  Next generation Unmanned Aerial Vehicles (UAVs) must reliably avoid moving
obstacles. Existing dynamic collision avoidance methods are effective where
obstacle trajectories are linear or known, but such restrictions are not
accurate to many real-world UAV applications. We propose an efficient method of
predicting an obstacle's motion based only on recent observations, via online
training of an LSTM neural network. Given such predictions, we define a
Nonlinear Probabilistic Velocity Obstacle (NPVO), which can be used select a
velocity that is collision free with a given probability. We take a step
towards formal verification of our approach, using statistical model checking
to approximate the probability that our system will mispredict an obstacle's
motion. Given such a probability, we prove upper bounds on the probability of
collision in multi-agent and reciprocal collision avoidance scenarios.
Furthermore, we demonstrate in simulation that our method avoids collisions
where state-of-the-art methods fail.
