Use the function

S

c

r

e

w

T

r

a

j

e

c

t

o

r

y

ScrewTrajectory in the given software to calculate a trajectory as a list of

N

$=$

$10$

N$=10$

S

E

$($

$3$

$)$

SE$(3)$ matrices, where each matrix represents the configuration of the end$-$effector at an instant in time. The first matrix is

X

s

t

a

r

t

$=$

$[$

$1$

$0$

$0$

$0$

$0$

$1$

$0$

$0$

$0$

$0$

$1$

$0$

$0$

$0$

$0$

$1$

$]$

X

start

$$

$=$

$$

$$

$$

$$

$$

$$

$1$

$0$

$0$

$0$

$$

$0$

$1$

$0$

$0$

$$

$0$

$0$

$1$

$0$

$$

$0$

$0$

$0$

$1$

$$

$$

$$

$$

$$

$$

$$

and the $10$th matrix is

X

e

n

d

$=$

$[$

$0$

$0$

$1$

$1$

$1$

$0$

$0$

$2$

$0$

$1$

$0$

$3$

$0$

$0$

$0$

$1$

$]$

$.$

X

end

$$

$=$

$$

$$

$$

$$

$$

$$

$0$

$1$

$0$

$0$

$$

$0$

$0$

$1$

$0$

$$

$1$

$0$

$0$

$0$

$$

$1$

$2$

$3$

$1$

$$

$$

$$

$$

$$

$$

$$

$.$

The motion is along a constant screw axis and the duration is

T

f

$=$

$10$

T

f

$$

$=10.$ The parameter

m

e

t

h

o

d

method equals $3$ for a cubic time scaling. Give the $9$th matrix $($one before

X

e

n

d

X

end

$$

$)$ in the returned trajectory. The maximum allowable error for any matrix entry is $0\mathrm{.}01,$ so give enough decimal places where necessary.

Use Python syntax to express a matrix in the answer box:

$[[1\mathrm{.}11,2\mathrm{.}22,3\mathrm{.}33],[4\mathrm{.}44,5\mathrm{.}55,6\mathrm{.}66],[7\mathrm{.}77,8\mathrm{.}88,9\mathrm{.}99]]$ for

$[$

$1\mathrm{.}11$

$2\mathrm{.}22$

$3\mathrm{.}33$

$4\mathrm{.}44$

$5\mathrm{.}55$

$6\mathrm{.}66$

$7\mathrm{.}77$

$8\mathrm{.}88$

$9\mathrm{.}99$

$]$

$$

$$

$$

$$

$1\mathrm{.}11$

$4\mathrm{.}44$

$7\mathrm{.}77$

$$

$2\mathrm{.}22$

$5\mathrm{.}55$

$8\mathrm{.}88$

$$

$3\mathrm{.}33$

$6\mathrm{.}66$

$9\mathrm{.}99$

$$

$$

$$

$$

$$

$.$