envs.cartpole_model
generative AI experiment - discretized cartpole transition and reward (P) matrix with adaptive angle binning created with chatGPT
Example usage: dpole = DiscretizedCartPole(10, 10, 10, .1, .5) # Example bin sizes for each variable and adaptive angle binning center/outer resolution
1""" 2generative AI experiment - discretized cartpole transition and reward (P) matrix with adaptive angle binning 3created with chatGPT 4 5Example usage: 6dpole = DiscretizedCartPole(10, 10, 10, .1, .5) # Example bin sizes for each variable and adaptive angle binning center/outer resolution 7 8""" 9 10import numpy as np 11 12 13class DiscretizedCartPole: 14 def __init__(self, 15 position_bins, 16 velocity_bins, 17 angular_velocity_bins, 18 angular_center_resolution, 19 angular_outer_resolution): 20 21 """ 22 Initializes the DiscretizedCartPole model. 23 24 Parameters: 25 - position_bins (int): Number of discrete bins for the cart's position. 26 - velocity_bins (int): Number of discrete bins for the cart's velocity. 27 - angular_velocity_bins (int): Number of discrete bins for the pole's angular velocity. 28 - angular_center_resolution (float): The resolution of angle bins near the center (around zero). 29 - angular_outer_resolution (float): The resolution of angle bins away from the center. 30 31 Attributes: 32 - state_space (int): Total number of discrete states in the environment. 33 - P (dict): Transition probability matrix where P[state][action] is a list of tuples (probability, next_state, 34 reward, done). 35 - transform_obs (lambda): Function to transform continuous observations into a discrete state index. 36 """ 37 self.position_bins = position_bins 38 self.velocity_bins = velocity_bins 39 self.angular_velocity_bins = angular_velocity_bins 40 self.action_space = 2 # Left or Right 41 42 # Define the range for each variable 43 self.position_range = (-2.4, 2.4) 44 self.velocity_range = (-3, 3) 45 self.angle_range = (-12 * np.pi / 180, 12 * np.pi / 180) 46 self.angular_velocity_range = (-1.5, 1.5) 47 self.angular_center_resolution = angular_center_resolution 48 self.angular_outer_resolution = angular_outer_resolution 49 50 # Use adaptive binning for the pole angle 51 self.angle_bins = self.adaptive_angle_bins(self.angle_range, self.angular_center_resolution, self.angular_outer_resolution) # Adjust these values as needed 52 53 self.state_space = np.prod([self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins]) 54 self.P = {state: {action: [] for action in range(self.action_space)} for state in range(self.state_space)} 55 self.setup_transition_probabilities() 56 self.n_states = len(self.angle_bins)*self.velocity_bins*self.position_bins*self.angular_velocity_bins 57 """ 58 Explanation of transform_obs lambda: 59 This lambda function will take cartpole observations, determine which bins they fall into, 60 and then convert bin coordinates into a single index. This makes it possible 61 to use traditional reinforcement learning and planning algorithms, designed for discrete spaces, with continuous 62 state space environments. 63 64 Parameters: 65 - obs (list): A list of continuous observations [position, velocity, angle, angular_velocity]. 66 67 Returns: 68 - int: A single integer representing the discretized state index. 69 """ 70 self.transform_obs = lambda obs: ( 71 np.ravel_multi_index(( 72 np.clip(np.digitize(obs[0], np.linspace(*self.position_range, self.position_bins)) - 1, 0, 73 self.position_bins - 1), 74 np.clip(np.digitize(obs[1], np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, 75 self.velocity_bins - 1), 76 np.clip(np.digitize(obs[2], self.angle_bins) - 1, 0, len(self.angle_bins) - 1), 77 # Use adaptive angle bins 78 np.clip(np.digitize(obs[3], np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 79 0, self.angular_velocity_bins - 1) 80 ), (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 81 ) 82 83 def adaptive_angle_bins(self, angle_range, center_resolution, outer_resolution): 84 """ 85 Generates adaptive bins for the pole's angle to allow for finer resolution near the center and coarser 86 resolution farther away. 87 88 Parameters: 89 - angle_range (tuple): The minimum and maximum angles in radians. 90 - center_resolution (float): Bin width near zero angle for higher resolution. 91 - outer_resolution (float): Bin width away from zero for lower resolution. 92 93 Returns: 94 - np.array: An array of bin edges with adaptive spacing. 