Best way to sync animation and movement?

I am relatively new to Unity - I have used it the past couple summers for research at my university, and so I'm not sure if this topic is over my head, or if there is a (relatively) simple way to implement animation/movement synchronization on a character. I have done a fair share of research and haven't found anything too groundbreaking, but maybe I just don't know what to search for.

I created a solution that works, but will not work for physics/collision calculations. The basic algorithm for my walk animation sync (the animation has no root transformation) is to update the position of the character so that whichever foot is on the ground has its bone position remain constant while the character moves essentially the negative Vector3 of the Vector3 which the bone is moving.

This solution is very simple, but I know that once the character begins moving into walls, things will get complicated. Would an appropriate solution be to simply Raycast to prevent the character moving into/through objects, or am I completely on the wrong track with this?

Thanks a lot!

-Paul