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#!/usr/bin/env python3 |
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# -*- coding: utf-8 -*- |
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""" |
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Created on Tue Feb 6 19:02:32 2024 |
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@author: marta |
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""" |
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import numpy as np |
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import plotly.graph_objects as go |
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from tqdm.notebook import tqdm |
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import plotly.express as px |
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import matplotlib as mpl |
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mpl.rcParams['figure.dpi'] = 300 |
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import matplotlib.pyplot as plt |
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import seaborn as sns |
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import os |
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from wand.image import Image as WImage |
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# sns.set(palette="husl",font_scale=1) |
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# %config InlineBackend.figure_format = 'retina' |
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import copy |
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np.random.seed(4032) |
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#%load_ext line_profiler |
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|
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#Define constants |
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#L = 2*np.pi # periodic domain size |
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L=10 |
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# define boundaries of simulation box |
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x0 = 0 |
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x1 = L |
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z0 = 0 |
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z1 = L |
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|
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# define reinforcement learning problem |
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N_states = 4 # number of states - one for each coarse-grained degree of vorticity |
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N_actions = 2 # number of actions - one for each coarse-grained swimming direction |
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# numerical parameters |
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dt = 0.0001 # timestep size |
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|
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#Utility functions |
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def moving_average(a, n=3) : |
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ret = np.cumsum(a, dtype=float) |
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ret[n:] = ret[n:] - ret[:-n] |
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return ret[n - 1:] / n |
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|
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# Runga-Kutta 4(5) integration for one step |
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# see https://stackoverflow.com/questions/54494770/how-to-set-fixed-step-size-with-scipy-integrate |
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def DoPri45Step(f,t,x,h): |
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k1 = f(t,x) |
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k2 = f(t + 1./5*h, x + h*(1./5*k1) ) |
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k3 = f(t + 3./10*h, x + h*(3./40*k1 + 9./40*k2) ) |
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k4 = f(t + 4./5*h, x + h*(44./45*k1 - 56./15*k2 + 32./9*k3) ) |
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k5 = f(t + 8./9*h, x + h*(19372./6561*k1 - 25360./2187*k2 + 64448./6561*k3 - 212./729*k4) ) |
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k6 = f(t + h, x + h*(9017./3168*k1 - 355./33*k2 + 46732./5247*k3 + 49./176*k4 - 5103./18656*k5) ) |
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v5 = 35./384*k1 + 500./1113*k3 + 125./192*k4 - 2187./6784*k5 + 11./84*k6 |
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k7 = f(t + h, x + h*v5) |
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v4 = 5179./57600*k1 + 7571./16695*k3 + 393./640*k4 - 92097./339200*k5 + 187./2100*k6 + 1./40*k7; |
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return v4,v5 |
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#Define useful data structures |
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#Define a dictionary of the possible states and their assigned indices |
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distance_states = ["ri", "rni"] #ri es rij<rct y rni es rij>rct |
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frecuency_states = ["wo", "wh"] #wo es w<wc y wh es w>wc |
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product_states = [(x,y) for x in distance_states for y in frecuency_states] # all possible states |
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state_lookup_table = {product_states[i]:i for i in range(len(product_states))} # returns index of given state |
