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Add optional robot radius to RRT/RRTStar path planners (#655)

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* Add optional robot radius to RRT/RRTStar path planners.
* update __init__ and check_collision to include radius
* during animation, if a robot radius is given then it is drawn

* Add test for robot radius

* Correct import error

* Correct missing robot_radius errors

* Address "expected 2 blank lines, found 1" error

* Address "line too long" errors

* Add missing argument description.

* Remove collision_check_with_xy and replace with check_collision

* Fix "missing whitespace after ','" error

* Update PathPlanning/ClosedLoopRRTStar/closed_loop_rrt_star_car.py

Co-authored-by: Atsushi Sakai <asakai.amsl+github@gmail.com>

Co-authored-by: Atsushi Sakai <asakai.amsl+github@gmail.com>
This commit is contained in:
Chris Mower
2022-04-19 04:53:24 +01:00
committed by GitHub
parent af2061a1e7
commit b53fdf75f6
10 changed files with 88 additions and 42 deletions
Download Patch File Download Diff File Expand all files Collapse all files

23
PathPlanning/ClosedLoopRRTStar/closed_loop_rrt_star_car.py
View File

@@ -37,11 +37,13 @@ class ClosedLoopRRTStar(RRTStarReedsShepp):
def __init__(self, start, goal, obstacle_list, rand_area, def __init__(self, start, goal, obstacle_list, rand_area,
max_iter=200, max_iter=200,
connect_circle_dist=50.0 connect_circle_dist=50.0,
robot_radius=0.0
): ):
super().__init__(start, goal, obstacle_list, rand_area, super().__init__(start, goal, obstacle_list, rand_area,
max_iter=max_iter, max_iter=max_iter,
connect_circle_dist=connect_circle_dist, connect_circle_dist=connect_circle_dist,
robot_radius=robot_radius
) )
self.target_speed = 10.0 / 3.6 self.target_speed = 10.0 / 3.6
@@ -127,7 +129,11 @@ class ClosedLoopRRTStar(RRTStarReedsShepp):
print("path is too long") print("path is too long")
find_goal = False find_goal = False
if not self.collision_check_with_xy(x, y, self.obstacle_list): tmp_node = self.Node(x, y, 0)
tmp_node.path_x = x
tmp_node.path_y = y
if not self.check_collision(
tmp_node, self.obstacle_list, self.robot_radius):
print("This path is collision") print("This path is collision")
find_goal = False find_goal = False
@@ -151,19 +157,6 @@ class ClosedLoopRRTStar(RRTStarReedsShepp):
return fgoalinds return fgoalinds
@staticmethod
def collision_check_with_xy(x, y, obstacle_list):
for (ox, oy, size) in obstacle_list:
for (ix, iy) in zip(x, y):
dx = ox - ix
dy = oy - iy
d = dx * dx + dy * dy
if d <= size ** 2:
return False # collision
return True # safe
def main(gx=6.0, gy=7.0, gyaw=np.deg2rad(90.0), max_iter=100): def main(gx=6.0, gy=7.0, gyaw=np.deg2rad(90.0), max_iter=100):
print("Start" + __file__) print("Start" + __file__)

8
PathPlanning/LQRRRTStar/lqr_rrt_star.py
View File

@@ -35,7 +35,8 @@ class LQRRRTStar(RRTStar):
goal_sample_rate=10, goal_sample_rate=10,
max_iter=200, max_iter=200,
connect_circle_dist=50.0, connect_circle_dist=50.0,
step_size=0.2 step_size=0.2,
robot_radius=0.0,
): ):
""" """
Setting Parameter Setting Parameter
@@ -44,6 +45,7 @@ class LQRRRTStar(RRTStar):
goal:Goal Position [x,y] goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...] obstacleList:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1]) self.start = self.Node(start[0], start[1])
@@ -58,6 +60,7 @@ class LQRRRTStar(RRTStar):
self.curvature = 1.0 self.curvature = 1.0
self.goal_xy_th = 0.5 self.goal_xy_th = 0.5
self.step_size = step_size self.step_size = step_size
self.robot_radius = robot_radius
self.lqr_planner = LQRPlanner() self.lqr_planner = LQRPlanner()
@@ -75,7 +78,8 @@ class LQRRRTStar(RRTStar):
nearest_ind = self.get_nearest_node_index(self.node_list, rnd) nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
new_node = self.steer(self.node_list[nearest_ind], rnd) new_node = self.steer(self.node_list[nearest_ind], rnd)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
near_indexes = self.find_near_nodes(new_node) near_indexes = self.find_near_nodes(new_node)
new_node = self.choose_parent(new_node, near_indexes) new_node = self.choose_parent(new_node, near_indexes)
if new_node: if new_node:

18
PathPlanning/RRT/rrt.py
View File

@@ -50,7 +50,8 @@ class RRT:
path_resolution=0.5, path_resolution=0.5,
goal_sample_rate=5, goal_sample_rate=5,
max_iter=500, max_iter=500,
play_area=None play_area=None,
robot_radius=0.0,
): ):
""" """
Setting Parameter Setting Parameter
@@ -60,6 +61,7 @@ class RRT:
obstacleList:obstacle Positions [[x,y,size],...] obstacleList:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
play_area:stay inside this area [xmin,xmax,ymin,ymax] play_area:stay inside this area [xmin,xmax,ymin,ymax]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1]) self.start = self.Node(start[0], start[1])
@@ -76,6 +78,7 @@ class RRT:
self.max_iter = max_iter self.max_iter = max_iter
self.obstacle_list = obstacle_list self.obstacle_list = obstacle_list
self.node_list = [] self.node_list = []
self.robot_radius = robot_radius
def planning(self, animation=True): def planning(self, animation=True):
""" """
@@ -93,7 +96,8 @@ class RRT:
new_node = self.steer(nearest_node, rnd_node, self.expand_dis) new_node = self.steer(nearest_node, rnd_node, self.expand_dis)
if self.check_if_outside_play_area(new_node, self.play_area) and \ if self.check_if_outside_play_area(new_node, self.play_area) and \
self.check_collision(new_node, self.obstacle_list): self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
self.node_list.append(new_node) self.node_list.append(new_node)
if animation and i % 5 == 0: if animation and i % 5 == 0:
@@ -103,7 +107,8 @@ class RRT:
self.node_list[-1].y) <= self.expand_dis: self.node_list[-1].y) <= self.expand_dis:
final_node = self.steer(self.node_list[-1], self.end, final_node = self.steer(self.node_list[-1], self.end,
self.expand_dis) self.expand_dis)
if self.check_collision(final_node, self.obstacle_list): if self.check_collision(
final_node, self.obstacle_list, self.robot_radius):
return self.generate_final_course(len(self.node_list) - 1) return self.generate_final_course(len(self.node_list) - 1)
if animation and i % 5: if animation and i % 5:
@@ -173,6 +178,8 @@ class RRT:
lambda event: [exit(0) if event.key == 'escape' else None]) lambda event: [exit(0) if event.key == 'escape' else None])
if rnd is not None: if rnd is not None:
plt.plot(rnd.x, rnd.y, "^k") plt.plot(rnd.x, rnd.y, "^k")
if self.robot_radius > 0.0:
self.plot_circle(rnd.x, rnd.y, self.robot_radius, '-r')
for node in self.node_list: for node in self.node_list:
if node.parent: if node.parent:
plt.plot(node.path_x, node.path_y, "-g") plt.plot(node.path_x, node.path_y, "-g")
@@ -225,7 +232,7 @@ class RRT:
return True # inside - ok return True # inside - ok
@staticmethod @staticmethod
def check_collision(node, obstacleList): def check_collision(node, obstacleList, robot_radius):
if node is None: if node is None:
return False return False
@@ -235,7 +242,7 @@ class RRT:
dy_list = [oy - y for y in node.path_y] dy_list = [oy - y for y in node.path_y]
d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)] d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)]
if min(d_list) <= size**2: if min(d_list) <= (size+robot_radius)**2:
return False # collision return False # collision
return True # safe return True # safe
@@ -262,6 +269,7 @@ def main(gx=6.0, gy=10.0):
rand_area=[-2, 15], rand_area=[-2, 15],
obstacle_list=obstacleList, obstacle_list=obstacleList,
# play_area=[0, 10, 0, 14] # play_area=[0, 10, 0, 14]
robot_radius=0.8
) )
path = rrt.planning(animation=show_animation) path = rrt.planning(animation=show_animation)

