__credits__ = ["Carlos Luis"]
from os import path
from typing import Optional
import numpy as np
import gym
from gym import spaces
from gym.envs.classic_control import utils
from gym.error import DependencyNotInstalled
DEFAULT_X = np.pi
DEFAULT_Y = 1.0
class PendulumEnv(gym.Env):
"""
### Description
The inverted pendulum swingup problem is based on the classic problem in control theory.
The system consists of a pendulum attached at one end to a fixed point, and the other end being free.
The pendulum starts in a random position and the goal is to apply torque on the free end to swing it
into an upright position, with its center of gravity right above the fixed point.
The diagram below specifies the coordinate system used for the implementation of the pendulum's
dynamic equations.
- `x-y`: cartesian coordinates of the pendulum's end in meters.
- `theta` : angle in radians.
- `tau`: torque in `N m`. Defined as positive _counter-clockwise_.
### Action Space
The action is a `ndarray` with shape `(1,)` representing the torque applied to free end of the pendulum.
| Num | Action | Min | Max |
|-----|--------|------|-----|
| 0 | Torque | -2.0 | 2.0 |
### Observation Space
The observation is a `ndarray` with shape `(3,)` representing the x-y coordinates of the pendulum's free
end and its angular velocity.
| Num | Observation | Min | Max |
|-----|------------------|------|-----|
| 0 | x = cos(theta) | -1.0 | 1.0 |
| 1 | y = sin(theta) | -1.0 | 1.0 |
| 2 | Angular Velocity | -8.0 | 8.0 |
### Rewards
The reward function is defined as:
*r = -(theta2 + 0.1 * theta_dt2 + 0.001 * torque2)*
where `$\theta$` is the pendulum's angle normalized between *[-pi, pi]* (with 0 being in the upright position).
Based on the above equation, the minimum reward that can be obtained is
*-(pi2 + 0.1 * 82 + 0.001 * 22) = -16.2736044*,
while the maximum reward is zero (pendulum is upright with zero velocity and no torque applied).
### Starting State
The starting state is a random angle in *[-pi, pi]* and a random angular velocity in *[-1,1]*.
### Episode Truncation
The episode truncates at 200 time steps.
### Arguments
- `g`: acceleration of gravity measured in *(m s-2)* used to calculate the pendulum dynamics.
The default value is g = 10.0 .
```
gym.make('Pendulum-v1', g=9.81)
```
### Version History
* v1: Simplify the math equations, no difference in behavior.
* v0: Initial versions release (1.0.0)
"""
metadata = {
"render_modes": ["human", "rgb_array"],
"render_fps": 30,
}
def __init__(self, render_mode: Optional[str] = None, g=10.0):
self.max_speed = 8
self.max_torque = 2.0
self.dt = 0.05
self.g = g
self.m = 1.0
self.l = 1.0
self.render_mode = render_mode
self.screen_dim = 500
self.screen = None
self.clock = None
self.isopen = True
high = np.array([1.0, 1.0, self.max_speed], dtype=np.float32)
# This will throw a warning in tests/envs/test_envs in utils/env_checker.py as the space is not symmetric
# or normalised as max_torque == 2 by default. Ignoring the issue here as the default settings are too old
# to update to follow the openai gym api
self.action_space = spaces.Box(
low=-self.max_torque, high=self.max_torque, shape=(1,), dtype=np.float32
)
self.observation_space = spaces.Box(low=-high, high=high, dtype=np.float32)
def step(self, u):
th, thdot = self.state # th := theta
g = self.g
m = self.m
l = self.l
dt = self.dt
u = np.clip(u, -self.max_torque, self.max_torque)[0]
self.last_u = u # for rendering
costs = angle_normalize(th) ** 2 + 0.1 * thdot**2 + 0.001 * (u**2)
newthdot = thdot + (3 * g / (2 * l) * np.sin(th) + 3.0 / (m * l**2) * u) * dt
newthdot = np.clip(newthdot, -self.max_speed, self.max_speed)
newth = th + newthdot * dt
self.state = np.array([newth, newthdot])
if self.render_mode == "human":
self.render()
return self._get_obs(), -costs, False, False, {}
def reset(self, *, seed: Optional[int] = None, options: Optional[dict] = None):
super().reset(seed=seed)
if options is None:
high = np.array([DEFAULT_X, DEFAULT_Y])
else:
# Note that if you use custom reset bounds, it may lead to out-of-bound
# state/observations.
x = options.get("x_init") if "x_init" in options else DEFAULT_X
y = options.get("y_init") if "y_init" in options else DEFAULT_Y
x = utils.verify_number_and_cast(x)
y = utils.verify_number_and_cast(y)
high = np.array([x, y])
low = -high # We enforce symmetric limits.
