def plan(self, start, goal, env):
"""Constructs a graph avoiding obstacles and then plans path from start to goal within the graph.
Args:
start (gennav.utils.RobotState): tuple with start point coordinates.
goal (gennav.utils.RobotState): tuple with end point coordinates.
env (gennav.envs.Environment): Base class for an envrionment.
Returns:
gennav.utils.Trajectory: The planned path as trajectory
dict: Dictionary containing additional information
"""
# Check if start and goal states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start,
message="Start state is in obstacle.")
if not env.get_status(goal):
raise InvalidGoalState(goal, message="Goal state is in obstacle.")
# construct graph
graph = self.construct(env)
# find collision free point in graph closest to start_point
min_dist = float("inf")
for node in graph.nodes:
dist = compute_distance(node.position, start.position)
traj = Trajectory([node, start])
if dist < min_dist and (env.get_traj_status(traj)):
min_dist = dist
s = node
# find collision free point in graph closest to end_point
min_dist = float("inf")
for node in graph.nodes:
dist = compute_distance(node.position, goal.position)
traj = Trajectory([node, goal])
if dist < min_dist and (env.get_traj_status(traj)):
min_dist = dist
e = node
# add start_point to path
path = [start]
traj = Trajectory(path)
# perform astar search
p = astar(graph, s, e)
if len(p.path) == 1:
raise PathNotFound(p, message="Path contains only one state")
else:
traj.path.extend(p.path)
# add end_point to path
traj.path.append(goal)
return traj, {}
def plan(self, start, goal, env):
"""Plans the path to be taken by the robot to get from start to goal in the form of waypoints
Args:
start (gennav.utils.RobotState) : starting state of the robot (x, y and z coordinates)
goal (gennav.utils.RobotState) : goal state of the robot (x, y and z coordinates)
env (gennav.envs.Environment) : Type of environment the robot is operating in
Returns:
trajectory (gennav.utils.Trajectory) : A list of waypoints(in the form of robot states) that the robot will follow to go to the goal from the start
dict: Dictionary containing additional information
"""
# Check if start and goal states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start,
message="Start state is in obstacle.")
if not env.get_status(goal):
raise InvalidGoalState(goal, message="Goal state is in obstacle.")
self.current = start
self.goal = goal
self.env = env
waypoints = [self.current]
while (math.sqrt((self.current.position.x - self.goal.position.x)**2 +
(self.current.position.y - self.goal.position.y)**2) >
self.error):
grad_attract = self.grad_attractive()
grad_repel = self.grad_repulsive()
grad = [0, 0]
grad[0] = grad_attract[0] + grad_repel[0]
grad[1] = grad_attract[1] + grad_repel[1]
self.current.position.x = self.current.position.x - self.STEP_SIZE * grad[
0]
self.current.position.y = self.current.position.y - self.STEP_SIZE * grad[
1]
waypoints.append(self.current)
trajectory = Trajectory(waypoints)
if len(trajectory.path) == 1:
raise PathNotFound(trajectory,
message="Path contains only one state")
return trajectory, {}
def plan(self, start, goal, env):
"""Path planning method
Args:
start (gennav.utils.common.RobotState): Starting state.
goal (gennav.utils.common.RobotState): Destination state
env (gennav.envs.Environment): Environment object
Returns:
gennav.utils.Trajectory: The path as a Trajectory
dict: Dictionary containing additional information like the node_list
"""
# Check if start and goal states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start,
message="Start state is in obstacle.")
if not env.get_status(goal):
raise InvalidGoalState(goal, message="Goal state is in obstacle.")
