Datasets:

claudios

/

dypybench_functions

like 1

lorien/grab

2d170c31a3335c2e29578b42a5d62ef3efc5d7ee

grab/util/cookies.py

MockRequest.origin_req_host

(self)

return self.get_origin_req_host()

def origin_req_host(self) -> str: return self.get_origin_req_host()

https://github.com/lorien/grab/blob/2d170c31a3335c2e29578b42a5d62ef3efc5d7ee/project1/grab/util/cookies.py#L102-L103

def origin_req_host(self) -> str: return self.get_origin_req_host()

lorien/grab

2d170c31a3335c2e29578b42a5d62ef3efc5d7ee

grab/util/cookies.py

MockRequest.host

(self)

return self.get_host()

def host(self) -> str: return self.get_host()

https://github.com/lorien/grab/blob/2d170c31a3335c2e29578b42a5d62ef3efc5d7ee/project1/grab/util/cookies.py#L106-L107

def host(self) -> str: return self.get_host()

lorien/grab

2d170c31a3335c2e29578b42a5d62ef3efc5d7ee

grab/util/cookies.py

MockResponse.__init__

(self, headers: HTTPMessage | HTTPHeaderDict)

Make a MockResponse for `cookielib` to read. :param headers: a httplib.HTTPMessage or analogous carrying the headers

Make a MockResponse for `cookielib` to read.

def __init__(self, headers: HTTPMessage | HTTPHeaderDict) -> None: """Make a MockResponse for `cookielib` to read. :param headers: a httplib.HTTPMessage or analogous carrying the headers """ self._headers = headers

https://github.com/lorien/grab/blob/2d170c31a3335c2e29578b42a5d62ef3efc5d7ee/project1/grab/util/cookies.py#L118-L123

def __init__(self, headers: HTTPMessage | HTTPHeaderDict) -> None: self._headers = headers

lorien/grab

2d170c31a3335c2e29578b42a5d62ef3efc5d7ee

grab/util/cookies.py

MockResponse.info

(self)

return self._headers

def info(self) -> HTTPMessage | HTTPHeaderDict: return self._headers

https://github.com/lorien/grab/blob/2d170c31a3335c2e29578b42a5d62ef3efc5d7ee/project1/grab/util/cookies.py#L125-L126

def info(self) -> HTTPMessage | HTTPHeaderDict: return self._headers

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

calc_grid_map_config

(ox, oy, xyreso)

return minx, miny, maxx, maxy, xw, yw

def calc_grid_map_config(ox, oy, xyreso): minx = round(min(ox) - EXTEND_AREA / 2.0) miny = round(min(oy) - EXTEND_AREA / 2.0) maxx = round(max(ox) + EXTEND_AREA / 2.0) maxy = round(max(oy) + EXTEND_AREA / 2.0) xw = int(round((maxx - minx) / xyreso)) yw = int(round((maxy - miny) / xyreso)) return minx, miny, maxx, maxy, xw, yw

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L18-L26

def calc_grid_map_config(ox, oy, xyreso): minx = round(min(ox) - EXTEND_AREA / 2.0) miny = round(min(oy) - EXTEND_AREA / 2.0) maxx = round(max(ox) + EXTEND_AREA / 2.0) maxy = round(max(oy) + EXTEND_AREA / 2.0) xw = int(round((maxx - minx) / xyreso)) yw = int(round((maxy - miny) / xyreso)) return minx, miny, maxx, maxy, xw, yw

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

atan_zero_to_twopi

(y, x)

return angle

def atan_zero_to_twopi(y, x): angle = math.atan2(y, x) if angle < 0.0: angle += math.pi * 2.0 return angle

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L43-L48

def atan_zero_to_twopi(y, x): angle = math.atan2(y, x) if angle < 0.0: angle += math.pi * 2.0 return angle

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

precasting

(minx, miny, xw, yw, xyreso, yawreso)

return precast

def precasting(minx, miny, xw, yw, xyreso, yawreso): precast = [[] for i in range(int(round((math.pi * 2.0) / yawreso)) + 1)] for ix in range(xw): for iy in range(yw): px = ix * xyreso + minx py = iy * xyreso + miny d = math.hypot(px, py) angle = atan_zero_to_twopi(py, px) angleid = int(math.floor(angle / yawreso)) pc = precastDB() pc.px = px pc.py = py pc.d = d pc.ix = ix pc.iy = iy pc.angle = angle precast[angleid].append(pc) return precast

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L51-L75

def precasting(minx, miny, xw, yw, xyreso, yawreso): precast = [[] for i in range(int(round((math.pi * 2.0) / yawreso)) + 1)] for ix in range(xw): for iy in range(yw): px = ix * xyreso + minx py = iy * xyreso + miny d = math.hypot(px, py) angle = atan_zero_to_twopi(py, px) angleid = int(math.floor(angle / yawreso)) pc = precastDB() pc.px = px pc.py = py pc.d = d pc.ix = ix pc.iy = iy pc.angle = angle precast[angleid].append(pc) return precast

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

generate_ray_casting_grid_map

(ox, oy, xyreso, yawreso)

return pmap, minx, maxx, miny, maxy, xyreso

def generate_ray_casting_grid_map(ox, oy, xyreso, yawreso): minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso) pmap = [[0.0 for i in range(yw)] for i in range(xw)] precast = precasting(minx, miny, xw, yw, xyreso, yawreso) for (x, y) in zip(ox, oy): d = math.hypot(x, y) angle = atan_zero_to_twopi(y, x) angleid = int(math.floor(angle / yawreso)) gridlist = precast[angleid] ix = int(round((x - minx) / xyreso)) iy = int(round((y - miny) / xyreso)) for grid in gridlist: if grid.d > d: pmap[grid.ix][grid.iy] = 0.5 pmap[ix][iy] = 1.0 return pmap, minx, maxx, miny, maxy, xyreso

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L78-L103

def generate_ray_casting_grid_map(ox, oy, xyreso, yawreso): minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso) pmap = [[0.0 for i in range(yw)] for i in range(xw)] precast = precasting(minx, miny, xw, yw, xyreso, yawreso) for (x, y) in zip(ox, oy): d = math.hypot(x, y) angle = atan_zero_to_twopi(y, x) angleid = int(math.floor(angle / yawreso)) gridlist = precast[angleid] ix = int(round((x - minx) / xyreso)) iy = int(round((y - miny) / xyreso)) for grid in gridlist: if grid.d > d: pmap[grid.ix][grid.iy] = 0.5 pmap[ix][iy] = 1.0 return pmap, minx, maxx, miny, maxy, xyreso

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

draw_heatmap

(data, minx, maxx, miny, maxy, xyreso)

def draw_heatmap(data, minx, maxx, miny, maxy, xyreso): x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso), slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)] plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues) plt.axis("equal")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L106-L110

def draw_heatmap(data, minx, maxx, miny, maxy, xyreso): x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso), slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)] plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues) plt.axis("equal")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

main

()

def main(): print(__file__ + " start!!") xyreso = 0.25 # x-y grid resolution [m] yawreso = np.deg2rad(10.0) # yaw angle resolution [rad] for i in range(5): ox = (np.random.rand(4) - 0.5) * 10.0 oy = (np.random.rand(4) - 0.5) * 10.0 pmap, minx, maxx, miny, maxy, xyreso = generate_ray_casting_grid_map( ox, oy, xyreso, yawreso) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) draw_heatmap(pmap, minx, maxx, miny, maxy, xyreso) plt.plot(ox, oy, "xr") plt.plot(0.0, 0.0, "ob") plt.pause(1.0)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L113-L133

def main(): print(__file__ + " start!!") xyreso = 0.25 # x-y grid resolution [m] yawreso = np.deg2rad(10.0) # yaw angle resolution [rad] for i in range(5): ox = (np.random.rand(4) - 0.5) * 10.0 oy = (np.random.rand(4) - 0.5) * 10.0 pmap, minx, maxx, miny, maxy, xyreso = generate_ray_casting_grid_map( ox, oy, xyreso, yawreso) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) draw_heatmap(pmap, minx, maxx, miny, maxy, xyreso) plt.plot(ox, oy, "xr") plt.plot(0.0, 0.0, "ob") plt.pause(1.0)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

precastDB.__init__

(self)

def __init__(self): self.px = 0.0 self.py = 0.0 self.d = 0.0 self.angle = 0.0 self.ix = 0 self.iy = 0

