Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 3 pot

... col(q 1 1 ,q 2 1 ,q 3 1 ) ∈ R 3 ,q 2 = col(q 1 2 ,q 2 2 ,q 3 2 ,q 4 2 ) ∈ R 4 , q 3 = col(q 1 3 ,q 2 3 ,q 3 3 ,q 4 3 ) ∈ R 4 and q = col(q 1 ,q 2 ,q 2 ) = (q 1 1 ,q 2 1 ,q 3 1 ,q 1 2 ,q 2 2 ,q 3 2 ,q 4 2 ,q 1 3 ,q 2 3 ,q 3 3 ,q 4 3 ) ... link and the support q 1 1 and between the particular links q 2 1 and q 3 1 . Analogously, we can introduce the interna...

Ngày tải lên: 10/08/2014, 05:20

... system, and even then the forces at Mathematical Modeling of Cooperative Systems 45 y 2 − y 3 = y 23 = Y 2 − Y 3 + Y 30 − Y 20 = Y 2 − Y 3 + s 3 =  1 − Y 20 − Y 30 ||Y 2 − Y 3 ||  (Y 2 − Y 3 ), ... 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...

Ngày tải lên: 10/08/2014, 05:20

... (−mg) ∂Y 2 ∂y 2     Y 2 =λ 1 Y 20 =λ 2 y 2 =−mg, Q 3 = F 3 ∂Y 3 ∂Y 3 = F 3 ∂Y 3 ∂y 3     Y 3 =λ 1 Y 30 =λ 2 y 3 = F 3 . (37 ) Mathematical Modeling of Cooperative Systems 53 Kinematic relations between the external and internal ... col(y 1 ,y 2 ,y 3 ), (32 )  = 1 2 ⎡ ⎣ Y 1 Y 2 Y 3 ⎤ ⎦ T ⎡ ⎣ π 12 −π 12 0 −π 12 π 12 + π 23 −π 23 0 −π 23 π 23 ⎤ ⎦ ·...

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 ... diag(K e1 ,K e2 ,K e3 , ),andex- panded vectors of the force F e = column(F e1 ,F e2 ,F e3 , ) and displacement  e = column( e1 , e2 , e3 , ). If the equations of stiffness of each...

Ngày tải lên: 10/08/2014, 05:20

... introducing (1 53) into the pre vious equation and, in view of (82), we obtain 2 ij a (Y Ii ,Y Ij ) =  A(a) 0 3 3 0 3 3 I 3 3   ij · (Y i − Y j )  T × K ij  A(a) 0 3 3 0 3 3 I 3 3   ij · ...  ij from (84) and, after transposition, we have 2 ij a (Y Ii ,Y Ij ) = (Y i − Y j ) T   1 − ρ ij 0  r ia − r ja   I 3 3 0 0 I 3 3  ×  A(a) T 0 3 3 0 3 3 I 3 3 ...

Ngày tải lên: 10/08/2014, 05:20

... Thus, Q 13 is the sym bol for the internal coordinate q 3 1 , whereas QS 13 and SS 13 are the symbols for its first and second derivatives ˙q 3 1 and ¨q 3 1 . Diagrams of the dependent variable and its derivatives ... 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 an...

Ngày tải lên: 10/08/2014, 05:20

... equations (217) and (218), differential equations should be solved. Using the indexing system defined in (206), (207) and (2 03) for the structure 158 Multi-Arm Cooperating Robots 1 63 Figure 25. Nominal ... A T r (A 0 0 − A s 0 )(G + col(F s c , 0)), ( 238 ) where A r (a) = diag(A(a), I 3 3 , A(a),I 3 3 ) ∈ R (6m+6)×(6m+6) , a r (a) = col(0 1 3 ,a, 0 1 3 ,a) ∈ R (6m+6)×1 , a =...

Ngày tải lên: 10/08/2014, 05:20

... 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 general motion 184 Multi-Arm Cooperating ... required, the contact forces can be given 174 Multi-Arm Cooperating Robots Figure 32 . Simulation results for motion (open-loop cooperative system) 186 Multi-...

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 2 03 – elastic; • in view of their redundanc y – non-redundant, and – redundant; • in view of joint compliance – with non-compliant...

Ngày tải lên: 10/08/2014, 05:20