Storing a 2d topdown map as integer or float matrix

Hi.

Im implementing a 2d topdown strategy game and consider storing the map as either a integer or floating matrix.
Storing it as an integer matrix would be easier for pathfinding and collision detection:

example (1 beeing walls and 0 being walkable path of tiles 32x32 pixels):


1,1,1,1,
1,0,0,1,
0,1,0,0

The drawback with integer is that the movement of the characters won’t be that smooth as with floating point. With floating point I could move the creatures 1-2 pixels, but using int, it would move 1 tile at a time which is 32 pixels)
Preferably I want to use float for the movement of the creatures but I think it will be more complex with both pathfinding and collision detection using float for the coordinates.

What do you suggest. Is it possible to mix the integer coordinate system for pathfinding but still use the float for smooth movement and positioning?