A mixed nonlinear complementarity technique for solving the dynamics of a dexterous manipulation system

• Autor(es):

  Buffo, F.E. (Southern National University. Department of Mathematics);

  Maciel, M.C. (Southern National University. Department of Mathematics).

• Fonte:

  Computational & Applied Mathematics; volume 25, número 1, páginas 79-95. 2006.

• Assuntos:

  linear complementarity problem;

  box constrained minimization;

  multi-rigid-body contact problem.

• Resumo:

  The versatility of a robot to perform a task is limited principally by the flexibilityof its end-effector. In the last years, research has been focused on the development of a hand with several fingers since these devices are capable of manipulating and grasping objects of different forms. A dexterous manipulation system, composed of a robot hand with several fingers and an object that will be held or manipulated, could be modeled as a set of rigid bodies in contact. The dynamics of several rigid bodies in contact tries to predict the accelerations and forces at the contact points of the set of rigid bodies with Coulomb friction. The calculation of such forces allows us to determine if the contact is maintained or disappears and to plan a determined action. The equations that describe the problem form a system of differential algebraic equations. In this contribution the problem is reformulated as a mixed nonlinear complementarity problem (MNCP). Then, an optimization problem with box constraints associated to the MNCP is presented using an adequate merit function. Conditions about the equivalence between the problems are established. Finally, the optimization problem is solved using a robust and efficient algorithm. Encouraging numerical results are reported.

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