Immobilizing 2D Serial Chains in Form Closure Grasps

Abstract: The immobilization of non-rigid objects is currently an active research area in robotics. This paper explores the problem by studying the immobilization of serial chains of rigid polygons connected by rotational joints. The chain is to be immobilized at a given placement by frictionless point fingers that may contact the polygons only along edge inte-riors or at concave vertices. In earlier work we established that any serial chain of n 6 = 3 polygons without parallel edges can be immobilized with n+2 frictionless point fingers. This paper establishes that this is the minimal number of frictionless point fingers required for the immobilization of such chains. The paper also establishes that serial chains of n = 3 polygons are indeed exceptional and require six rather than five point fingers for their immobilization. The paper next introduces a robust version of immobility, which requires that immobilization be maintained with respect to small finger placement errors. The paper describes how to robustly immobilize any serial chain of n polygons without parallel edges at the cost of only one additional frictionless point finger. The immobilization procedures described in the paper are constructive and readily implementable as part of grasp and manipulation planners.