DynaCon: The Embedding of the Adjoint Method in Multibody Dynamics

Regarding the increasing complexity of technical systems in modern engineering and science, simulations have become inevitable. Virtual experiments for simulating machines, engines or robots are an essential tool in applied sciences for the design and optimization of structures and machines. The actual physical or mechanical system is replaced by an equivalent multibody system which allows the modeling of the entire system of rigid and flexible bodies connected by joints and driven by forces and actuators. This means that, for a given set of initial conditions and time histories of external forces and actuators, the time history of the response of the whole virtual prototype can be computed. In recent years, considerable attention has been paid also to the arising inverse question, e.g., in case the time history of a control force is needed in order to allow a prescribed motion of an object in a minimum time or with minimum energy, possibly satisfying a specific path constraint simultaneously. Given the time history of the tension of a muscle fiber one might want to compute the muscular activity which produces that motion. Furthermore, an important problem is to identify specific material parameters of the muscle or a suspended bone. The underlying ideas of the latter mentioned biomechanical problems can be found in other relevant applications in robotics, aerospace or vehicle dynamics. The focus of the proposed project is the solution of such inverse multibody dynamics problems, intended as optimal control problems or parameter identifications for dynamical systems governed by differential- algebraic equations. Instead of the inefficient gradient computation from direct transcription, the adjoint method is persued, which is orders of magnitude more efficient. The scientific goal of the project is to define an innovative strategy for the solution of inverse multibody dynamic problems which possesses the characteristics of generality, robustness, accuracy and the possibility to embed the advantages in the field of multibody dynamics research. Of particular importance is the time- and memory-efficiency of the underlying numerical method concerning practical applicability in general purpose industrial level computations. Using the adjoint method, derivatives of the underlying mathematical formulation can be computed efficiently, even for large three dimensional simulations with millions of control parameters. The project combines innovative aspects from numerical mathematics in the context of inverse dynamics and time integration with pioneering ideas from the research field of multibody dynamics.

Regarding the increasing complexity of technical systems in modern engineering and science, simulations have become inevitable. Virtual experiments for simulating machines, engines or robots are an essential tool in applied sciences for the design and optimization of structures and machines. The actual physical or mechanical system is replaced by an equivalent multibody system which allows the modeling of the entire system of rigid and flexible bodies connected by joints and driven by forces and actuators. This means that, for a given set of initial conditions and time histories of external forces and actuators, the time history of the response of the whole virtual prototype can be computed. In recent years, considerable attention has been paid also to the arising inverse question, e.g., in case the time history of a control force is needed in order to allow a prescribed motion of an object in a minimum time or with minimum energy, possibly satisfying a specific path constraint simultaneously. Given the time history of the tension of a muscle fiber one might want to compute the muscular activity which produces that motion. Furthermore, an important problem is to identify specific material parameters of the muscle or a suspended bone. The underlying ideas of the latter mentioned biomechanical problems can be found in other relevant applications in robotics, aerospace or vehicle dynamics. The focus of the proposed project is the solution of such inverse multibody dynamics problems, intended as optimal control problems or parameter identifications for dynamical systems governed by differential-algebraic equations. Instead of the inefficient gradient computation from direct transcription, the adjoint method is persued, which is orders of magnitude more efficient. The scientific goal of the project is to define an innovative strategy for the solution of inverse multibody dynamic problems which possesses the characteristics of generality, robustness, accuracy and the possibility to embed the advantages in the field of multibody dynamics research. Of particular importance is the time- and memory-efficiency of the underlying numerical method concerning practical applicability in general purpose industrial level computations. Using the adjoint method, derivatives of the underlying mathematical formulation can be computed efficiently, even for large three dimensional simulations with millions of control parameters. The project combines innovative aspects from numerical mathematics in the context of inverse dynamics and time integration with pioneering ideas from the research field of multibody dynamics.