Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 11 pptx

... knowledge. It has already been mentioned that for the known right-hand sides of the re- lations (9), (10) and (11) , their left-hand sides are uniquely determined. If the cooperative work is solved ... 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 an...

Ngày tải lên: 10/08/2014, 05:20

... 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 ... contacts. The ‘non-uniqueness’ appears only in the description of the part of the system between the manipulator tips (grippers) and object. This suggests the 30 Multi-Arm Coopera...

Ngày tải lên: 10/08/2014, 05:20

... 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...

Ngày tải lên: 10/08/2014, 05:20

... 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...

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... h(q, ˙q) = τ + J T f c (167) 100 Multi-Arm Cooperating Robots 4 .11 Model of Cooperative System Dynamics for the Mobile Unloaded State Equations (113 ) or (115 ), (167) and (172) define the model of ... (w T 1a (Y, ˙ Y) w T ma (Y, ˙ Y)) T ∈ R 6m×1 , (116 ) where Y c denotes the expanded vector of contact position in the 6m-dimensional space and F c stands for the expanded vector of...

Ngày tải lên: 10/08/2014, 05:20

... 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...

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... 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...

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... 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...

Ngày tải lên: 10/08/2014, 05:20

... 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...

Ngày tải lên: 10/08/2014, 05:20