452 lines
14 KiB
Python
452 lines
14 KiB
Python
import math
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import numpy as np
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def sandbox(t):
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"""
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python simulator.py -m sandbox
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Un premier bac à sable pour faire des expériences
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La fonction reçoit le temps écoulé depuis le début (t) et retourne une position cible
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pour les angles des 12 moteurs
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- Entrée: t, le temps (secondes écoulées depuis le début)
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- Sortie: un tableau contenant les 12 positions angulaires cibles (radian) pour les moteurs
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"""
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# Par exemple, on envoie un mouvement sinusoidal
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targets = [0] * 12
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targets[0] = t ** 3
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targets[1] = 0
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targets[2] = 0
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targets[3] = t ** 3
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targets[4] = 0
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targets[5] = 0
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targets[6] = t ** 3
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targets[7] = 0
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targets[8] = 0
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targets[9] = t ** 3
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targets[10] = 0
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targets[11] = 0
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return targets
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def direct(alpha, beta, gamma):
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"""
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python simulator.py -m direct
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Le robot est figé en l'air, on ne contrôle qu'une patte
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Reçoit en argument la cible (alpha, beta, gamma) des degrés de liberté de la patte, et produit
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la position (x, y, z) atteinte par le bout de la patte
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- Sliders: les angles des trois moteurs (alpha, beta, gamma)
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- Entrées: alpha, beta, gamma, la cible (radians) des moteurs
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- Sortie: un tableau contenant la position atteinte par le bout de la patte (en mètres)
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"""
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return 0, 0, 0
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from math import *
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l1h = 0.049
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l1v = 0.032
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l1 = l1h
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l2h = 0.0605
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l2v = 0.02215
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l2 = sqrt(l2h ** 2 + l2v ** 2)
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l3h = 0.012
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l3v = 0.093
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l3 = sqrt(l3h ** 2 + l3v ** 2)
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tete_x = 0.095
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patte_y = 0.032
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patte_x = 0.079
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def inverse(x, y, z):
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"""
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python simulator.py -m inverse
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Le robot est figé en l'air, on ne contrôle qu'une patte
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Reçoit en argument une position cible (x, y, z) pour le bout de la patte, et produit les angles
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(alpha, beta, gamma) pour que la patte atteigne cet objectif
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- Sliders: la position cible x, y, z du bout de la patte
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- Entrée: x, y, z, une position cible dans le repère de la patte (mètres), provenant du slider
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- Sortie: un tableau contenant les 3 positions angulaires cibles (en radians)
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"""
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# Dimensions (m)
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z += l1v
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theta0 = atan2(y, x)
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l = sqrt((sqrt(x ** 2 + y ** 2) - l1) ** 2 + z ** 2)
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# l = sqrt((x - l1h*cos(theta0)) ** 2 + (y - l1h*sin(theta0)) ** 2 + (z + l1v) ** 2)
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param2 = -1 * (-(l ** 2) + l2 ** 2 + l3 ** 2) / (2 * l2 * l3)
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if param2 > 1 or param2 < -1:
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print("\033[94m" + f"Tentative d'acces a une position impossible (param2) ({x}, {y}, {z})" + "\033[0m")
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param2 = 1 if param2 > 1 else -1
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theta2 = acos(param2)
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param1 = (-l3 ** 2 + l2 ** 2 + l ** 2) / (2 * l2 * l)
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if param1 > 1 or param1 < -1:
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print("\033[94m" + f"Tentative d'acces a une position impossible (param1) ({x}, {y}, {z})" + "\033[0m")
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param1 = 1 if param1 > 1 else -1
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theta1 = acos(param1) + asin(z / l)
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# return [-theta0, theta1, theta2]
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angle1 = atan(l2v / l2h)
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return [-theta0, theta1 + angle1, theta2 + angle1 - pi / 2 + atan(l3h / l3v)]
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# return [0, angle1 , angle1 -pi/2 + atan(l3h/l3v)]
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def draw(t):
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"""
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python simulator.py -m draw
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Le robot est figé en l'air, on ne contrôle qu'une patte
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Le but est, à partir du temps donné, de suivre une trajectoire de triangle. Pour ce faire, on
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utilisera une interpolation linéaire entre trois points, et la fonction inverse précédente.
