Dynamic Modeling of Robotic Systems: A Dual Quaternion Formulation

Dynamic Modeling of Robotic Systems: A Dual Quaternion Formulation. Silva, F. F. A. Ph.D. Thesis, Federal University of Minas Gerais, Minas Gerais, Brazil, June, 2022.

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This thesis proposes a technique for the dynamic modeling of serial and branched robots using dual quaternion algebra. The modeling accounts for all lower-pair kinematic joints and six-degree-of-freedom joints, and the framework enables the systematic modular composition of dynamic models comprising several subsystems, each, in turn, composed of multiple rigid bodies. The proposed strategy is applicable even if some subsystems are regarded as black boxes, requiring only the twists and wrenches at the connection points between different subsystems. To help in the model composition, a unified graph representation that encodes the propagation of twists and wrenches between the subsystems is also proposed. The joint wrenches result from the calculation of the interconnection matrix of the graph, making the modeling procedure straightforward. The framework was validated using serial manipulators of 6-DoF and 50-DoF, a 9-DoF holonomic mobile manipulator, and a 38-DoF branched robot composed of 9 subsystems. The results were compared with Peter Corke’s Robotics Toolbox, Roy Featherstone’s Spatial V2, and the robot simulator V-REP/CoppeliaSim, demonstrating that the proposed formalism is as accurate as state-of-the-art libraries.

@phdthesis{Silva2022thesis,
  title = {Dynamic {{Modeling}} of {{Robotic Systems}}: {{A Dual Quaternion Formulation}}},
  author = {Silva, Frederico Fernandes Afonso},
  year = {2022},
  month = jun,
  address = {Minas Gerais, Brazil},
  copyright = {All rights reserved},
  school = {Federal University of Minas Gerais},
  abstract = {This thesis proposes a technique for the dynamic modeling of serial and branched robots  using dual quaternion algebra. The modeling accounts for all lower-pair kinematic joints  and six-degree-of-freedom joints, and the framework enables the systematic modular  composition of dynamic models comprising several subsystems, each, in turn, composed  of multiple rigid bodies. The proposed strategy is applicable even if some subsystems  are regarded as black boxes, requiring only the twists and wrenches at the connection  points between different subsystems. To help in the model composition, a unified graph  representation that encodes the propagation of twists and wrenches between the subsystems  is also proposed. The joint wrenches result from the calculation of the interconnection  matrix of the graph, making the modeling procedure straightforward. The framework  was validated using serial manipulators of 6-DoF and 50-DoF, a 9-DoF holonomic mobile  manipulator, and a 38-DoF branched robot composed of 9 subsystems. The results were  compared with Peter Corke’s Robotics Toolbox, Roy Featherstone’s Spatial V2, and the  robot simulator V-REP/CoppeliaSim, demonstrating that the proposed formalism is as  accurate as state-of-the-art libraries.},
  url = {https://www.researchgate.net/publication/362477656_Dynamic_Modeling_of_Robotic_Systems_A_Dual_Quaternion_Formulation#fullTextFileContent}
}

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