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: 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(Segway, self).__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 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.')
@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 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=1.0, l=1.0, g=9.8, mu=1e-2,
max_u=5.0, horizon=5000):
"""
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.
"""
# MDP parameters
self._m = m
self._l = l
self._g = g
self._mu = mu
self._random = random_start
self._dt = 0.01
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]))
gamma = .99
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)
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
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 InvertedPendulumDiscrete(Environment):
"""
The Inverted Pendulum 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):
"""
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;
mu (float, 1e-2): friction constant of the pendulum;
max_u (float, 50.): maximum allowed input torque;
noise_u (float, 10.): maximum noise on the action;
horizon (int, 3000): horizon of the problem.
"""
# 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)
gamma = .95
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:
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])
return self._state
def step(self, action):
if action == 0:
u = -self._max_u
elif action == 1:
u = 0.
else:
u = self._max_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
self._last_u = u
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.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 = state[1]
d_theta = omega
d_omega = (self._g * np.sin(theta) - self._alpha * self._m * self._l *
d_theta ** 2 * np.sin(2 * theta) * .5 - self._alpha * np.cos(
theta) * u) / (4 / 3 * self._l - self._alpha * self._m *
self._l * np.cos(theta) ** 2)
return d_theta, d_omega
class PreyPredator(Environment):
"""
A prey-predator environment environment. A Predator must catch a faster prey
in an environment with obstacles.
"""
def __init__(self):
self._rotation_radius = 0.6
self._catch_radius = 0.4
self._v_prey = 0.13
self._v_predator = 0.1
self._dt = 0.1
self._omega_prey = self._v_prey / self._rotation_radius
self._omega_predator = self._v_predator / self._rotation_radius
self._max_x = 5.0
self._max_y = 5.0
self._obstacles = [
(np.array([self._max_x/5,
self._max_y - 3.8*self._catch_radius]),
np.array([self._max_x,
self._max_y - 3.8*self._catch_radius])),
(np.array([-3/5*self._max_x,
self._max_y/4]),
np.array([-3/5*self._max_x,
-3/10*self._max_y])),
(np.array([-3/5*self._max_x + 3.8*self._catch_radius,
self._max_y / 4]),
np.array([-3/5*self._max_x + 3.8*self._catch_radius,
-3/10*self._max_y])),
(np.array([-3/5*self._max_x,
self._max_y/4]),
np.array([-3/5*self._max_x + 3.8*self._catch_radius,
self._max_y/4]))
]
# Add bounds of the map
self._obstacles += [(np.array([-self._max_x, -self._max_y]),
np.array([-self._max_x, self._max_y])),
(np.array([-self._max_x, -self._max_y]),
np.array([self._max_x, -self._max_y])),
(np.array([self._max_x, self._max_y]),
np.array([-self._max_x, self._max_y])),
(np.array([self._max_x, self._max_y]),
np.array([self._max_x, -self._max_y]))
]
high = np.array([self._max_x, self._max_y, np.pi,
self._max_x, self._max_y, np.pi])
# MDP properties
horizon = 500
gamma = 0.99
observation_space = spaces.Box(low=-high, high=high)
action_space = spaces.Box(low=np.array([0,
-self._omega_predator]),
high=np.array([self._v_predator,
self._omega_predator]))
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
width = 500
height = int(width * self._max_y / self._max_x)
self._viewer = Viewer(2*self._max_x, 2*self._max_y, width, height)
