CAD tip # 13221:

You can choose to "round" the geometric features (coordinates) to a fixed grid (e.g. 0.5 units) if they are within a specified tolerance (e.g. 0.01 units) around this grid, or you can snap to existing points within the specified tolerance.

Download the Attractor utility from Download, load it into your AutoCAD with APPLOAD a type the ATTRACTOR command. Select the grid rounding value or select existing "attractor" objects (resp. their points) to fix to (POINT, LINE, INSERT, LWPOLYLINE, POLYLINE, CIRCLE). You can also select previous attractors or all objects in a picked layer. Specify the tolerance (i.e. maximum distance where the points still will be snapped, attractor radius) and select the objects to be modified ("rounded", attracted) - of the type: POINT, LINE, INSERT, LWPOLYLINE, POLYLINE, ARC, CIRCLE, ELLIPSE, TEXT, MTEXT.

See an example where the symbols are being attracted to orange points in a circular array and to the vertices of the orange polyline. And on the other hand the cyan polyline is being snapped to the symbols.