Design and fabricate a humanoid robot and build the walk trajectory

Design and fabricate a humanoid robot and build the walk trajectory Le, Thanh Quanga a Department of Mechatronics, University of Technical Education of Ho Chi Minh City, VietNam, July

Design and fabricate a humanoid robot and build

the walk trajectory

Le, Thanh Quanga

a Department of Mechatronics, University of Technical Education of Ho Chi Minh City,

VietNam, July, 2012 lequangthanh010290@hotmail.com a

Abstrac t

To be able to calculate and control a

humanoid robot, one of the important

problems is modeling the robot Modeling

is establishing a system by using the

performing mathematics, so that we will

have the core awareness for solving

In addition, we need to calculate the

kinematics of the robot Solving the

inverse kinematics is the basic and

complex problems, because we do not

have the typical methods, they deal more

with the number of degrees of freedom,

positions and orientation of end points

and the difficulty in solving the complex

mathematical equations

Some other requirements are response times Forward and inverse kinematic equations for position and orientation use more Sin, Cosin, Arcsin, Arccos functions, which require more time to calculate

This report will determine how to model and resolve the forward and inverse kinematics base on Denavit - Hartenberg theory and adopt Levenberg-Marquardt theory about numeric matrix to solve forward and inverse kinematic equations for position and orientation

I Introductions

This project will design the mechanical part,

electrical part, software utility, design walk

trajectory and control a robot to walk like

this We need six degrees of freedom (DOF)

to define one point or body in space,3 DOF

of position and 3 DOF for orientation, 3

DOF of position are determined by using the

coordinate system With x, y, z coordinate, 3

DOF of orientation is described by rotary

angle around the coordinate axis There are some version of humanoid robot are built from the Ho Chi Minh City University of Technology, Viet Nam These versions have the advantages of using harmonic gearbox, which has the character of high ratio, error reduction at output, friction reduction at input DC servo motor enclosed with one encoder and one microchip

These chips communicate together by using

CAN network The disadvantages of them

are: heavy weight, spend more time to

calculate the trajectory directly

With modeling, they use translation matrixes

and rotary matrixes to demonstrate the

robot, and use analytic method for solving

the inverse kinematics

In this project, we will use

Denavid-Hartenberg theory to model the robot and

use numeric method for solving the inverse

kinematics By using RC servo motor, this

has light weight, easy to control…

II Results and Discussion

1 Modeling the robot:

We need to show how many degrees of

freedom the robot has?

Fig 1 Modeling of robot

Figure 1 indicates the typical modeling, in

real robot we have some angles do not

rotate For walk trajectory, we will care of

the position and orientation of hip and feet

So, we have the D-H tables for left and right foot

8 L 78 0 -90 Ɵ 7

Tab 1 D-H table for left foot

Tab 2 D-H table for right foot

Denevit – Hartenberg theory:[1]

Transposed matrix from N coordinate to N+1 coordinate:n T n1

Transposed matrix from R coordinate to H coordinate:

1. 2. 3 1 1 .2 3

R: Reference H: Hand of Robot

coordinate to H coordinate:

1

0 0

n n

T





R

H

T



We have the position of end point:

   

    

   

   

Inverse kinematic:

Position and orientation:

Fig 2 Position and orientation

With the same position , but in above figure,

the orientation of A is different We have the

forward kinematic equation of position and

orientation:

R

R





Euler(Φ, Ɵ ,Ψ) = Rot(z,Φ) Rot(y,Ɵ) Rot(x,Ψ)=

Euler( , , )



           

             

  

RPY( , , )

a o a o n a n a o n a n

a o a o a n a o n a n

a o n

           

           

  



Jacobi matrix:

With a robot have 2 mechanisms:

Fig 3 Two mechanisms robot

Coordinate of B:

1 1

1 2 1 2

1 2 1 2

B B

L C L C x

y L Sin L Sin

 

Differentiating this equation with respect to the two variables Ɵ1, Ɵ2:

B

B x

y

d



We have Jacobi matrix:

  1     

2

a o

B

B

x

y

d





 

D  J  D

   

1

1

1

1

1

1

D J D

D

J e

J e

























       

   



   

   

  

If we have inverse Jacobi matrix, we will

solve the inverse kinematics problem But

Jacobi matrix is non-square matrix, we may

not calculate it We attempt to find other

method to solve it Levenberg-Marquardt

has published one method to calculate the

inverse matrix, which is not square matrix

[2]

Fig 4 Algorithm of control

2 Design walk trajectory:

In walking project, the orbit of hip and foot must be ensuring like a human So, we must design the trajectory for hip and foot At first

we need to find one point, which does not change the position while walking The orbit

of hip and foot are defined by the equation

of order 3

x(t)= a.t3 + b.t2 + c.t +

We need to design walk trajectory in 2

planes Oxy and Oyz

Initializing of position and

orientation:

  00 00 00

, , , ,

, , , ,

     



Start

Calculate the errors:

0

set

e  f  f

J JJ I e



  

Fig 5 Trajectory of hip, foot on Oxy plane

Fig 6 Trajectory of hip, foot on Oyz plane

Fig 6.Chart of foot on x coordinate

Fig 7.Chart of foot on y coordinate

Fig 8 Chart of foot on zcoordinate

Fig 9.Chart of Hip on x coordinate

Fig 10 Chart of Hip on y coordinate

Fig 6.Chart of Hip on coordinate

3 Mechanism[3]

To reach the accuracy in control, the

mechanical design of robot is complex,

difficult Material of robot is aluminum,

using Solidwork software to design CAD

model The RC servo motors were used

Fig 10 Full CAD model of robot

Fig 11 Assembly of robot

Character of robot:

Agrees of freedom

16

Tab 3 D-H table for right foot

4 Control:

Use a computer to calculate the value for each step of walk project 2 dspic 30f6014A chip to control these motors

Fig 12 Block of hardware

Dspic 30F6014A (Master)

Dspic 30F6014A (Slave)

Servo 1

Servo 2

Servo 3

Servo 4

Servo 5

Servo 6

Servo 7

Servo 8

Servo 9

Servo 10 Servo 11 Servo 12

Servo 13

Servo 14 Servo 15

Servo 16

Fig 13 Electric hardware [4]

Simulation and experiment

Fig 14 Walking process in plane 1

Fig 15 Walking process in plane 2

Fig 16 Walking process in plane 3

Fig 17 Walking process in real

III Conclusions:

This project show the method to model,

solve the forward and inverse kinematic

equations of position and orientation

Finding the way to calculate the inverse

kinematic with orientation is so important

There are so many robot uses the

orientation in its act In painting robot, the

hand of robot is always parallel with thing

need to paint A serving robot handles a

glass of water, which is not fallen out…

The disadvantages of this project are: the trajectories were designed before update for chips permanently Because of low speed, these chips can not calculate the trajectory as online process while robot is walking The mechanism parts, electronic hardware were made by hand, the non- accuracy motors had

The flexibility of this method help us to

develop the robot, which can go up stair,

down stair, walk on non -plane surface

References

1 B.Niku, S., Introduction to Robotics

Analysis, Systems, Applications,

2001: United States of America

2 Gavin, H., The

Levenberg-Marquardt method for

nonlinear least squares

curve-fitting problems September

28,2011

3 CO LTD, K.K., Hardware manual

KHR-1, K.K CO LTD, Editor

Sep.2004

4 High-Performance, -.b and D.S

Controllers,

dsPIC30F6011A/6012A/6013A/601

4A

Data Sheet, Mocrochip, Editor 2008