20
PathPlanning/RRT/rrt_with_sobol_sampler.py
View File

@@ -62,7 +62,8 @@ class RRTSobol:
expand_dis=3.0, expand_dis=3.0,
path_resolution=0.5, path_resolution=0.5,
goal_sample_rate=5, goal_sample_rate=5,
max_iter=500): max_iter=500,
robot_radius=0.0):
""" """
Setting Parameter Setting Parameter
@@ -70,6 +71,7 @@ class RRTSobol:
goal:Goal Position [x,y] goal:Goal Position [x,y]
obstacle_list:obstacle Positions [[x,y,size],...] obstacle_list:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1]) self.start = self.Node(start[0], start[1])
@@ -83,6 +85,7 @@ class RRTSobol:
self.obstacle_list = obstacle_list self.obstacle_list = obstacle_list
self.node_list = [] self.node_list = []
self.sobol_inter_ = 0 self.sobol_inter_ = 0
self.robot_radius = robot_radius
def planning(self, animation=True): def planning(self, animation=True):
""" """
@@ -99,7 +102,8 @@ class RRTSobol:
new_node = self.steer(nearest_node, rnd_node, self.expand_dis) new_node = self.steer(nearest_node, rnd_node, self.expand_dis)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
self.node_list.append(new_node) self.node_list.append(new_node)
if animation and i % 5 == 0: if animation and i % 5 == 0:
@@ -109,7 +113,8 @@ class RRTSobol:
self.node_list[-1].y) <= self.expand_dis: self.node_list[-1].y) <= self.expand_dis:
final_node = self.steer(self.node_list[-1], self.end, final_node = self.steer(self.node_list[-1], self.end,
self.expand_dis) self.expand_dis)
if self.check_collision(final_node, self.obstacle_list): if self.check_collision(
final_node, self.obstacle_list, self.robot_radius):
return self.generate_final_course(len(self.node_list) - 1) return self.generate_final_course(len(self.node_list) - 1)
if animation and i % 5: if animation and i % 5:
@@ -183,6 +188,8 @@ class RRTSobol:
lambda event: [sys.exit(0) if event.key == 'escape' else None]) lambda event: [sys.exit(0) if event.key == 'escape' else None])
if rnd is not None: if rnd is not None:
plt.plot(rnd.x, rnd.y, "^k") plt.plot(rnd.x, rnd.y, "^k")
if self.robot_radius >= 0.0:
self.plot_circle(rnd.x, rnd.y, self.robot_radius, '-r')
for node in self.node_list: for node in self.node_list:
if node.parent: if node.parent:
plt.plot(node.path_x, node.path_y, "-g") plt.plot(node.path_x, node.path_y, "-g")
@@ -214,7 +221,7 @@ class RRTSobol:
return minind return minind
@staticmethod @staticmethod
def check_collision(node, obstacle_list): def check_collision(node, obstacle_list, robot_radius):
if node is None: if node is None:
return False return False
@@ -224,7 +231,7 @@ class RRTSobol:
dy_list = [oy - y for y in node.path_y] dy_list = [oy - y for y in node.path_y]
d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)] d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)]
if min(d_list) <= size**2: if min(d_list) <= (size+robot_radius)**2:
return False # collision return False # collision
return True # safe return True # safe
@@ -249,7 +256,8 @@ def main(gx=6.0, gy=10.0):
start=[0, 0], start=[0, 0],
goal=[gx, gy], goal=[gx, gy],
rand_area=[-2, 15], rand_area=[-2, 15],
obstacle_list=obstacle_list) obstacle_list=obstacle_list,
robot_radius=0.8)
path = rrt.planning(animation=show_animation) path = rrt.planning(animation=show_animation)
if path is None: if path is None:

6
PathPlanning/RRTDubins/rrt_dubins.py
View File

@@ -46,6 +46,7 @@ class RRTDubins(RRT):
def __init__(self, start, goal, obstacle_list, rand_area, def __init__(self, start, goal, obstacle_list, rand_area,
goal_sample_rate=10, goal_sample_rate=10,
max_iter=200, max_iter=200,
robot_radius=0.0
): ):
""" """
Setting Parameter Setting Parameter
@@ -54,6 +55,7 @@ class RRTDubins(RRT):
goal:Goal Position [x,y] goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...] obstacleList:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1], start[2]) self.start = self.Node(start[0], start[1], start[2])
@@ -67,6 +69,7 @@ class RRTDubins(RRT):
self.curvature = 1.0 # for dubins path self.curvature = 1.0 # for dubins path
self.goal_yaw_th = np.deg2rad(1.0) self.goal_yaw_th = np.deg2rad(1.0)
self.goal_xy_th = 0.5 self.goal_xy_th = 0.5
self.robot_radius = robot_radius
def planning(self, animation=True, search_until_max_iter=True): def planning(self, animation=True, search_until_max_iter=True):
""" """
@@ -82,7 +85,8 @@ class RRTDubins(RRT):
nearest_ind = self.get_nearest_node_index(self.node_list, rnd) nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
new_node = self.steer(self.node_list[nearest_ind], rnd) new_node = self.steer(self.node_list[nearest_ind], rnd)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
self.node_list.append(new_node) self.node_list.append(new_node)
if animation and i % 5 == 0: if animation and i % 5 == 0:

