A discrete variational approach to optimal control problems in multibody dynamics

Date

Dec 18, 2013

Time

5:00 PM - 6:00 PM

Speaker

Prof. Dr. Sigrid Leyendecker

Affiliation

Eleonore-Trefftz-Vorlesungen im Dresdner Mathematischen Seminar Prof. Dr. Sigrid Leyendecker Friedrich-Alexander Universität Erlangen-Nürnberg, Lehrstuhl für Technische Dynamik

Series

TUD Dresdner Mathematisches Seminar

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Description

Im Rahmen des Dresdner Mathematischen Seminars finden in diesem Semester eine Reihe von Eleonore-Trefftz-Vorlesungen statt, welche durch das Eleonore-Trefftz-Gastprofessorinnenprogramm der Exzellenzinitiative gefördert werden. The benefits of structure preserving algorithms - which can for example be derived via a discrete variational principle - for the numerical time-integration of mechanical systems are widely accepted in forward dynamic simulations. On the one hand, the fidelity of the approximate solution is improved compared to standard methods by inheriting certain characteristic properties of the continuous motion to the discrete trajectory. For example, the evolution of the system’s energy or momentum maps exactly represents externally applied forces, in particular they are conserved along the approximate motion of unforced systems. Furthermore, the symplectic structure underlying real dynamics is respected by certain mechanical integrators. On the other hand, the preservation of these quantities stabilises the numerical integration and thus enables longterm simulation. However, in the field of motion planning and optimal control via direct methods, so far, these benefits have been less used. The dynamic optimisation method DMOCC (Discrete Mechanics and Optimal Control for Constrained Systems) presented in this talk, does exploit the structure preserving properties of a variational integrator within an optimal control problem. It is applied to the optimal control of multibody dynamics, where the interconnections between different rigid or elastic structures are modelled as holonomic constraints. When simulating the dynamics of three-dimensional, possibly non-convex multibody systems, the detection and treatment of contact imposes quite a challenge. Monopedal jumping as well as the gait of a compass biped walker are considered as examples of hybrid systems, where the dynamics is subject to an inherent switch due to the closing or opening of contacts between the foot and the ground.

Links

• Dresdner Mathematisches Seminar
• Eleonore-Trefftz-Vorlesungen im Dresdner Mathematischen Seminar

Last modified: Dec 12, 2013, 4:14:31 PM