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The problem of automatically determining gripping positions for objects based upon geometrical knowledge of the object and its environment is addressed. Both the question of what constitutes a good grip and the efficiency of the computational algorithms are considered. Two new criteria for the stability of a grip are proposed: resilience to slippage, and twisting in the gripper due to external forces and torques. Resilience to slippage is expressed in terms of friction effects of the surfaces involved, the shape of the contact between the gripper and object, and the distance of the grip point from the center of mass of the object. Two new performance measures are introduced to reflect resilience to twisting. A general grip planning strategy is introduced that is both run-time efficient and robust.