Structure preserving optimal control of finger movements - Maas, Ramona; Leyendecker, Sigrid; Siebert, Tobias (Proceedings of the Euromech Colloquium 511 on Biomechanics of Human Motion, DVD, 16 pages, 2011)
A common tool to solve dynamical problems, in particular in biomechanic in- vestigations, is MATLAB/Simulink. Many integration methods, as used for example in MAT- LAB/Simulink, rely on standard discretisations of the continuous equations of motion. These methods often lead to time stepping schemes, that show numerical dissipation in energy and momentum. In contrast to that, we use a discrete variational principle to derive a time-stepping scheme. This method yields discrete analogues to the Euler- Lagrange equations and Noether’s theorem, which ensures that the structure of the underlying continuous dynamical system is preserved. Using this method, the simulation results are symplectic momentum consistent and exhibit a good energy behaviour. We implement a typical nonlinear Hill-type muscle model in the structure preserving simulation framework and investigate the differences to standard simulation of muscle actuated movements with MATLAB/Simulink, especially concerning the correct representation of energy and angu- lar momentum. A numerical example shows that the MATLAB/Simulink integrators artificially loose or gain energy and angular momentum, whereas all results of the symplectic momentum method are structure preserving. With this structure preserving simulation framework including actuation by muscle models, we investigate the trajectory of fingers during grasping movements. Since human movements are controlled by the central nervous system (CNS), we formulate finger movements as optimal con- trol problems for constrained forced motion with a physiologically motivated objective function as described in [1]. For the solution of the optimal control problem, we use DMOCC (Dis- crete Mechanics and Optimal Control for Constrained Systems, introduced in [2]), which can be distinguished from other direct transcription methods by its structure preserving formula- tion. This is a key feature of the method, since numerical dissipation could lead to over- or underestimation of the joint torques or muscle forces.
UnivIS-Import:2015-04-16:Pub.2010.tech.FT.ltd.struct_69
Keywords: structure preservation; grasping; DMOCC; optimal control; finger movement.