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L31-L37

def __init__(self): self.px = 0.0 self.py = 0.0 self.d = 0.0 self.angle = 0.0 self.ix = 0 self.iy = 0

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/raycasting_grid_map/raycasting_grid_map.py

precastDB.__str__

(self)

return str(self.px) + "," + str(self.py) + "," + str(self.d) + "," + str(self.angle)

def __str__(self): return str(self.px) + "," + str(self.py) + "," + str(self.d) + "," + str(self.angle)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/raycasting_grid_map/raycasting_grid_map.py#L39-L40

def __str__(self): return str(self.px) + "," + str(self.py) + "," + str(self.d) + "," + str(self.angle)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

kmeans_clustering

(rx, ry, nc)

return clusters

def kmeans_clustering(rx, ry, nc): clusters = Clusters(rx, ry, nc) clusters.calc_centroid() pre_cost = float("inf") for loop in range(MAX_LOOP): print("loop:", loop) cost = clusters.update_clusters() clusters.calc_centroid() d_cost = abs(cost - pre_cost) if d_cost < DCOST_TH: break pre_cost = cost return clusters

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L19-L34

def kmeans_clustering(rx, ry, nc): clusters = Clusters(rx, ry, nc) clusters.calc_centroid() pre_cost = float("inf") for loop in range(MAX_LOOP): print("loop:", loop) cost = clusters.update_clusters() clusters.calc_centroid() d_cost = abs(cost - pre_cost) if d_cost < DCOST_TH: break pre_cost = cost return clusters

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

calc_raw_data

(cx, cy, n_points, rand_d)

return rx, ry

def calc_raw_data(cx, cy, n_points, rand_d): rx, ry = [], [] for (icx, icy) in zip(cx, cy): for _ in range(n_points): rx.append(icx + rand_d * (random.random() - 0.5)) ry.append(icy + rand_d * (random.random() - 0.5)) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L85-L93

def calc_raw_data(cx, cy, n_points, rand_d): rx, ry = [], [] for (icx, icy) in zip(cx, cy): for _ in range(n_points): rx.append(icx + rand_d * (random.random() - 0.5)) ry.append(icy + rand_d * (random.random() - 0.5)) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

update_positions

(cx, cy)

return cx, cy

def update_positions(cx, cy): # object moving parameters DX1 = 0.4 DY1 = 0.5 DX2 = -0.3 DY2 = -0.5 cx[0] += DX1 cy[0] += DY1 cx[1] += DX2 cy[1] += DY2 return cx, cy

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L96-L108

def update_positions(cx, cy): # object moving parameters DX1 = 0.4 DY1 = 0.5 DX2 = -0.3 DY2 = -0.5 cx[0] += DX1 cy[0] += DY1 cx[1] += DX2 cy[1] += DY2 return cx, cy

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

main

()

def main(): print(__file__ + " start!!") cx = [0.0, 8.0] cy = [0.0, 8.0] n_points = 10 rand_d = 3.0 n_cluster = 2 sim_time = 15.0 dt = 1.0 time = 0.0 while time <= sim_time: print("Time:", time) time += dt # objects moving simulation cx, cy = update_positions(cx, cy) raw_x, raw_y = calc_raw_data(cx, cy, n_points, rand_d) clusters = kmeans_clustering(raw_x, raw_y, n_cluster) # for animation if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) clusters.plot_cluster() plt.plot(cx, cy, "or") plt.xlim(-2.0, 10.0) plt.ylim(-2.0, 10.0) plt.pause(dt) print("Done")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L111-L145

def main(): print(__file__ + " start!!") cx = [0.0, 8.0] cy = [0.0, 8.0] n_points = 10 rand_d = 3.0 n_cluster = 2 sim_time = 15.0 dt = 1.0 time = 0.0 while time <= sim_time: print("Time:", time) time += dt # objects moving simulation cx, cy = update_positions(cx, cy) raw_x, raw_y = calc_raw_data(cx, cy, n_points, rand_d) clusters = kmeans_clustering(raw_x, raw_y, n_cluster) # for animation if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) clusters.plot_cluster() plt.plot(cx, cy, "or") plt.xlim(-2.0, 10.0) plt.ylim(-2.0, 10.0) plt.pause(dt) print("Done")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

Clusters.__init__

(self, x, y, n_label)

def __init__(self, x, y, n_label): self.x = x self.y = y self.n_data = len(self.x) self.n_label = n_label self.labels = [random.randint(0, n_label - 1) for _ in range(self.n_data)] self.center_x = [0.0 for _ in range(n_label)] self.center_y = [0.0 for _ in range(n_label)]

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L39-L47

def __init__(self, x, y, n_label): self.x = x self.y = y self.n_data = len(self.x) self.n_label = n_label self.labels = [random.randint(0, n_label - 1) for _ in range(self.n_data)] self.center_x = [0.0 for _ in range(n_label)] self.center_y = [0.0 for _ in range(n_label)]

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

Clusters.plot_cluster

(self)

def plot_cluster(self): for label in set(self.labels): x, y = self._get_labeled_x_y(label) plt.plot(x, y, ".")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L49-L52

def plot_cluster(self): for label in set(self.labels): x, y = self._get_labeled_x_y(label) plt.plot(x, y, ".")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

Clusters.calc_centroid

(self)

def calc_centroid(self): for label in set(self.labels): x, y = self._get_labeled_x_y(label) n_data = len(x) self.center_x[label] = sum(x) / n_data self.center_y[label] = sum(y) / n_data

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L54-L59

def calc_centroid(self): for label in set(self.labels): x, y = self._get_labeled_x_y(label) n_data = len(x) self.center_x[label] = sum(x) / n_data self.center_y[label] = sum(y) / n_data

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

Clusters.update_clusters

(self)

return cost

def update_clusters(self): cost = 0.0 for ip in range(self.n_data): px = self.x[ip] py = self.y[ip] dx = [icx - px for icx in self.center_x] dy = [icy - py for icy in self.center_y] dist_list = [math.hypot(idx, idy) for (idx, idy) in zip(dx, dy)] min_dist = min(dist_list) min_id = dist_list.index(min_dist) self.labels[ip] = min_id cost += min_dist return cost

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L61-L77

def update_clusters(self): cost = 0.0 for ip in range(self.n_data): px = self.x[ip] py = self.y[ip] dx = [icx - px for icx in self.center_x] dy = [icy - py for icy in self.center_y] dist_list = [math.hypot(idx, idy) for (idx, idy) in zip(dx, dy)] min_dist = min(dist_list) min_id = dist_list.index(min_dist) self.labels[ip] = min_id cost += min_dist return cost

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/kmeans_clustering/kmeans_clustering.py

Clusters._get_labeled_x_y

(self, target_label)

return x, y

def _get_labeled_x_y(self, target_label): x = [self.x[i] for i, label in enumerate(self.labels) if label == target_label] y = [self.y[i] for i, label in enumerate(self.labels) if label == target_label] return x, y

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/kmeans_clustering/kmeans_clustering.py#L79-L82

def _get_labeled_x_y(self, target_label): x = [self.x[i] for i, label in enumerate(self.labels) if label == target_label] y = [self.y[i] for i, label in enumerate(self.labels) if label == target_label] return x, y

