Control of Multifinger Manipulation Theoretical And Experimental Studies Using

Cover Control of Multifinger Manipulation Theoretical And Experimental Studies Using
Control of Multifinger Manipulation Theoretical And Experimental Studies Using
James Demmel
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= E, X]/;^r. = r (2) where r, is the vector from the nominal center of torque to the position of the i"' finger, and x designates the vector obtained from x by rotating 90° counterclockwise.
Using the definition of the grip transformation G and introducing vectors F — {Fi, . . . , Fk) and w = (E, r), we can write them as G{F) = w. (3) We now seek a right inverse for G that will give us finger forces satisfying the frictionaJ constraints. The linear transformation G maps the set of vectors F ont
...o the set of object force/torque vectors w. We assume we have three noncolinear gripping points, so G is of full rank. Hence G has the pseudoinverse G"*" = G^{GG^)~^, and the solutions to Equation 3 can be written as G+w + e, (4) where e is a solution of the homogeneous equation Ge = 0. The vector e could be considered a set of purely gripping forces which hold the object in equilibrium (see [39]). It is not true though, that any solution of the 12 homogeneous equation will in fact grasp the object.

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