ME598 Introduction to Robots

Lab 2 Report

Group E

Group Members:

Renjie Xie

David Harman

Hao Wu

Jiachuan Peng

Submission Date: 3/28

Part 0: Configure and Test RAIS System with Manipulator

We used the robot arm with power supply 3

Specify the robot arm that we are using:

This figure shows the robot arm we are using, it represents its links and

joints with labeled sizes on the configuration.

Joint1: Base, Joint2: Shoulder, Joint3:Elbow, Joint4: Wrist pitch, Joint5:

Wrist roll

Part1: Validate Forward-Kinematics Model

Quantitative trials for comparing the simulated results from our

forward-kinematics function with actual robot position:

Position1:

simulated result

actual position

X: -6.2in Y: 0in Z: 12.65in

Position2:

simulated result

actual position

X: -7.5in Y: 0in Z: 11.5in

Position3:

simulated result

actual position

X: -10.1in Y: 0in Z: 7in

Position4:

simulated result

actual position

X: -10in Y: 0in Z: 6.75in

Position5:

simulated result

actual position

X: -10.2in Y: -1.6in Z: 7.2in

Position6:

simulated result

actual position

X: 0in Y: 0in Z: 14.5in

We find that the simulated data on Z direction always smaller than the

actual position data and the absolute value of simulated data on X

direction bigger than that of actual data. While the Y direction data is

exact as the actual.

We repeated each process three times from different starting

configurations and found that there always had some small discrepancies

between different routes for one end position, but those discrepancies

doesn’t affected much.

We think that the measure point we choose causes those discrepancies

because all drift direction of those differences are the same and those

discrepancies are in the range of [1 2]in. If we choose the same measure

point as the simulated one, the discrepancies could be minimized.

Part2: Inverse-Kinematic Model

The schematic of the robot arm with corresponding parameters:

In this configuration it shows the placed coordinate frames, labeled

joints, links, and rotation directions.

The derivation of the inverse-kinematic equations:

DH Parameters

The final transforming matrix is:

5*4*3*2*1 AAAAAT

Thus

Since the griper could be assumed to be pointing downward all the time,

the transforming matrix from frame 0 to frame 5 shall fulfill the following

form:

T'=

1000z100y0cossinx0sincos-

g

g

g

(In which θ equals θ1-θ5)

Thus the inverse kinematic equations are (5 variables requires 5

equations at least):

-cosθ=c1c234c5+s1s5; sinθ=-c1c234s5+s1c5;

-c1s234=0; -s1s234=0; -c234=-1; -s234c50; s234s5=0;

-d5c1s234+a3c1c23+a2c2c1=xg;

-d5s1s234+a3c1c23+a2c2s1=yg;

-d5c234-a3s23+d1-a2s2=zg;

Examples to check the output joints value:

1.

2

3.

The MATLAB code in the appendix.

Part3: Basic Path Planning

1. From the position (0, 4) to (-4, 0)

The path from the text file

90 0 90 78 0 50

90 0 90 78 0 0

7 0 90 15 0 0

7 0 90 78 0 0

7 0 90 78 0 50

0 0 0 0 0 50

The robot arm end-effector arrives at the position (0, 4) by inputting

each joint value (90 0 90 78 0), then closes the gripper and

moves to position (-4, 0) by inputting joint value (7 0 90 15 0)and

(7 0 90 78 0 0). Open the gripper to put the bolt and return to

home position (joint value: (0 0 0 0 0)).

2. From the position (-4, 0) to (0, -4)

The path from the text file

5 0 90 78 0 50

5 0 90 78 0 0

-90 0 90 15 0 0

-85 0 90 78 0 0

-85 0 90 78 0 50

0 0 0 0 0 50

The robot arm end-effector arrives at the position (-4, 0) by inputting

joint value (5 0 90 78 0 )(because the robot arm is not absolute

vertical, thus the first joint value is 5 instead of 0 for compensating the

tilt), then closes the gripper and moves to position (0, -4) by inputting

joint value (-90 0 90 15 0) and (-85 0 90 78 0 0). Open

the gripper to put the bolt and return to home position (joint value: (0

0 0 0 0)).

3. From the position (0, 4) to (-4, 0) and continue from the position (-4, 0)

to (0, -4)

The path on the text file

90 0 90 78 0 50

90 0 90 78 0 0

7 0 90 15 0 0

7 0 90 78 0 0

7 0 90 78 0 50

7 0 90 78 0 0

-90 0 90 15 0 0

-85 0 90 78 0 0

-85 0 90 78 0 50

0 0 0 0 0 50

The robot arm reaches the position (0, 4) first and closes the gripper to

catch the bolt and moves to the position (-4, 0), open the gripper to

release the bolt. Then, closes the gripper and sends the bolt to the

position (0, -4). Return to home position at the end.

We have tested each path three times and found that we could catch the

bolt and move to the destination almost accurately every time.

The path is inferred by combining the two paths mentioned above since

the intermediate configuration connecting the end position of first path

with the start position of second path, the robot arm could also move

continuously. Thus the path could the gathered to create a compound

path.

