Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Original System ◽  
Parent Body ◽  
Divide And Conquer ◽  
Loop Control ◽  
Generalized Coordinates ◽  
Divide And Conquer Algorithm ◽  
Generalized Force ◽  
New Formulation

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Computed Torque Control of Articulated Multibody Systems in the Generalized Divide and Conquer Algorithm Framework

2015 ◽  
Author(s):  
Cameron Kingsley ◽  
Mohammad Poursina
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Torque Control ◽  
Divide And Conquer ◽  
Controlled System ◽  
Divide And Conquer Algorithm ◽  
Computed Torque Control ◽  
And Control ◽  
Computed Torque

An extension to the Generalized-Divide-and-Conquer Algorithm (GDCA) is presented in this paper in conjunction with the Computed-Torque-Control-Law (CTCL) to model and control fully actuated multibody systems. CTCL uses the inverse dynamics to provide control inputs to the system while, the dynamics of the system must be formed and solved in each iteration. Herein, the GDCA is extended to form and solve the inverse dynamics to find control torques. Further, this method is also extended to efficiently solve the equations of motion of the controlled system. This significantly reduces the complexity of modeling, simulating, and controlling the fully actuated multibody systems to O(n) or O(logn) operations in each iteration in the serial and parallel implementations, respectively.

Parallel Efficiency of Lagrange Multipliers Based Divide and Conquer Algorithm for Dynamics of Multibody Systems

2011 ◽  
Author(s):  
Paweł Malczyk ◽  
Janusz Fra¸czek
Keyword(s):  
Parallel Computing ◽  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Open Loop ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Parallel Computer ◽  
Optimal Order ◽  
Parallel Efficiency ◽  
Divide And Conquer Algorithm

Efficient dynamics simulations of complex multibody systems are essential in many areas of computer aided engineering and design. As parallel computing resources has become more available, researchers began to reformulate existing algorithms or to create new parallel formulations. Recent works on dynamics simulation of multibody systems include sequential recursive algorithms as well as low order, exact or iterative parallel algorithms. The first part of the paper presents an optimal order parallel algorithm for dynamics simulation of open loop chain multibody systems. The proposed method adopts a Featherstone’s divide and conquer scheme by using Lagrange multipliers approach for constraint imposition and dependent set of coordinates for the system state description. In the second part of the paper we investigate parallel efficiency measures of the proposed formulation. The performance comparisons are made on the basis of theoretical floating-point operations count. The main part of the paper is concetrated on experimental investigation performed on parallel computer using OpenMP threads. Numerical experiments confirm good overall efficiency of the formulation in case of modest parallel computing resources available and demonstrate certain computational advantages over sequential versions.

Orthogonal Complement-Based Divide and Conquer Algorithm: A Detailed Investigation of Its Performance

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Growth Rate ◽  
Arbitrary Number ◽  
Multibody Systems ◽  
Divide And Conquer ◽  
Orthogonal Complement ◽  
Error Growth ◽  
Stabilization Method ◽  
Constraint Violation ◽  
Divide And Conquer Algorithm ◽  
Kinematic Loops

In this paper, we characterize the orthogonal complement-based divide-and-conquer (ODCA) [1] algorithm in terms of the constraint violation error growth rate and singularity handling capabilities. In addition, we present a new constraint stabilization method for the ODCA architecture. The proposed stabilization method is applicable to general multibody systems with arbitrary number of closed kinematic loops. We compare the performance of the ODCA with augmented [2] and reduction [3] methods. The results indicate that the performance of the ODCA falls between these two traditional techniques. Furthermore, using a numerical example, we demonstrate the effectiveness of the new stabilization scheme.

Efficient Operational Space Sensitivity Analysis of Dynamic Multibody Systems

2011 ◽  
Author(s):  
Rudranarayan M. Mukherjee
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Divide And Conquer ◽  
Parametric Perturbation ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Tree Topologies ◽  
Logarithmic Complexity

This paper presents a generalization of the divide and conquer algorithm for sensitivity analysis of dynamic multibody systems based on direct differentiation. While similar sensitivity analysis approach has been demonstrated for multi-rigid and multi-flexible systems in tree topologies and a limited set of kinematically closed loop topologies, this paper presents the generalization of these approaches to systems in generalized topologies including many coupled kinematically closed loops. This generalization retains the efficient complexity of the underlying formulations i.e. linear and logarithmic complexity in serial and parallel implementation. Other than the computational efficiency, the advantages of this method include concurrent sensitivity analysis with forward dynamics, no numerical artifacts arising from parametric perturbation and significantly reduced data storage compared to traditional methods. An interesting application of this work in control of multibody systems is discussed.

Dynamics and Control of Multi-Flexible-Body Systems in a Divide-and-Conquer Scheme

2015 ◽  
Author(s):  
Imad M. Khan ◽  
Kalyan C. Addepalli ◽  
Mohammad Poursina
Keyword(s):  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Constraint Forces ◽  
Control Laws ◽  
Motion Constraints ◽  
Divide And Conquer Algorithm ◽  
Dynamics And Control ◽  
Kinematic Loops

In this paper, we present an extension of the generalized divide-and-conquer algorithm (GDCA) for modeling constrained multi-flexible-body systems. The constraints of interest in this case are not the motion constraints or the presence of closed kinematic loops but those that arise due to inverse dynamics or control laws. The introductory GDCA paper introduced an efficient methodology to include generalized constraint forces in the handle equations of motion of the original divide-and-conquer algorithm for rigid multibody systems. Here, the methodology is applied to flexible bodies connected by kinematic joints. We develop necessary equations that define the algorithm and present a well known numerical example to validate the method.

scholarly journals Algebraic analysis of kinematics of multibody systems

2013 ◽  
Vol 4 (1) ◽  
pp. 33-47 ◽  
Author(s):  
S. Piipponen ◽  
J. Tuomela
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Commutative Algebra ◽  
Multibody Systems ◽  
Original System ◽  
Divide And Conquer ◽  
Polynomial Equations ◽  
3 Dimensional ◽  
Kinematical Analysis ◽  
Relevant Component

Abstract. The constructive commutative algebra is very useful in the kinematical analysis of the mechanisms because a large class of systems can be described using polynomial equations. We show that one can analyze quite complicated systems using a sort of divide and conquer strategy to decompose the system, and hence the configuration space, into simpler parts. The key observation is that it seems that typically systems indeed have a lot of distinct components, but usually only one of them is physically relevant. Hence if one finds the equations describing the component of interest the analysis of this system can be surprisingly simple compared to the original system. In particular typically the possible singularities of the original system disappear when one restricts the attention to the relevant component. On the technical side we show that some basic constraints used to define joints in 3 dimensional mechanisms can be decomposed to simpler parts. This has significant practical consequences because using these fundamental decompositions when writing the equations for complicated mechanisms decreases dramatically the complexity of the required computations.

Sign in / Sign up

Export Citation Format

Share Document