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Optimal Control Simulations of Lateral and Tip Pinch Grasping

: Phutane, U.; Roller, M.; Leyendecker, S.


Faragó, I.:
Progress in Industrial Mathematics at ECMI 2018 : 20th European Conference on Mathematics for Industry, ECMI 2018, Budapest, 18th to 22nd June 2018
Cham: Springer Nature, 2019 (The European Consortium for Mathematics in Industry 30)
ISBN: 978-3-030-27549-5 (Print)
ISBN: 978-3-030-27550-1 (Online)
European Conference on Mathematics for Industry (ECMI) <20, 2018, Budapest>
Fraunhofer ITWM ()

Grasping is a complex human movement. During grasping, when the hand closes around the object, the multibody system changes from a kinematic tree structure to a closed loop contact problem. To better understand work-related disorders or optimize execution of activities of daily life, an optimal control simulation to perform grasping is useful. We simulate the grasping action with a three-dimensional rigid multibody model composed of two fingers actuated by joint torques. The grasping movement is composed of a reaching phase (no contacts) and a grasping phase (closed contacts). The contact constraints are imposed first through distances between the fingers and the object surfaces and then through spherical joints. Thus, the dynamics of grasping is described by a hybrid dynamical system with a given switching sequence and unknown switching times. To determine a favourable trajectory for grasping action, we solve an optimal control problem (ocp). The ocp is solved using the direct transcription method DMOCC, leading to a structure preserving approximation of the continuous problem. An objective involving either the contact polygon centroid or the contol torques is minimized subject to discrete Euler-Lagrange equations, boundary conditions and path constraints. The dynamics of the object to grasp along with Coulomb friction is also taken into account.