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Merge pull request #151 from toolleeo/improved_arm_obstacle_navigation__visualization

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Added modified version of the arm obstacle avoidance simulation.
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Atsushi Sakai
2019-01-13 08:16:19 +09:00
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parent 7a17e3a120 a558096a83
commit 5a6970ecc6
1 changed files with 277 additions and 0 deletions
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ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation_2.py Normal file
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"""
Obstacle navigation using A* on a toroidal grid
Author: Daniel Ingram (daniel-s-ingram)
Tullio Facchinetti (tullio.facchinetti@unipv.it)
"""
from math import pi
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import from_levels_and_colors
import sys
plt.ion()
# Simulation parameters
M = 100
obstacles = [[1.75, 0.75, 0.6], [0.55, 1.5, 0.5], [0, -1, 0.7]]
def press(event):
"""Exit from the simulation."""
if event.key == 'q' or event.key == 'Q':
print('Quitting upon request.')
sys.exit(0)
def main():
# Arm geometry in the working space
link_length = [0.5, 1.5]
initial_link_angle = [0, 0]
arm = NLinkArm(link_length, initial_link_angle)
# (x, y) co-ordinates in the joint space [cell]
start = (10, 50)
goal = (58, 56)
grid = get_occupancy_grid(arm, obstacles)
route = astar_torus(grid, start, goal)
if len(route) >= 0:
animate(grid, arm, route)
def animate(grid, arm, route):
fig, axs = plt.subplots(1, 2)
fig.canvas.mpl_connect('key_press_event', press)
colors = ['white', 'black', 'red', 'pink', 'yellow', 'green', 'orange']
levels = [0, 1, 2, 3, 4, 5, 6, 7]
cmap, norm = from_levels_and_colors(levels, colors)
for i, node in enumerate(route):
plt.subplot(1, 2, 1)
grid[node] = 6
plt.cla()
plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
theta1 = 2 * pi * node[0] / M - pi
theta2 = 2 * pi * node[1] / M - pi
arm.update_joints([theta1, theta2])
plt.subplot(1, 2, 2)
arm.plot(plt, obstacles=obstacles)
plt.show()
# Uncomment here to save the sequence of frames
#plt.savefig('frame{:04d}.png'.format(i))
plt.pause(0.1)
def detect_collision(line_seg, circle):
"""
Determines whether a line segment (arm link) is in contact
with a circle (obstacle).
Credit to: http://doswa.com/2009/07/13/circle-segment-intersectioncollision.html
Args:
line_seg: List of coordinates of line segment endpoints e.g. [[1, 1], [2, 2]]
circle: List of circle coordinates and radius e.g. [0, 0, 0.5] is a circle centered
at the origin with radius 0.5
Returns:
True if the line segment is in contact with the circle
False otherwise
"""
a_vec = np.array([line_seg[0][0], line_seg[0][1]])
b_vec = np.array([line_seg[1][0], line_seg[1][1]])
c_vec = np.array([circle[0], circle[1]])
radius = circle[2]
line_vec = b_vec - a_vec
line_mag = np.linalg.norm(line_vec)
circle_vec = c_vec - a_vec
proj = circle_vec.dot(line_vec / line_mag)
if proj <= 0:
closest_point = a_vec
elif proj >= line_mag:
closest_point = b_vec
else:
closest_point = a_vec + line_vec * proj / line_mag
if np.linalg.norm(closest_point - c_vec) > radius:
return False
else:
return True
def get_occupancy_grid(arm, obstacles):
"""
Discretizes joint space into M values from -pi to +pi
and determines whether a given coordinate in joint space
would result in a collision between a robot arm and obstacles
in its environment.
Args:
arm: An instance of NLinkArm
obstacles: A list of obstacles, with each obstacle defined as a list
of xy coordinates and a radius.
Returns:
Occupancy grid in joint space
"""
grid = [[0 for _ in range(M)] for _ in range(M)]
theta_list = [2 * i * pi / M for i in range(-M // 2, M // 2 + 1)]
for i in range(M):
for j in range(M):
arm.update_joints([theta_list[i], theta_list[j]])
points = arm.points
collision_detected = False
for k in range(len(points) - 1):
for obstacle in obstacles:
line_seg = [points[k], points[k + 1]]
collision_detected = detect_collision(line_seg, obstacle)
if collision_detected:
break
if collision_detected:
break
grid[i][j] = int(collision_detected)
return np.array(grid)
def astar_torus(grid, start_node, goal_node):
"""
Finds a path between an initial and goal joint configuration using
the A* Algorithm on a tororiadal grid.