95 """ 96 min_angle, max_angle = angle_range 97 # Generate finer bins around zero 98 center_bins = np.arange(-center_resolution, center_resolution + 1e-6, center_resolution / 10) 99 # Generate sparser bins outside the center region 100 left_bins = np.linspace(min_angle, -center_resolution, 101 num=int((center_resolution - min_angle) / outer_resolution) + 1, endpoint=False) 102 right_bins = np.linspace(center_resolution, max_angle, 103 num=int((max_angle - center_resolution) / outer_resolution) + 1, endpoint=True) 104 return np.unique(np.concatenate([left_bins, center_bins, right_bins])) 105 106 def setup_transition_probabilities(self): 107 """ 108 Sets up the transition probabilities for the environment. This method iterates through all possible 109 states and actions, simulates the next state, and records the transition probability 110 (deterministic in this setup), reward, and termination status. 111 """ 112 for state in range(self.state_space): 113 position, velocity, angle, angular_velocity = self.index_to_state(state) 114 for action in range(self.action_space): 115 next_state, reward, done = self.compute_next_state(position, velocity, angle, angular_velocity, action) 116 self.P[state][action].append((1, next_state, reward, done)) 117 118 def index_to_state(self, index): 119 """ 120 Converts a single index into a multidimensional state representation. 121 122 Parameters: 123 - index (int): The flat index representing the state. 124 125 Returns: 126 - list: A list of indices representing the state in terms of position, velocity, angle, and angular velocity bins. 127 """ 128 totals = [self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins] 129 multipliers = np.cumprod([1] + totals[::-1])[:-1][::-1] 130 components = [int((index // multipliers[i]) % totals[i]) for i in range(4)] 131 return components 132 133 def compute_next_state(self, position_idx, velocity_idx, angle_idx, angular_velocity_idx, action): 134 """ 135 Computes the next state based on the current state indices and the action taken. Applies simplified physics calculations to determine the next state. 136 137 Parameters: 138 - position_idx (int): Current index of the cart's position. 139 - velocity_idx (int): Current index of the cart's velocity. 140 - angle_idx (int): Current index of the pole's angle. 141 - angular_velocity_idx (int): Current index of the pole's angular velocity. 142 - action (int): Action taken (0 for left, 1 for right). 143 144 Returns: 145 - tuple: Contains the next state index, the reward, and the done flag indicating if the episode has ended. 146 """ 147 position = np.linspace(*self.position_range, self.position_bins)[position_idx] 148 velocity = np.linspace(*self.velocity_range, self.velocity_bins)[velocity_idx] 149 angle = self.angle_bins[angle_idx] 150 angular_velocity = np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)[angular_velocity_idx] 151 152 # Simulate physics here (simplified) 153 force = 10 if action == 1 else -10 154 new_velocity = velocity + (force + np.cos(angle) * -10.0) * 0.02 155 new_position = position + new_velocity * 0.02 156 new_angular_velocity = angular_velocity + (-3.0 * np.sin(angle)) * 0.02 157 new_angle = angle + new_angular_velocity * 0.02 158 159 new_position_idx = np.clip(np.digitize(new_position, np.linspace(*self.position_range, self.position_bins)) - 1, 0, self.position_bins-1) 160 new_velocity_idx = np.clip(np.digitize(new_velocity, np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, self.velocity_bins-1) 161 new_angle_idx = np.clip(np.digitize(new_angle, self.angle_bins) - 1, 0, len(self.angle_bins)-1) 162 new_angular_velocity_idx = np.clip(np.digitize(new_angular_velocity, np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 0, self.angular_velocity_bins-1) 163 164 new_state_idx = np.ravel_multi_index((new_position_idx, new_velocity_idx, new_angle_idx, new_angular_velocity_idx), 165 (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 166 167 reward = 1 if np.abs(new_angle) < 12 * np.pi / 180 else -1 168 done = True if np.abs(new_angle) >= 12 * np.pi / 180 or np.abs(new_position) > 2.4 else False 169 170 return new_state_idx, reward, done
