Abstract: Robust and adaptive robotic peg-in-hole assembly under tight tolerance is critical to various industrial applications. Still, it remains an open challenge due to perception and physical uncertainties from contact-rich interactions that easily exceed the allowed clearance. In this paper, we study how to leverage the contact between the peg and its matching hole to eliminate uncertainties in the assembly process under unstructured settings. By exploring the role of compliance under contact constraints, we present a manipulation system that plans collision-inclusive interactions for the peg to 1) iteratively identify its task environment to localize the target hole and 2) exploit environmental contact constraints to refine insertion motions into the target hole without precise perception, facilitating a robust solution to peg-in-hole assembly. By conceptualizing the above process as the composition of funneling in different state spaces, we present a formal approach to construct manipulation funnels as an uncertainty-absorbing paradigm for peg-in-hole assembly. The proposed system effectively generalizes diverse peg-in-hole scenarios across varying scales, shapes, and materials in a learning-free manner. Extensive real-world experiments on a NIST Assembly Task Board validate its robustness in real-world applications.