class CartPole(Environment):
"""
The Inverted Pendulum on a Cart environment as presented in:
"Least-Squares Policy Iteration". Lagoudakis M. G. and Parr R.. 2003.
"""
def __init__(self,
m=2.,
M=8.,
l=.5,
g=9.8,
mu=1e-2,
max_u=50.,
noise_u=10.,
horizon=3000,
gamma=.95):
"""
Constructor.
Args:
m (float, 2.0): mass of the pendulum;
M (float, 8.0): mass of the cart;
l (float, .5): length of the pendulum;
g (float, 9.8): gravity acceleration constant;
max_u (float, 50.): maximum allowed input torque;
noise_u (float, 10.): maximum noise on the action;
horizon (int, 3000): horizon of the problem;
gamma (float, .95): discount factor.
"""
# MDP parameters
self._m = m
self._M = M
self._l = l
self._g = g
self._alpha = 1 / (self._m + self._M)
self._mu = mu
self._dt = .1
self._max_u = max_u
self._noise_u = noise_u
high = np.array([np.inf, np.inf])
# MDP properties
observation_space = spaces.Box(low=-high, high=high)
action_space = spaces.Discrete(3)
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
self._viewer = Viewer(2.5 * l, 2.5 * l)
self._last_u = None
self._state = None
super().__init__(mdp_info)
def reset(self, state=None):
if state is None:
angle = np.random.uniform(-np.pi / 8., np.pi / 8.)
self._state = np.array([angle, 0.])
else:
self._state = state
self._state[0] = normalize_angle(self._state[0])
self._last_u = 0
return self._state
def step(self, action):
if action == 0:
u = -self._max_u
elif action == 1:
u = 0.
else:
u = self._max_u
self._last_u = u
u += np.random.uniform(-self._noise_u, self._noise_u)
new_state = odeint(self._dynamics, self._state, [0, self._dt], (u, ))
self._state = np.array(new_state[-1])
self._state[0] = normalize_angle(self._state[0])
if np.abs(self._state[0]) > np.pi * .5:
reward = -1.
absorbing = True
else:
reward = 0.
absorbing = False
return self._state, reward, absorbing, {}
def render(self, mode='human'):
start = 1.25 * self._l * np.ones(2)
end = 1.25 * self._l * np.ones(2)
end[0] += self._l * np.sin(self._state[0])
end[1] += self._l * np.cos(self._state[0])
self._viewer.line(start, end)
self._viewer.square(start, 0, self._l / 10)
self._viewer.circle(end, self._l / 20)
direction = -np.sign(self._last_u) * np.array([1, 0])
value = np.abs(self._last_u)
self._viewer.force_arrow(start, direction, value, self._max_u,
self._l / 5)
self._viewer.display(self._dt)
def stop(self):
self._viewer.close()
def _dynamics(self, state, t, u):
theta = state[0]
omega = state[1]
d_theta = omega
d_omega = (self._g * np.sin(theta) - self._alpha * self._m * self._l *
.5 * d_theta**2 * np.sin(2 * theta) * .5 -
self._alpha * np.cos(theta) * u) / (
2 / 3 * self._l -
self._alpha * self._m * self._l * .5 * np.cos(theta)**2)
return d_theta, d_omega
class PuddleWorld(Environment):
"""
Puddle world as presented in:
"Off-Policy Actor-Critic". Degris T. et al.. 2012.
"""
def __init__(self, start=None, goal=None, goal_threshold=.1, noise_step=.025,
noise_reward=0, reward_goal=0., thrust=.05, puddle_center=None,
puddle_width=None, gamma=.99, horizon=5000):
"""
Constructor.
Args:
start (np.array, None): starting position of the agent;
goal (np.array, None): goal position;
goal_threshold (float, .1): distance threshold of the agent from the
goal to consider it reached;
noise_step (float, .025): noise in actions;
noise_reward (float, 0): standard deviation of gaussian noise in reward;
reward_goal (float, 0): reward obtained reaching goal state;
thrust (float, .05): distance walked during each action;
puddle_center (np.array, None): center of the puddle;
puddle_width (np.array, None): width of the puddle;
"""
# MDP parameters
self._start = np.array([.2, .4]) if start is None else start
self._goal = np.array([1., 1.]) if goal is None else goal
self._goal_threshold = goal_threshold
self._noise_step = noise_step
self._noise_reward = noise_reward
self._reward_goal = reward_goal
self._thrust = thrust
puddle_center = [[.3, .6], [.4, .5], [.8, .9]] if puddle_center is None else puddle_center
self._puddle_center = [np.array(center) for center in puddle_center]
puddle_width = [[.1, .03], [.03, .1], [.03, .1]] if puddle_width is None else puddle_width
self._puddle_width = [np.array(width) for width in puddle_width]
self._actions = [np.zeros(2) for _ in range(5)]
for i in range(4):
self._actions[i][i // 2] = thrust * (i % 2 * 2 - 1)
# MDP properties
action_space = Discrete(5)
observation_space = Box(0., 1., shape=(2,))
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
self._pixels = None
self._viewer = Viewer(1.0, 1.0)
super().__init__(mdp_info)
def reset(self, state=None):
if state is None:
self._state = self._start.copy()
else:
self._state = state
return self._state
def step(self, action):
idx = action[0]
self._state += self._actions[idx] + np.random.uniform(
low=-self._noise_step, high=self._noise_step, size=(2,))
self._state = np.clip(self._state, 0., 1.)
