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Optimal grasp selection, and control for stabilising a grasped object, with respect to slippage and external forces

This paper explores the problem of how to grasp an object, and then control a robot arm so as to stabilise that object, under conditions where: i) there is significant slippage between the object and the robot’s fingers; and ii) the object is perturbed by external forces. For an n degrees of freedom (dof) robot, we treat the robot plus grasped object as an (n+1) dof system, where the grasped object can rotate between the robot’s fingers via slippage. Firstly, we propose an optimisation-based algorithm that selects the best grasping location from a set of given candidates. The best grasp is one that will yield the minimum effort for the arm to keep the object in equilibrium against external perturbations. Secondly, we propose a controller which brings the (n+1) dof system to a task configuration, and then maintains that configuration robustly against matched and unmatched disturbances. To minimise slippage between gripper and grasped object, a sufficient criterion for selecting the control coefficients is proposed by adopting a set of inequalities, which are obtained solving a nonlinear minimisation problem, dependant on the static friction estimation. We demonstrate our approach on a simulated (2+1) planar robot, comprising two joints of the robot arm, plus the additional passive joint which is formed by the slippage between the object and the robot’s fingers. We also present an experiment with a real robot arm, grasping a flat object between the fingers of a parallel jaw gripper.