super(PreyPredator, self).__init__(mdp_info)
def reset(self, state=None):
if state is None:
self._state = np.array([0., 0., 0.,
self._max_x/2, self._max_y/2, np.pi/2])
self._state = np.array([3., 1., np.pi/2,
3., 2., np.pi/2])
ok = False
while not ok:
self._state = np.random.uniform(
low=self.info.observation_space.low,
high=self.info.observation_space.high)
delta_norm = np.linalg.norm(self._state[:2] - self._state[3:5])
ok = delta_norm > self._catch_radius
else:
self._state = state
self._state[2] = normalize_angle(self._state[2])
self._state[5] = normalize_angle(self._state[5])
return self._state
def step(self, action):
# compute new predator state
u = self._bound(action,
self.info.action_space.low,
self.info.action_space.high)
state_predator = self._state[:3]
state_predator = self._differential_drive_dynamics(state_predator, u)
# Compute new prey state
u_prey = self._prey_controller(self._state)
state_prey = self._state[3:]
state_prey = self._differential_drive_dynamics(state_prey, u_prey)
# Update state
self._state = np.concatenate([state_predator, state_prey], 0)
delta_norm_new = np.linalg.norm(self._state[:2]-self._state[3:5])
if delta_norm_new < self._catch_radius:
collision, _ = self._check_collision(self._state[:2],
self._state[3:5])
if collision is None:
absorbing = True
else:
absorbing = False
else:
absorbing = False
reward = -delta_norm_new
return self._state, reward, absorbing, {}
def _prey_controller(self, state):
delta_norm = np.linalg.norm(state[:2] - state[3:5])
if delta_norm > 3.0:
velocity_prey = 0
elif delta_norm > 1.5:
velocity_prey = self._v_prey / 2
else:
velocity_prey = self._v_prey
attack_angle = normalize_angle(np.arctan2(state[4] - state[1],
state[3] - state[0]))
angle_current = shortest_angular_distance(state[5], attack_angle)
if velocity_prey > 0:
# check attack angle collision
cos_theta = np.cos(attack_angle)
sin_theta = np.sin(attack_angle)
increment = 2.5*self._rotation_radius*np.array([cos_theta,
sin_theta])
collision, i = self._check_collision(state[3:5],
state[3:5]+increment)
if collision is not None:
obstacle = self._obstacles[i]
v_obst = self._segment_to_vector(*obstacle)
v_attack = state[3:5] - state[0:2]
angle = self._vector_angle(v_obst, v_attack)
if 0 <= angle <= np.pi/2 or angle <= -np.pi/2:
rotation_sign = +1
else:
rotation_sign = -1
evasion_angle = attack_angle + rotation_sign * np.pi/2
angle_current = shortest_angular_distance(state[5],
evasion_angle)
alpha = normalize_angle(state[5] + rotation_sign*np.pi/2)
cos_alpha = np.cos(alpha)
sin_alpha = np.sin(alpha)
increment = 1.5*self._rotation_radius * np.array(
[cos_alpha, sin_alpha])
lateral_collision, _ = self._check_collision(state[3:5],
state[3:5] +
increment)
if lateral_collision is not None:
rotation_sign *= -1
angle_current = rotation_sign * np.pi
omega_prey = angle_current / np.pi
u_prey = np.empty(2)
u_prey[0] = self._bound(velocity_prey, 0, self._v_prey)
u_prey[1] = self._bound(omega_prey, -self._omega_prey, self._omega_prey)
return u_prey
@staticmethod
def _cross_2d(vecr, vecs):
return vecr[0] * vecs[1] - vecr[1] * vecs[0]
@staticmethod
def _segment_to_vector(*segment):
a = segment[0]
b = segment[1]
if (b[0] > a[0]) or (b[0] == a[0] and b[1] > a[1]):
return b - a
else:
return a - b
@staticmethod
def _vector_angle(x, y):
angle = np.arctan2(x[1], x[0]) - np.arctan2(y[1], y[0])
return normalize_angle(angle)
def _check_collision(self, start, end):
collision = None
index = None
min_u = np.inf
for i, obstacle in enumerate(self._obstacles):
r = obstacle[1] - obstacle[0]
s = end - start
den = self._cross_2d(vecr=r, vecs=s)
if den != 0:
t = self._cross_2d((start - obstacle[0]), s) / den
u = self._cross_2d((start - obstacle[0]), r) / den
