# Optimal control simulations of tip pinch and lateral pinch grasping

Phutane U, Roller M, Leyendecker S (2018)

Publication Language: English

Publication Type: Conference contribution, Conference Contribution

Publication year: 2018

Conference Proceedings Title: Mathematics in Industry

Event location: Budapest

### Abstract

Grasping is a basic, though complex human movement performed with the hand through its many degrees of freedom.  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 living, 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 (the thumb and the index finger) along with the wrist and the forearm, modeled with the discrete null-space method. The model is actuated using joint torques. The grasping movement is composed of a reaching phase (no contact) and a grasping phase (closed contacts). The contact constraints are imposed first using functions to calculate the distance between the finger tips and the object surfaces and then through spherical joints. The durations of each phase is determined by the solution of an optimal control problem.  Thus, the dynamics is described by a hybrid dynamical system with a given switching sequence and unknown switching times. The optimal control problem is solved using the direct transcription method DMOCC (discrete mechanics and optimal control with constraints) leading to a structure preserving approximation. An objective function involving either the contact polygon centroid, the grasp matrix or the contact force is minimized subject to the 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. Investigations are done for two examples, namely lateral pinch and tip pinch grasps.

### How to cite

APA:

Phutane, U., Roller, M., & Leyendecker, S. (2018). Optimal control simulations of tip pinch and lateral pinch grasping. In Mathematics in Industry. Budapest, HU.

MLA:

Phutane, Uday, Michael Roller, and Sigrid Leyendecker. "Optimal control simulations of tip pinch and lateral pinch grasping." Proceedings of the European Consortium for Mathematics in Industry (ECMI) Conference, Budapest 2018.