Flexible Robot Dynamic Modeling

Several of the control strategies for flexible link robots described in the remainder of the book rely on an accurate dynamic model of the system. Creating a dynamic model that accounts for link flexibility adds additional challenges beyond the standard rigid link robot dynamics. The most apparent complexity arises due to the additional degrees-of-freedom associated with link deformations. Although in theory this adds an infinite number of degrees-of-freedom, in practice only a finite number are used to generate a model that is sufficiently accurate for predictive simulation and control design. Another complexity (and perhaps a less obvious one) is the appearance of first-order (not negligible) dynamic effects due to second-order kinematic and force effects that at first glance appear to be negligible. For simple robot configurations, these effects can be handled in several intuitive ways. However, for complicated geometries, a systematic approach is needed to ensure that coupling effects are not inadvertently lost. Much of this chapter is devoted to describing such an approach, called the method of quadratic modes.