Publications

@unpublished{Silva2024,
  title = {Dynamic {{Modeling}} of {{Branched Robots}} Using {{Modular Composition}}},
  author = {Silva, Frederico Fernandes Afonso and Adorno, Bruno Vilhena},
  year = {2024},
  month = jul,
  number = {arXiv:2208.01795},
  eprint = {2208.01795},
  primaryclass = {cs},
  publisher = {arXiv},
  urldate = {2024-07-26},
  abstract = {When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This paper proposes a systematic modular procedure for the dynamic modeling of branched robots comprising several subsystems, each composed of an arbitrary number of rigid bodies, providing the final dynamic model by reusing previous models of each branch. Unlike previous approaches, the proposed strategy is applicable even if some subsystems are regarded as black boxes, requiring only twists and their time derivatives, and wrenches at the connection points between those subsystems. To help in the model composition, we also propose a weighted directed graph representation where the weights encode the propagation of twists and their time derivatives, and wrenches between the subsystems. A simple linear operation on the graph interconnection matrix provides the dynamics of the whole system. Numerical results using a 24-DoF fixed-base branched robot composed of eight subsystems show that the proposed formalism is as accurate as a state-of-the-art library for robotic dynamic modeling. Additional results using a 30-DoF holonomic branched mobile manipulator composed of three subsystems demonstrate the fidelity of our model to a modern robotics simulator and its capability of dealing with black box subsystems. To further illustrate how the derived dynamic model can be used in closed-loop control, we also present a simple formulation of a model-based wrench-driven pose control for branched robots.},
  archiveprefix = {arXiv},
  copyright = {All rights reserved},
  keywords = {Computer Science - Robotics},
  url = {https://arxiv.org/abs/2208.01795},
  note = {Preprint.}
}

When modeling complex robot systems such as branched robots, whose kinematic structures are a tree, current techniques often require modeling the whole structure from scratch, even when partial models for the branches are available. This paper proposes a systematic modular procedure for the dynamic modeling of branched robots comprising several subsystems, each composed of an arbitrary number of rigid bodies, providing the final dynamic model by reusing previous models of each branch. Unlike previous approaches, the proposed strategy is applicable even if some subsystems are regarded as black boxes, requiring only twists and their time derivatives, and wrenches at the connection points between those subsystems. To help in the model composition, we also propose a weighted directed graph representation where the weights encode the propagation of twists and their time derivatives, and wrenches between the subsystems. A simple linear operation on the graph interconnection matrix provides the dynamics of the whole system. Numerical results using a 24-DoF fixed-base branched robot composed of eight subsystems show that the proposed formalism is as accurate as a state-of-the-art library for robotic dynamic modeling. Additional results using a 30-DoF holonomic branched mobile manipulator composed of three subsystems demonstrate the fidelity of our model to a modern robotics simulator and its capability of dealing with black box subsystems. To further illustrate how the derived dynamic model can be used in closed-loop control, we also present a simple formulation of a model-based wrench-driven pose control for branched robots.

@article{Silva2022,
  title = {Dynamics of {{Mobile Manipulators}} Using {{Dual Quaternion Algebra}}},
  author = {Silva, Frederico F. A. and {Quiroz-Oma{\~n}a}, Juan Jos{\'e} and Adorno, Bruno V.},
  year = {2022},
  month = dec,
  journal = {Journal of Mechanisms and Robotics},
  volume = {14},
  number = {6},
  eprint = {2007.08444},
  pages = {11},
  issn = {1942-4302},
  doi = {10.1115/1.4054320},
  abstract = {This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are propagated through high-level algebraic operations and works for any type of joints and arbitrary parameterizations. The second approach is based on Gauss's Principle of Least Constraint (GPLC) and includes arbitrary equality constraints. In addition to showing the connections of GPLC with Gibbs-Appell and Kane's equations, we use it to model a nonholonomic mobile manipulator. Our current formulations are more general than their counterparts in the state of the art, although GPLC is more computationally expensive, and simulation results show that they are as accurate as the classic recursive Newton-Euler algorithm.},
  archiveprefix = {arXiv},
  copyright = {All rights reserved},
  url = {https://arxiv.org/abs/2007.08444}
}

This paper presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton-Euler formulation and uses twists and wrenches, which are propagated through high-level algebraic operations and works for any type of joints and arbitrary parameterizations. The second approach is based on Gauss's Principle of Least Constraint (GPLC) and includes arbitrary equality constraints. In addition to showing the connections of GPLC with Gibbs-Appell and Kane's equations, we use it to model a nonholonomic mobile manipulator. Our current formulations are more general than their counterparts in the state of the art, although GPLC is more computationally expensive, and simulation results show that they are as accurate as the classic recursive Newton-Euler algorithm.

