

F3 F2F1

F4

DF

F3 F2F1

F4

(a) (c)(b)

D


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- 1 0 - 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0

- 2 0

- 1 5

- 1 0

- 5

0

5

1 0

1 5

2 0

2 5

Copyright: Panka j Sharma , Dr.Anupam Sa xe na and Dr. Ashish Dutta, IITKanpur


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Non-holonomic mobile robots with twowheels independently driven weredeveloped.

Each mobile robot worked as an agentcontrolled by wireless communication withthe central computer.

Overhead vision based coordination.


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An algorithm was proposed for the optimalcapture and transfer of a moving object to adesired goal, using the minimum number ofmobile robots.

The advantages as compared to earlier methodsare that resources are minimized and it leads tolesser deadlocks and networking time.


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Biped: A two legged robot with 8 or moreDOF for walking .

GAIT: A fixed pattern of foot placements Trajectory: The path (optimal?)taken by the

free foot to come from the rear to the front .

3. Humanoids as agents


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Energy optimal trajectory generation forcooperation with human / robot / agent.

Energy savings considering deformation of softsole or ground on biped stability.

New design considering springs at the joints for

reduced energy consumption.

Modes of cooperation in Multi agent systems.


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Lateral plane Front plane Isometric view


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Using DAlembertsprinciple:

- Where mi is the

mass of each link and

ri are the positionvectors.

=++ 0)()( TGrXrrmipii


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The ZMP approach is used to find the stable configuration during theGAIT. The ZMP is the point where the sum of all the forces and the moment of all

the masses of the biped is zero. The ZMP moves forward in the direction of the locomotion.


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is the joint angle from xi-1axis to the xiaxis about thezi-1axis.

di is the distance from the origin of the (i-1)th coordinate frame to the intersection of the z i-1axis with thexi

axis along the zi-1axis.

ai is the shortestdistance between zi-1 and zi axes.

is the offset angle from the z i-1 axis to thezi axis about thexi axis.

i

i


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Euler-Lagrangian equation

where

L is Lagrangian function, and is given by

KE is total kinetic energy of the biped robot,

PE is potential energy of the biped robot,

is generalized coordinates of the robot arm,

is first time derivative of the generalized coordinates,

i is the torque applied to the system at joint into drive linki.

i = 1, 2, 3, . . . .8ii i

d L L fordt

=

i

i

8

1

i i

i

L KE PE

=

=


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( ) ( ) ( )..

( ) ,t = + +D h c

where , corresponds to inertial acceleration

related symmetric matrix

is the non-linear centrifugal force vector.

is the gravity loading force vector.

is the torque applied at joint

( )D

( ), h

( )c

( )t


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The dynamic equation can be further modified by taking the reaction force

into account

where

The component is given by

where

N2is calculated using

( ) ( ) ( )..

( ) , ( )t rt = + + D h c K t

1 2, 8( , ....... )Tt t t=t

(2) 2,3,....,7

(3) 1,8

i

i

i

for it

for i

== =

T

M

0

2( ) i=2,3,....7i i i for= T R a N

2( ) i=1 and 8i i for= M a N

Link i

80

1 ( )i ii m= + =2OA N r g 0


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Energy optimal trajectory is found using GA.


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Intermediate points are obtained using GA

i f

pq

tfTime (sec)

Joint Angle (rad)

3

0

1,2,.........8k j jk k

C t for j=

= =

where Cjk is constant.


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| | | |W dt =

Objective function

Work done involves

Finding the joint angle, the joint velocity and the joint acceleration. Finding Torques by using the dynamic equations

ZMP should always be inside the supporting polygon,

Free foot should never go inside the ground,

The hip joints should always move forward

The hip joints should not come below the specified height


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Variation of each angle is a cubic spline.

Given the starting and end points, two

intermediate points are decided.

Constraints -a) Foot should not go below the ground

b) ZMP should be inside the footc) Min height of the hip is specifiedd) Hip should move forward


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The total work done is minimized bychecking the constraints.

In case of violation of a constraint a large

penalty is added to the function value.

Using Lagrangian-Euler formulation,dynamic equations can be written as:

= dtddonework ||

( ) ( , ) ( ) D H C = + +


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8 DOF Robot Angle assignment


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Parameters:

Population Size :50

Crossover ratio:0.95 Mutation ratio:0.05

Iterations : 280

Link Length:0.25 m

Step Length:0.25 m

obstacle


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Parameters:

Population Size :50

Crossover ratio:0.95 Mutation ratio:0.05

Iterations : 190

Link Length:0.25 m

Step Length:0.25 m


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Trajectory are computed on assumptionthat sole and ground are perfectly rigid.

