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Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 12

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Tham khảo tài liệu 'multi-arm cooperating robots- dynamics and control - zivanovic and vukobratovic part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 208 Multi-Arm Cooperating Robots - Part of the state vector Y col Yv Ys Y0 col Yv Ys0 col Yc Y0 G R 6m 6 1 of the elastic system Yu col Ys1 . Ys m-1 Y0 col Ys Y0 Ys0 G R . 282 - Part of the state vector Y of the elastic system equal to the position vector of contact points Yu Yc G R6mx1. 283 - In view of the one-to-one mapping of the internal coordinates q and position vector of contact points Yc expressed by the relation 172 in the form Yc q the choices equivalent to the previous ones are Yu col qs Y0 G R6mx1 284 Yu q G R6mx1. 285 Vector of elasticity forces. Between the vector of elasticity forces Fe co Fev Fes Fe0 coi Fev Fes0 col Fec Fe0 G R 6m 6 x1 and the state vector of elastic system Y there exists the relation 120 given by Fe Y K Y Y G R 6m 6 x 1 so that instead of the part of the state vector Y of the elastic system the controlled output can be part of the vector of elastic forces that is - Part of the vector of elasticity forces acting at the contact points of the followers and manipulated object MC given by Yu col Fes F0 Fes0 G R6mx1. 286 - Part of the vector of elasticity forces equal to the vector of elasticity forces acting at the contact points Yu Fec G R6mx1. 287 Vector of contact forces. In principle the correctness of this choice can be corroborated in the following way. By solving the differential equations 115 describing the elastic system dynamics the solution will be obtained in the form Y Y Fc G R 6m 6 x1 and having 172 in mind the relation qT YT T qT Y0T T Fc G R 6m 6 x1. will be obtained. By solving the system of differential equations 167 that describe the manipulator dynamics we get the solution q q T Fc G R6mx1 or from Cooperative System Control 209 172 Yc Yc t Fc G R6mx1. Elimination of the vector q i.e. of the vector Yc will yield the dependence Fc Fc t Y0 g R6mx1 which can be written as a function of the selected input vector T G R6mx1 as FỊ Y0T T FT Y0T T t g R 6m 6 x1. This means that the response to the drive T G R6mx1 is the .