Maas R, Leyendecker S (2010)

**Publication Type:** Conference contribution, other

**Publication year:** 2010

**Conference Proceedings Title:** Proceedings of the First Joint International Conference on Multibody System Dynamics

Trajectory planning of human motion is done unconsciously by the central nervous system (CNS). To get a better understanding about how the human CNS controls movements in a particular example, we investigate the trajectory of the index finger during grasping. In this regard, we describe the index finger, which consists of three phalanxes and three connecting joints, as an n-dimensional forced constrained multibody system. Varying forefinger movements are formulated as optimal control problems for constrained motion. At this stage, the actuation of the finger due to muscles is simply represented by bounded joint torques. However, the inclusion of muscle models is planned for the future. For the solution of the optimal control problem, DMOCC (Discrete Mechanics and Optimal Control for Constrained Systems, introduced in [8]) is used. DMOCC can be classified as a direct method, thus transforming the optimal control problem into a constrained optimisation problem. The algorithm yields a sequence of discrete configurations together with a sequence of actuating controls being optimal in the sense of minimising an objective function while the described (in-)equality constraints, and most importantly, the discrete equations of motion are fulfilled. Their structure preserving formulation distinguishes DMOCC from other direct transcription methods. It guarantees that certain characteristic properties of the real motion are inherited by the approximate trajectory. For example, the evolution of the systems momentum maps exactly represents externally applied controls and energy is not dissipated artificially. This is crucial, since numerical dissipation would lead to over- or underestimation of the joint torques. As in [4], the motion due to different objective functions like total control effort, torque change, kinetic energy and jerk in the fingertip is compared.

**APA:**

Maas, R., & Leyendecker, S. (2010). Structure preserving optimal control simulation of index finger dynamics. In *Proceedings of the First Joint International Conference on Multibody System Dynamics*. Lappeenranta, FI.

**MLA:**

Maas, Ramona, and Sigrid Leyendecker. "Structure preserving optimal control simulation of index finger dynamics." *Proceedings of the First Joint International Conference on Multibody System Dynamics, Lappeenranta* 2010.

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