Gymnasium/gym/envs/classic_control/cartpole.py

"""
Classic cart-pole system implemented by Rich Sutton et al.
Copied from http://incompleteideas.net/sutton/book/code/pole.c
permalink: https://perma.cc/C9ZM-652R
"""
import math
from typing import Optional, Union

import numpy as np
import pygame
from pygame import gfxdraw

import gym
from gym import spaces, logger
from gym.utils import seeding


class CartPoleEnv(gym.Env[np.ndarray, Union[int, np.ndarray]]):
    """
    ### Description
    This environment corresponds to the version of the cart-pole problem
    described by Barto, Sutton, and Anderson in ["Neuronlike Adaptive Elements That Can Solve Difficult Learning Control Problem"](https://ieeexplore.ieee.org/document/6313077).
    A pole is attached by an un-actuated joint to a cart, which moves along a
    frictionless track. The pendulum starts upright, and the goal is to prevent
    it from falling over by increasing and reducing the cart's velocity.

    ### Action Space
    The agent take a 1-element vector for actions.
    The action space is `(action)` in `[0, 1]`, where `action` is used to push
    the cart with a fixed amount of force:

    | Num | Action                 |
    |-----|------------------------|
    | 0   | Push cart to the left  |
    | 1   | Push cart to the right |

    Note: The amount the velocity is reduced or increased is not fixed as it depends on the angle the pole is pointing.
    This is because the center of gravity of the pole increases the amount of energy needed to move the cart underneath it

    ### Observation Space
    The observation is a `ndarray` with shape `(4,)` where the elements correspond to the following:

    | Num | Observation           | Min                  | Max                |
    |-----|-----------------------|----------------------|--------------------|
    | 0   | Cart Position         | -4.8*                 | 4.8*                |
    | 1   | Cart Velocity         | -Inf                 | Inf                |
    | 2   | Pole Angle            | ~ -0.418 rad (-24°)** | ~ 0.418 rad (24°)** |
    | 3   | Pole Angular Velocity | -Inf                 | Inf                |

    **Note:** above denotes the ranges of possible observations for each element, but in two cases this range exceeds the
    range of possible values in an un-terminated episode:
    - `*`: the cart x-position can be observed between `(-4.8, 4.8)`, but an episode terminates if the cart leaves the
    `(-2.4, 2.4)` range.
    - `**`: Similarly, the pole angle can be observed between  `(-.418, .418)` radians or precisely **±24°**, but an episode is
    terminated if the pole angle is outside the `(-.2095, .2095)` range or precisely **±12°**

    ### Rewards
    Reward is 1 for every step taken, including the termination step. The threshold is 475 for v1.

    ### Starting State
    All observations are assigned a uniform random value between (-0.05, 0.05)

    ### Episode Termination
    The episode terminates of one of the following occurs:

    1. Pole Angle is more than ±12°
    2. Cart Position is more than ±2.4 (center of the cart reaches the edge of the display)
    3. Episode length is greater than 500 (200 for v0)

    ### Arguments

    No additional arguments are currently supported.
    """

    metadata = {"render.modes": ["human", "rgb_array"], "video.frames_per_second": 50}

    def __init__(self):
        self.gravity = 9.8
        self.masscart = 1.0
        self.masspole = 0.1
        self.total_mass = self.masspole + self.masscart
        self.length = 0.5  # actually half the pole's length
        self.polemass_length = self.masspole * self.length
        self.force_mag = 10.0
        self.tau = 0.02  # seconds between state updates
        self.kinematics_integrator = "euler"

        # Angle at which to fail the episode
        self.theta_threshold_radians = 12 * 2 * math.pi / 360
        self.x_threshold = 2.4

        # Angle limit set to 2 * theta_threshold_radians so failing observation
        # is still within bounds.
        high = np.array(
            [
                self.x_threshold * 2,
                np.finfo(np.float32).max,
                self.theta_threshold_radians * 2,
                np.finfo(np.float32).max,
            ],
            dtype=np.float32,
        )

        self.action_space = spaces.Discrete(2)
        self.observation_space = spaces.Box(-high, high, dtype=np.float32)

        self.screen = None
        self.isopen = True
        self.state = None

        self.steps_beyond_done = None

    def step(self, action):
        err_msg = f"{action!r} ({type(action)}) invalid"
        assert self.action_space.contains(action), err_msg
        assert self.state is not None, "Call reset before using step method."
        x, x_dot, theta, theta_dot = self.state
        force = self.force_mag if action == 1 else -self.force_mag
        costheta = math.cos(theta)
        sintheta = math.sin(theta)