if 1 >= u >= 0 and 1 >= t >= 0:
if u < min_u:
collision = start + (u-1e-2)*s
min_u = u
index = i
return collision, index
def _differential_drive_dynamics(self, state, u):
delta = np.empty(3)
delta[0] = np.cos(state[2]) * u[0]
delta[1] = np.sin(state[2]) * u[0]
delta[2] = u[1]
new_state = state + delta
collision, _ = self._check_collision(state[:2], new_state[:2])
if collision is not None:
new_state[:2] = collision
new_state[0] = self._bound(new_state[0], -self._max_x, self._max_x)
new_state[1] = self._bound(new_state[1], -self._max_y, self._max_y)
new_state[2] = normalize_angle(new_state[2])
return new_state
def render(self, mode='human'):
center = np.array([self._max_x, self._max_y])
predator_pos = self._state[:2]
predator_theta = self._state[2]
prey_pos = self._state[3:5]
prey_theta = self._state[5]
# Predator
self._viewer.circle(center + predator_pos, self._catch_radius,
(255, 255, 255))
self._viewer.arrow_head(center + predator_pos, self._catch_radius,
predator_theta, (255, 0, 0))
# Prey
self._viewer.arrow_head(center + prey_pos, self._catch_radius,
prey_theta, (0, 0, 255))
# Obstacles
for obstacle in self._obstacles:
start = obstacle[0]
end = obstacle[1]
self._viewer.line(center + start, center + end)
self._viewer.display(self._dt)
class SegwayLinearMotion(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, goal_distance=1.0):
"""
Constructor.
Args:
random_start: whether to start from a random position or from the
horizontal one
"""
# MDP parameters
gamma = 0.99
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
self._goal_distance = goal_distance
high = np.array([2 * self._goal_distance, np.pi, 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 = 1500
mdp_info = MDPInfo(observation_space, action_space, gamma, horizon)
# Visualization
env_width = 4 * goal_distance
env_height = 2.5 * 2 * self.l
width = 800
height = int(width * env_height / env_width)
self._viewer = Viewer(env_width, env_height, width, height)
super(SegwayLinearMotion, self).__init__(mdp_info)
def reset(self, state=None):
if state is None:
if self._random:
angle = np.random.uniform(-np.pi / 4, np.pi / 4)
else:
angle = -np.pi / 8
self._state = np.array([-self._goal_distance, angle, 0., 0.])
else:
self._state = state
self._state[1] = normalize_angle(self._state[1])
return self._state
def step(self, action):
u = np.maximum(-self.max_u, np.minimum(self.max_u, action[0]))
new_state = odeint(self._dynamics, self._state, [0, self.dt], (u, ))
self._state = np.array(new_state[-1])
self._state[1] = normalize_angle(self._state[1])
if abs(self._state[1]) > np.pi / 2 \
or abs(self._state[0]) > 2*self._goal_distance:
absorbing = True
reward = -10000
else:
absorbing = False
Q = np.diag([10.0, 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):
position = state[0]
alpha = state[1]
d_alpha = state[2]
d_beta = state[3]
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
omegaR = d_beta
velocity = -omegaR * self.r
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(velocity)
dx.append(omegaP)
dx.append(dOmegaP)
dx.append(dOmegaR)
return dx
def render(self, mode='human'):
start = np.array([2 * self._goal_distance, 1.25 * 2 * self.l])
end = np.array(start)
goal = start + np.array([0, -self.r])
position = self._state[0]
start[0] += position
end[0] += -2 * self.l * np.sin(self._state[1]) + position
end[1] += 2 * self.l * np.cos(self._state[1])
self._viewer.line(start, end)
self._viewer.circle(start, self.r)
self._viewer.circle(goal, radius=0.01, color=(255, 0, 0))
self._viewer.display(self.dt)
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: 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(Segway, self).__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)