# Initialize start and goal nodes.
x_start = Node(state=start)
x_goal = Node(state=goal)
# Starting the tree:
node_list = [x_start]
# X_soln contains all the nodes near the goal
X_soln = []
for i in range(self.max_iter):
# defining the best cost as cbest
if len(X_soln) == 0:
cbest = float("inf")
else:
cbest = X_soln[0].cost + compute_distance(
X_soln[0].state.position, x_goal.state.position)
for node in X_soln:
if (node.cost + compute_distance(node.state.position,
x_goal.state.position) <
cbest):
cbest = node.cost + compute_distance(
node.state.position, x_goal.state.position)
# sample the new random point using the sample function
if cbest < float("inf"):
# Converting x_start and x_goal into arrays so that matrix calculations can be handled
x_start_array = np.array(
[x_start.state.position.x, x_start.state.position.y],
dtype=np.float32,
).reshape(2, 1)
x_goal_array = np.array(
[x_goal.state.position.x, x_goal.state.position.y],
dtype=np.float32).reshape(2, 1)
cmin = np.linalg.norm((x_goal_array - x_start_array))
x_center = (x_start_array + x_goal_array) / 2
a1 = (x_goal_array - x_start_array) / cmin
I1 = np.eye(len(x_start_array))[0].reshape(
len(x_start_array), 1)
M = np.dot(a1, I1.T)
[u, s, v] = np.linalg.svd(M)
# numpy returns the transposed value for v, so to convert it back
v = v.T
# Calculating the rotation to world frame matrix given by C = U*diag{1,....1.det(U)det(V)}*V.T where * denotes matrix multiplication
diag = np.eye(2)
diag[1, 1] = np.linalg.det(u) * np.linalg.det(v)
C = np.dot(np.dot(u, diag), v.T)
L = np.eye(2)
L[0, 0] = cbest / 2
L[1, 1] = np.sqrt(cbest**2 - cmin**2) / 2
rand_state = self.circular_sampler()
x_ball = np.array(
[rand_state.position.x, rand_state.position.y],
dtype=np.float32).reshape(2, 1)
x_rand_array = np.dot(np.dot(C, L), x_ball) + x_center
x_rand = RobotState()
x_rand.position.x = x_rand_array[0, 0]
x_rand.position.y = x_rand_array[1, 0]
x_rand_node = Node(state=x_rand)
else:
x_rand = self.rectangular_sampler()
x_rand_node = Node(state=x_rand)
# Finding the nearest node to the random point
distance_list = [
compute_distance(node.state.position,
x_rand_node.state.position)
for node in node_list
]
min_dist = distance_list[0]
min_index = 0
for index, distance in enumerate(distance_list):
if distance < min_dist:
min_dist = distance
min_index = index
x_nearest = node_list[min_index]
# Steering at a distance of self.expand_dis
theta = compute_angle(x_nearest.state.position,
x_rand_node.state.position)
x = x_nearest.state.position.x + self.expand_dis * math.cos(theta)
y = x_nearest.state.position.y + self.expand_dis * math.sin(theta)
t = RobotState(position=Point(x, y))
x_new = Node(state=t)
# Defining a temporary trajectory between the new node and its nearest node
traj = Trajectory(path=[x_nearest.state, x_new.state])
# Checking whether new node and the nearest node can be connected
if env.get_traj_status(traj):
# Adding new node to the node list
node_list.append(x_new)
# Defining the neighbours of x_new
X_near = []
for node in node_list:
if (compute_distance(
node.state.position, x_new.state.position)) < (
self.neighbourhood_radius
) and ( # If it is inside the neighbourhood radius
compute_distance(node.state.position,
x_new.state.position) != 0):
X_near.append(node)
x_min = x_nearest
c_min = x_min.cost + self.expand_dis
for x_near in X_near:
c_new = x_near.cost + compute_distance(
x_near.state.position, x_new.state.position)
if c_new < c_min:
traj = Trajectory(path=[x_near.state, x_new.state])
if env.get_traj_status(traj):
x_min = x_near
c_min = c_new
# Defining the parent node and cost of x_new
x_new.parent = x_min
x_new.cost = c_min
# Rewiring
for x_near in X_near:
c_near = x_near.cost
c_new = x_new.cost + compute_distance(
x_near.state.position, x_new.state.position)
if c_new < c_near:
traj = Trajectory(path=[x_new.state, x_near.state])
if env.get_traj_status(traj):
x_near.parent = x_new
x_near.cost = c_new
goal_traj = Trajectory(path=[x_new.state, x_goal.state])
if (compute_distance(x_goal.state.position,
x_new.state.position)
) < self.goal_distance and env.get_traj_status(goal_traj):
X_soln.append(x_new)
# X_soln contains all the solutions
if len(X_soln) == 0:
print("No solution found!")