Effect of soft sole can be detrimental to

bipeds stability.


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If the force distributionis as shown:

Total Reaction Force

Centroid of trapezium =

( )1 22

d

F F= +

2 1

2 1

(2 )3( )

cgd F Fd

F F+=

+Frontal Plane


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By balancing the forces and momentsabout point B

Solving these equations, we get:

( )

( )( )

1 2

2 11 2

1 2

2(2 )

2 2 3

d F F F

d d d F F F T F F

F F

= +

+= + +

+

1 2

2 2

6

6

F TFd d

F TF

d d

= + =


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If the force distributionis as shown:

Reaction Force

Distance of centroid

1

2F d=

3

d

=


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Balancing forces and moments, we get:

Solving these equations

1

1

2

2 2 3

F dF

Fd F d d T

=

= +

1

32 2

32

FF

d TF

d Td

F

=

=


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Due to uneven forcedistribution, one sideof sole deforms

more, resulting in anangle

It effects as if one

more DOF

Intended becomes

+


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F = Kx ; where k= YA/ h

X = deformation, A= area of foot,h= thickness of sole, Y = modulus ofelasticity.

F1

F2

F

T

0c

0=g. orrec on

procedure for


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Iterative method

for finding new

Required Torque

(from dynamic model)corresponding sole deformation =

total angle due to deformation

error =

0d

= T

0 zmp zmp0

0 zmp 0d

+

zmp0c

0zmp 0d

0 zmp 0 zmp 0

d

- ( )+

= +

( )

error < 0.01

IF

zmpcorrected angle = 0

NO

YES

p

deformed

angle


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Material which givesfeasible new are

suitable for sole

For balance infrontal plane, new

for differentmaterials are:

YoungsModulus

N/mm2

Final valueof angle 1

(Starting

value =

25)

5000 -23.34

6000 26.0944

7000 25.3365

8000 25.1805

9000 25.0383


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EN/mm2

Actualangle

2(35.58

)

5000 -

34.8531

10000 -

35.21

77

50000 -

35.50

93

100000 -

35.54


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It has been proved that the deformation ofthe sole is affected mainly by the torque inthe first ankle joint.

This may be due to two reasons:

- The torque is maximum at this joint.

- The foot is longer in the lateral plane

for this robot.


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The trajectory has been computed in thefollowing steps:

a) Compute the ZMP and make correctiononly to the first joint.

b) Find the optimal trajectory for the otherjoints using GA, for a given step length.


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Fixed foot

Free foot

Energy per step withoutdeformation= 3.87 WEnergy per step withdeformation= 2.91 W


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8DOF Biped with Springs atthe joints

All the joints are revolute

The link length are equal except

for the hip link

The ankle has two DOFs

The knee has one DOF The hip joint has one DOF


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Design of a biped with torsionalsprings at the joints similar tobiological joints with compliance.

Determination of energy optimal

trajectories.

Determination of optimal stiffnessand reference angles of thesprings.


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( ) ( ) ( )..

( ) ,t = + +D h c

where ,

corresponds to inertial acceleration

related symmetric matrix

is the non-linear centrifugal force vector.

is the gravity loading force vector.

is the torque applied at joint

( )D

( ), h

( )c

( )t


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In this work the torsional spring acts as the energy absorber and absorb theenergy in the potential form.

The flexible joint can reduce the work done during the gait

Where

corresponds to the torsional stiffness of the spring

corresponds to the reference angle.

( ) ( ) ( )

..

( ) , ( )t r

t = + + D h c K

tK

r

1 2 8[ , ,....., ]Tt t t t K K K =K


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a) Optimal trajectory for the rigid robot withno spring

a) Optimal trajectory of robot with same

stiffness at each joint.

a) Optimal trajectory of robot with optimalindividual joint stiffness

a) Optimal trajectory for optimal instanceposition, individual stiffness at each joint,reference angle and initial orientation.


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Link length, L = 0.2 m Hip length, h = 0.14 m Step length = 0.2 m Mass matrix = [0 1.3122 1.3122 2.7128 1.3122 1.3122 0 1.3348] Kg Length of the foot = 0.2 m Width of the foot = 0.07 m Without loss of generality the fixed foot is taken as the origin.

