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Department of Mechanical Engineering
National Taiwan University of Science and Technology
ME5609710 Robotics
Homework#4 (highest score is 100%)
E1. Explain the diMerences between the analytical Jacobian and the geometric Jacobian.
(4% extra credit)
E2. Briefly describe the solution method for the diMerential inverse kinematics problem.
(6% extra credit)
Q1. Derive the analytical Jacobian matrix of the Fanuc robot based on the forward
kinematics analysis from #HW2. ( 2 0%)
Q2. Present the geometric Jacobian matrix of the Fanus robot. (10%)
Q 3. Identify and describe three types of the singularity conditions in the Fanuc robot. (30%)
Q 4. Given the initial joint angles and final end-eMector poses
Initail joint angles ๐ !
!
[
]
Final pose ๐
"
"
Use the diMerential inverse kinematics method to solve the inverse kinematics problem.
Assum that over a small interval of time ๐ก, the end-eMector moves by โ๐ = ๐ "
#$%%&'(
Perform four interations to comput the final pose and joint values of the end-eMector. ( 3 0%)
Note:
- The joint velocity ๐ฬ (
[
)
,
.
]
/
) and the end-eMector velocity ๐ฃ
&
([๐ฃ
0
1
2
$
3
4
]
/
) can be assumed constant during the intervals.
- If your end-eMector coordinate system diMers from the one used in HW2_solution,
you may use your own settings. Adjust the transformation matrices accordingly for
the initial and final poses from your #HW2)
Q 5. Conduct an error analysis of the end-eMecot pose in both Catesian space for each
iteration. Let the error ๐ be defined as:
"
%
where ๐ "
is the desired pose, and ๐
%
represents the forward kinematic solution of
current joint configuration ๐.
Present a graph with error values on vertical-axis and the number of the iterations on
horizontal-axis to show the convergence of the inverse solution over the iterations. (10%)