path = []
path.append(x_start.state)
traj = Trajectory(path=path)
info_dict = {}
info_dict["node_list"] = node_list
if len(traj.path) == 1:
raise PathNotFound(path,
message="Path contains only one state")
return (traj, info_dict)
else:
print("Goal reached!")
Cbest = X_soln[0].cost
Xbest = X_soln[0]
node_list.append(x_goal)
for node in X_soln:
if node.cost < Cbest:
Cbest = node.cost
Xbest = node
x_goal.parent = Xbest
# Xbest is the optimum solution to the problem.
# Back tracing the path:
path = []
path.append(x_goal.state)
path.append(Xbest.state)
p = Xbest.parent
while p is not None:
path.append(p.state)
p = p.parent
path.append(x_start.state)
path.reverse()
# print("No. of solutions " + str(len(X_soln)))
trajectory = Trajectory(path=path)
info_dict = {}
info_dict["node_list"] = node_list
return (trajectory, info_dict)
def plan(self, start, end, env):
"""Plans path from start to goal avoiding obstacles.
Args:
start (gennav.utils.RobotState): Starting state
end (gennav.utils.RobotState): Goal state
env: (gennav.envs.Environment) Base class for an envrionment.
Returns:
gennav.utils.Trajectory: The planned path as trajectory
dict: Dictionary containing additional information
"""
# Check if start and end states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start,
message="Start state is in obstacle.")
if not env.get_status(end):
raise InvalidGoalState(end, message="Goal state is in obstacle.")
# Initialize graph
graph = Graph()
graph.add_node(start)
# Initialize node list with Starting Position
node_list = [start]
# Loop for maximum iterations to get the best possible path
for iter in range(self.max_iter):
rnd_node = self.sampler()
# Find nearest node to the sampled point
distance_list = [
compute_distance(node.position, rnd_node.position)
for node in node_list
]
try:
# for python2
nearest_node_index = min(xrange(len(distance_list)),
key=distance_list.__getitem__)
except NameError:
# for python 3
nearest_node_index = distance_list.index(min(distance_list))
nearest_node = node_list[nearest_node_index]
# Create new point in the direction of sampled point
theta = math.atan2(
rnd_node.position.y - nearest_node.position.y,
rnd_node.position.x - nearest_node.position.x,
)
new_node = RobotState(position=Point(
nearest_node.position.x + self.exp_dis * math.cos(theta),
nearest_node.position.y + self.exp_dis * math.sin(theta),
))
# Check whether new point is inside an obstacles
trj = Trajectory([nearest_node, new_node])
if not env.get_status(new_node) or not env.get_traj_status(trj):
continue
else:
node_list.append(new_node)
# FINDING NEAREST INDICES
nnode = len(node_list) + 1
# The circle in which to check parent node and rewiring
r = self.circle * math.sqrt((math.log(nnode) / nnode))
dist_list = [
compute_distance(node.position, new_node.position)
for node in node_list
]
# Getting all the indexes within r units of new_node
near_inds = [dist_list.index(i) for i in dist_list if i <= r**2]
graph.add_node(new_node)
graph.add_edge(nearest_node, new_node)
# Add all the collision free edges to the graph.
for ind in near_inds:
node_check = node_list[ind]
trj = Trajectory([new_node, node_check])
# If the above condition is met append the edge.
if env.get_traj_status(trj):
graph.add_edge(new_node, node_check)
if end not in graph.nodes:
min_cost = 2.0
closest_node = RobotState()
for node in graph.nodes:
temp = compute_distance(node.position, end.position)
if env.get_traj_status(Trajectory([node, end
])) and temp < min_cost:
min_cost = temp
closest_node = node
graph.add_edge(closest_node, end)
graph.add_node(end)
if start in graph.edges[end]:
graph.del_edge(start, end)
path = []
p = astar(graph, start, end)
path.extend(p.path)
if len(path) != 1:
print("Goal Reached!")
