Real-time capable model inversion of underactuated multibody systems using servo-constraints

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Underactuated multibody systems are mechanical systems which haves less control inputs than degrees of freedom. An inverse model provides for a given output trajectory the associated control inputs and the trajectories of all coordinates of the system. Inverse models are used as feedforward control in combination with feedback control for trajectory tracking of multibody systems. The aim of the proposed project is the development of real-time capable inverse models of underactuated multibody systems. Thereby the servo-constraint approach is used, which originates in multibody dynamics. This is a systematic numerical approach which is applicable to a wide range of systems. The mathematical model of multibody systems consists of the equation of motion with control inputs and the defined output equations. For the inverse model additional servo-constraints for the output are defined, such that these follow predefined trajectories. The systems considered in this project are either differentially flat systems or systems with stable internal dynamics. The biggest challenge in this project is the design and real-time solution of inverse models, which have a higher differential index and an internal dynamics. At the end of this project such systems should be treated, especially with several inputs and outputs. In the scope of this project it should also be investigated if the choice of coordinates, i.e minimal coordinates or redundant coordinates, has an influence on the solution and efficiency of the inverse model. Currently this is an open question since due to the servo-constraints always a differential algebraic equation arises. Using the simple example of a crane it has been already demonstrated that here redundant coordinates are not necessarily less efficient than using generalized coordinates. This will be especially interesting for more complex three-dimensional systems. Under given time step constraints the limits of real-time capable model inversion should be tested. Hereby for systems with internal dynamics it has to be considered that their characteristic might be fundamental faster than the forward dynamics. Finally, using basic experiments the accuracy of inverse models should be tested. Therefore a modular testbed will be set-up, which allows the testing of 4 structurally different systems.