Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach

1988 ◽  
Vol 55 (4) ◽  
pp. 899-904 ◽  
Author(s):  
S. K. Ider ◽  
F. M. L. Amirouche
Keyword(s):  
Null Space ◽  
Computationally Efficient ◽  
New Approach ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Linearly Independent ◽  
Kane's Equations ◽  
Constrained Dynamical Systems ◽  
Coordinate Reduction ◽  
Algebraic Constraint

In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Tao Xiong ◽  
Jianwan Ding ◽  
Yizhong Wu ◽  
Liping Chen ◽  
Wenjie Hou
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
The State ◽  
State Variables ◽  
Structural Decomposition ◽  
Multiple Degrees Of Freedom ◽  
Constraint Equations ◽  
Constrained Dynamical Systems ◽  
Algebraic Constraint

A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

Dynamics of Large Constrained Flexible Structures

1988 ◽  
Vol 110 (1) ◽  
pp. 78-83 ◽  
Author(s):  
F. M. L. Amirouche ◽  
R. L. Huston
Keyword(s):  
Structure Analysis ◽  
Flexible Structures ◽  
Orthogonal Complement ◽  
Space Structures ◽  
Governing Equations ◽  
Finite Segment ◽  
Closed Loops ◽  
Constraint Equations ◽  
Kane’S Equations ◽  
Kane's Equations

This paper presents an automated procedure useful in the study of large constrained flexible structures, undergoing large specified motions. The structure is looked upon as a “partially open tree” system, containing closed loops in some of the branches. The governing equations are developed using Kane’s equations as formulated by Huston et al. The accommodation of the constraint equations is based on the use of orthogonal complement arrays. The flexibility and oscillations of the bodies is modelled using finite segment modelling, structure analysis, and scaling techniques. The procedures developed are expected to be useful in applications including robotics, space structures, and biosystems.

Mobile manipulator modeling with Kane's approach

Robotica ◽  
2001 ◽  
Vol 19 (6) ◽  
pp. 675-690 ◽  
Author(s):  
Herbert G. Tanner ◽  
Kostas J. Kyriakopoulos
Keyword(s):  
Control Strategies ◽  
Nonholonomic Constraints ◽  
Dynamic Equations ◽  
Mobile Manipulator ◽  
Constraint Equations ◽  
Motion Constraints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Physical Insight ◽  
Complete Framework

A wheeled mobile manipulator system is modeled using Kane's dynamic equations. Kane's equations are constructed with minimum effort, are control oriented and provide both physical insight and fast simulations. The powerful tools of Kane's approach for incorporating nonholonomic motion constraints and bringing noncontributing forces into evidence are exploited. Both nonholonomic constraints associated with slipping and skidding as well as conditions for avoiding tipping over are included. The resulting equations, along with the set of constraint equations provide a safe and complete framework for developing control strategies for mobile manipulator systems.

TLISMNI/Adams algorithm for the solution of the differential/algebraic equations of constrained dynamical systems

2017 ◽  
Vol 232 (1) ◽  
pp. 129-149
Author(s):  
Ahmed A Shabana ◽  
Dayu Zhang ◽  
Gengxiang Wang
Keyword(s):  
Dynamical Systems ◽  
Numerical Integration ◽  
Sparse Matrix ◽  
Differential Algebraic Equations ◽  
Variable Step Size ◽  
Step Size ◽  
Constraint Equations ◽  
Adams Method ◽  
Constrained Dynamical Systems ◽  
Algebraic Constraint

This paper examines the performance of the 3rd and 4th order implicit Adams methods in the framework of the two-loop implicit sparse matrix numerical integration method in solving the differential/algebraic equations of heavily constrained dynamical systems. The variable-step size two-loop implicit sparse matrix numerical integration/Adams method proposed in this investigation avoids numerical force differentiation, ensures satisfying the nonlinear algebraic constraint equations at the position, velocity, and acceleration levels, and allows using sparse matrix techniques for efficiently solving the dynamical equations. The iterative outer loop of the two-loop implicit sparse matrix numerical integration/Adams method is aimed at achieving the convergence of the implicit integration formulae used to solve the independent differential equations of motion, while the inner loop is used to ensure the convergence of the iterative procedure used to satisfy the algebraic constraint equations. To solve the independent differential equations, two different implicit Adams integration formulae are examined in this investigation; a 3rd order implicit Adams-Moulton formula with a 2nd order explicit predictor Adams Bashforth formula, and a 4th order implicit Adams-Moulton formula with a 3rd order explicit predictor Adams Bashforth formula. A standard Newton–Raphson algorithm is used to satisfy the nonlinear algebraic constraint equations at the position level. The constraint equations at the velocity and acceleration levels are linear, and therefore, there is no need for an iterative procedure to solve for the dependent velocities and accelerations. The algorithm used for the error check and step-size change is described. The performance of the two-loop implicit sparse matrix numerical integration/Adams algorithm developed in this investigation is evaluated by comparison with the explicit predictor-corrector Adams method which has a variable-order and variable-step size. Simple and heavily constrained dynamical systems are used to evaluate the accuracy, robustness, damping characteristics, and effect of the outer-loop iterations of the proposed implicit schemes. The results obtained in this investigation show that the two-loop implicit sparse matrix numerical integration methods proposed in this study can be more efficient for stiff systems because of their ability to damp out high-frequency oscillations. Explicit integration methods, on the other hand, can be more efficient in the case of non-stiff systems.

scholarly journals Interference Cancellation Based Spectrum Sharing for Massive MIMO Communication Systems

