  This article establishes the novel D$^*_+$, a risk-aware and
platform-agnostic heterogeneous global path planner for robotic navigation in
complex environments. The proposed planner addresses a fundamental bottleneck
of occupancy-based path planners related to their dependency on accurate and
dense maps. More specifically, their performance is highly affected by poorly
reconstructed or sparse areas (e.g. holes in the walls or ceilings) leading to
faulty generated paths outside the physical boundaries of the 3-dimensional
space. As it will be presented, D$^*_+$ addresses this challenge with three
novel contributions, integrated into one solution, namely: a) the proximity
risk, b) the modeling of the unknown space, and c) the map updates. By adding a
risk layer to spaces that are closer to the occupied ones, some holes are
filled, and thus the problematic short-cutting through them to the final goal
is prevented. The novel established D$^*_+$ also provides safety marginals to
the walls and other obstacles, a property that results in paths that do not cut
the corners that could potentially disrupt the platform operation. D$^*_+$ has
also the capability to model the unknown space as risk-free areas that should
keep the paths inside, e.g in a tunnel environment, and thus heavily reducing
the risk of larger shortcuts through openings in the walls. D$^*_+$ is also
introducing a dynamic map handling capability that continuously updates with
the latest information acquired during the map building process, allowing the
planner to use constant map growth and resolve cases of planning over outdated
sparser map reconstructions...
