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Deterministic Pathfinding

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Hello, I currently am working on a multiplayer RTS (using lockstep), and now am stuck with local avoidance in pathfinding. How is it managed to calculate the paths of dozens of units without bumping into each other? Pathfinding itself is working like a charm (with lockstep principles used), but my units have no collision to each other so far, so they can run through other units. Every solution I have seen so far is using physic-collision with rigidbodys. But I don't want to have this solved by a physics engine I don't trust to be deterministic, so I need some kind of algorithm. I checked out "A* Pathfinding Project" and "Simple Path", which are working well without avoidance, but I don't know how to add code/alter code to make the collision detection non-physical. Am i missing something basically here?

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