  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 localisation
information, but also their manoeuvrability is constrained by their dynamics
and often suffer from uncertainty. In order to cope with these constraints,
this manuscript 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: (i) incrementally mapping the surroundings to build
an uncertainty-aware representation of the environment, and (ii) iteratively
(re)planning trajectories to goal that are kinodynamically feasible and
probabilistically safe through a multi-layered sampling-based planner in the
belief space. In-depth empirical analyses illustrate some important properties
of this approach, namely, (a) the multi-layered planning strategy enables rapid
exploration of the high-dimensional belief space while preserving asymptotic
optimality and completeness guarantees, and (b) the proposed routine for
probabilistic collision checking results in tighter probability bounds in
comparison to other uncertainty-aware planners in the literature. Furthermore,
real-world in-water experimental evaluation on a non-holonomic torpedo-shaped
autonomous underwater vehicle and simulated trials in the Stairwell scenario of
the DARPA Subterranean Challenge 2019 on a quadrotor unmanned aerial vehicle
demonstrate the efficacy of the method as well as its suitability for systems
with limited on-board computational power.
