  In automated manufacturing, robots must reliably assemble parts of various
geometries and low tolerances. Ideally, they plan the required motions
autonomously. This poses a substantial challenge due to high-dimensional state
spaces and non-linear contact-dynamics. Furthermore, object poses and model
parameters, such as friction, are not exactly known and a source of
uncertainty. The method proposed in this paper models the task of parts
assembly as a belief space planning problem over an underlying
impedance-controlled, compliant system. To solve this planning problem we
introduce an asymptotically optimal belief space planner by extending an
optimal, randomized, kinodynamic motion planner to non-deterministic domains.
Under an expansiveness assumption we establish probabilistic completeness and
asymptotic optimality. We validate our approach in thorough, simulated and
real-world experiments of multiple assembly tasks. The experiments demonstrate
our planner's ability to reliably assemble objects, solely based on CAD models
as input.
