"""classic Acrobot task""" from typing import Optional import numpy as np from numpy import cos, pi, sin from gym import core, logger, spaces from gym.error import DependencyNotInstalled __copyright__ = "Copyright 2013, RLPy http://acl.mit.edu/RLPy" __credits__ = [ "Alborz Geramifard", "Robert H. Klein", "Christoph Dann", "William Dabney", "Jonathan P. How", ] __license__ = "BSD 3-Clause" __author__ = "Christoph Dann " # SOURCE: # https://github.com/rlpy/rlpy/blob/master/rlpy/Domains/Acrobot.py from gym.envs.classic_control import utils class AcrobotEnv(core.Env): """ ### Description The Acrobot environment is based on Sutton's work in ["Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding"](https://papers.nips.cc/paper/1995/hash/8f1d43620bc6bb580df6e80b0dc05c48-Abstract.html) and [Sutton and Barto's book](http://www.incompleteideas.net/book/the-book-2nd.html). The system consists of two links connected linearly to form a chain, with one end of the chain fixed. The joint between the two links is actuated. The goal is to apply torques on the actuated joint to swing the free end of the linear chain above a given height while starting from the initial state of hanging downwards. As seen in the **Gif**: two blue links connected by two green joints. The joint in between the two links is actuated. The goal is to swing the free end of the outer-link to reach the target height (black horizontal line above system) by applying torque on the actuator. ### Action Space The action is discrete, deterministic, and represents the torque applied on the actuated joint between the two links. | Num | Action | Unit | |-----|---------------------------------------|--------------| | 0 | apply -1 torque to the actuated joint | torque (N m) | | 1 | apply 0 torque to the actuated joint | torque (N m) | | 2 | apply 1 torque to the actuated joint | torque (N m) | ### Observation Space The observation is a `ndarray` with shape `(6,)` that provides information about the two rotational joint angles as well as their angular velocities: | Num | Observation | Min | Max | |-----|------------------------------|---------------------|-------------------| | 0 | Cosine of `theta1` | -1 | 1 | | 1 | Sine of `theta1` | -1 | 1 | | 2 | Cosine of `theta2` | -1 | 1 | | 3 | Sine of `theta2` | -1 | 1 | | 4 | Angular velocity of `theta1` | ~ -12.567 (-4 * pi) | ~ 12.567 (4 * pi) | | 5 | Angular velocity of `theta2` | ~ -28.274 (-9 * pi) | ~ 28.274 (9 * pi) | where - `theta1` is the angle of the first joint, where an angle of 0 indicates the first link is pointing directly downwards. - `theta2` is ***relative to the angle of the first link.*** An angle of 0 corresponds to having the same angle between the two links. The angular velocities of `theta1` and `theta2` are bounded at ±4π, and ±9π rad/s respectively. A state of `[1, 0, 1, 0, ..., ...]` indicates that both links are pointing downwards. ### Rewards The goal is to have the free end reach a designated target height in as few steps as possible, and as such all steps that do not reach the goal incur a reward of -1. Achieving the target height results in termination with a reward of 0. The reward threshold is -100. ### Starting State Each parameter in the underlying state (`theta1`, `theta2`, and the two angular velocities) is initialized uniformly between -0.1 and 0.1. This means both links are pointing downwards with some initial stochasticity. ### Episode End The episode ends if one of the following occurs: 1. Termination: The free end reaches the target height, which is constructed as: `-cos(theta1) - cos(theta2 + theta1) > 1.0` 2. Truncation: Episode length is greater than 500 (200 for v0) ### Arguments No additional arguments are currently supported. ``` env = gym.make('Acrobot-v1') ``` By default, the dynamics of the acrobot follow those described in Sutton and Barto's book [Reinforcement Learning: An Introduction](http://incompleteideas.net/book/11/node4.html). However, a `book_or_nips` parameter can be modified to change the pendulum dynamics to those described in the original [NeurIPS paper](https://papers.nips.cc/paper/1995/hash/8f1d43620bc6bb580df6e80b0dc05c48-Abstract.html). ``` # To change the dynamics as described above env.env.book_or_nips = 'nips' ``` See the following note