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- Entrée: t, le temps (secondes écoulées depuis le début)
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- Sortie: un tableau contenant les 3 positions angulaires cibles (en radians)
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"""
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def interpol(x2, y2, z2, x1, y1, z1, t):
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return t * x1 + (1 - t) * x2, t * y1 + (1 - t) * y2, t * z1 + (1 - t) * z2
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p1 = [0.15, 0, 0]
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p2 = [0.1, 0.1, 0]
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p3 = [0.1, 0, 0.05]
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positions = [p1, p2, p3]
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ratio = (t % 1)
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partie = floor((t % 3))
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partie2 = (partie + 1) % 3
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# print(f"partie: {partie}, partie2: {partie2}")
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wanted_origin_x, wanted_origin_y, wanted_origin_z = positions[partie][0], positions[partie][1], positions[partie][
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2],
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wanted_dest_x, wanted_dest_y, wanted_dest_z = positions[partie2][0], positions[partie2][1], positions[partie2][2],
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# print(wanted_origin_x, wanted_origin_y, wanted_origin_z)
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# print(wanted_dest_x, wanted_dest_y, wanted_dest_z)
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# print(t)
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wanted_x, wanted_y, wanted_z = interpol(wanted_origin_x, wanted_origin_y, wanted_origin_z, wanted_dest_x,
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wanted_dest_y, wanted_dest_z, ratio)
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return inverse(wanted_x, wanted_y, wanted_z)
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def legs(targets_robot):
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"""
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python simulator.py -m legs
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Le robot est figé en l'air, on contrôle toute les pattes
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- Sliders: les 12 coordonnées (x, y, z) du bout des 4 pattes
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- Entrée: des positions cibles (tuples (x, y, z)) pour le bout des 4 pattes
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- Sortie: un tableau contenant les 12 positions angulaires cibles (radian) pour les moteurs
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"""
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targets = [0] * 18
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cos_val = [0, 0, -1, 0, 0, 1]
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sin_val = [-1, -1, 0, 1, 1, 0]
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offset_x = [-patte_x, -patte_x, -tete_x, -patte_x, -patte_x, -tete_x]
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offset_y = [patte_y, -patte_y, 0, patte_y, -patte_y, 0]
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for i in range(6):
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target_x, target_y, target_z = targets_robot[i]
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target_x_tmp = cos_val[i] * target_x - sin_val[i] * target_y
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target_y = sin_val[i] * target_x + cos_val[i] * target_y
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target_x = target_x_tmp
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target_x += offset_x[i]
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target_y += offset_y[i]
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alpha, beta, gamma = inverse(target_x, target_y, target_z)
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targets[3 * i] = alpha
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targets[3 * i + 1] = beta
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targets[3 * i + 2] = gamma
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return targets
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def interpol2(point2, point1, t):
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x1, y1, z1 = point1
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x2, y2, z2 = point2
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return t * x1 + (1 - t) * x2, t * y1 + (1 - t) * y2, t * z1 + (1 - t) * z2
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def walkV1(t, speed_x, speed_y, speed_rotation):
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"""
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python simulator.py -m walk
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Le but est d'intégrer tout ce que nous avons vu ici pour faire marcher le robot
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- Sliders: speed_x, speed_y, speed_rotation, la vitesse cible du robot
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- Entrée: t, le temps (secondes écoulées depuis le début)
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speed_x, speed_y, et speed_rotation, vitesses cibles contrôlées par les sliders
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- Sortie: un tableau contenant les 12 positions angulaires cibles (radian) pour les moteurs
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"""
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# t = t*speed_x * 20
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num_patte = 4
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slider_max = 0.200
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neutral_position = np.array([
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[0.1, 0.15, -0.16],
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[-0.1, 0.15, -0.16],
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[-0.2, -0.00, -0.16],
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[-0.1, -0.15, -0.16],
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[0.1, -0.15, -0.16],
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[0.2, 0, -0.16]
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])
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real_position = np.copy(neutral_position)
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movement_x = np.array([
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[0.0, 0, 0],
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[0.00, 0, 0],
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[-0.00, 0, 0],
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])
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movement_y = np.array([
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[0.0, 0, 0],
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[0, 0.00, 0],
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[0, -0.00, 0],
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])
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movement_z = np.array([
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[0, 0, 0],