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3584
Author(s):  
Milembolo Miantezila Junior ◽  
Bin Guo ◽  
Chenjie Zhang ◽  
Xuemei Bai
Keyword(s):  
Interference Cancellation ◽  
Communication Systems ◽  
Spectrum Sharing ◽  
Null Space ◽  
Base Station ◽  
Base Stations ◽  
Small Cells ◽  
Data Traffic ◽  
New Approach ◽  
Lte Advanced

Cellular network operators are predicting an increase in space of more than 200 percent to carry the move and tremendous increase of total users in data traffic. The growing of investments in infrastructure such as a large number of small cells, particularly the technologies such as LTE-Advanced and 6G Technology, can assist in mitigating this challenge moderately. In this paper, we suggest a projection study in spectrum sharing of radar multi-input and multi-output, and mobile LTE multi-input multi-output communication systems near m base stations (BS). The radar multi-input multi-output and mobile LTE communication systems split different interference channels. The new approach based on radar projection signal detection has been proposed for free interference disturbance channel with radar multi-input multi-output and mobile LTE multi-input multi-output by using a new proposed interference cancellation algorithm. We chose the channel of interference with the best free channel, and the detected signal of radar was projected to null space. The goal is to remove all interferences from the radar multi-input multi-output and to cancel any disturbance sources from a chosen mobile Communication Base Station. The experimental results showed that the new approach performs very well and can optimize Spectrum Access.

Real-Time Robot Capability Analysis

2005 ◽  
Author(s):  
Chalongrath Pholsiri ◽  
Chetan Kapoor ◽  
Delbert Tesar
Keyword(s):  
Decision Making ◽  
Path Planning ◽  
Real Time ◽  
Computationally Efficient ◽  
New Approach ◽  
Ellipsoid Method ◽  
Capability Analysis ◽  
Computationally Intensive ◽  
Planar Robots

Robot Capability Analysis (RCA) is a process in which force/motion capabilities of a manipulator are evaluated. It is very useful in both the design and operational phases of robotics. Traditionally, ellipsoids and polytopes are used to both graphically and numerically represent these capabilities. Ellipsoids are computationally efficient but tend to underestimate while polytopes are accurate but computationally intensive. This article proposes a new approach to RCA called the Vector Expansion (VE) method. The VE method offers accurate estimates of robot capabilities in real time and therefore is very suitable in applications like task-based decision making or online path planning. In addition, this method can provide information about the joint that is limiting a robot capability at a given time, thus giving an insight as to how to improve the performance of the robot. This method is then used to estimate capabilities of 4-DOF planar robots and the results discussed and compared with the conventional ellipsoid method. The proposed method is also successfully applied to the 7-DOF Mitsubishi PA10-7C robot.

PARALLEL, LOCALLY CONNECTED ALGORITHMS FOR NONLINEAR ADAPTIVE FILTERING

1993 ◽  
Vol 04 (01) ◽  
pp. 85-98 ◽  
Author(s):  
HASSAN M. AHMED ◽  
FAWAD RAUF
Keyword(s):  
Adaptive Filtering ◽  
Layered Structure ◽  
Adaptive Filters ◽  
Computationally Efficient ◽  
Local Connectivity ◽  
Linear Filters ◽  
New Approach ◽  
Vlsi Layout ◽  
State Dependent ◽  
Nonlinear Adaptive Filtering

A new adaptive modular realization for nonlinear filters is presented whereby construction is both computationally efficient and readily implemented. The proposed layered structure consists of locally connected, locally adapted linear filters. Modularity and local connectivity make efficient VLSI layout easy and amenable to automation. The layered structure is based on "state dependent embedding", a new approach to the design of series based nonlinear adaptive filters.

A New Approach for Fatigue Damage Modeling of Subsurface-Initiated Spalling in Large Rolling Contacts

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Aditya A. Walvekar ◽  
Neil Paulson ◽  
Farshid Sadeghi ◽  
Nick Weinzapfel ◽  
Martin Correns ◽  
...  
Keyword(s):  
Fatigue Damage ◽  
Damage Mechanics ◽  
Numerical Models ◽  
Rolling Contact ◽  
Fe Model ◽  
Triangle Mesh ◽  
Computationally Efficient ◽  
New Approach ◽  
Rolling Contacts ◽  
Delaunay Triangle

Large bearings employed in wind turbine applications have half-contact widths that are usually greater than 1 mm. Previous numerical models developed to investigate rolling contact fatigue (RCF) require significant computational effort to study large rolling contacts. This work presents a new computationally efficient approach to investigate RCF life scatter and spall formation in large bearings. The modeling approach incorporates damage mechanics constitutive relations in the finite element (FE) model to capture fatigue damage. It utilizes Voronoi tessellation to account for variability occurring due to the randomness in the material microstructure. However, to make the model computationally efficient, a Delaunay triangle mesh was used in the FE model to compute stresses during a rolling contact pass. The stresses were then mapped onto the Voronoi domain to evaluate the fatigue damage that leads to the formation of surface spall. The Delaunay triangle mesh was dynamically refined around the damaged elements to capture the stress concentration accurately. The new approach was validated against previous numerical model for small rolling contacts. The scatter in the RCF lives and the progression of fatigue spalling for large bearings obtained from the model show good agreement with experimental results available in the open literature. The ratio of L10 lives for different sized bearings computed from the model correlates well with the formula derived from the basic life rating for radial roller bearing as per ISO 281. The model was then extended to study the effect of initial internal voids on RCF life. It was found that for the same initial void density, the L10 life decreases with the increase in the bearing size.

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