path = Trajectory(path)
if len(path.path) == 1:
raise PathNotFound(path, message="Path contains only one state")
return path, {}
def plan(self, start, goal, env):
"""Path planning method
Args:
start (gennav.utils.common.RobotState): Starting state.
goal (gennav.utils.common.RobotState): Destination state
env (gennav.envs.Environment): Environment object
Returns:
gennav.utils.Trajectory: The path as a Trajectory
dict: Dictionary containing additional information like the node_list
"""
# Check if start and goal states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start, message="Start state is in obstacle.")
if not env.get_status(goal):
raise InvalidGoalState(goal, message="Goal state is in obstacle.")
# Initialize start and goal nodes.
x_start = Node(state=start)
x_goal = Node(state=goal)
# Starting the tree:
node_list = [x_start]
# X_soln contains all the nodes near the goal
X_soln = []
for i in range(self.max_iter):
# defining the best cost as cbest
if len(X_soln) == 0:
cbest = float("inf")
else:
cbest = X_soln[0].cost + compute_distance(
X_soln[0].state.position, x_goal.state.position
)
for node in X_soln:
if (
node.cost
+ compute_distance(node.state.position, x_goal.state.position)
< cbest
):
cbest = node.cost + compute_distance(
node.state.position, x_goal.state.position
)
# sample the new random point using the sample function
x_rand = self.rectangular_sampler()
x_rand_node = Node(state=x_rand)
# Finding the nearest node to the random point
distance_list = [
compute_distance(node.state.position, x_rand_node.state.position)
for node in node_list
]
min_dist = distance_list[0]
min_index = 0
for index, distance in enumerate(distance_list):
if distance < min_dist:
min_dist = distance
min_index = index
x_nearest = node_list[min_index]
# Steering at a distance of self.expand_dis
theta = compute_angle(x_nearest.state.position, x_rand_node.state.position)
x = x_nearest.state.position.x + self.expand_dis * math.cos(theta)
y = x_nearest.state.position.y + self.expand_dis * math.sin(theta)
t = RobotState(position=Point(x, y))
x_new = Node(state=t)
# Defining a temporary trajectory between the new node and its nearest node
traj = Trajectory(path=[x_nearest.state, x_new.state])
# Checking whether new node and the nearest node can be connected
if env.get_traj_status(traj):
# Adding new node to the node list
node_list.append(x_new)
# Defining the neighbours of x_new
X_near = []
for node in node_list:
if (compute_distance(node.state.position, x_new.state.position)) < (
self.neighbourhood_radius
) and ( # If it is inside the neighbourhood radius
compute_distance(node.state.position, x_new.state.position) != 0
):
X_near.append(node)
x_min = x_nearest
c_min = x_min.cost + self.expand_dis
for x_near in X_near:
c_new = x_near.cost + compute_distance(
x_near.state.position, x_new.state.position
)
if c_new < c_min:
traj = Trajectory(path=[x_near.state, x_new.state])
if env.get_traj_status(traj):
x_min = x_near
c_min = c_new
# Defining the parent node and cost of x_new
x_new.parent = x_min
x_new.cost = c_min
# Rewiring
for x_near in X_near:
c_near = x_near.cost
c_new = x_new.cost + compute_distance(
x_near.state.position, x_new.state.position
)
if c_new < c_near:
traj = Trajectory(path=[x_new.state, x_near.state])
if env.get_traj_status(traj):
x_near.parent = x_new
x_near.cost = c_new
goal_traj = Trajectory(path=[x_new.state, x_goal.state])
if (
compute_distance(x_goal.state.position, x_new.state.position)
) < self.goal_distance and env.get_traj_status(goal_traj):
X_soln.append(x_new)
# X_soln contains all the solutions
if len(X_soln) == 0:
print("No solution found!")
path = []
path.append(x_start.state)
traj = Trajectory(path=path)
info_dict = {}
info_dict["node_list"] = node_list
if len(traj.path) == 1:
raise PathNotFound(path, message="Path contains only one state")
return (traj, info_dict)
else:
print("Goal reached!")