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[0, 0, 0],
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[0, 0, 0]
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])
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step_duration = np.array([0.05, 0.3, 0.05])
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step_count = len(movement_z)
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movement_duration = np.sum(step_duration)
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assert len(
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step_duration) == step_count, f"all movements steps must have a length, currently, {len(step_duration)}/{step_count} have them"
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def get_current_step(t):
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time_passed = 0
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for i in range(len(step_duration)):
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time_passed += step_duration[i]
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if t % movement_duration < time_passed:
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return i
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def get_current_step_advancement(t):
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current_step = get_current_step(t)
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t = t % movement_duration
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for i in range(0, current_step):
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t -= step_duration[i]
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return t / step_duration[current_step]
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def get_next_step(t):
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return floor((get_current_step(t) + 1) % step_count)
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def rotate(patte):
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return [1, -1, -1, 1][
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patte] * movement_x # + [-1, 1, -1, 1][patte] * movement_y # mettre des 0 partout sur le Y fait une très belle rotation
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def normalize(matrix, slider_max, speed):
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return (matrix / slider_max) * speed
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offsets = np.array([0, 0.5, 0, 0.5]) * movement_duration # offset between each leg
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assert len(offsets) == num_patte, f"all offsets must be set, currently, {len(offsets)}/{num_patte} have them"
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for patte in range(num_patte):
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time = t + offsets[patte]
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mov_index_start = get_current_step(time)
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mov_index_end = get_next_step(time)
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mov_start_x = normalize(movement_x[mov_index_start], slider_max, speed_x)
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mov_end_x = normalize(movement_x[mov_index_end], slider_max, speed_x)
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mov_start_y = normalize(movement_y[mov_index_start], slider_max, speed_y)
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mov_end_y = normalize(movement_y[mov_index_end], slider_max, speed_y)
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mov_start_z = movement_z[mov_index_start]
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mov_end_z = movement_z[mov_index_end]
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mov_start_rotate = normalize(rotate(patte)[mov_index_start], 0.5, speed_rotation)
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mov_end_rotate = normalize(rotate(patte)[mov_index_end], 0.5, speed_rotation)
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mov_start = neutral_position[patte] + mov_start_z + mov_start_x + mov_start_y + mov_start_rotate
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mov_end = neutral_position[patte] + mov_end_z + mov_end_x + mov_end_y + mov_end_rotate
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(real_position[patte][0],
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real_position[patte][1],
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real_position[patte][2]) = interpol2(mov_start, mov_end, get_current_step_advancement(time))
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print(
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f"[{patte}] [{get_current_step(time)}->{get_next_step(time)}], start: {mov_start}, end: {mov_end}, current ({real_position[patte][0]}, {real_position[patte][1]}, {real_position[patte][2]})")
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return legs(real_position)
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def translate(tx, ty, tz):
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return np.array([
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[1.0, 0.0, 0.0, tx],
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[0.0, 1.0, 0.0, ty],
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[0.0, 0.0, 1.0, tz],
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[0.0, 0.0, 0.0, 1.0],
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])
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def Rx(alpha):
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return np.array([
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[1.0, 0.0, 0.0, 0.0],
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[0.0, np.cos(alpha), -np.sin(alpha), 0.0],
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[0.0, np.sin(alpha), np.cos(alpha), 0.0],
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[0.0, 0.0, 0.0, 1.0],
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])
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def Ry(alpha):
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return np.array([
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[np.cos(alpha), 0.0, -np.sin(alpha), 0.0],
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[0.0, 1.0, 0.0, 0.0],
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[np.sin(alpha), 0.0, np.cos(alpha), 0.0],
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[0.0, 0.0, 0.0, 1.0],
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])
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def Rz(alpha):
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return np.array([
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[np.cos(alpha), -np.sin(alpha), 0.0, 0.0],
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[np.sin(alpha), np.cos(alpha), 0.0, 0.0],
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[0.0, 0.0, 1.0, 0.0],
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[0.0, 0.0, 0.0, 1.0],
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])
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# multiplication de matrices: @
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# gauche: monde, droite: repere
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def walkV2(t, speed_x, speed_y, speed_rotation):
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def get_rotation_center(speed_x, speed_y, theta_point):
