Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question
minimum and maximum acceleration of the parameter s for the time-optimal path-constraint trajectory planning -(lagrangian
ode45 matrix
fill in the blanks where it says "Fill" in the first pitcure
![q_initial-(q_initial;0;0];
a_final-[q_final;0;0];
x_initial=[q_initial;s_initial'];
RHS=@ (t,x) [RPmanipulator (x (1:4), $FILL14%,ml,m2,11,12,rl);$FILL15%];
48
49 -
50 -
51
52 -
xlabel ('t')
legend ('ul (acc)','u2 (acc) ','ul (dec)','u2 (dec)','Location','southeast')
53 -
54 -
subplot (2,2,3)
55 -
hold on
[tl,xl]=ode45 (RHS, [0, tmin],x_initial,OPTIONS)
plot (tl, xl (:,1))
56
57 -
58
plot (tl,xl (:,2))
RHS=@ (t,x) [RPmanipulator (x (1:4), &FILL16%, ml,m2,Il,12,rl);%FILL17%];
[t2,x2]=ode45 (RHS, [tmin, tmin+tleft], $FILL188, OPTIONS)
plot (t2,x2 (:,1))
plot (t2, x2 (:,2))
59
60
61
62 -](https://content.bartleby.com/qna-images/question/7611a395-318b-4577-b358-b0b6f732a783/4d1964bc-435b-465f-95f4-bc66412820bc/6325yue_processed.png)
Transcribed Image Text:q_initial-(q_initial;0;0];
a_final-[q_final;0;0];
x_initial=[q_initial;s_initial'];
RHS=@ (t,x) [RPmanipulator (x (1:4), $FILL14%,ml,m2,11,12,rl);$FILL15%];
48
49 -
50 -
51
52 -
xlabel ('t')
legend ('ul (acc)','u2 (acc) ','ul (dec)','u2 (dec)','Location','southeast')
53 -
54 -
subplot (2,2,3)
55 -
hold on
[tl,xl]=ode45 (RHS, [0, tmin],x_initial,OPTIONS)
plot (tl, xl (:,1))
56
57 -
58
plot (tl,xl (:,2))
RHS=@ (t,x) [RPmanipulator (x (1:4), &FILL16%, ml,m2,Il,12,rl);%FILL17%];
[t2,x2]=ode45 (RHS, [tmin, tmin+tleft], $FILL188, OPTIONS)
plot (t2,x2 (:,1))
plot (t2, x2 (:,2))
59
60
61
62 -
![RPmanipulator.m x
LU.m X
findswitch.m x trajectory.m X
abc.m X
function RHS = RPmanipulator (q, u, ml, m2,I1,I2,rl)
* creates the righthand side of the Lagrange dynamics converted to ordinary
* differential equations
2
3
4
Sthe main equation was given in the general form qdotdot, it was 2nd order,
SWe need to define extra variables to get it down to Ind order:
$ q= ql q2 qldot q2dot
* RHS: right hand side gdot=RHS
* RHS1=qldot
* RHS2=q2dot
* RHS3=qldotdot=from Lagrange equation
* RHS4=q2dotdot=from Lagrange equation
5
7
10
11
12 -
g=9.8; $gravitational acc.
RHS= [g (4);
|a (4);
- (2*m2 *q (2) *q (3) *g(4) +g* (ml*rl+m2*q (2)) *cos (a (1)) -u (1))/ (Il+I2+ml*rl^2+m2*q(2) ^2);
13 -
14
15
16
- (-m2*g (2) *a(3) ^2+g*m2*sin (q (1))-u (2))/m2;
17
];
18 -
end
Current Folc](https://content.bartleby.com/qna-images/question/7611a395-318b-4577-b358-b0b6f732a783/4d1964bc-435b-465f-95f4-bc66412820bc/bmq1xte_processed.png)
Transcribed Image Text:RPmanipulator.m x
LU.m X
findswitch.m x trajectory.m X
abc.m X
function RHS = RPmanipulator (q, u, ml, m2,I1,I2,rl)
* creates the righthand side of the Lagrange dynamics converted to ordinary
* differential equations
2
3
4
Sthe main equation was given in the general form qdotdot, it was 2nd order,
SWe need to define extra variables to get it down to Ind order:
$ q= ql q2 qldot q2dot
* RHS: right hand side gdot=RHS
* RHS1=qldot
* RHS2=q2dot
* RHS3=qldotdot=from Lagrange equation
* RHS4=q2dotdot=from Lagrange equation
5
7
10
11
12 -
g=9.8; $gravitational acc.
RHS= [g (4);
|a (4);
- (2*m2 *q (2) *q (3) *g(4) +g* (ml*rl+m2*q (2)) *cos (a (1)) -u (1))/ (Il+I2+ml*rl^2+m2*q(2) ^2);
13 -
14
15
16
- (-m2*g (2) *a(3) ^2+g*m2*sin (q (1))-u (2))/m2;
17
];
18 -
end
Current Folc
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