I've decided to implement my own algorithm for optimal reciprocal collision avoidance. It doesn't use linear programming, but iteratively projects velocity on intersections of ORCA lines and checks if it is collision-free. It works great for relatively slow units, but fast units tend to stop under certain circumstances.
The problem arises when there are two or more obstacles with the same velocity, and their velocity obstacles are intersecting with each other, and the goal velocity is inside the both velocity obstacles, and the goal velocity is close to the edges of both of the velocity obstacles rather than …
