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zkK`N!!wFJED}{hC#C5(z;VcRoKlAJb^`p2=#&zLc(Wp|LyBv=-5Y9O%>(l=!x(>Sg z^Hj-VYMXmvBe$r8NGEbz 0) and (t<=10): # Accélération du leader + a = (Vd - Vmin) / 10 + vtleader = Vmin + a * t + vtold[-1] = vtleader + elif (t>= 16) and (t<=20): # Leader freine + a = - (Vd - Vmin) / 10 + vtleader = Vd + 2 * a * (t - 16) + vtold[-1] = vtleader + elif (t> 20) and (t<=30): # Accélération du leader + a = (Vd - Vmin) / 10 + vtleader = Vmin + a * (t-20) + vtold[-1] = vtleader + else: # Leader avance normalement + vtold[-1] = Vd + + vatt = vitesseatt(vtold) + vadop = vitesseadop(vtold, xxpold) + minimum = np.minimum(vatt, vadop) + print('minimum: ', minimum) + return minimum + + + +def position(fposition, newv): + newp = fposition + newv * dt + return newp + +xxbase = np.linspace(-nbv, 1, nbv) +xxpbase = np.linspace(0, 1, nbv) +yybase = np.linspace(0, 1, nbv) + +xxold = xxbase.copy() +xxpold = xxpbase.copy() +vtold = yybase.copy() + +while(t<=tf): + plt.figure(1,figsize=[16,9]) + # plt.clf() + plt.xlim([-1,41]) + plt.ylim([-0.5, Vd+1]) + + xx = px(xxold) + + vt = vitessereelle(t, vtold, xxpold) + + xxp = position(xxpold, vt) + + plt.scatter(xx, vt, c=colors) + + plt.plot([0,40],[Vd, Vd], color='k', linestyle='-', linewidth=1) + plt.xlabel('temps en s', fontsize = 16) + plt.ylabel('vitesse en m.s-¹', fontsize = 16) + plt.xticks(fontsize = 14) + plt.yticks(fontsize = 14) + # plt.title('Vitesse maximale désirée\nvitesse du leader : ' + str(Vd) + 'm.s-¹\ndistance entre deux voitures : ' + str(np.diff(xxpold)) + 'm\n\nTemps : ' + str(t)) + plt.draw() + if t == tf: + plt.savefig('gipps V2 (modélisation)/V1.png') + plt.pause(0.00001) + t += dt/fps + xxold = xx.copy() + xxpold = xxp.copy() + vtold = vt.copy() + +# images.merge() +# images2.merge(fps) \ No newline at end of file diff --git a/gipps V2 (modélisation)/gippsV2.py b/gipps V2 (modélisation)/gippsV2.py new file mode 100644 index 0000000..c189a3a --- /dev/null +++ b/gipps V2 (modélisation)/gippsV2.py @@ -0,0 +1,132 @@ +import numpy as np +import matplotlib.pyplot as plt +import time +from colour import Color +import imagesV2 as images + +fps = 4 + +# =========== +t0 = 0 +tf = 40 +dt = 1 +t = t0 +# =========== +nbv = 2 + +"""# =========== VARIABBLES +Xn(t) # position au temps t +Vn(t) # vitesse au temps t +An(t+Tr) # accel au temps t + Tr +ln # ? +k # ? +m # ? +""" + +# =========== CONSTANTES +An = 1.7 # accel max sampled from a normal distribution. N(1.7,0.3²) m/s² +Bn = -2 * An # frein max equated to - 2An +Sn = 6.5 # taille de la voiture plus marge sampled from a normal distribution. N(6.5,0.3²) m +Vd = 20.0 # vitesse désirée sampled from a normal distribution. N(20.0,3.2²) m/sec +Vmin = 1 +# X*n # position fin de freinage (calculable) +Tr = 2/3 + (2/3)/2 # temps de réaction + sûreté (= tau + θ = 2/3 + tau/2) +# B supposé égal à Bn-1 (si pas égal alors amplifications ??) + + +def rainbow_gradient(num_colors): + colors = [] + base_color = Color("violet") + gradient = list(base_color.range_to(Color("red"), num_colors)) + for