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# print(product_states) # to view mapping |
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|
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#Define an agent class for reinforcement learning |
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class Agent: |
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def __init__(self, Ns): |
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self.r = np.zeros(Ns) # reward for each stage |
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self.t = 0 # time |
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|
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# calculate reward given from entering a new state after a selected action is undertaken |
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def calc_reward(self): |
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# enforce implementation by subclass |
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if self.__class__ == AbstractClass: |
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raise NotImplementedError |
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def update_state(self): |
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# enforce implementation by subclass |
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if self.__class__ == AbstractClass: |
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raise NotImplementedError |
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def take_random_action(self): |
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# enforce implementation by subclass |
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if self.__class__ == AbstractClass: |
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raise NotImplementedError |
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def take_greedy_action(self, Q): |
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# enforce implementation by subclass |
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if self.__class__ == AbstractClass: |
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raise NotImplementedError |
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#Define swimmer class derived from agent |
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class Swimmer(Agent): |
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def __init__(self, Ns, ni, sigma): |
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# call init for superclass |
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super().__init__(Ns) |
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self.ni = ni |
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self.sigma = sigma |
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# local position within the periodic box. X = [x, z]^T with 0 <= x < 2 pi and 0 <= z < 2 pi |
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self.X = np.array([np.random.uniform(0, L), np.random.uniform(0, L), 0]) |
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# absolute position. -inf. <= x_total < inf. and -inf. <= z_total < inf. |
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self.X_total = self.X |
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# particle orientation |
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self.theta = np.random.uniform(0, 2*np.pi) # polar angle theta in the x-z plane |
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self.p = np.array([np.cos(self.theta), np.sin(self.theta)]) # p = [px, pz]^T |
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# translational and rotational velocity |
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self.U = np.zeros(3, float) |
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self.W = np.array([0., 0., 1.]) #Velocidad angular aleatoria |
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#distancia entre el swimmer y el obstáculo |
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self.R=np.random.uniform(0, 2.5, 1) |
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print(self.R) |
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# preferred swimming direction (equal to [1,0], [0,1], [-1,0], or [0,-1]) |
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self.ka = np.array([0,1]) |
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# history of local and global position. Only store information for this episode. |
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self.history_X = [self.X] |
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self.history_X_total = [self.X_total] |
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# local vorticity at the current location |
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_, _, self.w = tgv(self.X[0], self.X[1]) |
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# update coarse-grained state |
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self.update_state() |
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#obstáculos |
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self.obstacles= self.generate_obstacles() |
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#distancia entre el swimmer y el obstáculo |
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#self.R = [np.linalg.norm(self.X[:2] - np.array([obstacle_x, obstacle_y])) for obstacle_x, obstacle_y in zip(self.obstacles[::2], self.obstacles[1::2])] |
