Matlab, a software that is available on various computer platforms,
is a very powerful environment. Its environment is used for linear algebra
and graphical presentations. Application specific toolboxes provide extension
of its core functionality. Since Matlab has an interactive environment
and powerful graphical functions, it is very convenient to make robotic
simulation as well as experimental analysis with it.
The Robotics Toolbox allows a matlab user to create and manipulate
datatypes that are fundamental to robotics. Examples of these datatypes
are homogeneous transformations, quaternions and trajectories. For arbitrary
serial-link manipulators, the functions provided by the Toolbox include
forward and inverse kinematics, Jacobians, and forward and inverse dynamics.
This Toolbox has many functions which are very useful in Robotics,
especailly when it comes to areas such as kinematics and dynamics. When
conducting experiments with real robots, the toolbox is useful for simulation
and analyzing experimental results.
The Toolbox is written based on a general concept in which description
matrices are used to represent kinematics and dynamics of serial-link manipulators.
The user can create these matrices for any serial-link manipulator. The
well-known robots, i.e., the Puma 560 and the Stanford arm, are some of
the examples provided in the Toolbox. These matrices give a precise description
of a robot model and can accommodate the sharing of robot models across
the research community. As a result, the simulation results can be analyzed
and compared with the current ones in a better and more meaningful way.
The Toolbox is equipped with functions needed to manipulate important datatypes
such as vectors, homogeneous transformations and unit-quaternions. These
datatypes are used to represent 3-dimensional position and orientation.
In this project, my task is to understand and rewrite the toolbox to
accommodate for the configuration of the SIR1 robotics arm which served
as our research model.
In order to allow us to write a matrix that represents the configuration
of a robotic arm(SIR1), we have to understand the following dyn matrix
which describes the kinematics and dynamics of a manipulator in a general
way using the standard Denavit-Hartenberg conventions. Each row represents
one link of the manipulator and the columns are assigned according to the
following table.
| Column | Symbol | Description |
|
1 |
alpha |
link twist angle |
|
2 |
A |
link length |
|
3 |
theta |
link rotation angle |
|
4 |
D |
link offset distance |
|
5 |
sigma |
joint type; 0 for revolute, non-zero for prismatic |
|
6 |
m |
mass of the link |
|
7 |
rx |
link COG with respect to the link coordinate frame |
|
8 |
ry |
link COG with respect to the link coordinate frame |
|
9 |
rz |
link COG with respect to the link coordinate frame |
|
10 |
Ixx |
elements of link inertia tensor about the link COG |
|
11 |
Iyy |
elements of link inertia tensor about the link COG |
|
12 |
Izz |
elements of link inertia tensor about the link COG |
|
13 |
Ixy |
elements of link inertia tensor about the link COG |
|
14 |
Iyz |
elements of link inertia tensor about the link COG |
|
15 |
Ixz |
elements of link inertia tensor about the link COG |
|
16 |
Jm |
armature inertia |
|
17 |
G |
reduction gear ratio;joint speed/link speed |
|
18 |
B |
viscous friction, motor referred |
|
19 |
Tc+ |
coulomb friction (positive rotation), motor referred |
|
20 |
Tc- |
coulomb friction (negative rotation), motor referred |
The following configuration is for the SIR1 Robotics arm at University
of Bridgeport in Computer Science and Engineering Department.
% alpha A theta D sigma m rx ry rz Ixx Iyy Izz Ixy Iyz Ixz Jm
G B Tc+ Tc-
sir1 = [
pi/2 0 1.65*pi 0.205 0 0 0 0 0 0 0.35 0 0 0 0 200e-6 -62.6111 1.48e-3 .395
-.435
0 0.204 -pi*0.75 0 0 17.4 -.3638 .006 .2275 .13 .524 .539 0 0 0 200e-6
107.815 .817e-3 .126 -.071
0 0.250 -pi/2 0 0 4.8 -.0203 -.0141 .070 .066 .086 .0125 0 0 0 200e-6 -53.7063
1.38e-3 .132 -.105
pi/2 0 pi 0 0 0.82 0 .019 0 1.8e-3 1.3e-3 1.8e-3 0 0 0 33e-6 76.0364 71.2e-6
11.2e-3 -16.9e-3
0 0 2*pi 0.036 0 .09 0 0 .032 .15e-3 .15e-3 .04e-3 0 0 0 33e-6 76.686 36.7e-6
3.96e-3 -10.5e-3
];
In order to see the changes of the movements of SIR1, the following
commands are used:
qz=[0 0 0 0 0] % 0 represents revolute, whereas 1 represents prismatic
qr=[0 0 -pi/2 0 0]