14class DiscretizedCartPole: 15 def __init__(self, 16 position_bins, 17 velocity_bins, 18 angular_velocity_bins, 19 angular_center_resolution, 20 angular_outer_resolution): 21 22 """ 23 Initializes the DiscretizedCartPole model. 24 25 Parameters: 26 - position_bins (int): Number of discrete bins for the cart's position. 27 - velocity_bins (int): Number of discrete bins for the cart's velocity. 28 - angular_velocity_bins (int): Number of discrete bins for the pole's angular velocity. 29 - angular_center_resolution (float): The resolution of angle bins near the center (around zero). 30 - angular_outer_resolution (float): The resolution of angle bins away from the center. 31 32 Attributes: 33 - state_space (int): Total number of discrete states in the environment. 34 - P (dict): Transition probability matrix where P[state][action] is a list of tuples (probability, next_state, 35 reward, done). 36 - transform_obs (lambda): Function to transform continuous observations into a discrete state index. 37 """ 38 self.position_bins = position_bins 39 self.velocity_bins = velocity_bins 40 self.angular_velocity_bins = angular_velocity_bins 41 self.action_space = 2 # Left or Right 42 43 # Define the range for each variable 44 self.position_range = (-2.4, 2.4) 45 self.velocity_range = (-3, 3) 46 self.angle_range = (-12 * np.pi / 180, 12 * np.pi / 180) 47 self.angular_velocity_range = (-1.5, 1.5) 48 self.angular_center_resolution = angular_center_resolution 49 self.angular_outer_resolution = angular_outer_resolution 50 51 # Use adaptive binning for the pole angle 52 self.angle_bins = self.adaptive_angle_bins(self.angle_range, self.angular_center_resolution, self.angular_outer_resolution) # Adjust these values as needed 53 54 self.state_space = np.prod([self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins]) 55 self.P = {state: {action: [] for action in range(self.action_space)} for state in range(self.state_space)} 56 self.setup_transition_probabilities() 57 self.n_states = len(self.angle_bins)*self.velocity_bins*self.position_bins*self.angular_velocity_bins 58 """ 59 Explanation of transform_obs lambda: 60 This lambda function will take cartpole observations, determine which bins they fall into, 61 and then convert bin coordinates into a single index. This makes it possible 62 to use traditional reinforcement learning and planning algorithms, designed for discrete spaces, with continuous 63 state space environments. 64 65 Parameters: 66 - obs (list): A list of continuous observations [position, velocity, angle, angular_velocity]. 67 68 Returns: 69 - int: A single integer representing the discretized state index. 70 """ 71 self.transform_obs = lambda obs: ( 72 np.ravel_multi_index(( 73 np.clip(np.digitize(obs[0], np.linspace(*self.position_range, self.position_bins)) - 1, 0, 74 self.position_bins - 1), 75 np.clip(np.digitize(obs[1], np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, 76 self.velocity_bins - 1), 77 np.clip(np.digitize(obs[2], self.angle_bins) - 1, 0, len(self.angle_bins) - 1), 78 # Use adaptive angle bins 79 np.clip(np.digitize(obs[3], np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 80 0, self.angular_velocity_bins - 1) 81 ), (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 82 ) 83 84 def adaptive_angle_bins(self, angle_range, center_resolution, outer_resolution): 85 """ 86 Generates adaptive bins for the pole's angle to allow for finer resolution near the center and coarser 87 resolution farther away. 88 89 Parameters: 90 - angle_range (tuple): The minimum and maximum angles in radians. 91 - center_resolution (float): Bin width near zero angle for higher resolution. 92 - outer_resolution (float): Bin width away from zero for lower resolution. 93 94 Returns: 95 - np.array: An array of bin edges with adaptive spacing. 96 """ 97 min_angle, max_angle = angle_range 98 # Generate finer bins around zero 99 center_bins = np.arange(-center_resolution, center_resolution + 1e-6, center_resolution / 10) 100 # Generate sparser bins outside the center region 101 left_bins = np.linspace(min_angle, -center_resolution, 102 num=int((center_resolution - min_angle) / outer_resolution) + 1, endpoint=False) 103 right_bins = np.linspace(center_resolution, max_angle, 104 num=int((max_angle - center_resolution) / outer_resolution) + 1, endpoint=True) 105 return np.unique(np.concatenate([left_bins, center_bins, right_bins])) 106 107 def setup_transition_probabilities(self): 108 """ 109 Sets up the transition probabilities for the environment. This method iterates through all possible 110 states and actions, simulates the next state, and records the transition probability 111 (deterministic in this setup), reward, and termination status. 112 """ 113 for state in range(self.state_space): 114 position, velocity, angle, angular_velocity = self.index_to_state(state) 115 for action in range(self.action_space): 116 next_state, reward, done = self.compute_next_state(position, velocity, angle, angular_velocity, action) 117 self.P[state][action].append((1, next_state, reward, done)) 118 119 def index_to_state(self, index): 120 """ 121 Converts a single index into a multidimensional state representation. 