Innovative Optimization Methods for Multibody Systems

Modern multibody simulations enable scientists and industrial users to analyze the dynamic behavior of mechanical systems, which are far too complex both for writing down the equations of motions and for solving these equations analytically. Several commercial and research software tools are available for that purpose, which can be applied in vehicle dynamics, robotics, biomechanics etc. However, compared with other numerical engineering methods, multibody simulations have still a high potential for growing research and industrial recognition, because it is well suited for solving dynamical problems with large motions, rotations, deformations and the optimization and optimal control of such systems. In the last few years, the complexity of models in multibody dynamics has grown tremendously. In particular, simulations of large systems including as well flexible bodies, such as complete vehicles result in models with a vast number of degrees of freedom. In such cases, a simulation yielding only one motion of the system for given initial conditions may take even hours of computational time. If we are looking for a control which minimizes an objective function, e.g. the energy consumption or the time span for reaching a target state, we are dealing with an optimal control problem. There is an increasing demand in research for developing efficient and reliable algorithms for solving such problems in multibody dynamics. Among all optimal control problems, free end time problems are probably the most challenging ones. The goal of the proposed project is to develop a method for solving optimal control problems with free end time in multibody dynamics with applications in automotive and robotics. If we consider an industrial robot, for example, we might be interested in the optimal drive torques, while the target function could display energy consumption or measure the operation time. In this project we pay special attention to the latter class of problems and ask for controlling dynamic systems so that the time required is minimal. Efficient optimization algorithms for model-based design of multibody systems are the main focus of future technologies. In particular, time-optimal control problems are of great interest for a wide range of applications in engineering. On the one hand, this project promotes basic research in the field of optimal control, and on the other hand, it enables the transfer of theoretical methods into application in large-scale industrial problems and therefore allows the digital transformation of classical mechanics. Hence, the future vision of the proposed project is the application of classical mechanics in the sense of a digital tool ready for virtual production environment or works in multibody dynamics, as e.g. for smart vehicles or robots.