Description
Project Overview:
The objective of the second computer project is for you to gain experience with the challenges involved in implementing a kinematic simulation of an articulated object. Your program must generate the joint angles required
to move a planar, n-link robot so the robot’s hand follows a specified trajectory. Generating the joint angles will
require you to calculate Jacobians and perform both forward and inverse kinematics.
Description of Input Files:
Two files are provided in the project folder and will need to be inputs to your MATLAB script. The first file, which
is called arm, contains a subset of the Denavit-Hartenberg parameters for the robot arm in its initial configuration.
Specifically, the format for arm is as follows:
n λ
l1 θ1(0)
l2 θ2(0)
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.
.
.
.
.
ln θn(0)
where li
is the length of link i and θi(0) is the initial angle of joint i. Note the value of λ (for Damped Least
Squares) is included in the arm file.
The second input file is called trajectory and contains the desired end-effector trajectory for the robot. The file
format is as follows:
m λ
x(0) y(0)
x(1) y(1)
.
.
.
.
.
.
x(m) y(m)
where m is the number of desired positions specified for the robot. Note, m depends on the input file and should
be a variable within your program. The pair [x(i), y(i)] is the desired position of the end-effector at the ith frame.
From these two input files, you need to generate an output file called angles which specifies the joint angles
needed to reach each point in trajectory. The format of angles should be:
θ1(0) θ2(0) . . . θn(0)
θ1(1) θ2(1) . . . θn(1)
.
.
.
.
.
.
.
.
.
.
.
.
θ1(m) θ2(m) . . . θn(m)
where m corresponds to the number of points provided in trajectory and n again refers to the total number of joints.
In short – your code should read two files, arm and trajectory, and output a single file called angles as shown in
the block diagram of Figure 1.
Outline of General Procedure:
You will first need to import the provided input files, arm and trajectory. Consider using the fscanf command to
read the files or use dlmread as for Project 1. Make sure the imported data matches the corresponding format as
described. Using forward kinematics and the initial robot configuration described by arm, determine the location of
the end effector at t = 0 using forward kinematics. Compare the actual end-effector location to the desired location
as specified in trajectory to generate a position error.
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Figure 1: Box diagram of Input/Output for project
The next task is to reduce the position error by determining the joint angles required to reach the desired position, aka. perform inverse kinematics. You are to use the Damped Least Squares (DLS) technique which is iterative.
Within the DLS loop, you first need to form the Jacobian of the end-effector for the current robot configuration.
Using the Jacobian and given value of λ, perform DLS to calculate the change in joint angles, ∆θ which are added
to the initial angle values. Determine the robot’s end-effector position using the updated angle values and repeat
the angle update until the position error is satisfactorily small or you are unable to get any closer to the specified
point (i.e. the desired trajectory may not be within the robot’s reachable workspace). Store the total change in
joint angles as this is the first row in your output file. Repeat the entire process for the next point in trajectory.
Additional Comments:
You can evaluate the performance of your robot in many ways. One suggestion is to plot the desired position and
the actual position – a task accomplished by the single MATLAB script provided with the project. The script
check angles.m loads the angles file you generated, the arm parameters as needed for forward kinematics, along
with the trajectory file. From these files, a plot of the actual positions and desired positions is generated along with
a curve indicating the workspace boundary for your robot.
Another available check is provided through RobotStudio. In order to simulate your angles in RobotStudio, follow the RobotStudio Instructions provided in the project folder to unpack the RobotStudio Workspace.rspag package
provided in the project folder. After the workspace is unpacked, you will need to move the PositionGenerator.m
MATLAB script into the same folder as your other MATLAB scripts. Run PositionGenerator.m to reformat your
angles and trajectory files so they are compatible with RobotStudio. Make sure the newly generated files are placed
as described in the RobotStudio Instructions which may require manually moving the files.
What to Submit: When you are satisfied with the performance of you code, type a short README document as
described in the Project Guidelines document from the course website. Email the README file and a .zip folder
containing all MATLAB code to Megan at mremmons@rams.colostate.edu by the assignment deadline.
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