122 123 Parameters: 124 - index (int): The flat index representing the state. 125 126 Returns: 127 - list: A list of indices representing the state in terms of position, velocity, angle, and angular velocity bins. 128 """ 129 totals = [self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins] 130 multipliers = np.cumprod([1] + totals[::-1])[:-1][::-1] 131 components = [int((index // multipliers[i]) % totals[i]) for i in range(4)] 132 return components 133 134 def compute_next_state(self, position_idx, velocity_idx, angle_idx, angular_velocity_idx, action): 135 """ 136 Computes the next state based on the current state indices and the action taken. Applies simplified physics calculations to determine the next state. 137 138 Parameters: 139 - position_idx (int): Current index of the cart's position. 140 - velocity_idx (int): Current index of the cart's velocity. 141 - angle_idx (int): Current index of the pole's angle. 142 - angular_velocity_idx (int): Current index of the pole's angular velocity. 143 - action (int): Action taken (0 for left, 1 for right). 144 145 Returns: 146 - tuple: Contains the next state index, the reward, and the done flag indicating if the episode has ended. 147 """ 148 position = np.linspace(*self.position_range, self.position_bins)[position_idx] 149 velocity = np.linspace(*self.velocity_range, self.velocity_bins)[velocity_idx] 150 angle = self.angle_bins[angle_idx] 151 angular_velocity = np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)[angular_velocity_idx] 152 153 # Simulate physics here (simplified) 154 force = 10 if action == 1 else -10 155 new_velocity = velocity + (force + np.cos(angle) * -10.0) * 0.02 156 new_position = position + new_velocity * 0.02 157 new_angular_velocity = angular_velocity + (-3.0 * np.sin(angle)) * 0.02 158 new_angle = angle + new_angular_velocity * 0.02 159 160 new_position_idx = np.clip(np.digitize(new_position, np.linspace(*self.position_range, self.position_bins)) - 1, 0, self.position_bins-1) 161 new_velocity_idx = np.clip(np.digitize(new_velocity, np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, self.velocity_bins-1) 162 new_angle_idx = np.clip(np.digitize(new_angle, self.angle_bins) - 1, 0, len(self.angle_bins)-1) 163 new_angular_velocity_idx = np.clip(np.digitize(new_angular_velocity, np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 0, self.angular_velocity_bins-1) 164 165 new_state_idx = np.ravel_multi_index((new_position_idx, new_velocity_idx, new_angle_idx, new_angular_velocity_idx), 166 (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 167 168 reward = 1 if np.abs(new_angle) < 12 * np.pi / 180 else -1 169 done = True if np.abs(new_angle) >= 12 * np.pi / 180 or np.abs(new_position) > 2.4 else False 170 171 return new_state_idx, reward, done
15 def __init__(self, 16 position_bins, 17 velocity_bins, 18 angular_velocity_bins, 19 angular_center_resolution, 20 angular_outer_resolution): 21 22 """ 23 Initializes the DiscretizedCartPole model. 24 25 Parameters: 26 - position_bins (int): Number of discrete bins for the cart's position. 27 - velocity_bins (int): Number of discrete bins for the cart's velocity. 28 - angular_velocity_bins (int): Number of discrete bins for the pole's angular velocity. 29 - angular_center_resolution (float): The resolution of angle bins near the center (around zero). 30 - angular_outer_resolution (float): The resolution of angle bins away from the center. 31 32 Attributes: 33 - state_space (int): Total number of discrete states in the environment. 34 - P (dict): Transition probability matrix where P[state][action] is a list of tuples (probability, next_state, 35 reward, done). 36 - transform_obs (lambda): Function to transform continuous observations into a discrete state index. 