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direction = np.array([-speed_y, speed_x])
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return direction / max(0.001, theta_point)
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x0, y0 = get_rotation_center(speed_x, speed_y, speed_rotation)
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print(x0, y0)
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"""
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python simulator.py -m walk
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Le but est d'intégrer tout ce que nous avons vu ici pour faire marcher le robot
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- Sliders: speed_x, speed_y, speed_rotation, la vitesse cible du robot
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- Entrée: t, le temps (secondes écoulées depuis le début)
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speed_x, speed_y, et speed_rotation, vitesses cibles contrôlées par les sliders
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- Sortie: un tableau contenant les 12 positions angulaires cibles (radian) pour les moteurs
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"""
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# t = t*speed_x * 20
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num_patte = 4
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slider_max = 0.200
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neutral_position = np.array([
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[-0.06, 0.06, -0.13],
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[-0.06, -0.06, -0.13],
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[0.06, -0.06, -0.13], # [0.15, 0.15, -0.01],
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[0.06, 0.06, -0.13]
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])
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real_position = np.copy(neutral_position)
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movement_z = np.array([
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[0, 0, 0.02],
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[0, 0, -0.01],
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[0, 0, -0.01]
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])
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step_duration = np.array([0.05, 0.3, 0.05])
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step_count = len(movement_z)
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movement_duration = np.sum(step_duration)
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assert len(
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step_duration) == step_count, f"all movements steps must have a length, currently, {len(step_duration)}/{step_count} have them"
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def get_current_step(t):
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time_passed = 0
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for i in range(len(step_duration)):
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time_passed += step_duration[i]
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if t % movement_duration < time_passed:
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return i
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def get_current_step_advancement(t):
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current_step = get_current_step(t)
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t = t % movement_duration
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for i in range(0, current_step):
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t -= step_duration[i]
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return t / step_duration[current_step]
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def get_next_step(t):
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return floor((get_current_step(t) + 1) % step_count)
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offsets = np.array([0, 0.5, 0, 0.5]) * movement_duration # offset between each leg
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assert len(offsets) == num_patte, f"all offsets must be set, currently, {len(offsets)}/{num_patte} have them"
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for patte in range(num_patte):
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time = t + offsets[patte]
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mov_index_start = get_current_step(time)
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mov_index_end = get_next_step(time)
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mov_start_z = movement_z[mov_index_start]
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mov_end_z = movement_z[mov_index_end]
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mov_start = neutral_position[patte] + mov_start_z
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mov_end = neutral_position[patte] + mov_end_z
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(real_position[patte][0],
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real_position[patte][1],
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real_position[patte][2]) = interpol2(mov_start, mov_end, get_current_step_advancement(time))
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dthteta = speed_rotation * 2
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theta = dthteta * (get_current_step_advancement(time) - 0.5)
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# theta = 0
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print(theta)
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# rotating the vector
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x1, y1 = real_position[patte][0], real_position[patte][1]
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print(f"x1: {x1}, y1: {y1}")
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x1t, y1t = x1 - x0, y1 - y0
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x2t, y2t = x1t * cos(theta) + y1t * sin(theta), x1t * sin(theta) + y1t * cos(theta)
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x2, y2 = x2t + x0, y2t + y0
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print(f"x2: {x2}, y2: {y2}")
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if mov_index_start == 1:
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# theta += time
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# xp = d * cos(theta) + real_position[patte][0]
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real_position[patte][0] = x2
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real_position[patte][1] = y2
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# print(
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# f"[{patte}] [{get_current_step(time)}->{get_next_step(time)}], start: {mov_start}, end: {mov_end}, current ({real_position[patte][0]}, {real_position[patte][1]}, {real_position[patte][2]})")
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return legs(real_position)
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walk = walkV1
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if __name__ == "__main__":
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print("N'exécutez pas ce fichier, mais simulator.py")
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