Optimal control simulations of human hand grasping

The core objective of this work is to develop an optimal control setup to perform dynamic grasping simulations with a human hand. This is done primarily with a view to provide existing digital human modelling (DHM) environments such as IMMA (Intelligently Moving Manikin) the functionality to move beyond quasi-static simulations while performing assembly planning and ergonomic studies. The optimal control setup also finds applications be- yond DHM, particularly in the areas of medical diagnostics and rehabilitation. The optimal control approach is capable to provide sequences of trajectories and controls that are used to drive biomechanical systems while performing a particular task without the need of motion capture measurements. Such a sequence is obtained via the minimisation of an objective function. The spe- cific optimal control approach in this thesis makes use of structure preserving time-stepping schemes in describing the two distinct forms of dynamics of a mechanical system. The approximated solutions obtained by using afore- mentioned schemes inherit the characteristics of the continuous system, show angular momentum consistency and good long term energy behaviour.

The work begins with examining the kinematic behaviour of the thumb, which is the crucial to the grasping competence of primates. The focus then shifts to the understanding of grasping fundamentals that are mainly an outcome from the view of robotic manipulation tasks. In this part, we lay the foundation of unilateral multi-point contact systems. These are generated through kinematic models and characterize the force and velocity transmission properties between the hand the object through grasp quality measures. The hand and object multibody models along with the contact models become key components in the development of variational time integrators, derived through a discrete variational principle, to describe the dynamics of the hand reaching towards an object and then manipulating it. The discrete equations of motion representing the reaching and manipulation actions constitute a hybrid dynamical system to setup the grasping optimal control problem (OCP), where the switching occurs due to the enforcement of the contact constraints at an unknown time.