color in gradient: + hex_code = color.hex_l + colors.append(hex_code) + return colors +colors = rainbow_gradient(nbv) + +def px(tt): # Avance au cours du temps + tt += 1/fps + return tt + +def vitesseatt(vtold): # Vitesse qu'il peut réellement atteindre d'un point de vue dynamique + value = vtold + 2.5 * An * Tr * ( 1 - (vtold/Vd) ) * np.sqrt( ( 0.025 + (vtold/Vd) )) + return value + + +def vitesseadop(vtold, xxpold): # Vitesse qu'il est possible d'adopter en connaissant les contraintes de sécurité liées à la présence du véhicule leader + dst = np.diff(xxpold) + value = Bn * Tr + np.sqrt( ((Bn)**2) * ((Tr)**2) - Bn * ( 2 * dst) - vtold[0] * Tr - ( (xxold[-1])**2 / Bn ) ) + newvalue = np.insert(value, 1, vtold[1]) + print('newvalue: ', newvalue) + return newvalue + +def vitessereelle(t, vtold, xxpold): # Vitesse du véhicule + + if t==0: + vtold[-1] = 0.1 + elif (t> 0) and (t<=10): # Accélération du leader + a = (10 - Vmin) / 10 + vtleader = Vmin + a * t + vtold[-1] = vtleader + elif (t>= 16) and (t<=20): # Leader freine + a = - (10 - Vmin) / 10 + vtleader = 10 + 2 * a * (t - 16) + vtold[-1] = vtleader + elif (t> 20) and (t<=29): # Accélération du leader + a = (Vd - Vmin) / 10 + vtleader = Vmin + a * (t-19) + vtold[-1] = vtleader + elif (t> 29) and (t<=40): # Accélération du leader + vtold[-1] = 20 + else: # Leader avance normalement + vtold[-1] = 10 + + vatt = vitesseatt(vtold) + vadop = vitesseadop(vtold, xxpold) + minimum = np.minimum(vatt, vadop) + print('minimum: ', minimum) + return minimum + + + +def position(fposition, newv): + newp = fposition + newv * dt + return newp + +xxbase = np.linspace(-nbv, 1, nbv) +xxpbase = np.linspace(0, 1, nbv) +yybase = np.linspace(0, 1, nbv) + +xxold = xxbase.copy() +xxpold = xxpbase.copy() +vtold = yybase.copy() + +while(t<=tf): + plt.figure(1,figsize=[16,9]) + # plt.clf() + plt.xlim([-1,41]) + plt.ylim([-0.5, Vd+1]) + + xx = px(xxold) + + vt = vitessereelle(t, vtold, xxpold) + + xxp = position(xxpold, vt) + + plt.scatter(xx, vt, c=colors) + + plt.plot([0,40],[Vd, Vd], color='k', linestyle='-', linewidth=1) + plt.xlabel('temps en s', fontsize = 16) + plt.ylabel('vitesse en m.s-¹', fontsize = 16) + plt.xticks(fontsize = 14) + plt.yticks(fontsize = 14) + # plt.title('Vitesse maximale désirée\nvitesse du leader : ' + str(Vd) + 'm.s-¹\ndistance entre deux voitures : ' + str(np.diff(xxpold)) + 'm\n\nTemps : ' + str(t)) + if t == tf: + plt.savefig('gipps V2 (modélisation)/V2-' + str(fps) + '.png') + plt.pause(0.0001) + t += dt/fps + xxold = xx.copy() + xxpold = xxp.copy() + vtold = vt.copy() + +# images.merge(fps) \ No newline at end of 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+import numpy as np +import matplotlib.pyplot as plt + +# =========== CONSTANTES +An = 1.7 # accel max sampled from a normal distribution. N(1.7,0.3²) m/s² +Bn = -2 * An # frein max equated to - 2An +Sn = 6.5 # taille de la voiture plus marge sampled from a normal distribution. N(6.5,0.3²) m +Vd = 20.0 # vitesse désirée sampled from a normal