21
PathPlanning/RRTStar/rrt_star.py
View File

@@ -42,7 +42,8 @@ class RRTStar(RRT):
goal_sample_rate=20, goal_sample_rate=20,
max_iter=300, max_iter=300,
connect_circle_dist=50.0, connect_circle_dist=50.0,
search_until_max_iter=False): search_until_max_iter=False,
robot_radius=0.0):
""" """
Setting Parameter Setting Parameter
@@ -53,7 +54,8 @@ class RRTStar(RRT):
""" """
super().__init__(start, goal, obstacle_list, rand_area, expand_dis, super().__init__(start, goal, obstacle_list, rand_area, expand_dis,
path_resolution, goal_sample_rate, max_iter) path_resolution, goal_sample_rate, max_iter,
robot_radius=robot_radius)
self.connect_circle_dist = connect_circle_dist self.connect_circle_dist = connect_circle_dist
self.goal_node = self.Node(goal[0], goal[1]) self.goal_node = self.Node(goal[0], goal[1])
self.search_until_max_iter = search_until_max_iter self.search_until_max_iter = search_until_max_iter
@@ -77,7 +79,8 @@ class RRTStar(RRT):
math.hypot(new_node.x-near_node.x, math.hypot(new_node.x-near_node.x,
new_node.y-near_node.y) new_node.y-near_node.y)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
near_inds = self.find_near_nodes(new_node) near_inds = self.find_near_nodes(new_node)
node_with_updated_parent = self.choose_parent( node_with_updated_parent = self.choose_parent(
new_node, near_inds) new_node, near_inds)
@@ -128,7 +131,8 @@ class RRTStar(RRT):
for i in near_inds: for i in near_inds:
near_node = self.node_list[i] near_node = self.node_list[i]
t_node = self.steer(near_node, new_node) t_node = self.steer(near_node, new_node)
if t_node and self.check_collision(t_node, self.obstacle_list): if t_node and self.check_collision(
t_node, self.obstacle_list, self.robot_radius):
costs.append(self.calc_new_cost(near_node, new_node)) costs.append(self.calc_new_cost(near_node, new_node))
else: else:
costs.append(float("inf")) # the cost of collision node costs.append(float("inf")) # the cost of collision node
@@ -156,7 +160,8 @@ class RRTStar(RRT):
safe_goal_inds = [] safe_goal_inds = []
for goal_ind in goal_inds: for goal_ind in goal_inds:
t_node = self.steer(self.node_list[goal_ind], self.goal_node) t_node = self.steer(self.node_list[goal_ind], self.goal_node)
if self.check_collision(t_node, self.obstacle_list): if self.check_collision(
t_node, self.obstacle_list, self.robot_radius):
safe_goal_inds.append(goal_ind) safe_goal_inds.append(goal_ind)
if not safe_goal_inds: if not safe_goal_inds:
@@ -219,7 +224,8 @@ class RRTStar(RRT):
continue continue
edge_node.cost = self.calc_new_cost(new_node, near_node) edge_node.cost = self.calc_new_cost(new_node, near_node)
no_collision = self.check_collision(edge_node, self.obstacle_list) no_collision = self.check_collision(
edge_node, self.obstacle_list, self.robot_radius)
improved_cost = near_node.cost > edge_node.cost improved_cost = near_node.cost > edge_node.cost
if no_collision and improved_cost: if no_collision and improved_cost:
@@ -264,7 +270,8 @@ def main():
goal=[6, 10], goal=[6, 10],
rand_area=[-2, 15], rand_area=[-2, 15],
obstacle_list=obstacle_list, obstacle_list=obstacle_list,
expand_dis=1) expand_dis=1,
robot_radius=0.8)
path = rrt_star.planning(animation=show_animation) path = rrt_star.planning(animation=show_animation)
if path is None: if path is None:

