Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localization information but also their maneuverability is constrained by their dynamics and often suffers from uncertainty. In order to cope with these constraints, this article proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: 1) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment and 2) iteratively (re)planning trajectories to goal that is kinodynamically feasible and probabilistically safe through a multilayered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely: 1) the multilayered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees and 2) the proposed routine for probabilistic collision check-