Applying probability navigation function in dynamic uncertain environments

This paper introduces a novel motion planning algorithm for stochastic dynamic scenarios. We apply a Probability Navigation Function (PNF), discussed in the authors' previous research work, to dynamic environments. We first consider the ambient configuration space to be an n- dimensional ball; the robot and the obstacles loci are all known with a Gaussian probability distribution, and both the robot and the obstacles are assumed to have n-dimensional disc shapes. We fuse the geometries of the robot and the obstacles with the localization probability distribution using convolution. We then define a Probability Navigation Function (PNF) φ from the configuration space to R. We also provide a numerical method for the case where the obstacles and the robot shapes are non-symmetric and their probability distributions are non-Gaussian respectively. The PNF is applied to the dynamic case, where the obstacles are moving at different velocities, by calculating consecutive probability navigation functions according to a prediction of the obstacles' positions and their estimation error covariance. We then apply a simulated annealing scheme on the sequence of motion directions to choose an optimal path. We demonstrate our algorithm for various scenarios.