Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 8 doc

... Mq d -Mq d to the left-hand side and Mu-Mu to the right gives or ë=u-∆u+d, (4.4.44) where the inertia and nonlinear-term model mismatch terms are (4.4.45) (4.4. 46) 4.4 Computed-Torque Control Copyright ... its derivative. PD-Plus-Gravity Controller A useful controller in the computed-torque family is the PD-plus-gravity controller that results when M=I, N=G(q)-q d , with G(q) the g...

Ngày tải lên: 10/08/2014, 02:21

... Nonlinear Controllers There is a class of robot controllers that are not computed-torque-like controllers. These controllers are obtained directly from the robot equations without using the feedback-linearization ... Inc. Robust Control of Robotic Manipulators2 68 of q for robots with prismatic joints, and that (5.2.10) is satisfied by so that a=(à 2 - à 1 )/(à 2 +à 1 )) [Spo...

Ngày tải lên: 10/08/2014, 02:21

... q 1 2 + l 2 2 cos(q 1 2 + q 2 2 ) + l 3 2 cos(q 1 2 + q 2 2 + q 3 2 ) + l 4 2 cos(q 1 2 + q 2 2 + q 3 2 + q 4 2 ) z o2 + l 1 2 sin q 1 2 + l 2 2 sin(q 1 2 + q 2 2 ) + l 3 2 sin(q 1 2 + q 2 2 + ... l 1 2 cos q 1 2 + l 2 2 cos(q 1 2 + q 2 2 ) + l 3 2 cos(q 1 2 + q 2 2 + q 3 2 ) + l 4 2 cos(q 1 2 + q 2 2 + q 3 2 + q 4 2 ) z o2...

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 vect...

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 ... is to be solved by introducing the assump- 54 Multi-Arm C ooperating Robots i.e. the dependence F = ∂/∂y = Ky has been fully preserved. Thus, the prin- ciple of the minimum...

Ngày tải lên: 10/08/2014, 05:20

... a (r ia ,r ja ))(r ia r ja ) + ij 0 ì 0 , (89) 80 Multi-Arm Cooperating Robots 4 .5 Model of Elastic System Dynamics for the Immobile Unloaded State In this section, all the models of dynamics are derived using Lagrange’s ... 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 algor...

Ngày tải lên: 10/08/2014, 05:20

... A ia ) R 6 1 ,Y= col(Y 0 , ,Y m ) R 6m +6 L va (Y ) = diag(L v0a , ,L vma ) R (6m +6) ì(6m +6) , L via = diag(I 3ì3 ,L ia (A ia )) R 6 6 , v ia = col(r ia , ia (A ia )) = L via (Y i ) Y i R 6 1 , ia = ... R 6mì6m , detW ca (Y c ) = 0, w ca (Y, Y) = (w T 1a (Y, Y) w T ma (Y, Y)) T R 6mì1 , (1 16) where Y c denotes the expanded vector of contact position in the 6m-dimensional spac...

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 ... non- homogeneous system of differential equations involving dif ferential constraints. Such a system is solved by taking the left-hand side of the equality being given and see...

Ngày tải lên: 10/08/2014, 05:20

... equations (2 39) represents non-holonomic constraints. Solv- ing the nominal motion assumes the explicit calculation of the necessary contact 156 Multi-Arm Cooperating Robots 1 49 +[u 0 c −1 0 − ... that the positions of contact points 162 Multi-Arm Cooperating Robots 1 59 of matrices and vectors, with the subscript v for the leader (y v = y 1 ) and subscript s for the followe...

Ngày tải lên: 10/08/2014, 05:20

... 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; ã in view of their redundanc y non-redundant, and redundant; ã in view of joint compliance with non-compliant joint...

Ngày tải lên: 10/08/2014, 05:20

... the behavior of the non-controlled quantities q v , F cv and F cs and calculated driving torques τ . The conclusion about the behavior of the non-controlled quantities will be de- rived on the basis ... the moment when the control- realized asymptotic tracking of the controlled quanti- ties Y 0 and q s takes place. The goal is to estimate or determine the deviations of the non-controll...

Ngày tải lên: 10/08/2014, 05:20

... dt ⎞ ⎠ 230 Multi-Arm Cooperating Robots The control laws synthesized in the preceding section ensure the vector of in- crements Y s0 = col(Y s ,Y 0 ) and its deriv atives have an exponentially de- scending ... indirectly given by (312) and (315), whereby the non-controlled quantities (kinematic quantities of the leader, contact forces and driving torques) will not be 228 Mult...

Ngày tải lên: 10/08/2014, 05:20

... but it is the cooperative system control. Control schemes ‘leader/follower control and ‘master/slave control [14, 50], ‘motion/force control [51, 52], ‘coordinated control [15, 53, 54], are synthesized ... considered as part of the elastic interconnections of the object and manipulators. The object and elastic intercon- 252 Multi-Arm Cooperating Robots ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣...

Ngày tải lên: 10/08/2014, 05:20