Persona:
Jiménez Alburquerque, Fernando

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fjimenez@ind.uned.es
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Jiménez Alburquerque
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Fernando
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2016 - 20192
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Autor: Colombo, Leonardo ×

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Mostrando 1 - 2 de 2
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    Publicación
    Variational integrators for underactuated mechanical control systems with symmetries
    (American Institute of Mathematical Sciences, 2016-05-01) Colombo, Leonardo; Jiménez Alburquerque, Fernando; Martín de Diego, David
    Optimal control problems for underactuated mechanical systems can be seen as a higher-order variational problem subject to higher-order constraints (that is, when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces). In this paper we discuss the variational formalism for the class of underactuated mechanical control systems when the configuration space is a trivial principal bundle and the construction of variational integrators for such mechanical control systems. An interesting family of geometric integrators can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators, being one of their main properties the preservation of geometric features as the symplecticity, momentum preservation and good behavior of the energy. We construct variational integrators for higher-order mechanical systems on trivial principal bundles and their extension for higher-order constrained systems, paying particular attention to the case of underactuated mechanical systems.
  • Miniatura
    Publicación
    The variational discretization of the constrained higher-order Lagrange-Poincaré equations
    (American Institute of Mathematical Sciences, 2019-01-01) Bloch, Anthony; Colombo, Leonardo; Jiménez Alburquerque, Fernando
    In this paper we investigate a variational discretization for the class of mechanical systems in presence of symmetries described by the action of a Lie group which reduces the phase space to a (non-trivial) principal bundle. By introducing a discrete connection we are able to obtain the discrete constrained higher-order Lagrange-Poincaré equations. These equations describe the dynamics of a constrained Lagrangian system when the Lagrangian function and the constraints depend on higher-order derivatives such as the acceleration, jerk or jounces. The equations, under some mild regularity conditions, determine a well defined (local) flow which can be used to define a numerical scheme to integrate the constrained higher-order Lagrange-Poincaré equations. Optimal control problems for underactuated mechanical systems can be viewed as higher-order constrained variational problems. We study how a variational discretization can be used in the construction of variational integrators for optimal control of underactuated mechanical systems where control inputs act soley on the base manifold of a principal bundle (the shape space). Examples include the energy minimum control of an electron in a magnetic field and two coupled rigid bodies attached at a common center of mass.