Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 12 pptx
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 2 docx
... the cooperation participants.
Let the two manipulators hold the object from the previous example and let
22 Multi-Arm Cooperating Robots
acting forces on the object, F
c1
and F
c2
and, by small ... R
6m+6
represents the radius vector of the (6m + 6 )-
dimensional space of the elastic system, whose unloaded state 0 is fixed (immo-
bile).
12 Multi-Arm Cooperating Robots
11
gene...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 3 pot
... nodes and
system of forces) and the dimensional part (dimension [position/force]) that is in-
versely proportional to the elasticity module of the material and characteristics of
the cross-section ... motion, the derivatives of coordinates are differ-
34 Multi-Arm Cooperating Robots
3.1 Some Known Solutions to Cooperative Manipulation Models
In [12] and [13], the vector of force...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 4 ppt
... position and force of the
manipulated object are X
0
, Y
0
and F
I 0
, whereas Y
i
, F
i
, F
ci
and τ
i
, i = 1, 2are
the displacements of contact points, elastic forces, contact forces and manipula-
tor ... state quantities are the po-
sition and velocity of the object MC Y
2
and
˙
Y
2
. The elastic forces are at the same
time the contact forces F
1
=−f
c1
and F
3
=−f
c2
(f
c1...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 5 pdf
... direc-
tion y
z
i
. The total potential energy of the elastic system is only its deformation
82 Multi-Arm Cooperating Robots
73
efficient on-line algorithms for connecting such finite elements and ... stiffness matrix; y
0
and F
e0
are the vectors of displacements and forces at the
manipulated object MC, whereas y
c
and F
ec
are the expanded vectors of displace-
ments and forces...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 6 ppsx
... π
ij
(Y
i
,Y
j
) (129 )
92 Multi-Arm Cooperating Robots
of the elastic system with the change of nodes coordinates in the adopted coordi-
nate frame, i.e. at the translation and rotation of the ... contact of the manipulator tips and object in w hich no change of con-
tact point on the manipulated object is allowed, whereas the forces and moments
106 Multi-Arm Cooperating Robots...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 8 doc
... Simulation results for τ
1
1
= 50 [Nm] and τ
1
2
=−50 [Nm]
132 Multi-Arm Cooperating Robots
part referring to the physical quantity used in modeling and the number indicat-
ing the ordinal number of the ... F
y
1
and moment
M
1
in the direction of the displacements Y
x
1
, Y
y
1
and ϕ
1
of the first contact point.
136 Multi-Arm Cooperating Robots
131
Figure 22c. Simulation re...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 9 ppt
... Y
0
c
, Y
0
0
, velocities
˙
Y
0
c
,
164 Multi-Arm Cooperating Robots
can be calculated as a function of non-selected vectors of the followers’ displace-
ments and known vector. Let the displacement ... assumed that the positions of contact points
162 Multi-Arm Cooperating Robots
159
of matrices and vectors, with the subscript v for the leader (y
v
= y
1
) and subscript
s for th...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 10 pps
... stabilized first
and then Steps 10, 11 and 12 replaced by Steps 10a, 11a and 12a.
Step 10a.
By introducing the coordinates, velocities, and accelerations of the nodes, deter-
mined in Step 4, and the ... y
s
s0
=
col(y
s
s
,y
s
0
) and the force at the MC of the manipulated object at the end of grip-
168 Multi-Arm Cooperating Robots
Figure 30. Nominals for manipulated object...
Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 11 pptx
... of time for the
non-controlled object and of time and state for the controlled object. For the con-
200 Multi-Arm Cooperating Robots
For a linear system of n
x
ordinary first-order differential ... torques τ ,andthe
204 Multi-Arm Cooperating Robots
203
– elastic;
• in view of their redundanc y
– non-redundant, and
– redundant;
• in view of joint compliance
– with non-compliant jo...
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