absorbing = np.linalg.norm((self._state - self._goal),
ord=1) < self._goal_threshold
if not absorbing:
reward = np.random.randn() * self._noise_reward + self._get_reward(
self._state)
else:
reward = self._reward_goal
return self._state, reward, absorbing, {}
def render(self):
if self._pixels is None:
img_size = 100
pixels = np.zeros((img_size, img_size, 3))
for i in range(img_size):
for j in range(img_size):
x = i / img_size
y = j / img_size
pixels[i, img_size - 1 - j] = self._get_reward(
np.array([x, y]))
pixels -= pixels.min()
pixels *= 255. / pixels.max()
self._pixels = np.floor(255 - pixels)
self._viewer.background_image(self._pixels)
self._viewer.circle(self._state, 0.01,
color=(0, 255, 0))
goal_area = [
[-self._goal_threshold, 0],
[0, self._goal_threshold],
[self._goal_threshold, 0],
[0, -self._goal_threshold]
]
self._viewer.polygon(self._goal, 0, goal_area,
color=(255, 0, 0), width=1)
self._viewer.display(0.1)
def stop(self):
if self._viewer is not None:
self._viewer.close()
def _get_reward(self, state):
reward = -1.
for cen, wid in zip(self._puddle_center, self._puddle_width):
reward -= 2. * norm.pdf(state[0], cen[0], wid[0]) * norm.pdf(
state[1], cen[1], wid[1])
return reward
class AbstractGridWorld(Environment):
"""
Abstract class to build a grid world.
"""
def __init__(self, mdp_info, height, width, start, goal):
"""
Constructor.
Args:
height (int): height of the grid;
width (int): width of the grid;
start (tuple): x-y coordinates of the goal;
goal (tuple): x-y coordinates of the goal.
"""
assert not np.array_equal(start, goal)
assert goal[0] < height and goal[1] < width,\
'Goal position not suitable for the grid world dimension.'
self._state = None
self._height = height
self._width = width
self._start = start
self._goal = goal
# Visualization
self._viewer = Viewer(self._width, self._height, 500,
self._height * 500 // self._width)
super().__init__(mdp_info)
def reset(self, state=None):
if state is None:
state = self.convert_to_int(self._start, self._width)
self._state = state
return self._state
def step(self, action):
state = self.convert_to_grid(self._state, self._width)
new_state, reward, absorbing, info = self._step(state, action)
self._state = self.convert_to_int(new_state, self._width)
return self._state, reward, absorbing, info
def render(self):
for row in range(1, self._height):
for col in range(1, self._width):
self._viewer.line(np.array([col, 0]),
np.array([col, self._height]))
self._viewer.line(np.array([0, row]),
np.array([self._width, row]))
goal_center = np.array(
[.5 + self._goal[1], self._height - (.5 + self._goal[0])])
self._viewer.square(goal_center, 0, 1, (0, 255, 0))
start_grid = self.convert_to_grid(self._start, self._width)
start_center = np.array(
[.5 + start_grid[1], self._height - (.5 + start_grid[0])])
self._viewer.square(start_center, 0, 1, (255, 0, 0))
state_grid = self.convert_to_grid(self._state, self._width)
state_center = np.array(
[.5 + state_grid[1], self._height - (.5 + state_grid[0])])
self._viewer.circle(state_center, .4, (0, 0, 255))
self._viewer.display(.1)
def _step(self, state, action):
raise NotImplementedError('AbstractGridWorld is an abstract class.')
def _grid_step(self, state, action):
if action == 0:
if state[0] > 0:
state[0] -= 1
elif action == 1:
if state[0] + 1 < self._height:
state[0] += 1
elif action == 2:
if state[1] > 0:
state[1] -= 1
elif action == 3:
if state[1] + 1 < self._width:
state[1] += 1
@staticmethod
def convert_to_grid(state, width):
return np.array([state[0] // width, state[0] % width])
@staticmethod
def convert_to_int(state, width):
return np.array([state[0] * width + state[1]])
class Segway(Environment):
"""
The Segway environment (continuous version) as presented in:
"Deep Learning for Actor-Critic Reinforcement Learning". Xueli Jia. 2015.
