A gauge-invariant formulation for constrained robotic systems using square-root factorization and unitary transformation

Aghili, Farhad

doi:10.1109/iros.2008.4650682

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…Researchers [5, 7, 8, 30, 32] have used system-level matrices and operators to analyze and exploit the structure and sparsity of the mass matrix. Mass matrix factorization techniques and system-level global transforms to simplify the coupled equations of motion into diagonalized forms have also been explored [1, 2, 10, 20, 22, 33]. One common feature to most of these techniques has been the use of relative , instead of absolute coordinates [25] to parametrized the state of the system.…”

Section: Introductionmentioning

confidence: 99%

Graph theoretic foundations of multibody dynamics

Jain

2011

Multibody Syst Dyn

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This is the first part of two papers that use concepts from graph theory to obtain a deeper understanding of the mathematical foundations of multibody dynamics. The key contribution is the development of a unifying framework that shows that key analytical results and computational algorithms in multibody dynamics are a direct consequence of structural properties and require minimal assumptions about the specific nature of the underlying multibody system. This first part focuses on identifying the abstract graph theoretic structural properties of spatial operator techniques in multibody dynamics. The second part paper exploits these structural properties to develop a broad spectrum of analytical results and computational algorithms. Towards this, we begin with the notion of graph adjacency matrices and generalize it to define block-weighted adjacency (BWA) matrices and their 1-resolvents. Previously developed spatial operators are shown to be special cases of such BWA matrices and their 1-resolvents. These properties are shown to hold broadly for serial and tree topology multibody systems. Specializations of the BWA and 1-resolvent matrices are referred to as spatial kernel operators (SKO) and spatial propagation operators (SPO). These operators and their special properties provide the foundation for the analytical and algorithmic techniques developed in the companion paper. We also use the graph theory concepts to study the topology induced sparsity structure of these operators and the system mass matrix. Similarity transformations of these operators are also studied. While the detailed development is done for the case of rigid-link multibody systems, the extension of these techniques to a broader class of systems (e.g. deformable links) are illustrated.

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Section: Introductionmentioning

confidence: 99%

Graph theoretic foundations of multibody dynamics

Jain

2011

Multibody Syst Dyn

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“…As a result, the corresponding dynamic formulation in not invariant and a solution depends on measure units or a weighting matrix selected Aghili (2005); Angeles (2003); Lipkin and Duffy (1988); Luca and Manes (1994); Manes (1992). There also exist other techniques to describe the equations of motion in terms of quasi-velocities, i.e., a vector whose Euclidean norm is proportional to the square root of the system's kinetic energy, which can lead to simplification of these equations Aghili (2008;2007); Bedrossian (1992); Gu (2000); Gu and Loh (1987); Herman (2005); Herman and Kozlowski (2006); Jain and Rodriguez (1995); Junkins and Schaub (1997); Kodischeck (1985); Kozlowski (1998); Loduha and Ravani (1995); Papastavridis (1998) ;Rodriguez and Kertutz-Delgado (1992); Sinclair et al (2006);Spong (1992). A recent survey on some of these techniques can be found in Herman and Kozlowski (2006).…”

Section: Introductionmentioning

confidence: 99%

Modeling and Control of Mechanical Systems in Terms of Quasi-Velocities

Aghili¹

2010

Robotics 2010 Current and Future Challenges

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Graph theory roots of spatial operators for kinematics and dynamics

Jain

2010

2010 IEEE International Conference on Robotics and Automation

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19The passive sizing system consists of a series of low-profile pulleys attached to the front and back of the shoulder bearings on a spacesuit soft upper torso (SUT), textile cord or stainless steel cable, and a modified commercial ratchet mechanism. The cord/cable is routed through the pulleys and attached to the ratchet mechanism mounted on the front of the spacesuit within reach of the suited subject. Upon actuating the ratchet mechanism, the shoulder bearing breadth is changed, providing variable upper torso sizing.The active system consists of a series of pressurizable nastic cells embedded into the fabric layers of a spacesuit SUT. These cells are integrated to the front and back of the SUT and are connected to an air source with a variable regulator. When inflated, the nastic cells provide a change in the overall shoulder bearing breadth of the spacesuit and thus, torso sizing.The research focused on the development of a high-performance sizing and actuation system. This technology has application as a suit-sizing mechanism to Spacesuit Soft Upper Torso Sizing SystemsThis system has application in medical devices for immobilizing injured limbs or applying controlled pressure to areas of the body of a burn victim. Lyndon B. Johnson Space Center, Houston, TexasSpatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators -and the related mathematical analysis -have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems.The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models.Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems.In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematica...

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A gauge-invariant formulation for constrained robotic systems using square-root factorization and unitary transformation

Cited by 3 publications

References 25 publications

Graph theoretic foundations of multibody dynamics

Graph theoretic foundations of multibody dynamics

Modeling and Control of Mechanical Systems in Terms of Quasi-Velocities

Graph theory roots of spatial operators for kinematics and dynamics

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