Optimal Control in Proactive Chassis Dynamics: A Fixed Step Size Time-Stepping Scheme for Complementarity Problems

2014 ◽  
pp. 271-276 ◽  
Author(s):  
Johannes Michael ◽  
Matthias Gerdts
Keyword(s):  
Optimal Control ◽  
Complementarity Problems ◽  
Step Size ◽  
Time Stepping

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics

2007 ◽  
Author(s):  
Sigrid Leyendecker ◽  
Sina Ober-Blo¨baum ◽  
Jerrold E. Marsden ◽  
Michael Ortiz
Keyword(s):  
Optimal Control ◽  
Rigid Body ◽  
Null Space ◽  
Numerical Dissipation ◽  
Discrete Version ◽  
Dynamical Equations ◽  
Time Stepping ◽  
Minimal Dimension ◽  
Energy And Momentum ◽  
External Forces

This paper formulates the dynamical equations of mechanics subject to holonomic constraints in terms of the states and controls using a constrained version of the Lagrange-d’Alembert principle. Based on a discrete version of this principle, a structure preserving time-stepping scheme is derived. It is shown that this respect for the mechanical structure (such as a reliable computation of the energy and momentum budget, without numerical dissipation) is retained when the system is reduced to its minimal dimension by the discrete null space method. Together with initial and final conditions on the configuration and conjugate momentum, the reduced time-stepping equations serve as nonlinear equality constraints for the minimisation of a given cost functional. The algorithm yields a sequence of discrete configurations together with a sequence of actuating forces, optimally guiding the system from the initial to the desired final state. The resulting discrete optimal control algorithm is shown to have excellent energy and momentum properties, which are illustrated by two specific examples, namely reorientation and repositioning of a rigid body subject to external forces and the reorientation of a rigid body with internal momentum wheels.

Augmented Time-Stepping by Step-Size Adjustment and Extrapolation

2007 ◽  
Author(s):  
Christian Studer ◽  
Christoph Glocker
Keyword(s):  
Time Evolution ◽  
Integration Method ◽  
Switching Time ◽  
Mechanical Systems ◽  
Unilateral Contact ◽  
Step Size ◽  
Frictional Contacts ◽  
Time Stepping ◽  
Size Adjustment ◽  
Integration Order

Time-stepping schemes are widely used when integrating non-smooth systems. In this paper we discuss an augmented time-stepping scheme which uses step-size adjustment and extrapolation. The time evolution of non-smooth systems can be divided in different smooth parts, which are separated by switching points. We deduce the time-stepping method of Moreau, which is a common order-one integration method for non-smooth systems. We formulate the method using contact inclusions, and show how these inclusions can be solved by a projection. We show how time-steps which contain a switching point can be detected by observing the projection behaviour, and propose a step-size adjustment, which treats these switching time-steps with a minimal step-size Δtmin. Time-steps in smooth parts of the motion are run with a larger step-size, and an extrapolation method, which is based on the time-stepping scheme, is used to increase the integration order. The presented method is suitable for mechanical systems with unilateral and frictional contacts. For simplicity, we deduce the method considering solely mechanical systems with one unilateral contact.

Optimal Control for a Pitcher’s Motion Modeled as Constrained Mechanical System

2009 ◽  
Author(s):  
Sina Ober-Blo¨baum ◽  
Julia Timmermann
Keyword(s):  
Optimal Control ◽  
Muscle Force ◽  
Control Method ◽  
Control Effort ◽  
Constrained Mechanical Systems ◽  
Time Stepping ◽  
D’Alembert Principle ◽  
Optimal Control Method ◽  
Multi Body ◽  
Nonlinear Equality

In this contribution, a recently developed optimal control method for constrained mechanical systems is applied to determine optimal motions and muscle force evolutions for a pitcher’s arm. The method is based on a discrete constrained version of the Lagrange-d’Alembert principle leading to structure preserving time-stepping equations. A reduction technique is used to derive the nonlinear equality constraints for the minimization of a given objective function. Different multi-body models for the pitcher’s arm are investigated and compared with respect to the motion itself, the control effort, the pitch velocity, and the pitch duration time. In particular, the use of a muscle model allows for an identification of limits on the maximal forces that ensure more realistic optimal pitch motions.

Sign in / Sign up

Export Citation Format

Share Document