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

main

()

def main(): print("start!!") test_position_set() test_polygon_set() plt.show() print("done!!")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L255-L263

def main(): print("start!!") test_position_set() test_polygon_set() plt.show() print("done!!")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.__init__

(self, width, height, resolution, center_x, center_y, init_val=0.0)

__init__ :param width: number of grid for width :param height: number of grid for heigt :param resolution: grid resolution [m] :param center_x: center x position [m] :param center_y: center y position [m] :param init_val: initial value for all grid

__init__

def __init__(self, width, height, resolution, center_x, center_y, init_val=0.0): """__init__ :param width: number of grid for width :param height: number of grid for heigt :param resolution: grid resolution [m] :param center_x: center x position [m] :param center_y: center y position [m] :param init_val: initial value for all grid """ self.width = width self.height = height self.resolution = resolution self.center_x = center_x self.center_y = center_y self.left_lower_x = self.center_x - self.width / 2.0 * self.resolution self.left_lower_y = self.center_y - self.height / 2.0 * self.resolution self.ndata = self.width * self.height self.data = [init_val] * self.ndata

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L18-L39

def __init__(self, width, height, resolution, center_x, center_y, init_val=0.0): self.width = width self.height = height self.resolution = resolution self.center_x = center_x self.center_y = center_y self.left_lower_x = self.center_x - self.width / 2.0 * self.resolution self.left_lower_y = self.center_y - self.height / 2.0 * self.resolution self.ndata = self.width * self.height self.data = [init_val] * self.ndata

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.get_value_from_xy_index

(self, x_ind, y_ind)

get_value_from_xy_index when the index is out of grid map area, return None :param x_ind: x index :param y_ind: y index

get_value_from_xy_index

def get_value_from_xy_index(self, x_ind, y_ind): """get_value_from_xy_index when the index is out of grid map area, return None :param x_ind: x index :param y_ind: y index """ grid_ind = self.calc_grid_index_from_xy_index(x_ind, y_ind) if 0 <= grid_ind < self.ndata: return self.data[grid_ind] else: return None

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L41-L55

def get_value_from_xy_index(self, x_ind, y_ind): grid_ind = self.calc_grid_index_from_xy_index(x_ind, y_ind) if 0 <= grid_ind < self.ndata: return self.data[grid_ind] else: return None

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.get_xy_index_from_xy_pos

(self, x_pos, y_pos)

return x_ind, y_ind

get_xy_index_from_xy_pos :param x_pos: x position [m] :param y_pos: y position [m]

get_xy_index_from_xy_pos

def get_xy_index_from_xy_pos(self, x_pos, y_pos): """get_xy_index_from_xy_pos :param x_pos: x position [m] :param y_pos: y position [m] """ x_ind = self.calc_xy_index_from_position( x_pos, self.left_lower_x, self.width) y_ind = self.calc_xy_index_from_position( y_pos, self.left_lower_y, self.height) return x_ind, y_ind

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L57-L68

def get_xy_index_from_xy_pos(self, x_pos, y_pos): x_ind = self.calc_xy_index_from_position( x_pos, self.left_lower_x, self.width) y_ind = self.calc_xy_index_from_position( y_pos, self.left_lower_y, self.height) return x_ind, y_ind

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.set_value_from_xy_pos

(self, x_pos, y_pos, val)

return flag

set_value_from_xy_pos return bool flag, which means setting value is succeeded or not :param x_pos: x position [m] :param y_pos: y position [m] :param val: grid value

set_value_from_xy_pos

def set_value_from_xy_pos(self, x_pos, y_pos, val): """set_value_from_xy_pos return bool flag, which means setting value is succeeded or not :param x_pos: x position [m] :param y_pos: y position [m] :param val: grid value """ x_ind, y_ind = self.get_xy_index_from_xy_pos(x_pos, y_pos) if (not x_ind) or (not y_ind): return False # NG flag = self.set_value_from_xy_index(x_ind, y_ind, val) return flag

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L70-L87

def set_value_from_xy_pos(self, x_pos, y_pos, val): x_ind, y_ind = self.get_xy_index_from_xy_pos(x_pos, y_pos) if (not x_ind) or (not y_ind): return False # NG flag = self.set_value_from_xy_index(x_ind, y_ind, val) return flag

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.set_value_from_xy_index

(self, x_ind, y_ind, val)

set_value_from_xy_index return bool flag, which means setting value is succeeded or not :param x_ind: x index :param y_ind: y index :param val: grid value

set_value_from_xy_index

def set_value_from_xy_index(self, x_ind, y_ind, val): """set_value_from_xy_index return bool flag, which means setting value is succeeded or not :param x_ind: x index :param y_ind: y index :param val: grid value """ if (x_ind is None) or (y_ind is None): return False, False grid_ind = int(y_ind * self.width + x_ind) if 0 <= grid_ind < self.ndata: self.data[grid_ind] = val return True # OK else: return False

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L89-L108

def set_value_from_xy_index(self, x_ind, y_ind, val): if (x_ind is None) or (y_ind is None): return False, False grid_ind = int(y_ind * self.width + x_ind) if 0 <= grid_ind < self.ndata: self.data[grid_ind] = val return True # OK else: return False

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.set_value_from_polygon

(self, pol_x, pol_y, val, inside=True)

set_value_from_polygon Setting value inside or outside polygon :param pol_x: x position list for a polygon :param pol_y: y position list for a polygon :param val: grid value :param inside: setting data inside or outside

set_value_from_polygon

def set_value_from_polygon(self, pol_x, pol_y, val, inside=True): """set_value_from_polygon Setting value inside or outside polygon :param pol_x: x position list for a polygon :param pol_y: y position list for a polygon :param val: grid value :param inside: setting data inside or outside """ # making ring polygon if (pol_x[0] != pol_x[-1]) or (pol_y[0] != pol_y[-1]): np.append(pol_x, pol_x[0]) np.append(pol_y, pol_y[0]) # setting value for all grid for x_ind in range(self.width): for y_ind in range(self.height): x_pos, y_pos = self.calc_grid_central_xy_position_from_xy_index( x_ind, y_ind) flag = self.check_inside_polygon(x_pos, y_pos, pol_x, pol_y) if flag is inside: self.set_value_from_xy_index(x_ind, y_ind, val)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L110-L135

def set_value_from_polygon(self, pol_x, pol_y, val, inside=True): # making ring polygon if (pol_x[0] != pol_x[-1]) or (pol_y[0] != pol_y[-1]): np.append(pol_x, pol_x[0]) np.append(pol_y, pol_y[0]) # setting value for all grid for x_ind in range(self.width): for y_ind in range(self.height): x_pos, y_pos = self.calc_grid_central_xy_position_from_xy_index( x_ind, y_ind) flag = self.check_inside_polygon(x_pos, y_pos, pol_x, pol_y) if flag is inside: self.set_value_from_xy_index(x_ind, y_ind, val)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.calc_grid_index_from_xy_index

(self, x_ind, y_ind)

return grid_ind

def calc_grid_index_from_xy_index(self, x_ind, y_ind): grid_ind = int(y_ind * self.width + x_ind) return grid_ind

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L137-L139

def calc_grid_index_from_xy_index(self, x_ind, y_ind): grid_ind = int(y_ind * self.width + x_ind) return grid_ind

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.calc_grid_central_xy_position_from_xy_index

(self, x_ind, y_ind)

return x_pos, y_pos

def calc_grid_central_xy_position_from_xy_index(self, x_ind, y_ind): x_pos = self.calc_grid_central_xy_position_from_index( x_ind, self.left_lower_x) y_pos = self.calc_grid_central_xy_position_from_index( y_ind, self.left_lower_y) return x_pos, y_pos

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L141-L147

def calc_grid_central_xy_position_from_xy_index(self, x_ind, y_ind): x_pos = self.calc_grid_central_xy_position_from_index( x_ind, self.left_lower_x) y_pos = self.calc_grid_central_xy_position_from_index( y_ind, self.left_lower_y) return x_pos, y_pos

