Abstract
An efficient quantitative test for form closure valid for any
number of contact points is formulated as a linear program, the optimal
objective value of which provides a measure of how far a grasp is from
losing form closure. When the grasp does not have form closure,
manipulation planning requires a means for predicting the object's
stability and instantaneous velocity, given the joint velocities of the
hand. The classical approach to computing these quantities is to solve
the systems of kinematic inequalities corresponding to all possible
combinations of separating or sliding at the contacts. All combinations
resulting in the interpenetration of bodies or the infeasibility of the
equilibrium equations are rejected. The remaining combination is
consistent with all the constraints and is used to compute the velocity
of the manipulated object and the contact forces, which indicate whether
or not the object is stable. A linear program whose solution yields the
same information as the classical approach, usually without explicit
testing of all possible combinations of contact interactions, is
formulated
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