Elastic joints
This chapter deals with modelling and control of robot manipulators with joint flexibility. The presence of such a flexibility is a common aspect in many current industrial robots. When motion transmission elements such as harmonic drives, transmission be
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Elastic joints This chapter deals with modelling and control of robot manipulators with joint flexibility. The presence of such a flexibility is a common aspect in many current industrial robots. When motion transmission elements such as harmonic drives, transmission belts and long shafts are used, a dynamic time-varying displacement is introduced between the position of the driving actuator and that of the driven link. Most of the times, this intrinsic small deflection is regarded as a source of problems, especially when accurate trajectory tracking or high sensitivity to end-effector forces is mandatory. In fact, an oscillatory behaviour is usually observed when moving the links of a robot manipulator with non negligible joint flexibility. These vibrations are of small magnitude and occur at relatively high frequencies, but still within the bandwidth of interest for control. On the other hand, there are cases when compliant elements (in our case, at the joints) may become useful in a robotic structure, e.g., as a protection against unexpected "hard" contacts during assembly tasks. Moreover, when using harmonic drives, the negative side effect of flexibility is balanced by the benefit of working with a compact, in-line component, with high reduction ratio and large power transmission capability. From the modelling viewpoint, the above deformation can be characterized as being concentrated at the joints of the manipulator, and thus we often refer to this situation by the term elastic joints in lieu of flexible joints. This is a main feature to be recognized, because it will limit the complexity both of the model derivation and of the control synthesis. In particular, we emphasize the difference with lightweight manipulator links, where flexibility involves bodies of larger mass (as opposed to an elastic transmission shaft) undergoing deformations distributed over longer segments. In that
C. C. de Wit et al. (eds.), Theory of Robot Control © Springer-Verlag London Limited 1996
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CHAPTER 5. ELASTIC JOINTS
case, flexibility cannot be reduced to an effect concentrated at the joint. As we will see, this has relevant consequences in the control analysis and design; the case of flexible joints should then be treated separately from that of flexible links. We also remark that the assumption of perfect rigidity is an ideal one for all robot manipulators. However, the primary concern in deriving a mathematical model including any kind of flexibility is to evaluate quantitatively its relative effects, as superimposed to the rigid body motion. The additional modelling effort allows verifying whether a control law derived on the rigidity assumption (valid for rigid manipulators) will still work in practice, or should be modified and if so up to what extent. If high performance cannot be reached in this way, new specific control laws should be investigated, explicitly based on the more complete manipulator model. When compared to the rigid case, the dynamic model of robot manipulators with elastic joints (but rigid links)
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