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.calc_grid_central_xy_position_from_index

(self, index, lower_pos)

return lower_pos + index * self.resolution + self.resolution / 2.0

def calc_grid_central_xy_position_from_index(self, index, lower_pos): return lower_pos + index * self.resolution + self.resolution / 2.0

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L149-L150

def calc_grid_central_xy_position_from_index(self, index, lower_pos): return lower_pos + index * self.resolution + self.resolution / 2.0

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.calc_xy_index_from_position

(self, pos, lower_pos, max_index)

def calc_xy_index_from_position(self, pos, lower_pos, max_index): ind = int(np.floor((pos - lower_pos) / self.resolution)) if 0 <= ind <= max_index: return ind else: return None

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L152-L157

def calc_xy_index_from_position(self, pos, lower_pos, max_index): ind = int(np.floor((pos - lower_pos) / self.resolution)) if 0 <= ind <= max_index: return ind else: return None

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.check_occupied_from_xy_index

(self, xind, yind, occupied_val=1.0)

def check_occupied_from_xy_index(self, xind, yind, occupied_val=1.0): val = self.get_value_from_xy_index(xind, yind) if val is None or val >= occupied_val: return True else: return False

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L159-L166

def check_occupied_from_xy_index(self, xind, yind, occupied_val=1.0): val = self.get_value_from_xy_index(xind, yind) if val is None or val >= occupied_val: return True else: return False

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.expand_grid

(self)

def expand_grid(self): xinds, yinds = [], [] for ix in range(self.width): for iy in range(self.height): if self.check_occupied_from_xy_index(ix, iy): xinds.append(ix) yinds.append(iy) for (ix, iy) in zip(xinds, yinds): self.set_value_from_xy_index(ix + 1, iy, val=1.0) self.set_value_from_xy_index(ix, iy + 1, val=1.0) self.set_value_from_xy_index(ix + 1, iy + 1, val=1.0) self.set_value_from_xy_index(ix - 1, iy, val=1.0) self.set_value_from_xy_index(ix, iy - 1, val=1.0) self.set_value_from_xy_index(ix - 1, iy - 1, val=1.0)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L168-L183

def expand_grid(self): xinds, yinds = [], [] for ix in range(self.width): for iy in range(self.height): if self.check_occupied_from_xy_index(ix, iy): xinds.append(ix) yinds.append(iy) for (ix, iy) in zip(xinds, yinds): self.set_value_from_xy_index(ix + 1, iy, val=1.0) self.set_value_from_xy_index(ix, iy + 1, val=1.0) self.set_value_from_xy_index(ix + 1, iy + 1, val=1.0) self.set_value_from_xy_index(ix - 1, iy, val=1.0) self.set_value_from_xy_index(ix, iy - 1, val=1.0) self.set_value_from_xy_index(ix - 1, iy - 1, val=1.0)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.check_inside_polygon

(iox, ioy, x, y)

return inside

def check_inside_polygon(iox, ioy, x, y): npoint = len(x) - 1 inside = False for i1 in range(npoint): i2 = (i1 + 1) % (npoint + 1) if x[i1] >= x[i2]: min_x, max_x = x[i2], x[i1] else: min_x, max_x = x[i1], x[i2] if not min_x <= iox < max_x: continue tmp1 = (y[i2] - y[i1]) / (x[i2] - x[i1]) if (y[i1] + tmp1 * (iox - x[i1]) - ioy) > 0.0: inside = not inside return inside

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L186-L204

def check_inside_polygon(iox, ioy, x, y): npoint = len(x) - 1 inside = False for i1 in range(npoint): i2 = (i1 + 1) % (npoint + 1) if x[i1] >= x[i2]: min_x, max_x = x[i2], x[i1] else: min_x, max_x = x[i1], x[i2] if not min_x <= iox < max_x: continue tmp1 = (y[i2] - y[i1]) / (x[i2] - x[i1]) if (y[i1] + tmp1 * (iox - x[i1]) - ioy) > 0.0: inside = not inside return inside

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.print_grid_map_info

(self)

def print_grid_map_info(self): print("width:", self.width) print("height:", self.height) print("resolution:", self.resolution) print("center_x:", self.center_x) print("center_y:", self.center_y) print("left_lower_x:", self.left_lower_x) print("left_lower_y:", self.left_lower_y) print("ndata:", self.ndata)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L206-L214

def print_grid_map_info(self): print("width:", self.width) print("height:", self.height) print("resolution:", self.resolution) print("center_x:", self.center_x) print("center_y:", self.center_y) print("left_lower_x:", self.left_lower_x) print("left_lower_y:", self.left_lower_y) print("ndata:", self.ndata)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/grid_map_lib/grid_map_lib.py

GridMap.plot_grid_map

(self, ax=None)

return heat_map

def plot_grid_map(self, ax=None): grid_data = np.reshape(np.array(self.data), (self.height, self.width)) if not ax: fig, ax = plt.subplots() heat_map = ax.pcolor(grid_data, cmap="Blues", vmin=0.0, vmax=1.0) plt.axis("equal") # plt.show() return heat_map

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/grid_map_lib/grid_map_lib.py#L216-L225

def plot_grid_map(self, ax=None): grid_data = np.reshape(np.array(self.data), (self.height, self.width)) if not ax: fig, ax = plt.subplots() heat_map = ax.pcolor(grid_data, cmap="Blues", vmin=0.0, vmax=1.0) plt.axis("equal") # plt.show() return heat_map

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/point_cloud_sampling/point_cloud_sampling.py

voxel_point_sampling

(original_points: npt.NDArray, voxel_size: float)

return points

Voxel Point Sampling function. This function sample N-dimensional points with voxel grid. Points in a same voxel grid will be merged by mean operation for sampling. Parameters ---------- original_points : (M, N) N-dimensional points for sampling. The number of points is M. voxel_size : voxel grid size Returns ------- sampled points (M', N)

Voxel Point Sampling function. This function sample N-dimensional points with voxel grid. Points in a same voxel grid will be merged by mean operation for sampling.

def voxel_point_sampling(original_points: npt.NDArray, voxel_size: float): """ Voxel Point Sampling function. This function sample N-dimensional points with voxel grid. Points in a same voxel grid will be merged by mean operation for sampling. Parameters ---------- original_points : (M, N) N-dimensional points for sampling. The number of points is M. voxel_size : voxel grid size Returns ------- sampled points (M', N) """ voxel_dict = defaultdict(list) for i in range(original_points.shape[0]): xyz = original_points[i, :] xyz_index = tuple(xyz // voxel_size) voxel_dict[xyz_index].append(xyz) points = np.vstack([np.mean(v, axis=0) for v in voxel_dict.values()]) return points

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/point_cloud_sampling/point_cloud_sampling.py#L16-L38

def voxel_point_sampling(original_points: npt.NDArray, voxel_size: float): voxel_dict = defaultdict(list) for i in range(original_points.shape[0]): xyz = original_points[i, :] xyz_index = tuple(xyz // voxel_size) voxel_dict[xyz_index].append(xyz) points = np.vstack([np.mean(v, axis=0) for v in voxel_dict.values()]) return points

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/point_cloud_sampling/point_cloud_sampling.py

farthest_point_sampling

(orig_points: npt.NDArray, n_points: int, seed: int)

return orig_points[selected_ids, :]

Farthest point sampling function This function sample N-dimensional points with the farthest point policy. Parameters ---------- orig_points : (M, N) N-dimensional points for sampling. The number of points is M. n_points : number of points for sampling seed : random seed number Returns ------- sampled points (n_points, N)

Farthest point sampling function This function sample N-dimensional points with the farthest point policy.