"""
def __init__(self, random_start=False):
"""
Constructor.
Args:
random_start (bool, False): whether to start from a random position
or from the horizontal one.
"""
# MDP parameters
gamma = 0.97
self._Mr = 0.3 * 2
self._Mp = 2.55
self._Ip = 2.6e-2
self._Ir = 4.54e-4 * 2
self._l = 13.8e-2
self._r = 5.5e-2
self._dt = 1e-2
self._g = 9.81
self._max_u = 5
self._random = random_start
high = np.array([-np.pi / 2, 15, 75])
# MDP properties
observation_space = spaces.Box(low=-high, high=high)
action_space = spaces.Box(low=np.array([-self._max_u]),
high=np.array([self._max_u]))
horizon = 300
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
self._viewer = Viewer(5 * self._l, 5 * self._l)
self._last_x = 0
super().__init__(mdp_info)
def reset(self, state=None):
if state is None:
if self._random:
angle = np.random.uniform(-np.pi / 2, np.pi / 2)
else:
angle = -np.pi / 8
self._state = np.array([angle, 0., 0.])
else:
self._state = state
self._state[0] = normalize_angle(self._state[0])
self._last_x = 0
return self._state
def step(self, action):
u = self._bound(action[0], -self._max_u, self._max_u)
new_state = odeint(self._dynamics, self._state, [0, self._dt], (u, ))
self._state = np.array(new_state[-1])
self._state[0] = normalize_angle(self._state[0])
if abs(self._state[0]) > np.pi / 2:
absorbing = True
reward = -10000
else:
absorbing = False
Q = np.diag([3.0, 0.1, 0.1])
x = self._state
J = x.dot(Q).dot(x)
reward = -J
return self._state, reward, absorbing, {}
def _dynamics(self, state, t, u):
alpha = state[0]
d_alpha = state[1]
h1 = (self._Mr + self._Mp) * (self._r**2) + self._Ir
h2 = self._Mp * self._r * self._l * np.cos(alpha)
h3 = self._l**2 * self._Mp + self._Ip
omegaP = d_alpha
dOmegaP = -(h2 * self._l * self._Mp * self._r * np.sin(alpha) * omegaP
**2 - self._g * h1 * self._l * self._Mp * np.sin(alpha) +
(h2 + h1) * u) / (h1 * h3 - h2**2)
dOmegaR = (
h3 * self._l * self._Mp * self._r * np.sin(alpha) * omegaP**2 -
self._g * h2 * self._l * self._Mp * np.sin(alpha) +
(h3 + h2) * u) / (h1 * h3 - h2**2)
dx = list()
dx.append(omegaP)
dx.append(dOmegaP)
dx.append(dOmegaR)
return dx
def render(self, mode='human'):
start = 2.5 * self._l * np.ones(2)
end = 2.5 * self._l * np.ones(2)
dx = -self._state[2] * self._r * self._dt
self._last_x += dx
if self._last_x > 2.5 * self._l or self._last_x < -2.5 * self._l:
self._last_x = (2.5 * self._l +
self._last_x) % (5 * self._l) - 2.5 * self._l
start[0] += self._last_x
end[0] += -2 * self._l * np.sin(self._state[0]) + self._last_x
end[1] += 2 * self._l * np.cos(self._state[0])
if (start[0] > 5 * self._l and end[0] > 5 * self._l) \
or (start[0] < 0 and end[0] < 0):
start[0] = start[0] % 5 * self._l
end[0] = end[0] % 5 * self._l
self._viewer.line(start, end)
self._viewer.circle(start, self._r)
self._viewer.display(self._dt)
class InvertedPendulum(Environment):
"""
The Inverted Pendulum environment (continuous version) as presented in:
"Reinforcement Learning In Continuous Time and Space". Doya K.. 2000.
"Off-Policy Actor-Critic". Degris T. et al.. 2012.
"Deterministic Policy Gradient Algorithms". Silver D. et al. 2014.
"""
def __init__(self, random_start=False, m=1., l=1., g=9.8, mu=1e-2,
max_u=5., horizon=5000, gamma=.99):
"""
Constructor.
Args:
random_start (bool, False): whether to start from a random position
or from the horizontal one;
m (float, 1.0): mass of the pendulum;
l (float, 1.0): length of the pendulum;
g (float, 9.8): gravity acceleration constant;
mu (float, 1e-2): friction constant of the pendulum;
max_u (float, 5.0): maximum allowed input torque;
horizon (int, 5000): horizon of the problem;
gamma (int, .99): discount factor.