Cbest = X_soln[0].cost
Xbest = X_soln[0]
node_list.append(x_goal)
for node in X_soln:
if node.cost < Cbest:
Cbest = node.cost
Xbest = node
x_goal.parent = Xbest
# Xbest is the optimum solution to the problem.
# Back tracing the path:
path = []
path.append(x_goal.state)
path.append(Xbest.state)
p = Xbest.parent
while p is not None:
path.append(p.state)
p = p.parent
path.append(x_start.state)
path.reverse()
# print("No. of solutions " + str(len(X_soln)))
trajectory = Trajectory(path=path)
info_dict = {}
info_dict["node_list"] = node_list
return (trajectory, info_dict)
def plan(self, start, goal, env):
"""Plans path from start to goal avoiding obstacles.
Args:
start_point(gennav.utils.RobotState): with start point coordinates.
end_point (gennav.utils.RobotState): with end point coordinates.
env: (gennav.envs.Environment) Base class for an envrionment.
Returns:
gennav.utils.Trajectory: The planned path as trajectory
dict: Dictionary containing additional information like the node_list
"""
# Check if start and goal states are obstacle free
if not env.get_status(start):
raise InvalidStartState(start,
message="Start state is in obstacle.")
if not env.get_status(goal):
raise InvalidGoalState(goal, message="Goal state is in obstacle.")
# Initialize start and goal nodes
start_node = Node(state=start)
goal_node = Node(state=goal)
# Initialize node_list with start
node_list = [start_node]
# Loop to keep expanding the tree towards goal if there is no direct connection
traj = Trajectory(path=[start, goal])
if not env.get_traj_status(traj):
while True:
# Sample random state in specified area
rnd_state = self.sampler()
# Find nearest node to the sampled point
distance_list = [
compute_distance(node.state.position, rnd_state.position)
for node in node_list
]
try:
# for python2
nearest_node_index = min(xrange(len(distance_list)),
key=distance_list.__getitem__)
except NameError:
# for python 3
nearest_node_index = distance_list.index(
min(distance_list))
nearest_node = node_list[nearest_node_index]
# Create new point in the direction of sampled point
theta = math.atan2(
rnd_state.position.y - nearest_node.state.position.y,
rnd_state.position.x - nearest_node.state.position.x,
)
new_point = Point()
new_point.x = (nearest_node.state.position.x +
self.expand_dis * math.cos(theta))
new_point.y = (nearest_node.state.position.y +
self.expand_dis * math.sin(theta))
# Check whether new point is inside an obstacles
if not env.get_status(RobotState(position=new_point)):
continue
else:
new_node = Node.from_coordinates(new_point)
new_node.parent = nearest_node
node_list.append(new_node)
# Check if goal has been reached or if there is direct connection to goal
distance_to_goal = compute_distance(goal_node.state.position,
new_node.state.position)
traj = Trajectory(path=[RobotState(position=new_point), goal])
if distance_to_goal < self.expand_dis or env.get_traj_status(
traj):
goal_node.parent = node_list[-1]
node_list.append(goal_node)
print("Goal reached!")
break
else:
goal_node.parent = start_node
node_list = [start_node, goal_node]
# Construct path by traversing backwards through the tree
path = []
last_node = node_list[-1]
while last_node.parent is not None:
path.append(last_node.state)
last_node = last_node.parent
path.append(start)
info_dict = {}
info_dict["node_list"] = node_list
path = Trajectory(path[::-1])
if len(path.path) == 1:
raise PathNotFound(path, message="Path contains only one state")
return (path, info_dict)
