Multibody graph transformations and analysis

Jain, Abhinandan

doi:10.1007/s11071-011-0136-x

Cited by 15 publications

(6 citation statements)

References 14 publications

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“…The aggregation process is carried out in a way such that the transformed system's topology is that of a tree. The detailed description of the procedure for constraint embedding is described in [6].…”

Section: Dynamics With Loop Constraintsmentioning

confidence: 99%

“…A DAE solver is needed for solving the equations of motion in this formulation. An alternative method that avoids DAEs altogether is the constraint embedding (CE) dynamics algorithm [6]. This technique uses the TA model as a starting point.…”

mentioning

confidence: 99%

“…The third method that avoids DAEs altogether is the recently developed constraint embedding (CE) dynamics algorithm [6]. This technique uses the TA model as a starting point.…”

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confidence: 99%

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Hybrid Dynamics for Closed-Loop Multibody Systems

Jain

2023

Preprint

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A popular method for solving the dynamics of closed-loop systems is the {\it tree-augmented (TA)} dynamics algorithm. In this method, a minimal set of the inter-body constraints are ``cut'' to convert the system into a tree-topology system. The inter-body constraints within the tree are treated as hinges parameterized with a minimal set of coordinates. The overall dynamics model formulation consists of the minimal-coordinate dynamics model for the tree system together with the minimal set of bilateral closure constraints for the tree system. A DAE solver is needed for solving the equations of motion in this formulation. An alternative method that avoids DAEs altogether is the {\it constraint embedding (CE)} dynamics algorithm \cite{Jain2011b}. This technique uses the TA model as a starting point. However, TA model's bilateral constraints are eliminated by aggregating bodies affected by the bilateral constraint into compound bodies. The result system topology is once again a tree with only inter-body hinges and no bilateral constraints. The benefit of this approach is that the structure-based tree algorithms can be directly used to solve the dynamics, and this formulation requires the simpler ODE solver. While the CE algorithm is undoubtedly superior for systems with small loops - and especially ones where the loop kinematics has analytical solution. However when the loops become larger, or more complex (eg. meshes), the benefits of the CE approach over the TA approach decrease. For systems involving both small and large loops, the analyst is left with the unsatisfactory situation of choosing between either the TA or CE approaches. The main contribution of this paper is the development of a {\it hybrid dynamics method} which allows the use of TA and CE approaches to different loops in the multibody system. This allows the user to judiciously choose the better of the TA or CE approaches for each of the loops in the system.

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Section: Dynamics With Loop Constraintsmentioning

confidence: 99%

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confidence: 99%

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Hybrid Dynamics for Closed-Loop Multibody Systems

Jain

2023

Preprint

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“…It should be mentioned that T a ll is a lower triangular matrix and thus has simple inverse that maintains the topological structure of the original matrix and becomes an upper triangular matrix as follows [ 26 ]:

…”

Section: Multibody Formulation and System Equation Of Motionmentioning

confidence: 99%

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

Omar

2014

The Scientific World Journal

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Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

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“…Rodriguez [52], [51] built a unified framework based on the concept of filtering and smoothing to solve both inverse and forward dynamics problems. Based on the work by Rodriguez et al [53], Jain [30], [31], [32], [33] applied graph theory to dynamics problems, and analyzed various algorithms to solve dynamics problem in a unified formulation. Ascher et al [1] unified the derivation of CRBA and ABA as two elimination methods used to solve forward dynamics.…”

Section: Introduction and Related Workmentioning

confidence: 99%

A Factor-Graph Approach for Optimization Problems with Dynamics Constraints

Xie,

Escontrela,

Dellaert

2020

Preprint

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In this paper, we introduce dynamics factor graphs as a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynamics and contacts. A factor graph representation of dynamics problems provides an insightful visualization of their mathematical structure and can be used in conjunction with sparse nonlinear optimizers to solve challenging, highdimensional optimization problems in robotics. We can easily formulate kinodynamic motion planning as a trajectory optimization problem with factor graphs. We demonstrate the flexibility and descriptive power of dynamics factor graphs by applying them to control various dynamical systems, ranging from a simple cart pole to a 12-DoF quadrupedal robot.

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Multibody graph transformations and analysis

Cited by 15 publications

References 14 publications

Hybrid Dynamics for Closed-Loop Multibody Systems

Hybrid Dynamics for Closed-Loop Multibody Systems

Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

A Factor-Graph Approach for Optimization Problems with Dynamics Constraints

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