The hip height has taken to be 0.32m. The initial tilt of the biped is taken to be pi/9 and fixed all along the

simulation The distance of the free foot and hip joint is 0.1m and 0.05m on both the

side Reference position of the torsion spring is [0 0 /2 /2 3 /2 - /

2 0 0]rad


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K=0.25 Nm/rad, WD=5.4140 Watt K=0.5 Nm/rad, WD=4.3976 Watt K=1 Nm/rad, WD=5.7027 Watt


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K=1.5 Nm/rad, 6.1584 Watt K=2 Nm/rad, WD=8.4929 Watt K=3 Nm/rad, WD=10.7429 Watt


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K=0.25 Nm/rad, WD=5.6363 WattK=0.5 Nm/rad, WD=3.9654 Watt K=1 Nm/rad, WD=4.1297 Watt


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K=1.5 Nm/rad, WD=4.2784 Watt K=2 Nm/rad, WD=6.6247 WattK=3 Nm/rad, WD=7.4129 Watt


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K=0.25 Nm/rad, WD=4.1442 Watt K=0.5 Nm/rad, WD=3.5275 Watt K=1 Nm/rad, WD=4.6562 Watt


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K=1.5 Nm/rad, WD=4.6793 Watt K=2 Nm/rad, WD=4.9295 Watt K=3 Nm/rad, WD=8.4450 Watt


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The red, blue and green colored graph shows the variation of the work done with the

time step of 0.5, 1 and 2 sec respectively.


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GOALTo determine the optimal individual joint stiffness for obtainingenergy optimal gait

GA Parameters

Population size was set to 200, Maximum number of iterations was set to 4000,

Crossover probability = 0.95, and

Mutation probability = 0.05.


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WD=3.8577 WattWD=3.4036 Watt WD=5.8366 Watt


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Table 6.1:Stiffness at different joints

Joint No. 1 2 3 4 5 6 7 8

Stiffness

(Nm/rad)

Set 1 0.3838 1.3471 2.7807 2.1294 0.2171 0.7128 0.5361 2.8608

Set 2 2.4627 0.2471 2.1926 0.9228 0.5223 0.6539 2.4460 1.7384

Set 3 2.8773 0.5322 1.9642 1.5793 0.5955 0.2332 2.7530 0.7708

Average 1.9079 0.7088 2.3125 1.5438 0.4450 0.5333 1.9117 1.7900


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GOAL: To Determine Individual joint stiffness

The reference position of the torsional spring

The initial and final stances

The tilt angle of the biped robot GA parameters

Set no. Population size Maximum number of iterations

Crossoverprobability

Mutationprobability

Set1 50 4000 0.95 0.05

Set2 500 2000 0.95 0.05

Set3 200 2000 0.95 0.05


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WD=2.1605 Watt WD=1.8273 Watt WD=2.28Watt

Optimal stiffness of torsional springs at different joints


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Stiffness at different joints

Joint No. 1 2 3 4 5 6 7 8

Stiffness(Nm/rad)

Set 1 0.9587 1.7148 0.8393 2.9919 2.7364 0.6546 1.1190 2.1605

Set 2 2.65 1.4582 0.1581 2.5154 1.5139 1.0267 1.0901 1.6588

Set 3 2.3227 0.2807 0.7013 0.0953 2.8591 2.8329 1.2758 0.2723

Average 1.9771 1.1512 0.5662 1.8675 2.3698 1.5047 1.1616 1.3638

Optimal reference angles at different joints


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Reference angles at different joints

Joint No. 1 2 3 4 5 6 7 8

Angle

(rad)

Set 1 -0.0561 -1.2783 1.8674 -0.98 3.5185 -0.3786 1.1394 -0.3239

Set 2 -0.0082 -1.0817 1.8844 -0.8675 3.6571 -0.4165 1.5070 -0.1918

Set 3 -0.1075 -1.5424 1.9564 -0.0056 3.3750 -0.9179 0.9242 -0.3080

Average -0.057 -1.301 1.902 -0.206 3.5169 -0.571 1.1902 -0.275

Optimal Stance for T=1 sec


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Free Foot Hip

Initial Stance (m)

a

Final Stance (m)

b

Initial Stance (m)

c

Final Stance (m)

d

Height

(m)

Set 1 -0.0948 0.1072 -0.0561 0.0502 0.2978

Set 2 -0.0805 0.0852 -0.0469 0.0402 0.3060

Set 3 -0.0966 0.1090 -0.0512 0.0467 0.2928

Average -0.0906 0.1004 -0.514 0.0457 0.298

Initial Stance and Final Stance Position


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Initial Orientation (1) in radian

Set 1 -0.4397

Set 2 -0.4201

Set 3 -0.4510

Average -0.437

Initial Orientation of Biped


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As the time for GAIT increases from 0.5 sec to 2 sec thework done reduces from 6.9538 Watt to 4.3495 Watt for

rigid case.

