Generation of closed-form models for the control of flexible mechanisms: a numerical approach

In robotics, most high performances control strategies require a closed-form representation of the mechanical dynamic behaviour. This is even more critical when significant flexible effects are to be considered in the control algorithm. This paper presents a method to build closed-form dynamic equations for flexible multibody systems in terms of minimal coordinates. Relying on the Finite Element (FE) formulation, the method is able to tackle complex topologies with closed-loops in a systematic way. The method is based on an interpolation strategy. For a number of selected points in the configuration space, a full Finite Element model is built and reduced according to a component mode synthesis. Then, a piecewise polynomial model is adjusted to match the collected data. In order to guarantee the continuity of the model, a mode tracking strategy is implemented. After the presentation of the reduction procedure and of the interpolation strategy, a four-bar mechanism is analyzed as an illustrative example.