mae505: robotics final project – papers review. presented by: tao gan advisor: dr. venkat krovi....

MAE505: RoboticsFinal Project – Papers Review.

Presented By:Tao Gan

Advisor: Dr. Venkat Krovi.

Main Topic: Nonholonomic-Wheel Mobile Robot (WMR).Sub-Topics: Modeling, Redundancies, & Motion Control.

Focus on two papers:1. “Nonholonomic Mobile Manipulators: Kinematics,

Velocities and Redundancies,” - Journal of Intelligent and Robotic Systems Volume 36 , Issue 1 (January 2003) Pages: 45 – 63.- Authors: B. Bayle, J-Y. Fourquet and M. Renaud.- Present by: Leng-Feng Lee.

2. “Coordinating Locomotion and Manipulation of a Mobile Manipulator” -IEEE Transactions on Automatic Control, Vol. 39, No. 6, June 1994, pp. 1326-1332.- Authors: Yoshio Yamamoto and Xiaoping Yun.- Present by: Tao Gan.

Organization of Presentation:

In each paper, we will present the following:

- Introduction of the paper.- Formulation of the problem using an example.- Simulation setting used.- Simulation Result.- Discussion of the Simulation Result.

2nd paper: “Coordinating Locomotion and Manipulation of a Mobile Manipulator”

Introduction:

-When a person writes across a board, he/she positions his/her arm in a comfortable writing configuration by moving his/her body rather than reaching out the arm.

-The same situation happens in many case such as people transporting a heavy object cooperatively. -Therefore, when a mobile manipulator performs a manipulation task, it is desirable to bring the manipulator into certain preferred configurations by appropriately planning the motion of the mobile platform.


Modeling: Using an Example

Arial View

Modeling


Modeling:

Three variables describe the position and orientation of the platform

State Variables:

Two variables specify the angular positions for the driving wheels

),,,( , lrcc yxq


Modeling:Adding Nonholonomic Constraints

stop

No. 1C

No.2,3

C

No.1 constraint is that the platform must move in the direction of the axis of symmetry (holonomic).

No.2,3 constraints are the rolling constraints, i.e. the driving wheels do not slip(nonholonomic).

0sincos dxy cc

rcc rbyx sincos

lcc rbyx sincos


Modeling: Three Constraints

According to the q, the three constraints can be written in the form of

where

0)( qqA

rb

rb

d

qA

0sincos

0sincos

00cossin

)(


Modeling: State Space Representation

The Mobile plateform’s equation of motion are described by

N x N inertia matrix

N x 1 vector of position and velocity dependent forces

N x r input transformation matrixr-dimensional input vector

)()(),()( qAqEqqVqqM T

)(qM

),( qqV

)(qE


Modeling:Dynamic Equations

N x N inertia matrix


w

w

cc

c

c

I

I

Idmdm

dmm

dmm

qM

0000

0000

00cossin

00cos0

00sin0

)(


N x 1 vector of position and velocity dependent forces


N x r input transformation matrix

r-dimensional input vector


0

0

0

sin

cos

),(

2

2

dm

dm

qqVc

c

10

01

00

00

00

)(qE



Constraints matrix

S(q) are in the null space of A(q).


0)()( qSqA

10

01

)cossin()cossin(

)sincos()sincos(

)()()( 21 cc

dbcdbc

dbcdbc

qsqsqS


0)()( qSqA)(qSq

0)( qqA Differentiate and replace the one in the

))()(( VtSMtMSST


Premultiply byTS


))()(( VtSMtMSST Using state-space vector

Tlrlrcc

TTT yxqx ],,,,[ ,

1

2 )(

0

MSSf

Sx T

Suppose there is input u

uI

Sx

0

0

lineariz

e

What is u?


Trr yxqhy )(

Differentiate it.

)()()/)(( SJSJqqqhy hh

Decoupling Matrix

Differentiate it again.

y

)(1

vu

uv

This is u.

)()( yyKyyKyvy dp

dd

d


)(1 vu uI

Sx

0

0

Since we know u

Tlrlrcc yxx ],,,,[ ,

We can know every state variables in the system.


Simulation: Simulation Setting

1. Time Span: 0 – 60 sec

2. Path Trace: x = 6, y = t

3. Velocity: x_dot = 0,

y_dot = 1

4. Length of Link 1 = 5/sqrt(2),

Link 2= 5/sqrt(2),


Simulation: Simulation Setting

1. Time Span: 0 – 60 sec

2. Path Trace: x = t, y = t+t

3. Velocity: x_dot = 1,

y_dot = 1

4. Length of Link 1 = 5/sqrt(2),

Link 2= 5/sqrt(2),


Simulation:Simulation Result (case i)

Notice:

-Control of WMR with Nonholonomic Constraints with Error Correction.

-The velocity of point Po are shown.


Simulation:Simulation Result (case i)

Notice:

-It indicates that the mobile platform moved backward for a short period of time at the very beginning to achieve the needed heading angle.


Simulation:Simulation Result (case ii)



Notice:

-Control of WMR with Nonholonomic Constraints with Error Correction.

-The velocity of point Po are shown.



Notice:

-It indicates that the mobile platform moved backward for a short period of time at the very beginning to achieve the needed heading angle.


Conclusion:

-The second paper introduce a method of using Manipulability Measure of the Mobile Manipulator as the potential function included in the motion control of the WMR.

-We verified the effectiveness of the method by simulations on two representative trajectories

mae505: robotics final project – papers review. presented by: tao gan advisor: dr. venkat krovi....

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