I have n objects in 3D space and the same amount of target locations. I need to find a way to assign targets to each object and route them without collisions. It doesn't matter, which object goes to which target, just that there is only one for each target. No static obstacles in the space.
I've created a few algorithms for target selection, playing with graph theory (which I don't fully understand), Hopcroft Karp and others. I have kinda ok algorithm, but I'm not sure it's nearly optimal. I would consider it optimal, if it minimizes the largest distance. My current one minimizes total travel for all objects.
The objects start from standstill and move simultaneously. They can wait and move with different speeds, but max speed is set. To simplify the problem, I am happy with a solution with (near)constant speeds.
I've looked at A* and some of the classics, but so far I haven't found a workable one. Perhaps I'm misunderstanding something. My ideal solution would assign minimum number of waypoints with direct lines in between.
I think this is an NP problem, so I'm not after the optimal solution. I also don't have memory or computation time constraints. I'd be ecstatic to find something ready in Python, but I'd be happy for just algorithms or pointers.
To summarize: How to route n objects with max speeds to n targets in a way that avoids collisions. Preferably finding a solution with minimum total travel time.
I've tried some home-cooked algorithms and googled far and wide, but nothing seems to quite fit.