def farthest_point_sampling(orig_points: npt.NDArray, n_points: int, seed: int): """ Farthest point sampling function This function sample N-dimensional points with the farthest point policy. Parameters ---------- orig_points : (M, N) N-dimensional points for sampling. The number of points is M. n_points : number of points for sampling seed : random seed number Returns ------- sampled points (n_points, N) """ rng = np.random.default_rng(seed) n_orig_points = orig_points.shape[0] first_point_id = rng.choice(range(n_orig_points)) min_distances = np.ones(n_orig_points) * float("inf") selected_ids = [first_point_id] while len(selected_ids) < n_points: base_point = orig_points[selected_ids[-1], :] distances = np.linalg.norm(orig_points[np.newaxis, :] - base_point, axis=2).flatten() min_distances = np.minimum(min_distances, distances) distances_rank = np.argsort(-min_distances) # Farthest order for i in distances_rank: # From the farthest point if i not in selected_ids: # if not selected yes, select it selected_ids.append(i) break return orig_points[selected_ids, :]

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/point_cloud_sampling/point_cloud_sampling.py#L41-L74

def farthest_point_sampling(orig_points: npt.NDArray, n_points: int, seed: int): rng = np.random.default_rng(seed) n_orig_points = orig_points.shape[0] first_point_id = rng.choice(range(n_orig_points)) min_distances = np.ones(n_orig_points) * float("inf") selected_ids = [first_point_id] while len(selected_ids) < n_points: base_point = orig_points[selected_ids[-1], :] distances = np.linalg.norm(orig_points[np.newaxis, :] - base_point, axis=2).flatten() min_distances = np.minimum(min_distances, distances) distances_rank = np.argsort(-min_distances) # Farthest order for i in distances_rank: # From the farthest point if i not in selected_ids: # if not selected yes, select it selected_ids.append(i) break return orig_points[selected_ids, :]

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/point_cloud_sampling/point_cloud_sampling.py

poisson_disk_sampling

(orig_points: npt.NDArray, n_points: int, min_distance: float, seed: int, MAX_ITER=1000)

return orig_points[selected_ids, :]

Poisson disk sampling function This function sample N-dimensional points randomly until the number of points keeping minimum distance between selected points. Parameters ---------- orig_points : (M, N) N-dimensional points for sampling. The number of points is M. n_points : number of points for sampling min_distance : minimum distance between selected points. seed : random seed number MAX_ITER : Maximum number of iteration. Default is 1000. Returns ------- sampled points (n_points or less, N)

Poisson disk sampling function This function sample N-dimensional points randomly until the number of points keeping minimum distance between selected points.

def poisson_disk_sampling(orig_points: npt.NDArray, n_points: int, min_distance: float, seed: int, MAX_ITER=1000): """ Poisson disk sampling function This function sample N-dimensional points randomly until the number of points keeping minimum distance between selected points. Parameters ---------- orig_points : (M, N) N-dimensional points for sampling. The number of points is M. n_points : number of points for sampling min_distance : minimum distance between selected points. seed : random seed number MAX_ITER : Maximum number of iteration. Default is 1000. Returns ------- sampled points (n_points or less, N) """ rng = np.random.default_rng(seed) selected_id = rng.choice(range(orig_points.shape[0])) selected_ids = [selected_id] loop = 0 while len(selected_ids) < n_points and loop <= MAX_ITER: selected_id = rng.choice(range(orig_points.shape[0])) base_point = orig_points[selected_id, :] distances = np.linalg.norm( orig_points[np.newaxis, selected_ids] - base_point, axis=2).flatten() if min(distances) >= min_distance: selected_ids.append(selected_id) loop += 1 if len(selected_ids) != n_points: print("Could not find the specified number of points...") return orig_points[selected_ids, :]

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/point_cloud_sampling/point_cloud_sampling.py#L77-L113

def poisson_disk_sampling(orig_points: npt.NDArray, n_points: int, min_distance: float, seed: int, MAX_ITER=1000): rng = np.random.default_rng(seed) selected_id = rng.choice(range(orig_points.shape[0])) selected_ids = [selected_id] loop = 0 while len(selected_ids) < n_points and loop <= MAX_ITER: selected_id = rng.choice(range(orig_points.shape[0])) base_point = orig_points[selected_id, :] distances = np.linalg.norm( orig_points[np.newaxis, selected_ids] - base_point, axis=2).flatten() if min(distances) >= min_distance: selected_ids.append(selected_id) loop += 1 if len(selected_ids) != n_points: print("Could not find the specified number of points...") return orig_points[selected_ids, :]

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/point_cloud_sampling/point_cloud_sampling.py

plot_sampled_points

(original_points, sampled_points, method_name)

def plot_sampled_points(original_points, sampled_points, method_name): fig = plt.figure() ax = fig.add_subplot(projection='3d') ax.scatter(original_points[:, 0], original_points[:, 1], original_points[:, 2], marker=".", label="Original points") ax.scatter(sampled_points[:, 0], sampled_points[:, 1], sampled_points[:, 2], marker="o", label="Filtered points") plt.legend() plt.title(method_name) plt.axis("equal")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/point_cloud_sampling/point_cloud_sampling.py#L116-L126

def plot_sampled_points(original_points, sampled_points, method_name): fig = plt.figure() ax = fig.add_subplot(projection='3d') ax.scatter(original_points[:, 0], original_points[:, 1], original_points[:, 2], marker=".", label="Original points") ax.scatter(sampled_points[:, 0], sampled_points[:, 1], sampled_points[:, 2], marker="o", label="Filtered points") plt.legend() plt.title(method_name) plt.axis("equal")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/gaussian_grid_map/gaussian_grid_map.py

generate_gaussian_grid_map

(ox, oy, xyreso, std)

return gmap, minx, maxx, miny, maxy

def generate_gaussian_grid_map(ox, oy, xyreso, std): minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso) gmap = [[0.0 for i in range(yw)] for i in range(xw)] for ix in range(xw): for iy in range(yw): x = ix * xyreso + minx y = iy * xyreso + miny # Search minimum distance mindis = float("inf") for (iox, ioy) in zip(ox, oy): d = math.hypot(iox - x, ioy - y) if mindis >= d: mindis = d pdf = (1.0 - norm.cdf(mindis, 0.0, std)) gmap[ix][iy] = pdf return gmap, minx, maxx, miny, maxy

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/gaussian_grid_map/gaussian_grid_map.py#L19-L41

def generate_gaussian_grid_map(ox, oy, xyreso, std): minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso) gmap = [[0.0 for i in range(yw)] for i in range(xw)] for ix in range(xw): for iy in range(yw): x = ix * xyreso + minx y = iy * xyreso + miny # Search minimum distance mindis = float("inf") for (iox, ioy) in zip(ox, oy): d = math.hypot(iox - x, ioy - y) if mindis >= d: mindis = d pdf = (1.0 - norm.cdf(mindis, 0.0, std)) gmap[ix][iy] = pdf return gmap, minx, maxx, miny, maxy

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/gaussian_grid_map/gaussian_grid_map.py

calc_grid_map_config

(ox, oy, xyreso)

return minx, miny, maxx, maxy, xw, yw

def calc_grid_map_config(ox, oy, xyreso): minx = round(min(ox) - EXTEND_AREA / 2.0) miny = round(min(oy) - EXTEND_AREA / 2.0) maxx = round(max(ox) + EXTEND_AREA / 2.0) maxy = round(max(oy) + EXTEND_AREA / 2.0) xw = int(round((maxx - minx) / xyreso)) yw = int(round((maxy - miny) / xyreso)) return minx, miny, maxx, maxy, xw, yw

