  Path planning in dynamic environments is essential to high-risk applications
such as unmanned aerial vehicles, self-driving cars, and autonomous underwater
vehicles. In this paper, we generate collision-free trajectories for a robot
within any given environment with temporal and spatial uncertainties caused due
to randomly moving obstacles. We use two Poisson distributions to model the
movements of obstacles across the generated trajectory of a robot in both space
and time to determine the probability of collision with an obstacle. Measures
are taken to avoid an obstacle by intelligently manipulating the speed of the
robot at space-time intervals where a larger number of obstacles intersect the
trajectory of the robot. Our method potentially reduces the use of
computationally expensive collision detection libraries. Based on our
experiments, there has been a significant improvement over existing methods in
terms of safety, accuracy, execution time and computational cost. Our results
show a high level of accuracy between the predicted and actual number of
collisions with moving obstacles.
