The universal sl2 invariant and Milnor's invariant

We are interested in topological understandings of the quantum invariants.
Milnor's invariant is a classical invariant which is a generalization of the linking number.
Habegger and Masbaum showed that Milnor's invariants are obtained from a reduced version of Kontsevich integral.
The universal sl2 invariant is a quantum invariant taking values in the h-adic completed tensor powers of
the quantized enveloping algebra of sl2.
The coefficient of h^i of the universal sl2 invariant is a finite type invariant of degree i,
and thus theoretically is obtained from Kontsevich integral by using a weight system.
However, we have not yet known a constructive weight system for the universal sl2 invariant.
In this talk, we construct partial weight system of the universal sl2 invariant and study relationships between Milnor's invariants and the universal sl2 invariant.