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and rotational velocities of the following figures are
normalizedw.r.t. their physical limits.
5.1.TimeOptimalControl
Fig. 4 shows the normalized motor torques and
rotationalvelocitiesof timeoptimalcontrolproblem.
Fortimeoptimaloptimization tasks, it isobvious that
at least onemotor restriction is active. Thefinal time
isgivenby tf=0.83s.Moreover, allphysical limits
of the motors are well considered. Occurring joint
forces and torques of the first subsystem are shown
inFig. 5.
M1
M2
M3
0 0.2 0.4 0.6 0.8 1
-1
-0.5
0
0.5
1
q˙1
q˙2
q˙3
Fz
t in s
0 0.2 0.4 0.6 0.8 1
-1
-0.5
0
0.5
1
Figure 4: Normalized motor torques and rotational
velocities of the timeoptimal control
Fx
Fy
Fz
0 0.2 0.4 0.6 0.8 1
-40
-20
0
20
40
60
80
100
Mx
Mz
t in s
0 0.2 0.4 0.6 0.8 1
-2
-1
0
1
2
3
4
5
Figure5: Joint forcesandtorquesof the timeoptimal
control M1
M2
M3
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-1
-0.5
0
0.5
1
q˙1
q˙2
q˙3
t in s
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-1
-0.5
0
0.5
1
Figure 6: Normalized motor torques and rotational
velocities of the joint loadminimization
Fx
Fy
Fz
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-10
0
10
20
30
40
50
60
70
Mx
Mz
t in s
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
1
2
3
Figure 7: Joint forces and torques of the joint load
minimization
5.2.MinimizingJointLoads
In comparison to time optimal control, the final
time tf = 2s of this optimal control is predefined
due to thewalking speedof the analyzed biped. Fig.
6 and Fig. 7 shows the dynamical behavior of this
task. Motor restrictions are almost inactive and the
occurring joint forces and torques are reduced in
comparison toFig. 5.
5.3.Maximizing theVerticalTorqueof theTorso
As to the last subsection 5.2, the final time tf =
2s is also predefined in this task. Optimization re-
62
Joint Austrian Computer Vision and Robotics Workshop 2020
- Titel
- Joint Austrian Computer Vision and Robotics Workshop 2020
- Herausgeber
- Graz University of Technology
- Ort
- Graz
- Datum
- 2020
- Sprache
- englisch
- Lizenz
- CC BY 4.0
- ISBN
- 978-3-85125-752-6
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 188
- Kategorien
- Informatik
- Technik