distribution. N(20.0,3.2²) m/sec +# X*n # position fin de freinage (calculable) +Tr = 2/3 + (2/3)/2 # temps de réaction + sûreté (= tau + θ = 2/3 + tau/2) +# B supposé égal à Bn-1 (si pas égal alors amplifications ??) + + +vv = np.linspace(0, 36, 200) + +def vitesseatt(vv): # Vitesse qu'il peut réellement atteindre d'un point de vue dynamique + value = vv + 2.5 * An * Tr * ( 1 - (vv/Vd) ) * np.sqrt( ( 0.025 + (vv/Vd) )) + return value + + +def vitesseadop(vv): # Vitesse qu'il est possible d'adopter en connaissant les contraintes de sécurité liées à la présence du véhicule leader + value = 1 + return value + +def vitessereelle(vv): # Vitesse maximale désirée + vatt = vitesseatt(vv) + vadop = vitesseadop(vv) + return min(vatt, vadop) + +def plotter(nb): + plt.plot([0,nb],[vitesseatt(nb), vitesseatt(nb)], color='k', linestyle='-', linewidth=1) + plt.plot([nb, nb],[0, vitesseatt(nb)], color='k', linestyle='-', linewidth=1) + plt.scatter(nb, vitesseatt(nb)) + +plt.figure(figsize=[16,9]) +plt.xlim([0, 37]) +plt.ylim([0, 35]) + +plt.plot(vv, vitesseatt(vv), '-', color='red') #, label="Vitesse qu'il peut réellement atteindre d'un point de vue dynamique" +# plt.plot(vv, vitesseadop(vv), '-', color='green', label='No mask') + +plotter(10) +plotter(20) +plotter(30) + +# plt.legend(fontsize = 16, loc='upper center') +# plt.title('Variation de la vitesse de la voiture suivant en fonction de la voiture leader (première partie du modèle de Gipps)') +plt.xlabel('vitesse de la voiture leader en m.s-¹', fontsize = 16) +plt.ylabel('vitesse de la voiture qui suit en m.s-¹', fontsize = 16) +plt.xticks(fontsize = 14) +plt.yticks(fontsize = 14) +plt.savefig('gipps V2 (modélisation)/graph.png') +plt.draw() +plt.pause(4) \ No newline at end of file diff --git a/gipps V2 (modélisation)/imagesV1.py b/gipps V2 (modélisation)/imagesV1.py new file mode 100644 index 0000000..ded5506 --- /dev/null +++ b/gipps V2 (modélisation)/imagesV1.py @@ -0,0 +1,42 @@ +from PIL import Image +import os +import shutil + +try:os.remove('gipps/merged.png') +except:pass + +def merge_images(overlay_folder, output_path): + overlay_path = f"{overlay_folder}/1.png" + overlay = Image.open(overlay_path) + result_width, result_height = overlay.size + result = Image.new('RGB', (result_width, result_height), color=(255, 255, 255)) + x, y = 0, 0 + for i in range(1,40): + overlay_path = f"{overlay_folder}/{i}.png" + overlay = Image.open(overlay_path) + result.paste(overlay, (x, y), overlay) + result.save(output_path) + +def detrf(folder_path): + try: + if os.path.exists(folder_path): + shutil.rmtree(folder_path) + print(f"Folder '{folder_path}' successfully deleted.") + else: + print(f"Folder '{folder_path}' does not exist.") + + try: + os.makedirs(folder_path) + print(f"Folder '{folder_path}' successfully created.") + except OSError as e: + print(f"Error creating folder: {e}") + + except OSError as e: + print(f"Error deleting folder: {e}") + +def merge(): + overlay_folder = "gipps/result" + output_path = "gipps/merged.png" + merge_images(overlay_folder, output_path) + detrf('gipps/result') + print('merge done') \ No newline at end of file diff --git a/gipps V2 (modélisation)/imagesV2.py b/gipps V2 (modélisation)/imagesV2.py new file mode 100644 index 0000000..6462e0e --- /dev/null +++ b/gipps V2 (modélisation)/imagesV2.py @@ -0,0 +1,42 @@ +from PIL import Image +import os +import shutil + +try:os.remove('gipps/merged.png') +except:pass + +def merge_images(overlay_folder, output_path, fps): + overlay_path = f"{overlay_folder}/1.png" + overlay = Image.open(overlay_path) + result_width, result_height = overlay.size + result = Image.new('RGB', (result_width, result_height), color=(255, 255, 255)) + x, y = 0, 0 + for i in range(1,40*fps): + overlay_path = f"{overlay_folder}/{i}.png" + overlay = Image.open(overlay_path) + result.paste(overlay, (x, y), overlay) + result.save(output_path) + +def detrf(folder_path): + try: + if os.path.exists(folder_path): + shutil.rmtree(folder_path) + 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- Umin) / 10, - (Umax - Umin) / 10) vt = np.where(t <= 10, Umin + a * t, Umax + 2 * a * (t - 10)) - print('vt: ', vt) + # print('vt: ', vt) return vt diff --git a/pipes/dist sécuritéV2.py b/pipes/dist sécuritéV2.py new file mode 100644 index 0000000..8014d38 --- /dev/null +++ b/pipes/dist sécuritéV2.py @@ -0,0 +1,54 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.ticker as ticker + +# vt = 1.25 # 4,5 km/h +Umin = 1 # vitesse m/s +Umax = 36 # environ 130 km/h +Wm = 4.23 # longueur du véhicule en m (moyenne française) +t = np.linspace(0, 15, 400) + +def vitesse(t): + a = np.where(t <= 10, (Umax - Umin) / 10, - (Umax - Umin) / 10) + vt = np.where(t <= 10, Umin + a * t, Umax + 2 * a * (t - 10)) + # print('vt: ', vt) + return vt + + +def security(t): + vt = np.linspace(1, 36, 400) + # ici la vitesse est encore en m/s + miles_per_meter = 0.000621371 + seconds_per_hour = 3600 + vt = vt * miles_per_meter * seconds_per_hour + dist = Wm * (1 + (vt/(16.1/3.6))) + # print(dist) + return dist + + +fig, ax1 = plt.subplots(figsize=[16, 9]) +ax1.set_xlim([-1, 16]) +ax1.set_xlabel('Temps (s)', fontsize = 16) +ax1.set_ylabel('Distance de sécurité en m', color='b', fontsize = 16) +ax1.plot(t, security(t), label='Distance de sécurité', color='b') +ax1.tick_params(axis='y', labelcolor='blue', labelsize = 14) +ax1.tick_params(axis='x', labelcolor='black', labelsize = 14) + +ax2 = ax1.twinx() +ax2.set_ylabel('Vitesse de la voiture leader en m/s', color='r', fontsize = 16) +vitesse_data = np.linspace(1, 36, 400) +ax2.plot(t, vitesse_data, label='Vitesse de la voiture leader', color='r') +ax2.tick_params(axis='y', labelcolor='r', labelsize = 14) + + +ax1.set_ylim(-1, 100) +ax2.set_ylim(-1, 100) + +ax1.yaxis.set_major_locator(ticker.LinearLocator(numticks=10)) +ax2.yaxis.set_major_locator(ticker.LinearLocator(numticks=10)) + +# plt.title(label='Variation de la distance de sécurité en fonction de la vitesse du leader selon le modèle de Pipes', fontsize= 16) 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