37 """ 38 self.position_bins = position_bins 39 self.velocity_bins = velocity_bins 40 self.angular_velocity_bins = angular_velocity_bins 41 self.action_space = 2 # Left or Right 42 43 # Define the range for each variable 44 self.position_range = (-2.4, 2.4) 45 self.velocity_range = (-3, 3) 46 self.angle_range = (-12 * np.pi / 180, 12 * np.pi / 180) 47 self.angular_velocity_range = (-1.5, 1.5) 48 self.angular_center_resolution = angular_center_resolution 49 self.angular_outer_resolution = angular_outer_resolution 50 51 # Use adaptive binning for the pole angle 52 self.angle_bins = self.adaptive_angle_bins(self.angle_range, self.angular_center_resolution, self.angular_outer_resolution) # Adjust these values as needed 53 54 self.state_space = np.prod([self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins]) 55 self.P = {state: {action: [] for action in range(self.action_space)} for state in range(self.state_space)} 56 self.setup_transition_probabilities() 57 self.n_states = len(self.angle_bins)*self.velocity_bins*self.position_bins*self.angular_velocity_bins 58 """ 59 Explanation of transform_obs lambda: 60 This lambda function will take cartpole observations, determine which bins they fall into, 61 and then convert bin coordinates into a single index. This makes it possible 62 to use traditional reinforcement learning and planning algorithms, designed for discrete spaces, with continuous 63 state space environments. 64 65 Parameters: 66 - obs (list): A list of continuous observations [position, velocity, angle, angular_velocity]. 67 68 Returns: 69 - int: A single integer representing the discretized state index. 70 """ 71 self.transform_obs = lambda obs: ( 72 np.ravel_multi_index(( 73 np.clip(np.digitize(obs[0], np.linspace(*self.position_range, self.position_bins)) - 1, 0, 74 self.position_bins - 1), 75 np.clip(np.digitize(obs[1], np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, 76 self.velocity_bins - 1), 77 np.clip(np.digitize(obs[2], self.angle_bins) - 1, 0, len(self.angle_bins) - 1), 78 # Use adaptive angle bins 79 np.clip(np.digitize(obs[3], np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 80 0, self.angular_velocity_bins - 1) 81 ), (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 82 )
Initializes the DiscretizedCartPole model.
Parameters:
- position_bins (int): Number of discrete bins for the cart's position.
- velocity_bins (int): Number of discrete bins for the cart's velocity.
- angular_velocity_bins (int): Number of discrete bins for the pole's angular velocity.
- angular_center_resolution (float): The resolution of angle bins near the center (around zero).
- angular_outer_resolution (float): The resolution of angle bins away from the center.
Attributes:
- state_space (int): Total number of discrete states in the environment.
- P (dict): Transition probability matrix where P[state][action] is a list of tuples (probability, next_state, reward, done).
- transform_obs (lambda): Function to transform continuous observations into a discrete state index.
Explanation of transform_obs lambda: This lambda function will take cartpole observations, determine which bins they fall into, and then convert bin coordinates into a single index. This makes it possible to use traditional reinforcement learning and planning algorithms, designed for discrete spaces, with continuous state space environments.
Parameters:
- obs (list): A list of continuous observations [position, velocity, angle, angular_velocity].
Returns:
- int: A single integer representing the discretized state index.
84 def adaptive_angle_bins(self, angle_range, center_resolution, outer_resolution): 85 """ 86 Generates adaptive bins for the pole's angle to allow for finer resolution near the center and coarser 87 resolution farther away. 88 89 Parameters: 90 - angle_range (tuple): The minimum and maximum angles in radians. 91 - center_resolution (float): Bin width near zero angle for higher resolution. 92 - outer_resolution (float): Bin width away from zero for lower resolution. 93 94 Returns: 95 - np.array: An array of bin edges with adaptive spacing. 96 """ 97 min_angle, max_angle = angle_range 98 # Generate finer bins around zero 99 center_bins = np.arange(-center_resolution, center_resolution + 1e-6, center_resolution / 10) 100 # Generate sparser bins outside the center region 101 left_bins = np.linspace(min_angle, -center_resolution, 102 num=int((center_resolution - min_angle) / outer_resolution) + 1, endpoint=False) 103 right_bins = np.linspace(center_resolution, max_angle, 104 num=int((max_angle - center_resolution) / outer_resolution) + 1, endpoint=True) 105 return np.unique(np.concatenate([left_bins, center_bins, right_bins]))
Generates adaptive bins for the pole's angle to allow for finer resolution near the center and coarser resolution farther away.
Parameters:
- angle_range (tuple): The minimum and maximum angles in radians.
- center_resolution (float): Bin width near zero angle for higher resolution.
- outer_resolution (float): Bin width away from zero for lower resolution.
Returns:
- np.array: An array of bin edges with adaptive spacing.