For a time step of 0.5 sec, 1 sec and 2 sec the minimum

work done is 4.3976 Watt, 3.9654 Watt and 3.5275 Watt

respectively when the stiffness at each joint is 0.5 Nm/rad

For optimal stiffness at each joint the minimum work done

is 3.4036 Watt.

Optimizing all the parameters namely stance position,

stiffness at each joint, reference angle and initial tilt the

minimum work done is 1.8273 Watt


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1. Performing a task in coordination (withforce /moment interaction)

2. Performing a task in formation (no forces /

moments involved)

3. Others (interacting with people using vision,

speech etc.).


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Concept of ZMP is valid only for one biped.

In case of multiple bipeds the conditions ofbalance are not very clear.

One idea is to ensure that the ZMP is inbetween all the biped and environment

contact points.

What happens if one robot looses contact?


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The system is balanced as long as the ZMP isinside the common feet polygons.

Sensory information determines position of

the common object / environment (inclinationor vision sensors)


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Major concern is the time of convergence :days !

Interaction is still highly constrained.

Future is to develop real time controlalgorithms.

Finger exoskeleton for rehabilitationf k i


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of stroke patients


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Design optimal mechanical system Use EMG from muscles Use EEG from brain as a switch foractivation.

Proximal Phalanx Four Bar


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DEPARTMENT OF ELECTRICAL ENGINEERING

Middle Phalanx Four Bar


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Distal Phalanx Four Bar


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Index Finger Four Bar


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Index Finger Four Bar


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Objective:

To design the Optimized Exoskeleton for the Index finger based on Four BarDesign using Path Generation

GA Optimization Details:

Iterations: 4000 for each four bar

Population Size: 100

Generation: 700

Cross-Over Fraction: 0.8

Proximal Phalanx Four Bar (contd)

Error = 1.9 cm2


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Middle Phalanx Four Bar (contd)


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Distal Phalanx Four Bar (contd)


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Reconfigurable prosthetic socket

)heel contact (b)mid stance (c) toe off

extensionmoment at the

groundreaction force

A

CB

D

Fig.1 Diagram of walking cycle with lowerlimb prosthesis& Design concept of the MR

Fig.14

Two main problems:

1. Misalignment

2. Change in stump

size


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Fig. 15 Correction of misalignment of the socket.

Instrumented socket with


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Instrumented socket with

slip and force sensors

Slip

Sensors


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VAS 0 1 1 2

2 3

3 4 4 5 5 6


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(b) 63[kPa]

(a) 38[kPa]

PT(L) 0.72

PT(C) 0.63

PT(M) 1.54HF 1.81

TL 1.72

TC 1.09

TM 1.54

TL 1.54

TC 1.45TM 1.63

TL 1.54

TC 1.81

TM 1.36

FP 3.81

FP 3.36FP 3.36

FP 3.18

Average 1.89

PT(L) 0.54

PT(C) 0.36

PT(M) 0.54

HF 0.72

TL 0.72

TC 0.54

TM 0.81

TL 0.54

TC 0.72

TM 0.90

TL 0.72

TC 1.09

TM 1.00

FP 2.27

FP 2.18

FP 2.45

FP 1.90

Average 1.37

6 7 7 8


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(a) (b)

patellar tendon

tibial crest

fossa poplitea

stump end

tube fittings


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0

5

10

15

0 50 100 150

pressure [kPa]

displacemen

t[mm]

0[T]

0.12[T]

0.12[T]2

0.12[T]3

0.12[T]40[T]

0.12[T]

0.24[T]

0.36[T]

0.48[T]Rigid

socket

Soft

Flexible

socket

Active

socket


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Two rovers and a Lander on the moon.

Navigation

Kinematics , Dynamics and Control.

System of systems


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ashish dutta

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