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/gaussian_grid_map/gaussian_grid_map.py#L44-L52

def calc_grid_map_config(ox, oy, xyreso): minx = round(min(ox) - EXTEND_AREA / 2.0) miny = round(min(oy) - EXTEND_AREA / 2.0) maxx = round(max(ox) + EXTEND_AREA / 2.0) maxy = round(max(oy) + EXTEND_AREA / 2.0) xw = int(round((maxx - minx) / xyreso)) yw = int(round((maxy - miny) / xyreso)) return minx, miny, maxx, maxy, xw, yw

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/gaussian_grid_map/gaussian_grid_map.py

draw_heatmap

(data, minx, maxx, miny, maxy, xyreso)

def draw_heatmap(data, minx, maxx, miny, maxy, xyreso): x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso), slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)] plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues) plt.axis("equal")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/gaussian_grid_map/gaussian_grid_map.py#L55-L59

def draw_heatmap(data, minx, maxx, miny, maxy, xyreso): x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso), slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)] plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues) plt.axis("equal")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/gaussian_grid_map/gaussian_grid_map.py

main

()

def main(): print(__file__ + " start!!") xyreso = 0.5 # xy grid resolution STD = 5.0 # standard diviation for gaussian distribution for i in range(5): ox = (np.random.rand(4) - 0.5) * 10.0 oy = (np.random.rand(4) - 0.5) * 10.0 gmap, minx, maxx, miny, maxy = generate_gaussian_grid_map( ox, oy, xyreso, STD) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) draw_heatmap(gmap, minx, maxx, miny, maxy, xyreso) plt.plot(ox, oy, "xr") plt.plot(0.0, 0.0, "ob") plt.pause(1.0)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/gaussian_grid_map/gaussian_grid_map.py#L62-L82

def main(): print(__file__ + " start!!") xyreso = 0.5 # xy grid resolution STD = 5.0 # standard diviation for gaussian distribution for i in range(5): ox = (np.random.rand(4) - 0.5) * 10.0 oy = (np.random.rand(4) - 0.5) * 10.0 gmap, minx, maxx, miny, maxy = generate_gaussian_grid_map( ox, oy, xyreso, STD) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) draw_heatmap(gmap, minx, maxx, miny, maxy, xyreso) plt.plot(ox, oy, "xr") plt.plot(0.0, 0.0, "ob") plt.pause(1.0)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

main

()

def main(): # simulation parameters sim_time = 30.0 # simulation time dt = 0.2 # time tick angle_resolution = np.deg2rad(3.0) # sensor angle resolution v1 = VehicleSimulator(-10.0, 0.0, np.deg2rad(90.0), 0.0, 50.0 / 3.6, 3.0, 5.0) v2 = VehicleSimulator(20.0, 10.0, np.deg2rad(180.0), 0.0, 50.0 / 3.6, 4.0, 10.0) l_shape_fitting = LShapeFitting() lidar_sim = LidarSimulator() time = 0.0 while time <= sim_time: time += dt v1.update(dt, 0.1, 0.0) v2.update(dt, 0.1, -0.05) ox, oy = lidar_sim.get_observation_points([v1, v2], angle_resolution) rects, id_sets = l_shape_fitting.fitting(ox, oy) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect( 'key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.axis("equal") plt.plot(0.0, 0.0, "*r") v1.plot() v2.plot() # Plot range observation for ids in id_sets: x = [ox[i] for i in range(len(ox)) if i in ids] y = [oy[i] for i in range(len(ox)) if i in ids] for (ix, iy) in zip(x, y): plt.plot([0.0, ix], [0.0, iy], "-og") plt.plot([ox[i] for i in range(len(ox)) if i in ids], [oy[i] for i in range(len(ox)) if i in ids], "o") for rect in rects: rect.plot() plt.pause(0.1) print("Done")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L211-L265

def main(): # simulation parameters sim_time = 30.0 # simulation time dt = 0.2 # time tick angle_resolution = np.deg2rad(3.0) # sensor angle resolution v1 = VehicleSimulator(-10.0, 0.0, np.deg2rad(90.0), 0.0, 50.0 / 3.6, 3.0, 5.0) v2 = VehicleSimulator(20.0, 10.0, np.deg2rad(180.0), 0.0, 50.0 / 3.6, 4.0, 10.0) l_shape_fitting = LShapeFitting() lidar_sim = LidarSimulator() time = 0.0 while time <= sim_time: time += dt v1.update(dt, 0.1, 0.0) v2.update(dt, 0.1, -0.05) ox, oy = lidar_sim.get_observation_points([v1, v2], angle_resolution) rects, id_sets = l_shape_fitting.fitting(ox, oy) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect( 'key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.axis("equal") plt.plot(0.0, 0.0, "*r") v1.plot() v2.plot() # Plot range observation for ids in id_sets: x = [ox[i] for i in range(len(ox)) if i in ids] y = [oy[i] for i in range(len(ox)) if i in ids] for (ix, iy) in zip(x, y): plt.plot([0.0, ix], [0.0, iy], "-og") plt.plot([ox[i] for i in range(len(ox)) if i in ids], [oy[i] for i in range(len(ox)) if i in ids], "o") for rect in rects: rect.plot() plt.pause(0.1) print("Done")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting.__init__

(self)

def __init__(self): # Parameters self.criteria = self.Criteria.VARIANCE self.min_dist_of_closeness_criteria = 0.01 # [m] self.d_theta_deg_for_search = 1.0 # [deg] self.R0 = 3.0 # [m] range segmentation param self.Rd = 0.001

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L39-L45

def __init__(self): # Parameters self.criteria = self.Criteria.VARIANCE self.min_dist_of_closeness_criteria = 0.01 # [m] self.d_theta_deg_for_search = 1.0 # [deg] self.R0 = 3.0 # [m] range segmentation param self.Rd = 0.001

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting.fitting

(self, ox, oy)

return rects, id_sets

def fitting(self, ox, oy): # step1: Adaptive Range Segmentation id_sets = self._adoptive_range_segmentation(ox, oy) # step2 Rectangle search rects = [] for ids in id_sets: # for each cluster cx = [ox[i] for i in range(len(ox)) if i in ids] cy = [oy[i] for i in range(len(oy)) if i in ids] rects.append(self._rectangle_search(cx, cy)) return rects, id_sets

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L47-L59

def fitting(self, ox, oy): # step1: Adaptive Range Segmentation id_sets = self._adoptive_range_segmentation(ox, oy) # step2 Rectangle search rects = [] for ids in id_sets: # for each cluster cx = [ox[i] for i in range(len(ox)) if i in ids] cy = [oy[i] for i in range(len(oy)) if i in ids] rects.append(self._rectangle_search(cx, cy)) return rects, id_sets

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting._calc_area_criterion

(c1, c2)

return alpha

def _calc_area_criterion(c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) alpha = -(c1_max - c1_min) * (c2_max - c2_min) return alpha

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L62-L70

def _calc_area_criterion(c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) alpha = -(c1_max - c1_min) * (c2_max - c2_min) return alpha

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting._calc_closeness_criterion

(self, c1, c2)

return beta

def _calc_closeness_criterion(self, c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) # Vectorization D1 = np.minimum(c1_max - c1, c1 - c1_min) D2 = np.minimum(c2_max - c2, c2 - c2_min) d = np.maximum(np.minimum(D1, D2), self.min_dist_of_closeness_criteria) beta = (1.0 / d).sum() return beta

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L72-L84

def _calc_closeness_criterion(self, c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) # Vectorization D1 = np.minimum(c1_max - c1, c1 - c1_min) D2 = np.minimum(c2_max - c2, c2 - c2_min) d = np.maximum(np.minimum(D1, D2), self.min_dist_of_closeness_criteria) beta = (1.0 / d).sum() return beta

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting._calc_variance_criterion

(c1, c2)

return gamma

def _calc_variance_criterion(c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) # Vectorization D1 = np.minimum(c1_max - c1, c1 - c1_min) D2 = np.minimum(c2_max - c2, c2 - c2_min) E1 = D1[D1 < D2] E2 = D2[D1 >= D2] V1 = - np.var(E1) if len(E1) > 0 else 0. V2 = - np.var(E2) if len(E2) > 0 else 0. gamma = V1 + V2 return gamma

