Structure-preserving optimal control of multibody systems

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The goal of the present research project is to develop new numerical methods for the optimal control of multibody systems. Energy-efficient movements are important to save resources. In particular, the question is how to control a specific multibody system to minimize the energy consumption. The related optimal control problem can be solved by applying computer simulation. Examples range from robotics to biomechanical locomotion systems. Another example is the optimal attitude control of a spacecraft.The aim of the project is to extend the notion of structure-preserving schemes for the numerical integration of the equations of motion to the realm of optimal control. Structure-preserving numerical methods inherit fundamental physical properties from the underlying mechanical system. Due to their inherent pyhsical consistency, structure-preserving schemes typically lead to superior numerical performance.Optimal control problems typically exhibit characteristic structural properties as well. However, so far, these properties have not been exploited in the development of numerical methods. The research proposal aims at the development of new numerical methods which satisfy fundamental structural properties of the optimal control problem. In particular, the newly proposed structure-preserving approach to optimal control problems should lead to improved numerical stability and convergence properties.