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i might be talking completely out of my butt here, i'm certainly out of my depth anyhow. however, jim what you are explaining about your problem sounds massively complex and almost infinite of avoidance of collisions.
you may have already been down this route, and please do excuse my lack of knowledge in this field but, is it at all possible to break these functions down.
based on object going from a to b, could something be achieved by looking at the objects current position and looking at it's immediate available movement and positions possible for maybe a certain amount of moves/time? basically in steps breaking the whole process down into more managable segments. so maybe at a certain time object 'a' could only be a certain place while object 'b' could be a certain other place avoiding all possibilities of collision of object 'a' within this certain time frame/amount of moves?
did that make any sense to anyone? sorry for my basic talk, as u can see i'm not technical in this side of things lol.
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