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L87-L102

def _calc_variance_criterion(c1, c2): c1_max = max(c1) c2_max = max(c2) c1_min = min(c1) c2_min = min(c2) # Vectorization D1 = np.minimum(c1_max - c1, c1 - c1_min) D2 = np.minimum(c2_max - c2, c2 - c2_min) E1 = D1[D1 < D2] E2 = D2[D1 >= D2] V1 = - np.var(E1) if len(E1) > 0 else 0. V2 = - np.var(E2) if len(E2) > 0 else 0. gamma = V1 + V2 return gamma

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting._rectangle_search

(self, x, y)

return rect

def _rectangle_search(self, x, y): X = np.array([x, y]).T d_theta = np.deg2rad(self.d_theta_deg_for_search) min_cost = (-float('inf'), None) for theta in np.arange(0.0, np.pi / 2.0 - d_theta, d_theta): c = X @ rot_mat_2d(theta) c1 = c[:, 0] c2 = c[:, 1] # Select criteria cost = 0.0 if self.criteria == self.Criteria.AREA: cost = self._calc_area_criterion(c1, c2) elif self.criteria == self.Criteria.CLOSENESS: cost = self._calc_closeness_criterion(c1, c2) elif self.criteria == self.Criteria.VARIANCE: cost = self._calc_variance_criterion(c1, c2) if min_cost[0] < cost: min_cost = (cost, theta) # calc best rectangle sin_s = np.sin(min_cost[1]) cos_s = np.cos(min_cost[1]) c1_s = X @ np.array([cos_s, sin_s]).T c2_s = X @ np.array([-sin_s, cos_s]).T rect = RectangleData() rect.a[0] = cos_s rect.b[0] = sin_s rect.c[0] = min(c1_s) rect.a[1] = -sin_s rect.b[1] = cos_s rect.c[1] = min(c2_s) rect.a[2] = cos_s rect.b[2] = sin_s rect.c[2] = max(c1_s) rect.a[3] = -sin_s rect.b[3] = cos_s rect.c[3] = max(c2_s) return rect

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L104-L149

def _rectangle_search(self, x, y): X = np.array([x, y]).T d_theta = np.deg2rad(self.d_theta_deg_for_search) min_cost = (-float('inf'), None) for theta in np.arange(0.0, np.pi / 2.0 - d_theta, d_theta): c = X @ rot_mat_2d(theta) c1 = c[:, 0] c2 = c[:, 1] # Select criteria cost = 0.0 if self.criteria == self.Criteria.AREA: cost = self._calc_area_criterion(c1, c2) elif self.criteria == self.Criteria.CLOSENESS: cost = self._calc_closeness_criterion(c1, c2) elif self.criteria == self.Criteria.VARIANCE: cost = self._calc_variance_criterion(c1, c2) if min_cost[0] < cost: min_cost = (cost, theta) # calc best rectangle sin_s = np.sin(min_cost[1]) cos_s = np.cos(min_cost[1]) c1_s = X @ np.array([cos_s, sin_s]).T c2_s = X @ np.array([-sin_s, cos_s]).T rect = RectangleData() rect.a[0] = cos_s rect.b[0] = sin_s rect.c[0] = min(c1_s) rect.a[1] = -sin_s rect.b[1] = cos_s rect.c[1] = min(c2_s) rect.a[2] = cos_s rect.b[2] = sin_s rect.c[2] = max(c1_s) rect.a[3] = -sin_s rect.b[3] = cos_s rect.c[3] = max(c2_s) return rect

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

LShapeFitting._adoptive_range_segmentation

(self, ox, oy)

return S

def _adoptive_range_segmentation(self, ox, oy): # Setup initial cluster S = [] for i, _ in enumerate(ox): C = set() R = self.R0 + self.Rd * np.linalg.norm([ox[i], oy[i]]) for j, _ in enumerate(ox): d = np.hypot(ox[i] - ox[j], oy[i] - oy[j]) if d <= R: C.add(j) S.append(C) # Merge cluster while True: no_change = True for (c1, c2) in list(itertools.permutations(range(len(S)), 2)): if S[c1] & S[c2]: S[c1] = (S[c1] | S.pop(c2)) no_change = False break if no_change: break return S

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L151-L175

def _adoptive_range_segmentation(self, ox, oy): # Setup initial cluster S = [] for i, _ in enumerate(ox): C = set() R = self.R0 + self.Rd * np.linalg.norm([ox[i], oy[i]]) for j, _ in enumerate(ox): d = np.hypot(ox[i] - ox[j], oy[i] - oy[j]) if d <= R: C.add(j) S.append(C) # Merge cluster while True: no_change = True for (c1, c2) in list(itertools.permutations(range(len(S)), 2)): if S[c1] & S[c2]: S[c1] = (S[c1] | S.pop(c2)) no_change = False break if no_change: break return S

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

RectangleData.__init__

(self)

def __init__(self): self.a = [None] * 4 self.b = [None] * 4 self.c = [None] * 4 self.rect_c_x = [None] * 5 self.rect_c_y = [None] * 5

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L180-L186

def __init__(self): self.a = [None] * 4 self.b = [None] * 4 self.c = [None] * 4 self.rect_c_x = [None] * 5 self.rect_c_y = [None] * 5

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

RectangleData.plot

(self)

def plot(self): self.calc_rect_contour() plt.plot(self.rect_c_x, self.rect_c_y, "-r")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L188-L190

def plot(self): self.calc_rect_contour() plt.plot(self.rect_c_x, self.rect_c_y, "-r")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

RectangleData.calc_rect_contour

(self)

def calc_rect_contour(self): self.rect_c_x[0], self.rect_c_y[0] = self.calc_cross_point( self.a[0:2], self.b[0:2], self.c[0:2]) self.rect_c_x[1], self.rect_c_y[1] = self.calc_cross_point( self.a[1:3], self.b[1:3], self.c[1:3]) self.rect_c_x[2], self.rect_c_y[2] = self.calc_cross_point( self.a[2:4], self.b[2:4], self.c[2:4]) self.rect_c_x[3], self.rect_c_y[3] = self.calc_cross_point( [self.a[3], self.a[0]], [self.b[3], self.b[0]], [self.c[3], self.c[0]]) self.rect_c_x[4], self.rect_c_y[4] = self.rect_c_x[0], self.rect_c_y[0]

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L192-L202

def calc_rect_contour(self): self.rect_c_x[0], self.rect_c_y[0] = self.calc_cross_point( self.a[0:2], self.b[0:2], self.c[0:2]) self.rect_c_x[1], self.rect_c_y[1] = self.calc_cross_point( self.a[1:3], self.b[1:3], self.c[1:3]) self.rect_c_x[2], self.rect_c_y[2] = self.calc_cross_point( self.a[2:4], self.b[2:4], self.c[2:4]) self.rect_c_x[3], self.rect_c_y[3] = self.calc_cross_point( [self.a[3], self.a[0]], [self.b[3], self.b[0]], [self.c[3], self.c[0]]) self.rect_c_x[4], self.rect_c_y[4] = self.rect_c_x[0], self.rect_c_y[0]

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/rectangle_fitting.py

RectangleData.calc_cross_point

(a, b, c)

return x, y

def calc_cross_point(a, b, c): x = (b[0] * -c[1] - b[1] * -c[0]) / (a[0] * b[1] - a[1] * b[0]) y = (a[1] * -c[0] - a[0] * -c[1]) / (a[0] * b[1] - a[1] * b[0]) return x, y

