  Robots often have to deal with the challenges of operating in dynamic and
sometimes unpredictable environments. Although an occupancy map of the
environment is sufficient for navigation of a mobile robot or manipulation
tasks with a robotic arm in static environments, robots operating in dynamic
environments demand richer information to improve robustness, efficiency, and
safety. For instance, in path planning, it is important to know the direction
of motion of dynamic objects at various locations of the environment for safer
navigation or human-robot interaction. In this paper, we introduce directional
statistics into robotic mapping to model circular data. Primarily, in
collateral to occupancy grid maps, we propose directional grid maps to
represent the location-wide long-term angular motion of the environment. Being
highly representative, this defines a probability measure-field over the
longitude-latitude space rather than a scalar-field or a vector field. Withal,
we further demonstrate how the same theory can be used to model angular
variations in the spatial domain, temporal domain, and spatiotemporal domain.
We carried out a series of experiments to validate the proposed models using a
variety of robots having different sensors such as RGB cameras and LiDARs on
simulated and real-world settings in both indoor and outdoor environments.

Robotics