@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}
}

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.

@inproceedings{Silva2019,
  title = {Wrench {{Control}} Based on {{Dual Quaternion Algebra}}},
  booktitle = {Workshop on {{Applications}} of {{Dual Quaternion Algebra}} to {{Robotics}}},
  author = {Silva, Frederico Fernandes Afonso and Adorno, Bruno Vilhena},
  year = {2019},
  address = {Belo Horizonte, Brasil},
  doi = {10.5281/zenodo.3566650},
  copyright = {All rights reserved},
  abstract = {This paper proposes a wrench control strategy that takes advantage of the recurrence equations of the dual quaternion Newton-Euler formalism. A simple application for end-effector admittance control is presented to illustrate the proposed method. Simulations on a KUKA LWR robot are performed showing the effectiveness of the proposed method.},
  url = {https://zenodo.org/records/3566650}
}

This paper proposes a wrench control strategy that takes advantage of the recurrence equations of the dual quaternion Newton-Euler formalism. A simple application for end-effector admittance control is presented to illustrate the proposed method. Simulations on a KUKA LWR robot are performed showing the effectiveness of the proposed method.

@article{Silva2018,
  title = {Whole-Body {{Control}} of a {{Mobile Manipulator Using Feedback Linearization}} and {{Dual Quaternion Algebra}}},
  author = {Silva, Frederico Fernandes Afonso and Adorno, Bruno Vilhena},
  year = {2018},
  month = aug,
  journal = {Journal of Intelligent \& Robotic Systems},
  volume = {91},
  number = {2},
  pages = {249--262},
  publisher = {Journal of Intelligent \& Robotic Systems},
  issn = {0921-0296},
  doi = {10.1007/s10846-017-0686-3},
  abstract = {This paper presents the whole-body control of a nonholonomic mobile manipulator using feedback lin- earization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the desired end-effector pose, acts as a dynamic trajectory generator for the end-effector, and input signals for both nonholonomic mobile base and manipulator arm are gener- ated by using the pseudoinverse of the whole-body Jacobian matrix. In order to deal with the nonholonomic constraints, the input signal to the mobile base generated by the whole- body motion control is properly remapped to ensure feasi- bility. The Lyapunov stability for the proposed controller is presented and experimental results on a real platform are performed in order to compare the proposed scheme to a tra- ditional classic whole-body linear kinematic controller. The results show that, for similar convergence rate, the nonlin- ear controller is capable of generating smoother movements while having lower control effort than the linear controller.},
  copyright = {All rights reserved},
  keywords = {dual quaternion,Dual quaternion,Mobile manipulat,Mobile manipulator,nonlinear control,Nonlinear control,Whole-body control},
  url = {https://www.researchgate.net/publication/320202323_Whole-body_Control_of_a_Mobile_Manipulator_Using_Feedback_Linearization_and_Dual_Quaternion_Algebra#fullTextFileContent}
}

This paper presents the whole-body control of a nonholonomic mobile manipulator using feedback lin- earization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the desired end-effector pose, acts as a dynamic trajectory generator for the end-effector, and input signals for both nonholonomic mobile base and manipulator arm are gener- ated by using the pseudoinverse of the whole-body Jacobian matrix. In order to deal with the nonholonomic constraints, the input signal to the mobile base generated by the whole- body motion control is properly remapped to ensure feasi- bility. The Lyapunov stability for the proposed controller is presented and experimental results on a real platform are performed in order to compare the proposed scheme to a tra- ditional classic whole-body linear kinematic controller. The results show that, for similar convergence rate, the nonlin- ear controller is capable of generating smoother movements while having lower control effort than the linear controller.