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def generate_obstacles(self): |
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obstacles=[] #el numero de obstáculos será 10*10 |
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cell_spacing= L/4 |
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for i in range(4): |
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for j in range(4): |
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obstacle_x= i*cell_spacing |
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obstacle_y= j*cell_spacing |
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obstacles.append(obstacle_x) |
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obstacles.append(obstacle_y) |
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return obstacles |
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def interaction_with_obstacles(self,obstacles,kappa,alpha,beta,gamma,Pe,dt): |
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F= np.array([0.,0.,0.]) |
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for i in range(len(obstacles)//2): |
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#F1 |
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obstacle_position = np.array([obstacles[2*i],obstacles[2*i+1], 0]) |
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r=self.X - obstacle_position |
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r_norm=np.linalg.norm(r) |
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Re= (.5*self.sigma)**2*np.linalg.norm(self.W)/self.ni |
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S=1/(1+np.exp(-kappa*((Re/r_norm**3)-Re))) |
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F1=alpha*(Re/r_norm**3)*np.cross(self.U,self.W)*S |
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#F2 |
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F2=beta*np.cross(self.W,r)/r_norm**3 |
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#F de atracción |
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F_attr= gamma*(np.exp(-r_norm/kappa)/r_norm**2)*(kappa+r_norm)*r |
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#Fuerza total |
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F+=F1+F2+F_attr |
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xi=np.random.normal(0,1, size=2) #vector de números aleatorios generados a partir de una distribución normal estándar con dos componentes, xi creo que es un vector de ruido estocástico (modela el ruido térmico) |
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dr_therm = np.sqrt(2*self.sigma**2*dt/Pe)*xi |
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dr = F[:-1]*dt + dr_therm |
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#actualizamos la posición del spinner |
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self.X[:-1] += dr |
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self.U = np.array([dr[0]/dt, dr[1]/dt, 0]) |
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all_dists = np.empty(len(obstacles)//2) |
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for i in range(len(obstacles)//2): |
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all_dists[i] = np.linalg.norm(self.X-np.array([obstacles[2*i],obstacles[2*i+1], 0])) |
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self.R = np.amin(all_dists) |
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#comprobamos que el spinner siga dentro del box periódico |
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self.check_in_box() |
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def reinitialize(self): |
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self.X = np.array([np.random.uniform(0, L), np.random.uniform(0, L)]) |
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self.X_total = self.X |
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self.theta = np.random.uniform(0, 2*np.pi) # polar angle theta in the x-z plane |
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self.p = np.array([np.cos(self.theta), np.sin(self.theta)]) # p = [px, pz]^T # orientación del nadador |
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self.U = np.zeros(2) |
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self.W = np.array([0, 0, 1]) |
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self.ka = np.array([0,1]) |
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self.history_X = [self.X] |
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self.history_X_total = [self.X_total] |
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self.R=np.random.uniform(0, 2.5) |
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self.t = 0 |
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def update_kinematics(self, Φ, Ψ, D0 = 0, Dr = 0, int_method = "euler"): # Actualiza la posición y orientación del nadador según un método de integración especificado. |
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if int_method == "rk45": |
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y0 = np.concatenate((self.X,self.p)) |
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_, v5 = DoPri45Step(self.calc_velocity_rk45,self.t,y0,dt) |
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y = y0 + dt*v5 |
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self.X = y[:2] |
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self.p = y[2:] |
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dx = self.X - self.history_X[-1] |
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self.X_total = self.X_total + dx |