The video address

https://youtu.be/uMU8d3zsCS0

Part 4: multiple object path planning

Specify the obstacle starting positions

1. (3, 4.5) 2. (5, 3) 3.(2, 6)

The bin position

(4, 9)

The path on the text file

59 10 80 67 0 50

59 10 80 67 0 0

59 10 51 67 0 0

-66 31 21 45 2 0

-66 31 21 45 2 50

-34 31 21 45 2 50

-29 23 58 80 2 50

-29 23 58 80 2 0

-34 31 21 45 2 0

-66 31 21 45 2 0

-66 31 21 45 2 50

-86 31 21 45 2 50

-86 28 35 89 2 50

-70 28 35 89 2 50

-70 35 39 89 2 50

-70 35 39 89 2 0

-81 15 39 89 2 0

-86 21 40 37 2 0

-67 22 23 62 2 0

-67 22 23 62 2 50

0 0 0 0 0 50

First move the robot arm end-effector to the position 1 (3, 4.5) by

inputting joint values (59 10 80 67 0 ), then close gripper to catch

the bolt and input joint values (66 31 21 45 2) to send bolt into

the bin.

Second, reach position 2 (5, 3) gradually through joint values (-34 31

21 45 2), (-29 23 58 80 2), (-29 23 58 80 2), (-34 31

21 45 2). Then catch the bolt and move to the bin position by

inputting joint values(-66 31 21 45 2).

Third, to the position 3 (2, 6) step by step using joint values(-86 31 21

45 2 ), (-86 28 35 89 2 ), (-70 28 35 89 2), (-70 35 39

89 2), continuously catch the bolt and release it into the bin.

At last back to the home as the joint values are(0 0 0 0 0 ).

The intermediate configuration are connected since the end of former

path is the start of next path.

The record address

https://youtu.be/EUzFYp-6d58

Bonus:

Specify the obstacle XYZ starting positions

1. (3, 4.5, 0) 2. (5, 3, 1) 3.(2, 6, 0.5)

The bin position

(4, 9)

The path on the text file

59 10 80 67 0 50

59 10 80 67 0 0

59 10 51 67 0 0

-66 31 21 45 2 0

-66 31 21 45 2 50

-29 21 38 34 2 50

-29 21 38 98 2 50

-29 21 38 98 2 0

-29 12 31 48 2 0

-64 18 40 39 2 0

-64 18 40 39 2 50

-89 18 40 39 2 50

-89 7 62 70 2 50

-70 7 62 70 2 50

-70 14 68 66 2 50

-70 14 68 66 2 0

-85 14 59 66 2 0

-85 2 40 66 2 0

-65 20 30 38 2 0

-65 20 30 38 2 50

0 0 0 0 0 50

The process are the same as the part 4 mentioned above. Since the

objects 2 and 3 have height, thus joint values are changed in order to

catch the bolt.

To the position 1,we input joint value(59 10 80 67 0 ).

Position 1 to the bin: joint values of the path are (59 10 51 67 0),

(-66 31 21 45 2).

To the position 2, we input joint values (-29 21 38 34 2), (-29 21

38 98 2).

Position 2 to the bin: joint values of the path are (-29 21 38 98 2),

(-29 12 31 48 2), (-64 18 40 39 2).

To the position3, we input joint values(-89 18 40 39 2), (-89 7

62 70 2), (-70 7 62 70 2), (-70 14 68 66 2).

Position 3 to the bin: joint values of the path are (-85 14 59 66 2),

(-85 2 40 66 2), (-65 20 30 38 2).

Back to the home, we input joint values (0 0 0 0 0).

The intermediate configuration are connected since the end of former

path is the start of next path.

The record address

https://youtu.be/aaSsaLSDHNs

Part5: Student Feedback

We think that this lab is important for us to understand the robot motion

and control, we have tested the theory that we could plan the robot path

by inputting joint values calculated from inverse-kinematic equations.

We have taken two weeks to complete this exercise, and we

encountered some difficulties such as the ruler data is hard for us to read

exactly during measurement since the ruler is always tilted a little, and

the gripper was broken on our first robot arm so we needed to change

the machine and started all processes again. The biggest trouble we have

met is that we hardly to maintain same results for repeated processes

even every condition didn’t change, the bolt is also to hard to be caught

without dropping. Also, when we test our codes, we found that the

result was not correspond exactly o the statics of RAIS model.

The exercise could be improved if it sets more obstacles and complicated

goals for us to achieve because it could improve our skills much.

Appendix(MATLAB function code)

% function J = ME598_GrpE_InvKin(x,y,z,theta5)%% a2=3.61;% a3=3.08;% d1=2.91;% d5=5.45;

function J = ME598_GrpE_InvKin(xyz)x = xyz(1); y = xyz(2); z = xyz(3);a1 = 2.91; a2 = 3.61;a3 = 3.08; a4 = 5.45;% Calculating basic coefs for inverse kinematicsr = z + a4 - a1;s = sqrt(x^2 + y^2);

D = (r^2 + s^2 - a2^2 - a3^2) / (2*a2*a3);% Calculating rotating angles for each jointstheta1 = atan2(y, x);theta3 = atan2(sqrt(1 - D^2), D);

theta2 = abs(atan2(r, s) - atan2(a2 + a3*cos(theta3),a3*sin(theta3)));theta4 = pi - theta2 - theta3;theta5 = 0;J = wrapTo180(rad2deg([theta1 theta2 theta3 theta4 theta5]));