Motion Planning in 3D Environments Using Visibility Velocity Obstacles

Abstract—In this paper, we present a unique method
combining visibility analysis in 3D environments with dynamic
motion planning algorithm, named Visibility Velocity
Obstacles (VVO). Our method is based on two major steps.
The first step is based on analytic visibility boundaries
calculation in 3D environments, taking into account sensors'
capabilities including probabilistic consideration. In the second
step, we generate VVO transferring visibility boundaries from
the position space to the velocity space, for each object. Each
VVO represents velocity's set of possible future collision and
visibility boundaries. Based on our analysis in velocity space,
we plan our trajectory by selecting robot's future velocity at
each time step, tracking each specific target by considering
visibility constraints as an integral part of the velocities space.
We formulate the tracked target in the environment as part of
our planner and include visibility analysis for the next time
step as part of our planning in the same search space. We
define visibility aspects as part of velocity space, where all the
objects are modeled from the visibility point of view. We
introduce a potential trajectory planner combining unified 3D
visibility analysis for target tracking as part of dynamic motion
planning.