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# check if still in the periodic box |
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self.check_in_box() |
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# ensure the vector p has unit length |
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self.p /= (self.p[0]**2 + self.p[1]**2)**(1/2) |
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# update polar angle |
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x = self.p[0] |
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yy = self.p[1] |
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self.theta = np.arctan2(yy,x) if yy >= 0 else (np.arctan2(yy,x) + 2*np.pi) |
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# store positions |
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self.history_X.append(self.X) |
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self.history_X_total.append(self.X_total) |
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elif int_method == "euler": |
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# calculate new translational and rotational velocity |
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self.calc_velocity(Φ, Ψ) |
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self.update_position(int_method, D0) |
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self.update_orientation(int_method, Dr) |
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else: |
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raise Exception("Integration method must be 'Euler' or 'rk45'") |
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self.t = self.t + dt |
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def calc_velocity_rk45(self, t, y): #calcula la velocidad del nadador en un determinado tiempo 't' y estado 'y' utilizando Rk45 |
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x = y[0] |
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z = y[1] |
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px = y[2] |
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pz = y[3] |
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ux, uz, self.w = tgv(x, z) #tgv proporciona velocidades de flujo en la posición (x,z), w es la vorticidad |
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#cálculo de las velocidades translacionales |
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U0 = ux + Φ*px #ux y uz son las velocidades del flujo |
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U1 = uz + Φ*pz |
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#cálculo de las velocidades rotacionales |
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ka_dot_p = self.ka[0]*px + self.ka[1]*pz #alineación del vector de nado preferido con la dirección del nadador |
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W0 = 1/2/Ψ*(self.ka[0] - ka_dot_p*px) + 1/2*pz*self.w |
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W1 = 1/2/Ψ*(self.ka[1] - ka_dot_p*pz) + 1/2*-px*self.w |
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return np.array([U0, U1, W0, W1]) |
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def update_position(self, int_method, D0): #D0 representa la difusión |
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# use explicit euler to update |
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dx = dt*self.U |
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if D0 > 0: dx = dx + np.sqrt(2*D0*dt)*np.random.normal(size=2) #posible efecto de la difusión browniana |
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self.X = self.X + dx |
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self.X_total = self.X_total + dx |
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# check if still in the periodic box |
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self.check_in_box() |
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# store positions |
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self.history_X.append(self.X) |
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self.history_X_total.append(self.X_total) |
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def update_orientation(self, int_method, Dr): |
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self.p = self.p + dt*self.W #W velocidad angular |
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# ensure the vector p has unit length |
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self.p /= (self.p[0]**2 + self.p[1]**2)**(1/2) |
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# if rotational diffusion is present |
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if Dr > 0: #Dr representa difucion rotacional |
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px = self.p[0] |
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pz = self.p[1] |
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cross = px*pz |
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A = np.array([[1-px**2, -cross], [-cross, 1-pz**2]]) #A es una matriz |
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v = np.sqrt(2*Dr*dt)*np.random.normal(size=2) #v es un vector de valores aleatorios |
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self.p[0] = self.p[0] + A[0,0]*v[0] + A[0,1]*v[1] #Se calcula un cambio aleatorio en la orientación usando A y v |
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self.p[1] = self.p[1] + A[1,0]*v[0] + A[1,1]*v[1] |
