Motion planning in dynamic uncertain environment using probability navigation function

This paper introduces a novel motion planning algorithm for stochastic dynamic scenarios. We extend Rimon and Koditechek´s concept of a navigation function to such scenarios. Such a function can be used when considering spherical and start-shaped geometries for the robot, obstacles and work space. Our main idea is to take into account both the probabilities and the geometries of the objects acting in the work space by formulating a probability density function p_tot that encloses both. We consider of p_tot as a metric between the robot and the obstacles, minimizing it in the course of the motion. Additionally, we define a safe probability value for collision δ. By analytically investigating p_tot defined in Rⁿ we find a convenient approximation for a safe distance p_δ in the sense of that metric. Lastly, we present some experiments applying our algorithm in various scenarios.