On the internal dynamics of flexible manipulators based on symmetric dichotomy

The symmetric acausal/causal dichotomy for the linearised stable internal dynamics of a class of flexible manipulators is studied. Computational issues, including the convergence of the iterative computation scheme and the symmetry computation of the desired internal dynamic trajectory, are addressed and the implication of the noncausal invertibility on tip trajectory planning is investigated. To explore the potential advantages offered by the inversion-based trajectory tracking control, it is highly desirable to have an internal dynamic model in an acausal/causal decoupled form. Also, this acausal/causal dichotomy should be explicit to provide a clear insight into the internal dynamics. This should also be useful for efficient computation and be able to guide tip trajectory planning. The symmetric dichotomy based internal dynamic model is developed to achieve these desirable characteristics. Case studies are carried out to illustrate the validity of the symmetric dichotomy based model for the internal dynamics