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self.p /= (self.p[0]**2 + self.p[1]**2)**(1/2) |
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# update polar angle |
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x = self.p[0] |
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y = self.p[1] |
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self.theta = np.arctan2(y,x) if y >= 0 else (np.arctan2(y,x) + 2*np.pi) |
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def calc_velocity(self, Φ, Ψ): |
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ux, uz, self.w = tgv(self.X[0], self.X[1]) |
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# careful - computing in the following way is significantly slower: self.U = np.array(ux, uz) + Φ*self.p |
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self.U[0] = ux + Φ*self.p[0] |
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self.U[1] = uz + Φ*self.p[1] |
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px = self.p[0] |
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pz = self.p[1] |
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ka_dot_p = self.ka[0]*px + self.ka[1]*pz |
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self.W[0] = 1/2/Ψ*(self.ka[0] - ka_dot_p*px) + 1/2*pz*self.w |
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self.W[1] = 1/2/Ψ*(self.ka[1] - ka_dot_p*pz) + 1/2*-px*self.w |
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def check_in_box(self): # Este método verifica si el nadador todavía está dentro del cuadro periódico |
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if self.X[0] < x0: |
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self.X[0] += L |
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elif self.X[0] > x1: |
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self.X[0] -= L |
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if self.X[1] < z0: |
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self.X[1] += L |
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elif self.X[1] > z1: |
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self.X[1] -= L |
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def calc_reward(self, n): |
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self.r[n] = self.history_X_total[-1][1]-self.history_X_total[-2][1] |
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def update_state(self): |
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#self.distance_obstacles() |
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#componente z de la velocidad angular |
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W_z = self.W[2] |
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if W_z <= 0.175*self.ni/(.5*self.sigma*self.sigma): |
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W_state = "wo" |
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elif W_z > 0.175*self.ni/(.5*self.sigma*self.sigma): |
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W_state = "wh" |
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else: |
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raise Exception("Invalid value of w detected: ", W_z) |
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if self.R <= 1.25: |
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R_state = "ri" |
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elif self.R > 1.25: |
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R_state = "rni" |
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else: |
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raise Exception ("Invalid value of r detected: ", self.R) |
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self.my_state = (R_state, W_state) |
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def take_greedy_action(self, Q): |
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state_index = state_lookup_table[self.my_state] |
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action_index = np.argmax(Q[state_index]) # find largest entry in this row of Q (i.e. this state) |
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Wc=0.175*self.ni/(.5*self.sigma*self.sigma) |
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if action_index == 0: # aumenta 1/8W |
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self.W[2] += 1./8*Wc |
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elif action_index == 1: # disminuye 1/8W |
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self.W[2] -= 1./8*Wc |
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else: |
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raise Exception ("Action index out of bounds: ", action_index) |
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return action_index |
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def take_random_action(self): |
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action_index = np.random.randint(0, 2, 1) |
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Wc=0.175*self.ni/(.5*self.sigma*self.sigma) |
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if action_index == 0: # aumenta 1/8W |
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self.W[2] += 1./8*Wc |
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else: # disminuye 1/8W |
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self.W[2] -= 1./8*Wc |
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return action_index |
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#Define Taylor-Green vortex |