8
PathPlanning/RRTStarDubins/rrt_star_dubins.py
View File

@@ -46,7 +46,8 @@ class RRTStarDubins(RRTStar):
def __init__(self, start, goal, obstacle_list, rand_area, def __init__(self, start, goal, obstacle_list, rand_area,
goal_sample_rate=10, goal_sample_rate=10,
max_iter=200, max_iter=200,
connect_circle_dist=50.0 connect_circle_dist=50.0,
robot_radius=0.0,
): ):
""" """
Setting Parameter Setting Parameter
@@ -55,6 +56,7 @@ class RRTStarDubins(RRTStar):
goal:Goal Position [x,y] goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...] obstacleList:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1], start[2]) self.start = self.Node(start[0], start[1], start[2])
@@ -69,6 +71,7 @@ class RRTStarDubins(RRTStar):
self.curvature = 1.0 # for dubins path self.curvature = 1.0 # for dubins path
self.goal_yaw_th = np.deg2rad(1.0) self.goal_yaw_th = np.deg2rad(1.0)
self.goal_xy_th = 0.5 self.goal_xy_th = 0.5
self.robot_radius = robot_radius
def planning(self, animation=True, search_until_max_iter=True): def planning(self, animation=True, search_until_max_iter=True):
""" """
@@ -84,7 +87,8 @@ class RRTStarDubins(RRTStar):
nearest_ind = self.get_nearest_node_index(self.node_list, rnd) nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
new_node = self.steer(self.node_list[nearest_ind], rnd) new_node = self.steer(self.node_list[nearest_ind], rnd)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
near_indexes = self.find_near_nodes(new_node) near_indexes = self.find_near_nodes(new_node)
new_node = self.choose_parent(new_node, near_indexes) new_node = self.choose_parent(new_node, near_indexes)
if new_node: if new_node:

11
PathPlanning/RRTStarReedsShepp/rrt_star_reeds_shepp.py
View File

@@ -45,7 +45,8 @@ class RRTStarReedsShepp(RRTStar):
def __init__(self, start, goal, obstacle_list, rand_area, def __init__(self, start, goal, obstacle_list, rand_area,
max_iter=200, max_iter=200,
connect_circle_dist=50.0 connect_circle_dist=50.0,
robot_radius=0.0
): ):
""" """
Setting Parameter Setting Parameter
@@ -54,6 +55,7 @@ class RRTStarReedsShepp(RRTStar):
goal:Goal Position [x,y] goal:Goal Position [x,y]
obstacleList:obstacle Positions [[x,y,size],...] obstacleList:obstacle Positions [[x,y,size],...]
randArea:Random Sampling Area [min,max] randArea:Random Sampling Area [min,max]
robot_radius: robot body modeled as circle with given radius
""" """
self.start = self.Node(start[0], start[1], start[2]) self.start = self.Node(start[0], start[1], start[2])
@@ -63,6 +65,7 @@ class RRTStarReedsShepp(RRTStar):
self.max_iter = max_iter self.max_iter = max_iter
self.obstacle_list = obstacle_list self.obstacle_list = obstacle_list
self.connect_circle_dist = connect_circle_dist self.connect_circle_dist = connect_circle_dist
self.robot_radius = robot_radius
self.curvature = 1.0 self.curvature = 1.0
self.goal_yaw_th = np.deg2rad(1.0) self.goal_yaw_th = np.deg2rad(1.0)
@@ -82,7 +85,8 @@ class RRTStarReedsShepp(RRTStar):
nearest_ind = self.get_nearest_node_index(self.node_list, rnd) nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
new_node = self.steer(self.node_list[nearest_ind], rnd) new_node = self.steer(self.node_list[nearest_ind], rnd)
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
near_indexes = self.find_near_nodes(new_node) near_indexes = self.find_near_nodes(new_node)
new_node = self.choose_parent(new_node, near_indexes) new_node = self.choose_parent(new_node, near_indexes)
if new_node: if new_node:
@@ -117,7 +121,8 @@ class RRTStarReedsShepp(RRTStar):
if new_node is None: if new_node is None:
return return
if self.check_collision(new_node, self.obstacle_list): if self.check_collision(
new_node, self.obstacle_list, self.robot_radius):
self.node_list.append(new_node) self.node_list.append(new_node)
def draw_graph(self, rnd=None): def draw_graph(self, rnd=None):

13
tests/test_rrt_star.py
View File

@@ -19,5 +19,18 @@ def test_no_obstacle():
assert path is not None assert path is not None
def test_no_obstacle_and_robot_radius():
obstacle_list = []
# Set Initial parameters
rrt_star = m.RRTStar(start=[0, 0],
goal=[6, 10],
rand_area=[-2, 15],
obstacle_list=obstacle_list,
robot_radius=0.8)
path = rrt_star.planning(animation=False)
assert path is not None
if __name__ == '__main__': if __name__ == '__main__':
conftest.run_this_test(__file__) conftest.run_this_test(__file__)

2
tests/test_rrt_star_reeds_shepp.py
View File

@@ -1,5 +1,5 @@
import conftest # Add root path to sys.path import conftest # Add root path to sys.path
import rrt_star_reeds_shepp as m from PathPlanning.RRTStarReedsShepp import rrt_star_reeds_shepp as m
def test1(): def test1():