Solution: According to the meaning of the question, set A represents a set of points in a series of circles, and set B represents a set of straight lines. In order to make two sets not empty, a straight line needs to intersect with a circle, from which m≤0 or m≥ 1/2 can be obtained.

When m≤0, there is [(2-2m)/√ 2] > -m and [(2-2m-1)/√ 2] > _ m；

There are [√ 2 _ √ 2m] > _m，√2/2 _√2m & gt； _m，

If m≤0, then 2 > 2m+ 1, A∩B=? ,

When m≥ 1/2, there are |2-2m/√2|≤m or | 2-2m-1√ 2 |≤ m,

The solution is: 2-√2≤m≤2+√2, 1-√2/2≤m≤ 1+√2/2,

If m≥ 12, the range of m is [1/2,2+√ 2];

The comprehensive range of m is [1/2,2+√ 2];

So the answer is [1/2,2+√ 2]