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# given position, return local velocity and vorticity |
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def tgv(x, z): |
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ux = -1/2*np.cos(x)*np.sin(z) |
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uz = 1/2*np.sin(x)*np.cos(z) |
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w = -np.cos(x)*np.cos(z) |
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return ux, uz, w |
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def training(alpha0, Φ, Ψ, Ns=4000, Ne=5000, gamma=0.999, eps0=0.0, D0=0, Dr=0, n_updates=1000, \ |
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RIC=False, method="Qlearning", lr_decay=None, omega=0.85, eps_decay=False, Qin=None): |
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# n_updates - how often to plot the trajectory undertaken by the particle during the learning process |
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# Ne - number of episodes |
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# Ns - number of steps in an episode |
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# alpha0 - learning rate (or starting learning rate when employing LR decay) |
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# gamma - discount factor, i.e. how much we weigh future to present rewards. Close to 0 = myopic view. |
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# eps0 - fraction of the time we allow for exploration in selecting the following action. 0 = always greedy. |
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# D0 - translational diffusivity |
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# Dr - rotational diffusivity |
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# RIC - Reset of Initial Conditions. First time a state-action pair is encountered, set Q[s,a] = reward |
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# method - choose from Q-learning, Double Q-learning (, or Expected SARSA |
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# lr_decay - whether or not to use learning rate decay. Options are none, or polynomial (lr=1/#(s,a)**omega) |
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# omega - exponent used in lr_decay: lr = 1/#(s,a)**omega |
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# eps_decay - whether or not to decay epsilon linearly: eff_eps = eps0/k for the k-th step |
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# Qin - initial Q matrix. Useful for testing performance after an extensive exploration phase. |
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# if using the expected SARSA method, turn on epsilon decay since eps = 0 is simply Q-learning anyway |
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if method=="expSARSA": |
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eps_decay = True |
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if eps0 == 0: eps0 = 1 |
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# Total reward for each episode |
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hist_R_tot_smart = np.zeros(Ne) |
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hist_R_tot_naive= np.zeros(Ne) |
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# learning gain per episode |
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Σ = np.zeros(Ne) |
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smart_stored_histories = [] # store position = f(t) every so often for an episode (smart particles) |
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naive_stored_histories = [] # store position = f(t) every so often for an episode (naive particles) |
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# number of times each state-action pair has been explored |
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state_action_counter = np.zeros((N_states,N_actions)) |
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# initialize a naive and a smart gyrotactic particle |
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naive = Swimmer(Ns) |
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smart = Swimmer(Ns) |
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# initialize Q matrix to large value |
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if method=="doubleQ": |
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Q1 = L*Ns*np.ones((4, 2)) |
||||
Q2 = L*Ns*np.ones((4, 2)) |
||||
else: |
||||
Q = L*Ns*np.ones((4, 2)) # 4 states, 2 possible actions. Each column is an action, w. |
||||
|
||||
if Qin is not None: Q = Qin |
||||
|
||||
# store average Q for each episode to track convergence |
||||
avg_Q_history = np.zeros((Ne,4,2)) |
||||
|
||||
# store initial position and orientation for each episode |
||||
initial_coords = np.zeros((Ne,3)) |
||||
|
||||
# iterate over episodes |
||||
k = 0 |
||||
for ep in tqdm(range(Ne)): |
||||
|
||||
# assign random orientation and position |
||||
smart.reinitialize() |
||||
naive.reinitialize() |
||||
naive = copy.deepcopy(smart) # have naive and smart share initial conditions for visualization purposes |
||||
|
||||
# store initialization |
||||
initial_coords[ep,0:2] = smart.X |
||||
initial_coords[ep,2] = smart.theta |
||||
|
||||
# save selected actions and particle orientation for last episodes |
||||
if ep == Ne - 1: |
||||
chosen_actions = np.zeros(Ns) |
||||
theta_history = np.zeros(Ns) |
||||
|
||||
# iterate over stages within an episode |
||||
