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Merge pull request #163 from takayuki5168/bipedal
implemented bipedal walking
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Atsushi Sakai
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Bipedal/__init__.py
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Bipedal/__init__.py
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Bipedal/bipedal_planner/animation.gif
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Bipedal/bipedal_planner/animation.gif
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Bipedal/bipedal_planner/bipedal_planner.py
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Bipedal/bipedal_planner/bipedal_planner.py
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"""
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Bipedal Walking with modifying designated footsteps
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author: Takayuki Murooka (takayuki5168)
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"""
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import numpy as np
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import math
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from matplotlib import pyplot as plt
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import matplotlib.patches as pat
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from mpl_toolkits.mplot3d import Axes3D
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import mpl_toolkits.mplot3d.art3d as art3d
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class BipedalPlanner(object):
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def __init__(self):
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self.ref_footsteps = None
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self.g = 9.8
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def set_ref_footsteps(self, ref_footsteps):
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self.ref_footsteps = ref_footsteps
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def inverted_pendulum(self, x, x_dot, px_star, y, y_dot, py_star, z_c, time_width):
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time_split = 100
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for i in range(time_split):
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delta_time = time_width / time_split
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x_dot2 = self.g / z_c * (x - px_star)
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x += x_dot * delta_time
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x_dot += x_dot2 * delta_time
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y_dot2 = self.g / z_c * (y - py_star)
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y += y_dot * delta_time
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y_dot += y_dot2 * delta_time
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if i % 10 == 0:
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self.com_trajectory.append([x, y])
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return x, x_dot, y, y_dot
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def walk(self, T_sup=0.8, z_c=0.8, a=10, b=1, plot=False):
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if self.ref_footsteps is None:
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print("No footsteps")
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return
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# set up plotter
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if plot:
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fig = plt.figure()
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ax = Axes3D(fig)
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com_trajectory_for_plot = []
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self.com_trajectory = []
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self.ref_p = [] # reference footstep positions
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self.act_p = [] # actual footstep positions
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px, py = 0., 0. # reference footstep position
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px_star, py_star = px, py # modified footstep position
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xi, xi_dot, yi, yi_dot = 0., 0., 0.01, 0. # TODO yi should be set as +epsilon, set xi, yi as COM
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time = 0.
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n = 0
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self.ref_p.append([px, py, 0])
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self.act_p.append([px, py, 0])
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for i in range(len(self.ref_footsteps)):
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# simulate x, y and those of dot of inverted pendulum
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xi, xi_dot, yi, yi_dot = self.inverted_pendulum(xi, xi_dot, px_star, yi, yi_dot, py_star, z_c, T_sup)
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# update time
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time += T_sup
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n += 1
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# calculate px, py, x_, y_, vx_, vy_
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f_x, f_y, f_theta = self.ref_footsteps[n - 1]
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rotate_mat = np.array([[math.cos(f_theta), -math.sin(f_theta)],
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[math.sin(f_theta), math.cos(f_theta)]])
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if n == len(self.ref_footsteps):
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f_x_next, f_y_next, f_theta_next = 0., 0., 0.
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else:
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f_x_next, f_y_next, f_theta_next = self.ref_footsteps[n]
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rotate_mat_next = np.array([[math.cos(f_theta_next), -math.sin(f_theta_next)],
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[math.sin(f_theta_next), math.cos(f_theta_next)]])
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T_c = math.sqrt(z_c / self.g)
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C = math.cosh(T_sup / T_c)
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S = math.sinh(T_sup / T_c)
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px, py = list(np.array([px, py]) + np.dot(rotate_mat, np.array([f_x, -1 * math.pow(-1, n) * f_y])))
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x_, y_ = list(np.dot(rotate_mat_next, np.array([f_x_next / 2., math.pow(-1, n) * f_y_next / 2.])))