"""
# MDP parameters
self._m = m
self._l = l
self._g = g
self._mu = mu
self._random = random_start
self._dt = .01
self._max_u = max_u
self._max_omega = 5 / 2 * np.pi
high = np.array([np.pi, self._max_omega])
# MDP properties
observation_space = spaces.Box(low=-high, high=high)
action_space = spaces.Box(low=np.array([-max_u]),
high=np.array([max_u]))
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
self._viewer = Viewer(2.5 * l, 2.5 * l)
self._last_u = None
super().__init__(mdp_info)
def reset(self, state=None):
if state is None:
if self._random:
angle = np.random.uniform(-np.pi, np.pi)
else:
angle = np.pi / 2
self._state = np.array([angle, 0.])
else:
self._state = state
self._state[0] = normalize_angle(self._state[0])
self._state[1] = self._bound(self._state[1], -self._max_omega,
self._max_omega)
self._last_u = 0.0
return self._state
def step(self, action):
u = self._bound(action[0], -self._max_u, self._max_u)
new_state = odeint(self._dynamics, self._state, [0, self._dt],
(u,))
self._state = np.array(new_state[-1])
self._state[0] = normalize_angle(self._state[0])
self._state[1] = self._bound(self._state[1], -self._max_omega,
self._max_omega)
reward = np.cos(self._state[0])
self._last_u = u.item()
return self._state, reward, False, {}
def render(self, mode='human'):
start = 1.25 * self._l * np.ones(2)
end = 1.25 * self._l * np.ones(2)
end[0] += self._l * np.sin(self._state[0])
end[1] += self._l * np.cos(self._state[0])
self._viewer.line(start, end)
self._viewer.circle(start, self._l / 40)
self._viewer.circle(end, self._l / 20)
self._viewer.torque_arrow(start, -self._last_u, self._max_u,
self._l / 5)
self._viewer.display(self._dt)
def stop(self):
self._viewer.close()
def _dynamics(self, state, t, u):
theta = state[0]
omega = self._bound(state[1], -self._max_omega, self._max_omega)
d_theta = omega
d_omega = (-self._mu * omega + self._m * self._g * self._l * np.sin(
theta) + u) / (self._m * self._l**2)
return d_theta, d_omega
class RoomToyEnv(Environment):
def __init__(self, size=5., goal=[2.5, 2.5], goal_radius=0.6):
# Save important environment information
self._size = size
self._goal = np.array(goal)
self._goal_radius = goal_radius
# Create the action space.
action_space = Discrete(4) # 4 actions: N, S, W, E
# Create the observation space. It's a 2D box of dimension (size x size).
# You can also specify low and high array, if every component has different limits
shape = (2,)
observation_space = Box(0, size, shape)
# Create the MDPInfo structure, needed by the environment interface
mdp_info = MDPInfo(observation_space, action_space, gamma=0.99, horizon=100)
super().__init__(mdp_info)
# Create a state class variable to store the current state
self._state = None
# Create the viewer
self._viewer = Viewer(size, size)
def reset(self, state=None):
if state is None:
# Generate randomly a state inside the state space, but not inside the goal
self._state = np.random.rand(2) * self._size
# Check if it's inside the goal radius and repeat the sample if necessary
while np.linalg.norm(self._state - self._goal) < self._goal_radius:
self._state = np.random.rand(2) * self._size
else:
# If an initial state is provided, set it and return, after checking it's valid.
assert np.all(state < self._size) and np.all(state > 0)
assert np.linalg.norm(state - self._goal) > self._goal_radius
self._state = state
# Return the current state
return self._state
def step(self, action):
# convert the action in a N, S, W, E movement
movement = np.zeros(2)
if action == 0:
movement[1] += 0.1
elif action == 1:
movement[1] -= 0.1
elif action == 2:
movement[0] -= 0.1
elif action == 3:
movement[0] += 0.1
else:
assert ValueError('The environment has only 4 actions')
# Apply the movement with some noise:
self._state += movement + np.random.randn(2)*0.05
# Clip the state space inside the boundaries.
low = self.info.observation_space.low
high = self.info.observation_space.high
self._state = Environment._bound(self._state, low, high)
# Compute distance form goal
goal_distance = np.linalg.norm(self._state - self._goal)
# Compute the reward as distance penalty from goal
reward = -goal_distance
# Set the absorbing flag if goal is reached
absorbing = goal_distance < self._goal_radius
# Return all the information + empty dictionary (used to pass additional information)
return self._state, reward, absorbing, {}
def render(self):
# Draw a red circle for the agent
self._viewer.circle(self._state, 0.1, color=(255, 0, 0))
# Draw a green circle for the goal
self._viewer.circle(self._goal, self._goal_radius, color=(0, 255, 0))
# Display the image for 0.1 seconds
self._viewer.display(0.1)