for stage in range(Ns): |
||||
|
||||
# select an action eps-greedily. Note naive never changes its action/strategy (i.e. trying to swim up) |
||||
Qinput = Q1 + Q2 if method=="doubleQ" else Q |
||||
k = k + 1 # k-th update |
||||
|
||||
eff_eps = eps0/k**omega if eps_decay else eps0 # decrease amount of exploration as time proceeds |
||||
if np.random.uniform(0, 1) < eff_eps: |
||||
action = smart.take_random_action() |
||||
else: |
||||
action = smart.take_greedy_action(Qinput) |
||||
|
||||
# record action and orientation on last episode |
||||
if ep == Ne - 1: |
||||
chosen_actions[stage] = action |
||||
theta_history[stage] = smart.theta |
||||
|
||||
# record index of the prior state |
||||
old_s = state_lookup_table[smart.my_state] |
||||
|
||||
# given selected action, update the state |
||||
naive.update_kinematics(Φ, Ψ, D0, Dr) |
||||
smart.update_kinematics(Φ, Ψ, D0, Dr) |
||||
smart.update_state() # only need to update smart particle since naive has ka = [0, 1] always |
||||
|
||||
# calculate reward based on new state |
||||
naive.calc_reward(stage) |
||||
smart.calc_reward(stage) |
||||
|
||||
new_s = state_lookup_table[smart.my_state] |
||||
state_action_counter[new_s,action] += 1 |
||||
|
||||
# employ learning rate decay if applicable |
||||
alpha = alpha0/(1+state_action_counter[old_s,action])**omega if lr_decay else alpha0 |
||||
|
||||
# update Q matrix |
||||
if method=="doubleQ": |
||||
if np.random.uniform(0, 1) < 0.5: # update Q1 |
||||
if Q1[old_s, action] == L*Ns and RIC==True: # apply Reset of Initial Conditions (RIC) |
||||
Q1[old_s, action] = smart.r[stage] |
||||
else: |
||||
Q1[old_s, action] = Q1[old_s, action] + alpha*(smart.r[stage] + \ |
||||
gamma*np.max(Q2[new_s,:])-Q1[old_s,action]) |
||||
else: # update Q2 |
||||
if Q2[old_s, action] == L*Ns and RIC==True: |
||||
Q2[old_s, action] = smart.r[stage] |
||||
else: |
||||
Q2[old_s, action] = Q2[old_s, action] + alpha*(smart.r[stage] + \ |
||||
gamma*np.max(Q1[new_s,:])-Q2[old_s,action]) |
||||
if method=="expSARSA": |
||||
# calculate V, the expected Q value for the next state-actio pair |
||||
V = 0 |
||||
greedy_action = np.argmax(Q[new_s]) # would-be greedy action for new state |
||||
for new_action in range(N_actions): |
||||
pi = (1 - eff_eps) + eff_eps/N_actions if new_action == greedy_action else eff_eps/N_actions |
||||
V = V + pi*Q[new_s, new_action] |
||||
|
||||
if Q[old_s, action] == L*Ns and RIC==True: |
||||
Q[old_s, action] = smart.r[stage] |
||||
else: |
||||
Q[old_s, action] = Q[old_s, action] + alpha*(smart.r[stage] + gamma*V - Q[old_s,action]) |
||||
else: |
||||
if Q[old_s, action] == L*Ns and RIC==True: |
||||
Q[old_s, action] = smart.r[stage] |
||||
else: |
||||
Q[old_s, action] = Q[old_s, action] + alpha*(smart.r[stage] + \ |
||||
gamma*np.max(Q[new_s,:])-Q[old_s,action]) |
||||
|
||||
# store average Q for each episode to track convergence |
||||
avg_Q_history[ep] = avg_Q_history[ep] + Q1 + Q2 if method=="doubleQ" else avg_Q_history[ep] + Q |
||||
|
||||
avg_Q_history[ep] = avg_Q_history[ep]/Ns |
||||
|
||||
|
||||
# calculate Rtot for this episode |
||||
R_tot_naive = np.sum(naive.r) |
||||
R_tot_smart = np.sum(smart.r) |
||||
|
||||
# calculate learning gain for this episode |
||||
Σ[ep] = R_tot_smart/R_tot_naive - 1 |
||||
hist_R_tot_smart[ep] = R_tot_smart |
||||
hist_R_tot_naive[ep] = R_tot_naive |
||||
|
||||
# plot trajectory every so often |
||||
if ep%n_updates==0 or ep==Ne-1: |
||||
smart_history_X_total = np.array(smart.history_X_total) |
||||
smart_stored_histories.append((ep,smart_history_X_total)) |
||||
naive_history_X_total = np.array(naive.history_X_total) |
||||
naive_stored_histories.append((ep,naive_history_X_total)) |
||||
|
||||
# save optimal policy |
||||
if ep==Ne-1: |
||||
filename = "Policies/Q_alpha_" + str(alpha).replace(".","d") + "_Ns_" + str(Ns) + "_Ne_" + str(Ne) + \ |
||||
"_Φ_" + str(Φ).replace(".","d") + "_Ψ_" + str(Ψ).replace(".","d") + "_eps_" \ |
||||
+ str(eff_eps).replace(".","d") + "_epsdecay_" + str(eps_decay) |
||||
if lr_decay: filename = filename + "_omega_" + str(omega) |
||||
if method=="doubleQ": filename = filename + "_" + str(method) |
||||
if RIC: filename = filename + "_RIC_" + str(RIC) |
||||
Qout = Q1 + Q2 if method=="doubleQ" else Q |
||||
np.save(filename, Qout) |
||||
|
||||
return Qout, Σ, smart, naive, hist_R_tot_smart, hist_R_tot_naive, smart_stored_histories, naive_stored_histories, \ |
||||
state_action_counter, chosen_actions, avg_Q_history, initial_coords, theta_history |
||||
#Plot |
||||
|
||||
Q = np.random.rand(4, 2) |
||||
|
||||
#Q = np.array([[1, 0], |
||||
#[2, 1], |
||||
#[0, 0], |
||||
#[1, 2]]) |
||||
|
||||
print(Q) |
||||
|
||||
Ns = 5000 |
||||
spinner = Swimmer(Ns, 1, 1) |
||||
traj = [] |
||||
obstacles = spinner.generate_obstacles() |
||||
for i in range(Ns): |
||||
spinner.interaction_with_obstacles(obstacles, 2.5, 1, 1., 2.5e-4, 10000, 0.001) |
||||
traj.append(spinner.X[0]) |
||||
traj.append(spinner.X[1]) |
||||
|
||||
action_index = spinner.take_greedy_action(Q) |
||||
|
||||
|
||||
spinner.update_state() |
||||
|
||||
#print("Mi estado", spinner.my_state) |
||||
#print("Valor de Wz después de tomar la acción:", spinner.W[2]) |
||||
|
||||
fig, ax= plt.subplots(1,1) |
||||
ax.plot(traj[::2], traj[1::2], '.') |
||||
ax.plot(obstacles[::2], obstacles[1::2], '.') |
||||
ax.set_aspect('equal') |
||||
print(obstacles[::2]) |
||||
plt.show() |
||||
|
||||
|
||||
#comprobación de que W va cambiando |
||||
|
||||
Loading…
Reference in new issue