self.state = self.np_random.uniform(low=low, high=high)
self.last_u = None
if self.render_mode == "human":
self.render()
return self._get_obs(), {}
def _get_obs(self):
theta, thetadot = self.state
return np.array([np.cos(theta), np.sin(theta), thetadot], dtype=np.float32)
def render(self):
if self.render_mode is None:
gym.logger.warn(
"You are calling render method without specifying any render mode. "
"You can specify the render_mode at initialization, "
f'e.g. gym("{self.spec.id}", render_mode="rgb_array")'
)
return
try:
import pygame
from pygame import gfxdraw
except ImportError:
raise DependencyNotInstalled(
"pygame is not installed, run `pip install gym[classic_control]`"
)
if self.screen is None:
pygame.init()
if self.render_mode == "human":
pygame.display.init()
self.screen = pygame.display.set_mode(
(self.screen_dim, self.screen_dim)
)
else: # mode in "rgb_array"
self.screen = pygame.Surface((self.screen_dim, self.screen_dim))
if self.clock is None:
self.clock = pygame.time.Clock()
self.surf = pygame.Surface((self.screen_dim, self.screen_dim))
self.surf.fill((255, 255, 255))
bound = 2.2
scale = self.screen_dim / (bound * 2)
offset = self.screen_dim // 2
rod_length = 1 * scale
rod_width = 0.2 * scale
l, r, t, b = 0, rod_length, rod_width / 2, -rod_width / 2
coords = [(l, b), (l, t), (r, t), (r, b)]
transformed_coords = []
for c in coords:
c = pygame.math.Vector2(c).rotate_rad(self.state[0] + np.pi / 2)
c = (c[0] + offset, c[1] + offset)
transformed_coords.append(c)
gfxdraw.aapolygon(self.surf, transformed_coords, (204, 77, 77))
gfxdraw.filled_polygon(self.surf, transformed_coords, (204, 77, 77))
gfxdraw.aacircle(self.surf, offset, offset, int(rod_width / 2), (204, 77, 77))
gfxdraw.filled_circle(
self.surf, offset, offset, int(rod_width / 2), (204, 77, 77)
)
rod_end = (rod_length, 0)
rod_end = pygame.math.Vector2(rod_end).rotate_rad(self.state[0] + np.pi / 2)
rod_end = (int(rod_end[0] + offset), int(rod_end[1] + offset))
gfxdraw.aacircle(
self.surf, rod_end[0], rod_end[1], int(rod_width / 2), (204, 77, 77)
)
gfxdraw.filled_circle(
self.surf, rod_end[0], rod_end[1], int(rod_width / 2), (204, 77, 77)
)
fname = path.join(path.dirname(__file__), "assets/clockwise.png")
img = pygame.image.load(fname)
if self.last_u is not None:
scale_img = pygame.transform.smoothscale(
img,
(scale * np.abs(self.last_u) / 2, scale * np.abs(self.last_u) / 2),
)
is_flip = bool(self.last_u > 0)
scale_img = pygame.transform.flip(scale_img, is_flip, True)
self.surf.blit(
scale_img,
(
offset - scale_img.get_rect().centerx,
offset - scale_img.get_rect().centery,
),
)
# drawing axle
gfxdraw.aacircle(self.surf, offset, offset, int(0.05 * scale), (0, 0, 0))
gfxdraw.filled_circle(self.surf, offset, offset, int(0.05 * scale), (0, 0, 0))
self.surf = pygame.transform.flip(self.surf, False, True)
self.screen.blit(self.surf, (0, 0))
if self.render_mode == "human":
pygame.event.pump()
self.clock.tick(self.metadata["render_fps"])
pygame.display.flip()
else: # mode == "rgb_array":
return np.transpose(
np.array(pygame.surfarray.pixels3d(self.screen)), axes=(1, 0, 2)
)
def close(self):
if self.screen is not None:
import pygame
pygame.display.quit()
pygame.quit()
self.isopen = False
def angle_normalize(x):
return ((x + np.pi) % (2 * np.pi)) - np.pi