python_exercise_3_4.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
MIT License

Copyright (c) 2022 Jongrae.K

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""

import numpy as np
import matplotlib.pyplot as plt

# number of samples
num_sample = 500

# map size
map_width = 10
map_height = 5

# x,y coordinates of start and destination of the path to be calculated
xy_start = np.array([0,0])
xy_dest = np.array([9,4])

# spread num_sample random points over the map area
xy_points = np.random.rand(num_sample,2)
xy_points[::,0] = xy_points[::,0]*map_width
xy_points[::,1] = xy_points[::,1]*map_height

# stacking them all together with start and destination
xy_points = np.vstack((xy_start,xy_dest,xy_points))
start_node = 0
end_node = 1

# recycle delaunay code by chaining to voronoi
# construct graph using voronoi
from scipy.spatial import Voronoi
vor = Voronoi(xy_points)
xy_points = vor.vertices
num_sample = xy_points.shape[0]
xy_points_org_4_draw = xy_points

#-----------------------------------------------------------------------------
# circular obstacle at [3,3], radius 1.5 & define the boundary
obs_xy = [3,3]
obs_rad = 1.5
th = np.arange(0,2*np.pi+0.01,0.01)
x_obs_0 = obs_rad*np.cos(th)+obs_xy[0]
y_obs_0 = obs_rad*np.sin(th)+obs_xy[1]
xy_obs_0 = np.vstack((x_obs_0,y_obs_0)).T

# non-convex obstacle boundary
x_obs_1 = np.array([6,8,8,5,5,7,7,6,6])
y_obs_1 = np.array([1,1,4,4,3,3,2,2,1])
xy_obs_1 = np.vstack((x_obs_1,y_obs_1)).T

# define obstacle using Path in matplotlib.path
from matplotlib.path import Path
Obs_0 = Path(xy_obs_0)
Obs_1 = Path(xy_obs_1)

# found points are not inside the circular obstacle
mask_0 = ~Obs_0.contains_points(xy_points)
mask_1 = ~Obs_1.contains_points(xy_points)
mask_all = np.logical_and(mask_0,mask_1)
#-----------------------------------------------------------------------------

# edges
temp_index = np.array(vor.ridge_vertices)

# remove edges inside the boundary: this part needs to be updated for
# faster execusion
temp_index_update = []
set_index = np.arange(num_sample)
set_index = set_index[~mask_all]
for add_idx_p1_p2 in enumerate(temp_index):
    add_idx = add_idx_p1_p2[0]
    p1_idx = add_idx_p1_p2[1][0]
    p2_idx = add_idx_p1_p2[1][1]
    if not(np.isin(p1_idx,set_index) or np.isin(p2_idx,set_index)):
        temp_index_update.append(temp_index[add_idx])
#--------------------------------------------------------------
        
temp_index_update = np.array(temp_index_update)
temp_idx = temp_index_update[:,0]
temp_jdx = temp_index_update[:,1]

# remove edges outside of the boundary
cut_mask = temp_idx <= num_sample-1
temp_idx = temp_idx[cut_mask]
temp_jdx = temp_jdx[cut_mask]
cut_mask = temp_jdx <= num_sample-1
temp_idx = temp_idx[cut_mask]
temp_jdx = temp_jdx[cut_mask]

cut_mask = temp_idx >= 0
temp_idx = temp_idx[cut_mask]
temp_jdx = temp_jdx[cut_mask]
cut_mask = temp_jdx >= 0
temp_idx = temp_idx[cut_mask]
temp_jdx = temp_jdx[cut_mask]    

dd_all = np.sqrt(np.sum((xy_points[temp_idx]-xy_points[temp_jdx])**2,1))
cut_dist = np.mean(dd_all)+1*np.std(dd_all)

# distance thereshold for removing longer paths
cut_mask_ij = dd_all<cut_dist
temp_xy_ij = np.vstack((temp_idx[cut_mask_ij],temp_jdx[cut_mask_ij]))

# corresponding distance to the paths
dist_ij = dd_all[cut_mask_ij]

# change format into row, column and the distance
xy_index = temp_xy_ij.T
row_org = xy_index[:,0]
col_org = xy_index[:,1]
row = np.hstack((row_org,col_org))
col = np.hstack((col_org,row_org))
dist = dist_ij
dist = np.hstack((dist,dist))
num_node = xy_points.shape[0]

# construct the distance matrix
from scipy.sparse import csr_matrix
dist_sparse = csr_matrix((dist,(row,col)), shape=(num_node,num_node))

# update start_node and end_node to the closest points in the list
start_node = np.argmin(np.sum((xy_points-xy_start)**2,1))
end_node = np.argmin(np.sum((xy_points-xy_dest)**2,1))


# calculate the shortest path
from scipy.sparse.csgraph import dijkstra
dist, pred = dijkstra(dist_sparse, indices = start_node, return_predecessors=True)
print(f'distance from node #{start_node:0d} to node #{end_node:0d}: {dist[end_node]:4.2f}')

# obtain the shortest path
path = []
i=end_node
if np.isinf(dist[end_node]):
    print('the path does not exist!')
else:
    while i!=start_node:
        path.append(i)
        i = pred[i]
    path.append(start_node)
    print('path=',path[::-1])

opt_path = np.asarray(path[::-1])

# plot all paths, obstacles
plt.figure()
x_p1_p2=np.array([xy_points_org_4_draw[temp_xy_ij[0]][:,0], xy_points_org_4_draw[temp_xy_ij[1]][:,0]])
y_p1_p2=np.array([xy_points_org_4_draw[temp_xy_ij[0]][:,1], xy_points_org_4_draw[temp_xy_ij[1]][:,1]])
plt.plot(x_p1_p2,y_p1_p2,'b-')    
plt.plot(x_obs_0,y_obs_0,'r',linewidth=4)
plt.plot(x_obs_1,y_obs_1,'r',linewidth=4)
plt.plot(xy_start[0],xy_start[1],'x')
plt.plot(xy_dest[0],xy_dest[1],'o')
plt.text(0,0.2,'Initial Location')
plt.text(7.5,4.2,'Destination')
plt.axis([-0.2,10,-0.2,5])

# plot the optimal path
for idx in range(0,opt_path.size-1,1):
    p_idx = opt_path[idx]
    q_idx = opt_path[idx+1]
    op_xx = [xy_points[p_idx,0], xy_points[q_idx,0]]
    op_yy = [xy_points[p_idx,1], xy_points[q_idx,1]]
    plt.plot(op_xx,op_yy,'g',linewidth=4)
    
# connect the starting point and the end point to the path
op_xx = [xy_points[start_node,0], xy_start[0]]
op_yy = [xy_points[start_node,1], xy_start[1]]
plt.plot(op_xx,op_yy,'g',linewidth=4)
op_xx = [xy_points[end_node,0], xy_dest[0]]
op_yy = [xy_points[end_node,1], xy_dest[1]]
plt.plot(op_xx,op_yy,'g',linewidth=4)