Directional Grid Maps: Modeling Multimodal Angular Uncertainty in Dynamic Environments

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.