Please make a Matlab code for just e$.)$ using corke matlab robotics toolbox. funct rpy$2$tr$()$ and transl$().$ i already did a$-$d MATLAB EXERCISE $2$B

a$)$ Write a MATLAB program to calculate the homogeneous transformation matrix

${?}_B^{A}T$ when the user enters $Z-Y-x$ Euler angles $--$ and the position vector

${?}^A{P}_B.$ Test for two examples:

i$)=10,=20,=30,$ and ${?}^A{P}_B=\{[1,2,3]{\}}^T.$

ii$)$ For $=20(==0),{?}^A{P}_B=\{[3,0,1]{\}}^T.$

b$)$ For $=20(==0),{?}^A{P}_B=\{[3,0,1]{\}}^T,$ and ${?}^{B}P=\{[1,0,1]{\}}^T,$ use MATLAB to

calculate ${?}^{A}P$; demonstrate with a sketch that your results are correct. Also, using

the same numbers, demonstrate all three interpretations of the homogeneous

transformation matrix $-$ the $($b$)$ assignment is the second interpretation, transform

mapping.

c$)$ Write a MATLAB program to calculate the inverse homogeneous transformation

matrix ${?}_B^A{T}^{-1}={?}_A^{B}T,$ using the symbolic formula. Compare your result with a

numerical MATLAB function $($e$.$g$.,$ inv$).$ Demonstrate that both methods yield

correct results $($i$.$e$.,{?}_B^A{T}_B^A{T}^{-1}={?}_B^A{T}_B^{-1}{?}^{A}T=I_4).$ Demonstrate this for examples $($i$)$

and $($ii$)$ from $($a$)$ above.

d$)$ Define ${?}_B^{A}T$ to be the result from $($a$)($i$)$ and ${?}_C^{B}T$ to be the result from $($a$)($ii$).$

i$)$ Calculate ${?}_C^{A}T,$ and show the relationship via a transform graph. Do the same

for ${?}_A^{C}T.$

ii$)$ Given ${?}_C^{A}T$ and ${?}_C^{B}T$ from $($d$)($i$)-$assume you don't know ${?}_B^{A}T,$ calculate it$,$ and

compare your result with the answer you know.

iii$)$ Given ${?}_C^{A}T$ and ${?}_B^{A}T$ from $($d$)($i$)-$assume you don't know ${?}_C^{B}T,$ calculate it$,$ and

compare your result with the answer you know.

e$)$ Check all results by means of the Corke MATLAB Robotics Toolbox. Try

functions $rpy2tr()$ and transl$().$