example of smooth moving over a grid in pygame

pygame_move_smooth.py

import sys
import pygame
import math
from pygame.locals import *


TILE_SIZE = 32
WIDTH = 32 * 20
HEIGHT = 32 * 10

BLACK = Color(0, 0, 0)
BLUE = Color(0, 0, 200)

playerLocation = [10, 5]

pygame.init()
screen = pygame.display.set_mode([WIDTH, HEIGHT])
offset = 0.0

IS_MOVING = False
MOVE_SPEED = 1

while 1:
	for event in pygame.event.get():
		if event.type == pygame.QUIT:
			sys.exit()
		if event.type == pygame.KEYDOWN and not IS_MOVING:
			if event.key == K_ESCAPE:
				sys.exit()
			elif event.key == K_LEFT:
				IS_MOVING = True
				currentMovePosition = [playerLocation[0] * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				targetMovePosition = [(playerLocation[0] - 1) * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				moveIncrement = [MOVE_SPEED * -1, 0]
			elif event.key == K_RIGHT:
				IS_MOVING = True
				currentMovePosition = [playerLocation[0] * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				targetMovePosition = [(playerLocation[0] + 1) * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				moveIncrement = [MOVE_SPEED, 0]
			elif event.key == K_DOWN:
				IS_MOVING = True
				currentMovePosition = [playerLocation[0] * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				targetMovePosition = [playerLocation[0] * TILE_SIZE, (playerLocation[1] + 1) * TILE_SIZE]
				moveIncrement = [0, MOVE_SPEED]
			elif event.key == K_UP:
				IS_MOVING = True
				currentMovePosition = [playerLocation[0] * TILE_SIZE, playerLocation[1] * TILE_SIZE]
				targetMovePosition = [playerLocation[0] * TILE_SIZE, (playerLocation[1] - 1) * TILE_SIZE]
				moveIncrement = [0, MOVE_SPEED * -1]

	if IS_MOVING:
		currentMovePosition[0] += moveIncrement[0]
		currentMovePosition[1] += moveIncrement[1]
		if currentMovePosition[0] == targetMovePosition[0] and currentMovePosition[1] == targetMovePosition[1]:
			IS_MOVING = False
			playerLocation[0] = targetMovePosition[0] / TILE_SIZE
			playerLocation[1] = targetMovePosition[1] / TILE_SIZE

		playerPos = Rect(currentMovePosition[0], currentMovePosition[1], TILE_SIZE, TILE_SIZE)
	else:
		playerPos = Rect(playerLocation[0] * TILE_SIZE, playerLocation[1] * TILE_SIZE, TILE_SIZE, TILE_SIZE)


	screen.fill(BLACK)
	pygame.draw.rect(screen, BLUE, playerPos)

	pygame.display.flip()
	pygame.time.wait(10)