The homotopy sequence for regular singular stratified bundles

A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the 'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an analogous homotopy exact sequence for fundamental group schemes classifying regular singular stratified bundles, under the additional assumption that the morphism in question can be (partially) compactified to a log smooth morphism.