Temporal finite elements for target control dynamics of mechanisms

This paper discusses a temporal finite element description in the analysis of dynamics of mechanical systems, with a special emphasis on problems where target control is desired. This is defined as a situation where forces are sought for the movement of a structure from an initial to one or more specified target states. The primary applications lie in robotics and in bio-mechanical forward simulations of musculoskeletal systems. A temporal discretization of the movement and forces is introduced. By interpolating simultaneously displacements and velocities in the spatial discrete degrees of freedom, a collocation over the time interval can be used to decide the necessary system. The needed control can be optimized for chosen criteria on the integrated force components. The temporal interpolation of control forces and discrete displacements introduces a degree of continuity in the obtained results. The viewpoint allows variation of many aspects of problem formulation, and leads to efficient solutions for systems of high complexity but moderate size.