Wilking's completeness conjecture for dual foliations

Let $M$ be a complete Riemannian manifold with nonnegative sectional curvature, and let $\mathcal{F}$ be a singular Riemannian foliation on $M$. The dual foliation is the foliation whose leaf through $x\in M$ consists of points joined to $x$ by curves everywhere perpendicular to the leaves of $\mathcal{F}$. Wilking's completeness conjecture. The dual foliation has complete leaves. The conjecture extends known completeness results for orbit decompositions of isometric group actions, compact nonsingular foliations, and fibers of Sharafutdinov retractions; the cited paper proves it for Riemannian foliations on nonnegatively curved symmetric spaces, while the general case remains open.