How to make smooth movement in pygame

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You have a game loop, so use it. Just move the character by a certain position in each frame. For instance mov the character by step per frame:

step = 1

if x2 + step <= x:
    x2 += step
elif x2 - step >= x:
    x2 -= step
else:
    x2 = x

if y2 + step <= y:
    y2 += step
elif y2 - step >= y:
    y2 -= step
else:
    y2 = y

For a more sophisticated solution, you’ve to compute the Euclidean distance form the point to the target. Use pygame.math.Vector2 for the computation.

Compute the distance from between the follower and the sprite and the unit direction vector from (follower_x, follower_y) to (mainsprite_x, mainsprite_y). The Unit Vector can be computed by dividing the direction vector by the distance or by normalizing (normalize()) the direction vector:

target_vector = Vector2(mainsprite_x, mainsprite_y)
follower_vector = Vector2(follower_x, follower_y)

distance = follower_vector.distance_to(target_vector)
direction_vector = target_vector - follower_vector
if distance > 0:
    direction_vector /= distance

Now you can define an exact step_distance and move to follower int direction of the sprite:

if distance > 0:
    new_follower_vector = follower_vector + direction_vector * step_distance.

Define a maximum_distance and a minimum_distance. The minimum step distance is:

min_step = max(0, distance - maximum_distance)

The maximum step distance is

max_step = distance - minimum_distance

Put it all together:

minimum_distance    = 0
maximum_distance    = 10000
target_vector       = Vector2(mainsprite_x, mainsprite_y)
follower_vector     = Vector2(follower_x, follower_y)
new_follower_vector = Vector2(follower_x, follower_y)

distance = follower_vector.distance_to(target_vector)
if distance > minimum_distance:
    direction_vector    = (target_vector - follower_vector) / distance
    min_step            = max(0, distance - maximum_distance)
    max_step            = distance - minimum_distance
    step_distance       = min_step + (max_step - min_step) * LERP_FACTOR
    new_follower_vector = follower_vector + direction_vector * step_distance

Minimal example: repl.it/@Rabbid76/PyGame-FollowMouseSmoothly

import pygame

LERP_FACTOR      = 0.05
minimum_distance = 25
maximum_distance = 100

def FollowMe(pops, fpos):
    target_vector       = pygame.math.Vector2(*pops)
    follower_vector     = pygame.math.Vector2(*fpos)
    new_follower_vector = pygame.math.Vector2(*fpos)

    distance = follower_vector.distance_to(target_vector)
    if distance > minimum_distance:
        direction_vector    = (target_vector - follower_vector) / distance
        min_step            = max(0, distance - maximum_distance)
        max_step            = distance - minimum_distance
        step_distance       = min_step + (max_step - min_step) * LERP_FACTOR
        new_follower_vector = follower_vector + direction_vector * step_distance

    return (new_follower_vector.x, new_follower_vector.y) 

pygame.init()
window = pygame.display.set_mode((500, 500))
clock = pygame.time.Clock()

follower = (100, 100)
run = True
while run:
    clock.tick(60)
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            run = False

    player   = pygame.mouse.get_pos()
    follower = FollowMe(player, follower)

    window.fill(0)  
    pygame.draw.circle(window, (0, 0, 255), player, 10)
    pygame.draw.circle(window, (255, 0, 0), (round(follower[0]), round(follower[1])), 10)
    pygame.display.flip()

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