and the [implementation](https://github.com/openai/gym/blob/master/gym/envs/classic_control/acrobot.py) for details: > The dynamics equations were missing some terms in the NIPS paper which are present in the book. R. Sutton confirmed in personal correspondence that the experimental results shown in the paper and the book were generated with the equations shown in the book. However, there is the option to run the domain with the paper equations by setting `book_or_nips = 'nips'` ### Version History - v1: Maximum number of steps increased from 200 to 500. The observation space for v0 provided direct readings of `theta1` and `theta2` in radians, having a range of `[-pi, pi]`. The v1 observation space as described here provides the sine and cosine of each angle instead. - v0: Initial versions release (1.0.0) (removed from gym for v1) ### References - Sutton, R. S. (1996). Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding. In D. Touretzky, M. C. Mozer, & M. Hasselmo (Eds.), Advances in Neural Information Processing Systems (Vol. 8). MIT Press. https://proceedings.neurips.cc/paper/1995/file/8f1d43620bc6bb580df6e80b0dc05c48-Paper.pdf - Sutton, R. S., Barto, A. G. (2018 ). Reinforcement Learning: An Introduction. The MIT Press. """ metadata = { "render_modes": ["human", "rgb_array"], "render_fps": 15, } dt = 0.2 LINK_LENGTH_1 = 1.0 # [m] LINK_LENGTH_2 = 1.0 # [m] LINK_MASS_1 = 1.0 #: [kg] mass of link 1 LINK_MASS_2 = 1.0 #: [kg] mass of link 2 LINK_COM_POS_1 = 0.5 #: [m] position of the center of mass of link 1 LINK_COM_POS_2 = 0.5 #: [m] position of the center of mass of link 2 LINK_MOI = 1.0 #: moments of inertia for both links MAX_VEL_1 = 4 * pi MAX_VEL_2 = 9 * pi AVAIL_TORQUE = [-1.0, 0.0, +1] torque_noise_max = 0.0 SCREEN_DIM = 500 #: use dynamics equations from the nips paper or the book book_or_nips = "book" action_arrow = None domain_fig = None actions_num = 3 def __init__(self, render_mode: Optional[str] = None): self.render_mode = render_mode self.screen = None self.clock = None self.isopen = True high = np.array( [1.0, 1.0, 1.0, 1.0, self.MAX_VEL_1, self.MAX_VEL_2], dtype=np.float32 ) low = -high self.observation_space = spaces.Box(low=low, high=high, dtype=np.float32) self.action_space = spaces.Discrete(3) self.state = None def reset(self, *, seed: Optional[int] = None, options: Optional[dict] = None): super().reset(seed=seed) # Note that if you use custom reset bounds, it may lead to out-of-bound # state/observations. low, high = utils.maybe_parse_reset_bounds( options, -0.1, 0.1 # default low ) # default high self.state = self.np_random.uniform(low=low, high=high, size=(4,)).astype( np.float32 ) if self.render_mode == "human": self.render() return self._get_ob(), {} def step(self, a): s = self.state assert s is not None, "Call reset before using AcrobotEnv object." torque = self.AVAIL_TORQUE[a] # Add noise to the force action if self.torque_noise_max > 0: torque += self.np_random.uniform( -self.torque_noise_max, self.torque_noise_max ) # Now, augment the state with our force action so it can be passed to # _dsdt s_augmented = np.append(s, torque) ns = rk4(self._dsdt, s_augmented, [0, self.dt]) ns[0] = wrap(ns[0], -pi, pi) ns[1] = wrap(ns[1], -pi, pi) ns[2] = bound(ns[2], -self.MAX_VEL_1, self.MAX_VEL_1) ns[3] = bound(ns[3], -self.MAX_VEL_2, self.MAX_VEL_2) self.state = ns terminated = self._terminal() reward = -1.0 if not terminated else 0.0 if self.render_mode == "human": self.render() return (self._get_ob(), reward, terminated, False, {}) def _get_ob(self): s = self.state assert s is not None, "Call reset before using AcrobotEnv object." return np.array( [cos(s[0]), sin(s[0]), cos(s[1]), sin(s[1]), s[2], s[3]], dtype=np.float32 ) def _terminal(self): s = self.state assert s is not None, "Call reset before using AcrobotEnv object." return bool(-cos(s[0]) - cos(s[1] + s[0]) > 1.0) def _dsdt(self, s_augmented): m1 = self.LINK_MASS_1 m2 = self.LINK_MASS_2 l1 = self.LINK_LENGTH_1 lc1 = self.LINK_COM_POS_1 lc2 = self.LINK_COM_POS_2 I1 = self.LINK_MOI I2 = self.LINK_MOI g = 9.8 a = s_augmented[-1] s = s_augmented[:-1] theta1 = s[0] theta2 = s[1] dtheta1 = s[2] dtheta2 = s[3] d1 = ( m1 * lc1**2 + m2 * (l1**2 + lc2**2 + 2 * l1 * lc2 * cos(theta2)) + I1 + I2 ) d2 = m2 * (lc2**2 + l1 * lc2 * cos(theta2)) + I2 phi2 = m2 * lc2 * g * cos(theta1 + theta2 - pi / 2.0) phi1 = ( -m2 * l1 * lc2 * dtheta2**2 * sin(theta2) - 2 * m2 * l1 * lc2 * dtheta2 * dtheta1 * sin(theta2) + (m1 * lc1 + m2 * l1) * g * cos(theta1 - pi / 2) + phi2 ) if self.book_or_nips == "nips": # the following line is consistent with the description in the # paper ddtheta2 = (a + d2 / d1 * phi1 - phi2) / (m2 * lc2**2 + I2 - d2**2 / d1) else: # the following line is consistent with the java implementation and the # book ddtheta2 = ( a + d2 / d1 * phi1 - m2 * l1 * lc2 * dtheta1**2 * sin(theta2) - phi2 ) / (m2 * lc2**2 + I2 - d2**2 / d1) ddtheta1 = -(d2 * ddtheta2 + phi1) / d1 return dtheta1, dtheta2, ddtheta1, ddtheta2, 0.0 def render(self): if self.render_mode is None: 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() surf = pygame.Surface((self.SCREEN_DIM, self.SCREEN_DIM)) surf.fill((255, 255, 255)) s = self.state bound = self.LINK_LENGTH_1 + self.LINK_LENGTH_2 + 0.2 # 2.2 for default scale = self.SCREEN_DIM / (bound * 2) offset = self.SCREEN_DIM / 2 if s is None: return None p1 = [ -self.LINK_LENGTH_1 * cos(s[0]) * scale, self.LINK_LENGTH_1 * sin(s[0]) * scale, ] p2 = [ p1[0] - self.LINK_LENGTH_2 * cos(s[0] + s[1]) * scale, p1[1] + self.LINK_LENGTH_2 * sin(s[0] + s[1]) * scale, ] xys = np.array([[0, 0], p1, p2])[:, ::-1] thetas = [s[0] - pi / 2, s[0] + s[1] - pi / 2] link_lengths = [self.LINK_LENGTH_1 * scale, self.LINK_LENGTH_2 * scale] pygame.draw.line( surf, start_pos=(-2.2 * scale + offset, 1 * scale + offset), end_pos=(2.2 * scale + offset, 1 * scale + offset), color=(0, 0, 0), ) for ((x, y), th, llen) in zip(xys, thetas, link_lengths): x = x + offset y = y + offset l, r, t, b = 0, llen, 0.1 * scale, -0.1 * scale coords = [(l, b), (l, t), (r, t), (r, b)] transformed_coords = [] for coord in coords: coord = pygame.math.Vector2(coord).rotate_rad(th) coord = (coord[0] + x, coord[1] + y) transformed_coords.append(coord) gfxdraw.aapolygon(surf, transformed_coords, (0, 204, 204)) gfxdraw.filled_polygon(surf, transformed_coords, (0, 204, 204)) gfxdraw.aacircle(surf, int(x), int(y), int(0.1 * scale), (204, 204, 0)) gfxdraw.filled_circle(surf, int(x), int(y), int(0.1 * scale), (204, 204, 0)) surf = pygame.transform.flip(surf, False, True) self.screen.blit(surf, (0, 0)) if self.render_mode == "human": pygame.event.pump() self.clock.tick(self.metadata["render_fps"]) pygame.display.flip() elif self.render_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 wrap(x, m, M): """Wraps ``x`` so m <= x <= M; but unlike ``bound()`` which truncates, ``wrap()`` wraps x around the coordinate system defined by m,M.\n For example, m = -180, M = 180 (degrees), x = 360 --> returns 0. Args: x: a scalar m: minimum possible value in range M: maximum possible value in range Returns: x: a scalar, wrapped """ diff = M - m while x > M: x = x - diff while x < m: x = x + diff return x def bound(x, m, M=None): """Either have m as scalar, so bound(x,m,M) which returns m <= x <= M *OR* have m as length 2 vector, bound(x,m, ) returns m[0] <= x <= m[1]. Args: x: scalar m: The lower bound M: The upper bound Returns: x: scalar, bound between min (m) and Max (M) """ if M is None: M = m[1] m = m[0] # bound x between min (m) and Max (M) return min(max(x, m), M) def rk4(derivs, y0, t): """ Integrate 1-D or N-D system of ODEs using 4-th order Runge-Kutta. Example for 2D system: >>> def derivs(x): ... d1 = x[0] + 2*x[1] ... d2 = -3*x[0] + 4*x[1] ... return d1, d2 >>> dt = 0.0005 >>> t = np.arange(0.0, 2.0, dt) >>> y0 = (1,2) >>> yout = rk4(derivs, y0, t) Args: derivs: the derivative of the system and has the signature ``dy = derivs(yi)`` y0: initial state vector t: sample times Returns: yout: Runge-Kutta approximation of the ODE """ try: Ny = len(y0) except TypeError: yout = np.zeros((len(t),), np.float_) else: yout = np.zeros((len(t), Ny), np.float_) yout[0] = y0 for i in np.arange(len(t) - 1): this = t[i] dt = t[i + 1] - this dt2 = dt / 2.0 y0 = yout[i] k1 = np.asarray(derivs(y0)) k2 = np.asarray(derivs(y0 + dt2 * k1)) k3 = np.asarray(derivs(y0 + dt2 * k2)) k4 = np.asarray(derivs(y0 + dt * k3)) yout[i + 1] = y0 + dt / 6.0 * (k1 + 2 * k2 + 2 * k3 + k4) # We only care about the final timestep and we cleave off action value which will be zero return yout[-1][:4]