How does the undo operation work?

Question

I have a for loop that each time it will move or rotate several objects randomly, if some conditions not satisfied, it will undo all operations.

for obj in group_obj.objects:
            move_rotate(obj, T, T_0)

            accessableArea(obj)
        
        new_c = total_cost(group_obj)
        if i == 0:
            old_c = c_0
        if Metropolis(old_c, new_c):
            old_c = new_c
        else:
            for i in range(len(group_obj.objects)):
                bpy.ops.ed.undo()

This is move & rotate function

def move_rotate(object, T, T_0):
"""
Description:move and rotate object randomly

"""
if len(object.name.split("_")) < 3:

    std = math.sqrt(T/10)
    m = np.random.normal(0, std, 1)
    if np.random.randint(2):
        object.location.x += m
    else:
        object.location.y += m
    # rootate
    std = math.pi * (T/T_0)
    r = np.random.normal(0, std, 1)
    object.rotation_euler.z += r

It will report this error

RuntimeError: Operator bpy.ops.ed.undo.poll() failed, context is incorrect

Another question is, it seems blneder considered all operations down by script as one operation, Each time I run over the script press undo the sence will return to origin instead of last step.

Update: Based on @X Y's answer, I made some improvement:

while T > T_F:
    for i in range(num):
        count = 0
        for obj in group.objects:
            bpy.ops.ed.undo_push()
            # repeat move&rotate until it won't cross the wall
            while True:
                
                move_rotate(obj, T, T_0)

                if check_if_cross_wall(obj):
                    bpy.ops.ed.undo()
                    continue

                break
                

            count += 1
            accessableArea(obj)
        
        new_c = total_cost(group)
        if i == 0:
            old_c = c_0
        if Metropolis(old_c, new_c):
            old_c = new_c
        else:
            bpy.ops.ed.undo()

    T = T * alpha

move & rotate function keep it as is.

report StructRNA of type Object has been removed.

Answer 1

Create a Restore point

import bpy

# make sure it has a active object
bpy.context.object.location.x += 1

bpy.ops.ed.undo_push(message = "Restore point 1")

bpy.context.object.location.x += 2

bpy.ops.ed.undo_push(message = "Restore point 2")


# restore part, use interface or run bpy.ops
def UNDO():
    try:
        bpy.ops.ed.undo()
        print("success")
    except:
        print("fail")

# undo 1 step
UNDO()
# because click to run script also create a store point
# so, Restore point 2 is gone!

Fix ReferenceError

import bpy

def UNDO():
    try:
        bpy.ops.ed.undo()
        print("success")
    except:
        print("fail")


bpy.ops.ed.undo_push(message = "Restore point 1")
obj = bpy.data.objects["Cube"]
obj.location.x += 1

UNDO()
print(obj) # obj cannot be used anymore (after undo)
# so need get the object again
obj = bpy.data.objects["Cube"]
print(obj.name)