Tham khảo tài liệu 'control problems in robotics and automation - b. siciliano and . valavanis (eds) part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 84 A. De Luca In particular the complete dynamic model of robots with elastic joints fails to satisfy the necessary conditions for input-output decoupling and or full linearization by static state feedback 15 as opposed to the case of rigid robots for which these methods are equivalent to the well-known computed torque technique. Use of the larger class of dynamic state feedback controllers is helpful because elastic joint robots are in fact input-output invertible systems without zero dynamics. However the linearizing dynamic compensator has been derived so far only for very simple manipulators while a general synthesis method is still missing. In Sect. 2. we will provide a constructive answer to this problem. Furthermore we will be able to characterize in a precise way a tight upper bound for the dimension of the needed dynamic compensator. On the other hand the mapping between the joint torque input and the end-effector position output in robots with flexible links is associated with an unstable zero dynamics 14 the nonlinear equivalent of non-minimum phase zeros in a linear setting. The straightforward application of inversionbased control leads in this case to an unbounded increase of the internal arm deformation and eventually to control explosion. Different approaches have been presented in order to overcome this problem while exactly tracking the desired tip motion of multi-link manipulators inversion in the frequency domain iterative learning control nonlinear regulation or a combination of these. In all cases the key feature is the computation of the bounded link deformations and of the joint motions producing the desired trajectory of the manipulator tip. Based on this idea Sect. 3. presents in a unified framework three different but rather equivalent solutions to the end-effector trajectory tracking problem. We report also some illustrative experimental results obtained on a prototype two-link planar manipulator with flexible forearm available in our .
