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 multiagent and reciprocal collision avoidance scenarios. Furthermore, we demonstrate in simulation that our method avoids collisions where state-of-the-art methods fail.
In this paper, we present a formal approach to reciprocal n-body collision avoidance, where multiple mobile robots need to avoid collisions with each other while moving in a common workspace. In our formulation, each robot acts fully independently, and does not communicate with other robots. Based on the definition of velocity obstacles [5], we derive sufficient conditions for collision-free motion by reducing the problem to solving a low-dimensional linear program. We test our approach on several dense and complex simulation scenarios involving thousands of robots and compute collision-free actions for all of them in only a few milliseconds. To the best of our knowledge, this method is the first that can guarantee local collision-free motion for a large number of robots in a cluttered workspace.