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.

Logarithmic Complexity Sensitivity Analysis of Flexible Multibody Systems

2009 ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Modal Shape ◽  
Flexible Multibody

This paper presents a recursive direct differentiation method for sensitivity analysis of flexible multibody systems. Large rotations and translations in the system are modeled as rigid body degrees of freedom while the deformation field within each body is approximated by superposition of modal shape functions. The equations of motion for the flexible members are differentiated at body level and the sensitivity information is generated via a recursive divide and conquer scheme. The number of differentiations required in this method is minimal. The method works concurrently with the forward dynamics simulation of the system and requires minimum data storage. The use of divide and conquer framework makes the method linear and logarithmic in complexity for serial and parallel implementation, respectively, and ideally suited for general topologies. The method is applied to a flexible two arm robotic manipulator to calculate sensitivity information and the results are compared with the finite difference approach.

Operational Space Impulse Momentum Algorithm for Flexible Multibody Systems With Generalized Topologies

2011 ◽  
Author(s):  
Rudranarayan M. Mukherjee
Keyword(s):  
Multibody Systems ◽  
Divide And Conquer ◽  
Closed Loops ◽  
Operational Space ◽  
Bilateral Constraints ◽  
Tree Topologies ◽  
Rigid Multibody Systems ◽  
Divide And Conquer Scheme ◽  
Tree Map ◽  
Rigid Multibody

This paper presents a new methodology for modeling discontinuous dynamics of flexible and rigid multibody systems based on the impulse momentum formulation. The new methodology is based on the seminal idea of the divide and conquer scheme for modeling the forward dynamics of rigid multibody systems. While a similar impulse momentum approach has been demonstrated for multibody systems in tree topologies, this paper presents the generalization of the approach to systems in generalized topologies including many coupled kinematically closed loops. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The generalized impulse momenta equations of flexible bodies are derived using a projection method.

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.

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.

Distributed Operational Space Formulation of Serial Manipulators

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Kishor D. Bhalerao ◽  
James Critchley ◽  
Denny Oetomo ◽  
Roy Featherstone ◽  
Oussama Khatib
Keyword(s):  
Parallel Algorithms ◽  
Time Complexity ◽  
Degrees Of Freedom ◽  
Null Space ◽  
Divide And Conquer ◽  
Serial Manipulators ◽  
Divide And Conquer Algorithm ◽  
Operational Space ◽  
Space Formulation ◽  
Space Dynamics

This paper presents a new parallel algorithm for the operational space dynamics of unconstrained serial manipulators, which outperforms contemporary sequential and parallel algorithms in the presence of two or more processors. The method employs a hybrid divide and conquer algorithm (DCA) multibody methodology which brings together the best features of the DCA and fast sequential techniques. The method achieves a logarithmic time complexity (O(log(n)) in the number of degrees of freedom (n) for computing the operational space inertia (Λe) of a serial manipulator in presence of O(n) processors. The paper also addresses the efficient sequential and parallel computation of the dynamically consistent generalized inverse (J¯e) of the task Jacobian, the associated null space projection matrix (Ne), and the joint actuator forces (τnull) which only affect the manipulator posture. The sequential algorithms for computing J¯e, Ne, and τnull are of O(n), O(n2), and O(n) computational complexity, respectively, while the corresponding parallel algorithms are of O(log(n)), O(n), and O(log(n)) time complexity in the presence of O(n) processors.

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