Blender - An empty acts as a "force field" towards a group of objects.

blender_forcefield.py

import bpy
import mathutils
from random import randint

def my_handler(scene):
    # I couldn't register a class as handler or use global variables
    # so I'm using hidden empties as  global variables to store the
    # previous positions when required.
    old_loc_name = "old_empty"
    if old_loc_name not in bpy.data.objects:
        print("Creating new")
        o = bpy.data.objects.new(old_loc_name,None)
        # Uncomment if you want the empty to appear
        # in your scene manager. By default it's commented
        # to prevent it from becoming too cluttered.
        #bpy.context.scene.collection.objects.link(o)
    old_loc = bpy.data.objects[old_loc_name].location
    target = bpy.data.objects["Empty"].location # Get target's location
    bpy.data.objects[old_loc_name].location = target
    # Empty position changed
    # Check cubes to update them
    distance = 5
    move_inc = 0.3
    noise_factor = 0.4
    # Noise vector
    noise_vec = mathutils.Vector((randint(-1000,1000)/1000,randint(-1000,1000)/1000,randint(-1000,1000)/1000))*1
    # Affects every object that is a MESH and has 'Cube' in the name
    for cube in [x for x in bpy.data.objects if 'Cube' in x.name and x.type=="MESH"]:
        t_vec = cube.location-target
        origin_name = cube.name+"_origin"
        # Get the original position of this cube
        # or create a new empty for it if it doesn't already exist
        if origin_name not in bpy.data.objects:
            o = bpy.data.objects.new(origin_name,None)
            o.location = cube.location
            # Uncomment if you want the empty to appear
            # in your scene manager. By default it's commented
            # to prevent it from becoming too cluttered.
            #bpy.context.scene.collection.objects.link(o)
        else:
            o = bpy.data.objects[origin_name]
        o_vec = cube.location-o.location
        
        # If cube is in range of target, move to the opposite direction
        # else try to return to origins
        if t_vec.length < distance:
            t_vec_n = mathutils.Vector.normalized(t_vec)
            # Noise shift
            n_vec = (mathutils.Vector.orthogonal(t_vec_n)+noise_vec)*noise_factor
            cube.location += t_vec_n*move_inc+n_vec
        else:
            if o_vec.length > move_inc:
                o_vec_n = -mathutils.Vector.normalized(o_vec)*move_inc
                cube.location += o_vec_n

# Uncomment this if you need to clear every the cube's origins
"""
for o in bpy.data.objects:
    if '_origin' in o.name:
        bpy.data.objects.remove(o)
"""
bpy.app.handlers.frame_change_pre.clear()
bpy.app.handlers.frame_change_pre.append(my_handler)