Minimum Energy Control of Multibody Systems Utilizing Storage Elements

2009 ◽  
Author(s):  
Werner Schiehlen ◽  
Makoto Iwamura
Keyword(s):  
Multibody Systems ◽  
Optimal Trajectory ◽  
Design Method ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Operating Time ◽  
Minimum Energy Control ◽  
Robot Systems ◽  
Optimal Design Method ◽  
The Relationship

In this paper, we consider the problem to minimize the energy consumption for controlled multibody systems utilizing passive elastic elements for energy storage useful for robot systems in manufacturing. Firstly, based on the linearized equations of motion, we analyze the relationship between the consumed energy and the operating time, and the optimal trajectory using optimal control theory. Then, we verify the analytical solution by comparing with the numerical one computed considering the full nonlinear dynamics. After that we derive a condition for the operating time to be optimal, and propose the optimal design method for springs. Finally, we show the effectiveness of the design method by applying it to a 2DOF manipulator.

Review of Contemporary Approaches for Constraint Enforcement in Multibody Systems

2007 ◽  
Vol 3 (1) ◽  
Author(s):  
Olivier A. Bauchau ◽  
André Laulusa
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Constraint Violation ◽  
New Techniques ◽  
Index Reduction ◽  
Reduction Techniques ◽  
Constraint Enforcement ◽  
The Relationship

A hallmark of multibody dynamics is that most formulations involve a number of constraints. Typically, when redundant generalized coordinates are used, equations of motion are simpler to derive but constraint equations are present. Approaches to dealing with high index differential algebraic equations, based on index reduction techniques, are reviewed and discussed. Constraint violation stabilization techniques that have been developed to control constraint drift are also reviewed. These techniques are used in conjunction with algorithms that do not exactly enforce the constraints. Control theory forms the basis for a number of these methods. Penalty based techniques have also been developed, but the augmented Lagrangian formulation presents a more solid theoretical foundation. In contrast to constraint violation stabilization techniques, constraint violation elimination techniques enforce exact satisfaction of the constraints, at least to machine accuracy. Finally, as the finite element method has gained popularity for the solution of multibody systems, new techniques for the enforcement of constraints have been developed in that framework. The goal of this paper is to review the features of these methods, assess their accuracy and efficiency, underline the relationship among the methods, and recommend approaches that seem to perform better than others.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Development of Optimal Design Method for Steel Double-Beam Floor System Considering Rotational Constraints

2021 ◽  
Vol 11 (7) ◽  
pp. 3266
Author(s):  
Insub Choi ◽  
Dongwon Kim ◽  
Junhee Kim
Keyword(s):  
Optimal Design ◽  
Design Process ◽  
Design Method ◽  
Steel Beams ◽  
High Gravity ◽  
Double Beam ◽  
Iterative Analysis ◽  
Floor Systems ◽  
Optimal Design Method ◽  
Floor System

Under high gravity loads, steel double-beam floor systems need to be reinforced by beam-end concrete panels to reduce the material quantity since rotational constraints from the concrete panel can decrease the moment demand by inducing a negative moment at the ends of the beams. However, the optimal design process for the material quantity of steel beams requires a time-consuming iterative analysis for the entire floor system while especially keeping in consideration the rotational constraints in composite connections between the concrete panel and steel beams. This study aimed to develop an optimal design method with the LM (Length-Moment) index for the steel double-beam floor system to minimize material quantity without the iterative design process. The LM index is an indicator that can select a minimum cross-section of the steel beams in consideration of the flexural strength by lateral-torsional buckling. To verify the proposed design method, the material quantities between the proposed and code-based design methods were compared at various gravity loads. The proposed design method successfully optimized the material quantity of the steel double-beam floor systems without the iterative analysis by simply choosing the LM index of the steel beams that can minimize objective function while satisfying the safety-related constraint conditions. In particular, under the high gravity loads, the proposed design method was superb at providing a quantity-optimized design option. Thus, the proposed optimal design method can be an alternative for designing the steel double-beam floor system.

CFD analysis and RSM optimization of obstacle layout in Tesla micromixer

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Xiaowen Wang ◽  
Lihong Yang ◽  
Fujia Sun
Keyword(s):  
Chemical Reaction ◽  
Chemical Engineering ◽  
Design Method ◽  
Mixing Rate ◽  
Special Flow ◽  
Surface Method ◽  
Rsm Optimization ◽  
Effective Technology ◽  
Optimal Design Method ◽  
Lateral Offset

Abstract As a kind of fast and efficient mixing equipment, micromixer has been applied to chemical reaction detection. Its application can not only save experimental samples but also reduce the experimental time. In micromixers, Tesla structure is widely used due to its simple structure and special flow mechanism. In this paper, CFD and response surface method are used to analyze and verify the flow field of the configuration of adding diamond obstacles in the Tesla mixer. The results show that the order of layout parameter weight from large to small is obstacle size > vertical offset > horizontal offset. And the Desirability was 0.806, the optimal diamond obstacle size is 46.35 μm and the optimal lateral offset is 18.78 μm. In addition, a constant value OF 20 μm is predicted as the optimal vertical offset of the micromixer. Compared with the Tesla-type micromixer without obstacles, the diamond-shaped barrier Tesla-type micromixer designed in this paper has higher mixing rate and lower pressure drop under the same conditions, which can be applied to chemical reactors, and can also help to improve the accuracy of chemical reaction. It can be demonstrated that the presented optimal design method of obstacles layout in Tesla mixer is a simple and effective technology to improve the liquid mixing in microfluidic devices, and it has a broad application prospect in chemical engineering.

Research on the Optimal Design Method of the Main Components for the Wheelchair Pickup

2013 ◽  
Vol 791-793 ◽  
pp. 799-802
Author(s):  
Ya Ping Wang ◽  
H.R. Shi ◽  
L. Gao ◽  
Z. Wang ◽  
X.Y. Jia ◽  
...  
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Basic Function ◽  
Design Parameters ◽  
Algorithm Optimization ◽  
Optimization Analysis ◽  
Research Designs ◽  
Optimal Design Method ◽  
Main Components

With the increasing of the aging of population all over the world, and With the inconvenience coming from diseases and damage, there will be more and more people using the wheelchair as a tool for transport. When it cant be short of the wheelchair in the daily life, the addition of the function will bring the elevation of the quality of life for the unfortunate. Staring with this purpose, the research designs a pickup with planetary bevel gear for the wheelchair. After determining the basic function of the wheelchair aids, the study determines the design parameters by using the knowledge of parametric design and completes the model for the system with Pro/E, on the other hand, it completes key components optimization analysis which is based on genetic algorithm optimization.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

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