Tham khảo tài liệu 'multi-arm cooperating robots- dynamics and control - zivanovic and vukobratovic part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 228 Multi-Arm Cooperating Robots The control laws synthesized in the preceding section ensure the vector of increments AYi0 col AY. A To and its derivatives have an exponentially descending character. Because of the character of the change of AY. 0 and its derivatives the vector AFds0 also has an exponentially descending character converging to a zero value. For the non-singular matrix ck the value AYV is calculated from the last equation of 335 . Because of a linear dependence on the quantities AFd0 AT- and AT0 the deviation AYV will also have an exponentially descending character converging to zero. Because of that the non-controlled output quantity Yv will asymptotically converge to the nominal trajectory of the leader s contact point Y0. By an analogous procedure on the basis of the second equation of 335 it can be concluded that the increments of the contact forces of the followers AFc have also an exponentially descending character converging to the zero values . the contact forces of the followers converge asymptotically to their nominal values F0S. Thus we have proved the asymptotic tracking of all the non-controlled quantities of the elastic system in the case of tracking the nominal trajectories of the manipulated object MC and nominal trajectories of the followers contact points. Exactly the same conclusion could be derived if the trajectories of the other m nodes were selected as nominals . the nominal trajectories of the contact points Yc0 col YV0 t Y t only when selecting the vector of controlled outputs Yu q. Estimation of the driving torques constraints. Constraints on the driving torques can be estimated by norming some expression by an expression of the cooperative system dynamics in which they are explicitly contained 316 295 296 or by norming the expression for the description of the manipulator dynamics 167 . The simplest way is to norm 167 hrII H q q h q q yr q nH cII- Since in the course of time after the initial deviation qs0 is .
