  A handlebody-link is a disjoint union of embeddings of handlebodies in $S^3$
and an HL-homotopy is an equivalence relation on handlebody-links generated by
self-crossing changes. The second author and Ryo Nikkuni classified the set of
HL-homotopy classes of 2-component handlebody-links completely using the
linking numbers for handlebody-links. In this paper, we construct a family of
invariants for HL-homotopy classes of general handlebody-links, by using
Milnor's link-homotopy invariants. Moreover, we give a bijection between the
set of HL-homotopy classes of almost trivial handlebody-links and tensor
product space modulo some general linear actions, especially for 3- or more
component handlebody-links. Through this bijection we construct comparable
invariants of HL-homotopy classes.