107 def setup_transition_probabilities(self): 108 """ 109 Sets up the transition probabilities for the environment. This method iterates through all possible 110 states and actions, simulates the next state, and records the transition probability 111 (deterministic in this setup), reward, and termination status. 112 """ 113 for state in range(self.state_space): 114 position, velocity, angle, angular_velocity = self.index_to_state(state) 115 for action in range(self.action_space): 116 next_state, reward, done = self.compute_next_state(position, velocity, angle, angular_velocity, action) 117 self.P[state][action].append((1, next_state, reward, done))
Sets up the transition probabilities for the environment. This method iterates through all possible states and actions, simulates the next state, and records the transition probability (deterministic in this setup), reward, and termination status.
119 def index_to_state(self, index): 120 """ 121 Converts a single index into a multidimensional state representation. 122 123 Parameters: 124 - index (int): The flat index representing the state. 125 126 Returns: 127 - list: A list of indices representing the state in terms of position, velocity, angle, and angular velocity bins. 128 """ 129 totals = [self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins] 130 multipliers = np.cumprod([1] + totals[::-1])[:-1][::-1] 131 components = [int((index // multipliers[i]) % totals[i]) for i in range(4)] 132 return components
Converts a single index into a multidimensional state representation.
Parameters:
- index (int): The flat index representing the state.
Returns:
- list: A list of indices representing the state in terms of position, velocity, angle, and angular velocity bins.
134 def compute_next_state(self, position_idx, velocity_idx, angle_idx, angular_velocity_idx, action): 135 """ 136 Computes the next state based on the current state indices and the action taken. Applies simplified physics calculations to determine the next state. 137 138 Parameters: 139 - position_idx (int): Current index of the cart's position. 140 - velocity_idx (int): Current index of the cart's velocity. 141 - angle_idx (int): Current index of the pole's angle. 142 - angular_velocity_idx (int): Current index of the pole's angular velocity. 143 - action (int): Action taken (0 for left, 1 for right). 144 145 Returns: 146 - tuple: Contains the next state index, the reward, and the done flag indicating if the episode has ended. 147 """ 148 position = np.linspace(*self.position_range, self.position_bins)[position_idx] 149 velocity = np.linspace(*self.velocity_range, self.velocity_bins)[velocity_idx] 150 angle = self.angle_bins[angle_idx] 151 angular_velocity = np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)[angular_velocity_idx] 152 153 # Simulate physics here (simplified) 154 force = 10 if action == 1 else -10 155 new_velocity = velocity + (force + np.cos(angle) * -10.0) * 0.02 156 new_position = position + new_velocity * 0.02 157 new_angular_velocity = angular_velocity + (-3.0 * np.sin(angle)) * 0.02 158 new_angle = angle + new_angular_velocity * 0.02 159 160 new_position_idx = np.clip(np.digitize(new_position, np.linspace(*self.position_range, self.position_bins)) - 1, 0, self.position_bins-1) 161 new_velocity_idx = np.clip(np.digitize(new_velocity, np.linspace(*self.velocity_range, self.velocity_bins)) - 1, 0, self.velocity_bins-1) 162 new_angle_idx = np.clip(np.digitize(new_angle, self.angle_bins) - 1, 0, len(self.angle_bins)-1) 163 new_angular_velocity_idx = np.clip(np.digitize(new_angular_velocity, np.linspace(*self.angular_velocity_range, self.angular_velocity_bins)) - 1, 0, self.angular_velocity_bins-1) 164 165 new_state_idx = np.ravel_multi_index((new_position_idx, new_velocity_idx, new_angle_idx, new_angular_velocity_idx), 166 (self.position_bins, self.velocity_bins, len(self.angle_bins), self.angular_velocity_bins)) 167 168 reward = 1 if np.abs(new_angle) < 12 * np.pi / 180 else -1 169 done = True if np.abs(new_angle) >= 12 * np.pi / 180 or np.abs(new_position) > 2.4 else False 170 171 return new_state_idx, reward, done
Computes the next state based on the current state indices and the action taken. Applies simplified physics calculations to determine the next state.
Parameters:
- position_idx (int): Current index of the cart's position.
- velocity_idx (int): Current index of the cart's velocity.
- angle_idx (int): Current index of the pole's angle.
- angular_velocity_idx (int): Current index of the pole's angular velocity.
- action (int): Action taken (0 for left, 1 for right).
Returns:
- tuple: Contains the next state index, the reward, and the done flag indicating if the episode has ended.