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vx_, vy_ = list(np.dot(rotate_mat_next, np.array([(1 + C) / (T_c * S) * x_, (C - 1) / (T_c * S) * y_])))
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self.ref_p.append([px, py, f_theta])
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# calculate reference COM
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xd, xd_dot = px + x_, vx_
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yd, yd_dot = py + y_, vy_
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# calculate modified footsteps
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D = a * math.pow(C - 1, 2) + b * math.pow(S / T_c, 2)
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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)
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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)
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self.act_p.append([px_star, py_star, f_theta])
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# plot
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if plot:
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# for plot trajectory, plot in for loop
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for c in range(len(self.com_trajectory)):
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if c > len(com_trajectory_for_plot):
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# set up plotter
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plt.cla()
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ax.set_zlim(0, z_c * 2)
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ax.set_aspect('equal', 'datalim')
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# update com_trajectory_for_plot
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com_trajectory_for_plot.append(self.com_trajectory[c])
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# plot com
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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")
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# plot inverted pendulum
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ax.plot([px_star, com_trajectory_for_plot[-1][0]],
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[py_star , com_trajectory_for_plot[-1][1]],
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[0, z_c], color="green", linewidth=3)
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ax.scatter([com_trajectory_for_plot[-1][0]],
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[com_trajectory_for_plot[-1][1]],
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[z_c], color="green", s=300)
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# foot rectangle for self.ref_p
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foot_width = 0.06
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foot_height = 0.04
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for j in range(len(self.ref_p)):
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angle = self.ref_p[j][2] + math.atan2(foot_height, foot_width) - math.pi
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r = math.sqrt(math.pow(foot_width / 3., 2) + math.pow(foot_height / 2., 2))
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rec = pat.Rectangle(xy = (self.ref_p[j][0] + r * math.cos(angle), self.ref_p[j][1] + r * math.sin(angle)),
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width=foot_width, height=foot_height, angle=self.ref_p[j][2] * 180 / math.pi, color="blue", fill=False, ls=":")
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ax.add_patch(rec)
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art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z")
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# foot rectangle for self.act_p
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for j in range(len(self.act_p)):
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angle = self.act_p[j][2] + math.atan2(foot_height, foot_width) - math.pi
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r = math.sqrt(math.pow(foot_width / 3., 2) + math.pow(foot_height / 2., 2))
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rec = pat.Rectangle(xy = (self.act_p[j][0] + r * math.cos(angle), self.act_p[j][1] + r * math.sin(angle)),
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width=foot_width, height=foot_height, angle=self.act_p[j][2] * 180 / math.pi, color="blue", fill=False)
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ax.add_patch(rec)
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art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z")
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plt.draw()
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plt.pause(0.001)
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if plot:
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plt.show()
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if __name__ == "__main__":
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bipedal_planner = BipedalPlanner()
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footsteps = [[0.0, 0.2, 0.0],
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[0.3, 0.2, 0.0],
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[0.3, 0.2, 0.2],
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[0.3, 0.2, 0.2],
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[0.0, 0.2, 0.2]]
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bipedal_planner.set_ref_footsteps(footsteps)
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bipedal_planner.walk(plot=True)
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12
README.md
12
README.md
@@ -58,6 +58,8 @@ Python codes for robotics algorithm.
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* [Aerial Navigation](#aerial-navigation)
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* [drone 3d trajectory following](#drone-3d-trajectory-following)
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* [rocket powered landing](#rocket-powered-landing)
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* [Bipedal](#bipedal)
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* [bipedal planner with inverted pendulum](#bipedal-planner-with-inverted-pendulum)
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* [License](#license)
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* [Use-case](#use-case)
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* [Contribution](#contribution)
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@@ -525,6 +527,16 @@ Ref:
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- [notebook](https://github.com/AtsushiSakai/PythonRobotics/blob/master/AerialNavigation/rocket_powered_landing/rocket_powered_landing.ipynb)
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# Bipedal
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## bipedal planner with inverted pendulum
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This is an bipedal planner of modifying footsteps with inverted pendulum.
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You can set the footsteps and automatically planner will modify those.
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# License
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MIT
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