Args:
grid: An occupancy grid (ndarray)
start_node: Initial joint configuation (tuple)
goal_node: Goal joint configuration (tuple)
Returns:
Obstacle-free route in joint space from start_node to goal_node
"""
grid[start_node] = 4
grid[goal_node] = 5
parent_map = [[() for _ in range(M)] for _ in range(M)]
X, Y = np.meshgrid([i for i in range(M)], [i for i in range(M)])
heuristic_map = np.abs(X - goal_node[1]) + np.abs(Y - goal_node[0])
for i in range(heuristic_map.shape[0]):
for j in range(heuristic_map.shape[1]):
heuristic_map[i, j] = min(heuristic_map[i, j],
i + 1 + heuristic_map[M - 1, j],
M - i + heuristic_map[0, j],
j + 1 + heuristic_map[i, M - 1],
M - j + heuristic_map[i, 0]
)
explored_heuristic_map = np.full((M, M), np.inf)
distance_map = np.full((M, M), np.inf)
explored_heuristic_map[start_node] = heuristic_map[start_node]
distance_map[start_node] = 0
while True:
grid[start_node] = 4
grid[goal_node] = 5
current_node = np.unravel_index(
np.argmin(explored_heuristic_map, axis=None), explored_heuristic_map.shape)
min_distance = np.min(explored_heuristic_map)
if (current_node == goal_node) or np.isinf(min_distance):
break
grid[current_node] = 2
explored_heuristic_map[current_node] = np.inf
i, j = current_node[0], current_node[1]
neighbors = []
if i - 1 >= 0:
neighbors.append((i - 1, j))
else:
neighbors.append((M - 1, j))
if i + 1 < M:
neighbors.append((i + 1, j))
else:
neighbors.append((0, j))
if j - 1 >= 0:
neighbors.append((i, j - 1))
else:
neighbors.append((i, M - 1))
if j + 1 < M:
neighbors.append((i, j + 1))
else:
neighbors.append((i, 0))
for neighbor in neighbors:
if grid[neighbor] == 0 or grid[neighbor] == 5:
distance_map[neighbor] = distance_map[current_node] + 1
explored_heuristic_map[neighbor] = heuristic_map[neighbor]
parent_map[neighbor[0]][neighbor[1]] = current_node
grid[neighbor] = 3
'''
plt.cla()
plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
plt.show()
plt.pause(1e-5)
'''
if np.isinf(explored_heuristic_map[goal_node]):
route = []
print("No route found.")
else:
route = [goal_node]
while parent_map[route[0][0]][route[0][1]] is not ():
route.insert(0, parent_map[route[0][0]][route[0][1]])
print("The route found covers %d grid cells." % len(route))
return route
class NLinkArm(object):
"""
Class for controlling and plotting a planar arm with an arbitrary number of links.
"""
def __init__(self, link_lengths, joint_angles):
self.n_links = len(link_lengths)
if self.n_links != len(joint_angles):
raise ValueError()
self.link_lengths = np.array(link_lengths)
self.joint_angles = np.array(joint_angles)
self.points = [[0, 0] for _ in range(self.n_links + 1)]
self.lim = sum(link_lengths)
self.update_points()
def update_joints(self, joint_angles):
self.joint_angles = joint_angles
self.update_points()
def update_points(self):
for i in range(1, self.n_links + 1):
self.points[i][0] = self.points[i - 1][0] + \
self.link_lengths[i - 1] * \
np.cos(np.sum(self.joint_angles[:i]))
self.points[i][1] = self.points[i - 1][1] + \
self.link_lengths[i - 1] * \
np.sin(np.sum(self.joint_angles[:i]))
self.end_effector = np.array(self.points[self.n_links]).T
def plot(self, myplt, obstacles=[]):
myplt.cla()
for obstacle in obstacles:
circle = myplt.Circle(
(obstacle[0], obstacle[1]), radius=0.5 * obstacle[2], fc='k')
myplt.gca().add_patch(circle)
for i in range(self.n_links + 1):
if i is not self.n_links:
myplt.plot([self.points[i][0], self.points[i + 1][0]],
[self.points[i][1], self.points[i + 1][1]], 'r-')
myplt.plot(self.points[i][0], self.points[i][1], 'k.')
myplt.xlim([-self.lim, self.lim])
myplt.ylim([-self.lim, self.lim])
myplt.draw()
#myplt.pause(1e-5)
if __name__ == '__main__':
main()