""" Bipedal Walking with modifying designated footsteps author: Takayuki Murooka (takayuki5168) """ import numpy as np import math from matplotlib import pyplot as plt import matplotlib.patches as pat from mpl_toolkits.mplot3d import Axes3D import mpl_toolkits.mplot3d.art3d as art3d class BipedalPlanner(object): def __init__(self): self.ref_footsteps = None self.g = 9.8 def set_ref_footsteps(self, ref_footsteps): self.ref_footsteps = ref_footsteps def inverted_pendulum(self, x, x_dot, px_star, y, y_dot, py_star, z_c, time_width): time_split = 100 for i in range(time_split): delta_time = time_width / time_split x_dot2 = self.g / z_c * (x - px_star) x += x_dot * delta_time x_dot += x_dot2 * delta_time y_dot2 = self.g / z_c * (y - py_star) y += y_dot * delta_time y_dot += y_dot2 * delta_time if i % 10 == 0: self.com_trajectory.append([x, y]) return x, x_dot, y, y_dot def walk(self, T_sup=0.8, z_c=0.8, a=10, b=1, plot=False): if self.ref_footsteps is None: print("No footsteps") return # set up plotter if plot: fig = plt.figure() ax = Axes3D(fig) com_trajectory_for_plot = [] self.com_trajectory = [] self.ref_p = [] # reference footstep positions self.act_p = [] # actual footstep positions px, py = 0.0, 0.0 # reference footstep position px_star, py_star = px, py # modified footstep position xi, xi_dot, yi, yi_dot = 0.0, 0.0, 0.01, 0.0 time = 0.0 n = 0 self.ref_p.append([px, py, 0]) self.act_p.append([px, py, 0]) for i in range(len(self.ref_footsteps)): # simulate x, y and those of dot of inverted pendulum xi, xi_dot, yi, yi_dot = self.inverted_pendulum( xi, xi_dot, px_star, yi, yi_dot, py_star, z_c, T_sup) # update time time += T_sup n += 1 # calculate px, py, x_, y_, vx_, vy_ f_x, f_y, f_theta = self.ref_footsteps[n - 1] rotate_mat = np.array([[math.cos(f_theta), -math.sin(f_theta)], [math.sin(f_theta), math.cos(f_theta)]]) if n == len(self.ref_footsteps): f_x_next, f_y_next, f_theta_next = 0., 0., 0. else: f_x_next, f_y_next, f_theta_next = self.ref_footsteps[n] rotate_mat_next = np.array([[math.cos(f_theta_next), -math.sin(f_theta_next)], [math.sin(f_theta_next), math.cos(f_theta_next)]]) T_c = math.sqrt(z_c / self.g) C = math.cosh(T_sup / T_c) S = math.sinh(T_sup / T_c) px, py = list(np.array( [px, py]) + np.dot(rotate_mat, np.array([f_x, -1 * math.pow(-1, n) * f_y]))) x_, y_ = list(np.dot(rotate_mat_next, np.array( [f_x_next / 2., math.pow(-1, n) * f_y_next / 2.]))) vx_, vy_ = list(np.dot(rotate_mat_next, np.array( [(1 + C) / (T_c * S) * x_, (C - 1) / (T_c * S) * y_]))) self.ref_p.append([px, py, f_theta]) # calculate reference COM xd, xd_dot = px + x_, vx_ yd, yd_dot = py + y_, vy_ # calculate modified footsteps D = a * math.pow(C - 1, 2) + b * math.pow(S / T_c, 2) px_star = -a * (C - 1) / D * (xd - C * xi - T_c * S * xi_dot) - \ b * S / (T_c * D) * (xd_dot - S / T_c * xi - C * xi_dot) py_star = -a * (C - 1) / D * (yd - C * yi - T_c * S * yi_dot) - \ b * S / (T_c * D) * (yd_dot - S / T_c * yi - C * yi_dot) self.act_p.append([px_star, py_star, f_theta]) # plot if plot: # for plot trajectory, plot in for loop for c in range(len(self.com_trajectory)): if c > len(com_trajectory_for_plot): # set up plotter plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) ax.set_zlim(0, z_c * 2) ax.set_aspect('equal', 'datalim') # update com_trajectory_for_plot com_trajectory_for_plot.append(self.com_trajectory[c]) # plot com ax.plot([p[0] for p in com_trajectory_for_plot], [p[1] for p in com_trajectory_for_plot], [ 0 for p in com_trajectory_for_plot], color="red") # plot inverted pendulum ax.plot([px_star, com_trajectory_for_plot[-1][0]], [py_star, com_trajectory_for_plot[-1][1]], [0, z_c], color="green", linewidth=3) ax.scatter([com_trajectory_for_plot[-1][0]], [com_trajectory_for_plot[-1][1]], [z_c], color="green", s=300) # foot rectangle for self.ref_p foot_width = 0.06 foot_height = 0.04 for j in range(len(self.ref_p)): angle = self.ref_p[j][2] + \ math.atan2(foot_height, foot_width) - math.pi r = math.sqrt( math.pow(foot_width / 3., 2) + math.pow(foot_height / 2., 2)) rec = pat.Rectangle(xy=(self.ref_p[j][0] + r * math.cos(angle), self.ref_p[j][1] + r * math.sin(angle)), width=foot_width, height=foot_height, angle=self.ref_p[j][2] * 180 / math.pi, color="blue", fill=False, ls=":") ax.add_patch(rec) art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z") # foot rectangle for self.act_p for j in range(len(self.act_p)): angle = self.act_p[j][2] + \ math.atan2(foot_height, foot_width) - math.pi r = math.sqrt( math.pow(foot_width / 3., 2) + math.pow(foot_height / 2., 2)) rec = pat.Rectangle(xy=(self.act_p[j][0] + r * math.cos(angle), self.act_p[j][1] + r * math.sin(angle)), width=foot_width, height=foot_height, angle=self.act_p[j][2] * 180 / math.pi, color="blue", fill=False) ax.add_patch(rec) art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z") plt.draw() plt.pause(0.001) if plot: plt.show() if __name__ == "__main__": bipedal_planner = BipedalPlanner() footsteps = [[0.0, 0.2, 0.0], [0.3, 0.2, 0.0], [0.3, 0.2, 0.2], [0.3, 0.2, 0.2], [0.0, 0.2, 0.2]] bipedal_planner.set_ref_footsteps(footsteps) bipedal_planner.walk(plot=True)