@mastersthesis{Silva2017,
  title = {Whole-Body {{Control}} of a {{Mobile Manipulator Using Feedback Linearization}} and {{Dual Quaternion Algebra}}},
  author = {Silva, Frederico Fernandes Afonso},
  year = {2017},
  doi = {10.13140/RG.2.2.23936.58884},
  abstract = {This master thesis presents the whole-body control of a nonholonomic mobile manipulator using feedback linearization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the desired end-effector pose, acts as a dynamic trajectory generator for the end-effector, and input signals for both nonholonomic mobile base and manipulator arm are generated by using the pseudoinverse of the whole-body Jacobian matrix. In order to deal with the nonholonomic constraints, the input signal to the mobile base generated by the whole-body motion control is properly remapped to ensure feasibility. Joint constraints, which are present in the real platform, are treated by means of constraints in the Jacobian matrix. The Lyapunov stability for the closed-loop system is presented, utilizing Lyapunov's Direct Method and Matrosov's theorem, and experimental results on a real platform are performed in order to compare the proposed scheme to a traditional classic whole-body linear kinematic controller. The results show that, for similar convergence rate, the nonlinear controller is capable of generating smoother movements while having lower control effort than the linear controller.},
  copyright = {All rights reserved},
  school = {Universidade Federal de MInas Gerais},
  keywords = {dual quaternions.,feedback linearization,kinematic control,nonholonomic mobile manipulator,Nonlinear control},
  url = {https://www.researchgate.net/publication/338018160_Whole-body_Control_of_a_Mobile_Manipulator_Using_Feedback_Linearization_and_Dual_Quaternion_Algebra#fullTextFileContent}
}

This master thesis presents the whole-body control of a nonholonomic mobile manipulator using feedback linearization and dual quaternion algebra. The controller, whose reference is a unit dual quaternion representing the desired end-effector pose, acts as a dynamic trajectory generator for the end-effector, and input signals for both nonholonomic mobile base and manipulator arm are generated by using the pseudoinverse of the whole-body Jacobian matrix. In order to deal with the nonholonomic constraints, the input signal to the mobile base generated by the whole-body motion control is properly remapped to ensure feasibility. Joint constraints, which are present in the real platform, are treated by means of constraints in the Jacobian matrix. The Lyapunov stability for the closed-loop system is presented, utilizing Lyapunov's Direct Method and Matrosov's theorem, and experimental results on a real platform are performed in order to compare the proposed scheme to a traditional classic whole-body linear kinematic controller. The results show that, for similar convergence rate, the nonlinear controller is capable of generating smoother movements while having lower control effort than the linear controller.

@inproceedings{Silva2016,
  title = {Whole-{{Body Control}} of a {{Mobile Manipulator Using Feedback Linearization Based}} on {{Dual Quaternions}}},
  booktitle = {2016 {{XIII Latin American Robotics Symposium}} and {{IV Brazilian Robotics Symposium}} ({{LARS}}/{{SBR}})},
  author = {Silva, Frederico Fernandes Afonso and Adorno, Bruno Vilhena},
  year = {2016},
  month = oct,
  pages = {293--298},
  publisher = {IEEE},
  address = {Recife},
  doi = {10.1109/LARS-SBR.2016.56},
  abstract = {This paper presents a whole-body pose control of a mobile manipulator using a cascade scheme with two control loops. In the outer loop there is a nonlinear controller based on dual-quaternion feedback linearization---whose reference is a unit dual quaternion representing the desired end effector's pose---that acts as a dynamic trajectory generator and generates input signals for both nonholonomic mobile base and manip- ulator arm; the inner loop uses the input signals generated by the outer-loop as reference for an input-output linearizing controller that explicitly takes into account the nonholonomic constraints of the mobile base. Experimental results on a real platform are performed in order to compare the proposed scheme to a traditional whole-body kinematic controller using the pseudoinverse of the Jacobian matrix. The results show that the abrupt initial movement that is a characteristic of the classic approach, when the initial error is too large, is mitigated by the use of the nonlinear control.},
  copyright = {All rights reserved},
  isbn = {978-1-5090-3656-1},
  url = {https://www.researchgate.net/publication/312435840_Whole-Body_Control_of_a_Mobile_Manipulator_Using_Feedback_Linearization_Based_on_Dual_Quaternions#fullTextFileContent}
}

This paper presents a whole-body pose control of a mobile manipulator using a cascade scheme with two control loops. In the outer loop there is a nonlinear controller based on dual-quaternion feedback linearization—whose reference is a unit dual quaternion representing the desired end effector's pose—that acts as a dynamic trajectory generator and generates input signals for both nonholonomic mobile base and manip- ulator arm; the inner loop uses the input signals generated by the outer-loop as reference for an input-output linearizing controller that explicitly takes into account the nonholonomic constraints of the mobile base. Experimental results on a real platform are performed in order to compare the proposed scheme to a traditional whole-body kinematic controller using the pseudoinverse of the Jacobian matrix. The results show that the abrupt initial movement that is a characteristic of the classic approach, when the initial error is too large, is mitigated by the use of the nonlinear control.