        # For the interested reader:
        # https://coneural.org/florian/papers/05_cart_pole.pdf
        temp = (
            force + self.polemass_length * theta_dot ** 2 * sintheta
        ) / self.total_mass
        thetaacc = (self.gravity * sintheta - costheta * temp) / (
            self.length * (4.0 / 3.0 - self.masspole * costheta ** 2 / self.total_mass)
        )
        xacc = temp - self.polemass_length * thetaacc * costheta / self.total_mass

        if self.kinematics_integrator == "euler":
            x = x + self.tau * x_dot
            x_dot = x_dot + self.tau * xacc
            theta = theta + self.tau * theta_dot
            theta_dot = theta_dot + self.tau * thetaacc
        else:  # semi-implicit euler
            x_dot = x_dot + self.tau * xacc
            x = x + self.tau * x_dot
            theta_dot = theta_dot + self.tau * thetaacc
            theta = theta + self.tau * theta_dot

        self.state = (x, x_dot, theta, theta_dot)

        done = bool(
            x < -self.x_threshold
            or x > self.x_threshold
            or theta < -self.theta_threshold_radians
            or theta > self.theta_threshold_radians
        )

        if not done:
            reward = 1.0
        elif self.steps_beyond_done is None:
            # Pole just fell!
            self.steps_beyond_done = 0
            reward = 1.0
        else:
            if self.steps_beyond_done == 0:
                logger.warn(
                    "You are calling 'step()' even though this "
                    "environment has already returned done = True. You "
                    "should always call 'reset()' once you receive 'done = "
                    "True' -- any further steps are undefined behavior."
                )
            self.steps_beyond_done += 1
            reward = 0.0

        return np.array(self.state, dtype=np.float32), reward, done, {}

    def reset(
        self,
        *,
        seed: Optional[int] = None,
        return_info: bool = False,
        options: Optional[dict] = None,
    ):
        super().reset(seed=seed)
        self.state = self.np_random.uniform(low=-0.05, high=0.05, size=(4,))
        self.steps_beyond_done = None
        if not return_info:
            return np.array(self.state, dtype=np.float32)
        else:
            return np.array(self.state, dtype=np.float32), {}

    def render(self, mode="human"):
        screen_width = 600
        screen_height = 400

        world_width = self.x_threshold * 2
        scale = screen_width / world_width
        polewidth = 10.0
        polelen = scale * (2 * self.length)
        cartwidth = 50.0
        cartheight = 30.0

        x = self.state

        if self.screen is None:
            pygame.init()
            self.screen = pygame.display.set_mode((screen_width, screen_height))
        self.surf = pygame.Surface((screen_width, screen_height))
        self.surf.fill((255, 255, 255))

        l, r, t, b = -cartwidth / 2, cartwidth / 2, cartheight / 2, -cartheight / 2
        axleoffset = cartheight / 4.0
        cartx = x[0] * scale + screen_width / 2.0  # MIDDLE OF CART
        carty = 100  # TOP OF CART
        cart_coords = [(l, b), (l, t), (r, t), (r, b)]
        cart_coords = [(c[0] + cartx, c[1] + carty) for c in cart_coords]
        gfxdraw.aapolygon(self.surf, cart_coords, (0, 0, 0))
        gfxdraw.filled_polygon(self.surf, cart_coords, (0, 0, 0))

        l, r, t, b = (
            -polewidth / 2,
            polewidth / 2,
            polelen - polewidth / 2,
            -polewidth / 2,
        )

        pole_coords = []
        for coord in [(l, b), (l, t), (r, t), (r, b)]:
            coord = pygame.math.Vector2(coord).rotate_rad(-x[2])
            coord = (coord[0] + cartx, coord[1] + carty + axleoffset)
            pole_coords.append(coord)
        gfxdraw.aapolygon(self.surf, pole_coords, (202, 152, 101))
        gfxdraw.filled_polygon(self.surf, pole_coords, (202, 152, 101))

        gfxdraw.aacircle(
            self.surf,
            int(cartx),
            int(carty + axleoffset),
            int(polewidth / 2),
            (129, 132, 203),
        )
        gfxdraw.filled_circle(
            self.surf,
            int(cartx),
            int(carty + axleoffset),
            int(polewidth / 2),
            (129, 132, 203),
        )

        gfxdraw.hline(self.surf, 0, screen_width, carty, (0, 0, 0))

        self.surf = pygame.transform.flip(self.surf, False, True)
        self.screen.blit(self.surf, (0, 0))
        if mode == "human":
            pygame.display.flip()

        if mode == "rgb_array":
            return np.transpose(
                np.array(pygame.surfarray.pixels3d(self.screen)), axes=(1, 0, 2)
            )
        else:
            return self.isopen

    def close(self):
        if self.screen is not None:
            pygame.quit()
            self.isopen = False