Incrementality and Hierarchies in the Enrollment of Multiple Synergies for Grasp Planning

Postural hand synergies or eigenpostures are joint angle covariation patterns observed in common grasping tasks. A typical definition associates the geometry of synergy vectors and their hierarchy (relative statistical weight) with the principal component analysis of an experimental covariance matrix. In a reduced complexity representation, the accuracy of hand posture reconstruction is incrementally improved as the number of synergies is increased according to the hierarchy. In this work, we explore whether and how hierarchy and incrementality extend from posture description to grasp force distribution. To do so, we study the problem of optimizing grasps w.r.t. hand/object relative pose and force application, using hand models with an increasing number of synergies, ordered according to a widely used postural basis. The optimization is performed numerically, on a data set of simulated grasps of four objects with a 19-DoF anthropomorphic hand. Results show that the hand/object relative poses that minimize (possibly locally) the grasp optimality index remain roughly the same as more synergies are considered. This suggests that an incremental learning algorithm could be conceived, leveraging on the solution of lower dimensionality problems to progressively address more complex cases as more synergies are added. Second, we investigate whether the adopted hierarchy of postural synergies is indeed the best also for force distribution. Results show that this is not the case.