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/rectangle_fitting.py#L205-L208

def calc_cross_point(a, b, c): x = (b[0] * -c[1] - b[1] * -c[0]) / (a[0] * b[1] - a[1] * b[0]) y = (a[1] * -c[0] - a[0] * -c[1]) / (a[0] * b[1] - a[1] * b[0]) return x, y

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator.__init__

(self, i_x, i_y, i_yaw, i_v, max_v, w, L)

def __init__(self, i_x, i_y, i_yaw, i_v, max_v, w, L): self.x = i_x self.y = i_y self.yaw = i_yaw self.v = i_v self.max_v = max_v self.W = w self.L = L self._calc_vehicle_contour()

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L22-L30

def __init__(self, i_x, i_y, i_yaw, i_v, max_v, w, L): self.x = i_x self.y = i_y self.yaw = i_yaw self.v = i_v self.max_v = max_v self.W = w self.L = L self._calc_vehicle_contour()

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator.update

(self, dt, a, omega)

def update(self, dt, a, omega): self.x += self.v * np.cos(self.yaw) * dt self.y += self.v * np.sin(self.yaw) * dt self.yaw += omega * dt self.v += a * dt if self.v >= self.max_v: self.v = self.max_v

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L32-L38

def update(self, dt, a, omega): self.x += self.v * np.cos(self.yaw) * dt self.y += self.v * np.sin(self.yaw) * dt self.yaw += omega * dt self.v += a * dt if self.v >= self.max_v: self.v = self.max_v

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator.plot

(self)

def plot(self): plt.plot(self.x, self.y, ".b") # convert global coordinate gx, gy = self.calc_global_contour() plt.plot(gx, gy, "--b")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L40-L45

def plot(self): plt.plot(self.x, self.y, ".b") # convert global coordinate gx, gy = self.calc_global_contour() plt.plot(gx, gy, "--b")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator.calc_global_contour

(self)

return gx, gy

def calc_global_contour(self): gxy = np.stack([self.vc_x, self.vc_y]).T @ rot_mat_2d(self.yaw) gx = gxy[:, 0] + self.x gy = gxy[:, 1] + self.y return gx, gy

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L47-L52

def calc_global_contour(self): gxy = np.stack([self.vc_x, self.vc_y]).T @ rot_mat_2d(self.yaw) gx = gxy[:, 0] + self.x gy = gxy[:, 1] + self.y return gx, gy

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator._calc_vehicle_contour

(self)

def _calc_vehicle_contour(self): self.vc_x = [] self.vc_y = [] self.vc_x.append(self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x.append(self.L / 2.0) self.vc_y.append(-self.W / 2.0) self.vc_x.append(-self.L / 2.0) self.vc_y.append(-self.W / 2.0) self.vc_x.append(-self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x.append(self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x, self.vc_y = self._interpolate(self.vc_x, self.vc_y)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L54-L74

def _calc_vehicle_contour(self): self.vc_x = [] self.vc_y = [] self.vc_x.append(self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x.append(self.L / 2.0) self.vc_y.append(-self.W / 2.0) self.vc_x.append(-self.L / 2.0) self.vc_y.append(-self.W / 2.0) self.vc_x.append(-self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x.append(self.L / 2.0) self.vc_y.append(self.W / 2.0) self.vc_x, self.vc_y = self._interpolate(self.vc_x, self.vc_y)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

VehicleSimulator._interpolate

(x, y)

return rx, ry

def _interpolate(x, y): rx, ry = [], [] d_theta = 0.05 for i in range(len(x) - 1): rx.extend([(1.0 - theta) * x[i] + theta * x[i + 1] for theta in np.arange(0.0, 1.0, d_theta)]) ry.extend([(1.0 - theta) * y[i] + theta * y[i + 1] for theta in np.arange(0.0, 1.0, d_theta)]) rx.extend([(1.0 - theta) * x[len(x) - 1] + theta * x[1] for theta in np.arange(0.0, 1.0, d_theta)]) ry.extend([(1.0 - theta) * y[len(y) - 1] + theta * y[1] for theta in np.arange(0.0, 1.0, d_theta)]) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L77-L91

def _interpolate(x, y): rx, ry = [], [] d_theta = 0.05 for i in range(len(x) - 1): rx.extend([(1.0 - theta) * x[i] + theta * x[i + 1] for theta in np.arange(0.0, 1.0, d_theta)]) ry.extend([(1.0 - theta) * y[i] + theta * y[i + 1] for theta in np.arange(0.0, 1.0, d_theta)]) rx.extend([(1.0 - theta) * x[len(x) - 1] + theta * x[1] for theta in np.arange(0.0, 1.0, d_theta)]) ry.extend([(1.0 - theta) * y[len(y) - 1] + theta * y[1] for theta in np.arange(0.0, 1.0, d_theta)]) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

LidarSimulator.__init__

(self)

def __init__(self): self.range_noise = 0.01

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L96-L97

def __init__(self): self.range_noise = 0.01

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

LidarSimulator.get_observation_points

(self, v_list, angle_resolution)

return rx, ry

def get_observation_points(self, v_list, angle_resolution): x, y, angle, r = [], [], [], [] # store all points for v in v_list: gx, gy = v.calc_global_contour() for vx, vy in zip(gx, gy): v_angle = math.atan2(vy, vx) vr = np.hypot(vx, vy) * random.uniform(1.0 - self.range_noise, 1.0 + self.range_noise) x.append(vx) y.append(vy) angle.append(v_angle) r.append(vr) # ray casting filter rx, ry = self.ray_casting_filter(angle, r, angle_resolution) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L99-L120

def get_observation_points(self, v_list, angle_resolution): x, y, angle, r = [], [], [], [] # store all points for v in v_list: gx, gy = v.calc_global_contour() for vx, vy in zip(gx, gy): v_angle = math.atan2(vy, vx) vr = np.hypot(vx, vy) * random.uniform(1.0 - self.range_noise, 1.0 + self.range_noise) x.append(vx) y.append(vy) angle.append(v_angle) r.append(vr) # ray casting filter rx, ry = self.ray_casting_filter(angle, r, angle_resolution) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/rectangle_fitting/simulator.py

LidarSimulator.ray_casting_filter

(theta_l, range_l, angle_resolution)

return rx, ry

def ray_casting_filter(theta_l, range_l, angle_resolution): rx, ry = [], [] range_db = [float("inf") for _ in range( int(np.floor((np.pi * 2.0) / angle_resolution)) + 1)] for i in range(len(theta_l)): angle_id = int(round(theta_l[i] / angle_resolution)) if range_db[angle_id] > range_l[i]: range_db[angle_id] = range_l[i] for i in range(len(range_db)): t = i * angle_resolution if range_db[i] != float("inf"): rx.append(range_db[i] * np.cos(t)) ry.append(range_db[i] * np.sin(t)) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/rectangle_fitting/simulator.py#L123-L140

def ray_casting_filter(theta_l, range_l, angle_resolution): rx, ry = [], [] range_db = [float("inf") for _ in range( int(np.floor((np.pi * 2.0) / angle_resolution)) + 1)] for i in range(len(theta_l)): angle_id = int(round(theta_l[i] / angle_resolution)) if range_db[angle_id] > range_l[i]: range_db[angle_id] = range_l[i] for i in range(len(range_db)): t = i * angle_resolution if range_db[i] != float("inf"): rx.append(range_db[i] * np.cos(t)) ry.append(range_db[i] * np.sin(t)) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/circle_fitting/circle_fitting.py

circle_fitting

(x, y)

return (cxe, cye, re, error)

Circle Fitting with least squared input: point x-y positions output cxe x center position cye y center position re radius of circle error: prediction error

Circle Fitting with least squared input: point x-y positions output cxe x center position cye y center position re radius of circle error: prediction error

def circle_fitting(x, y): """ Circle Fitting with least squared input: point x-y positions output cxe x center position cye y center position re radius of circle error: prediction error """ sumx = sum(x) sumy = sum(y) sumx2 = sum([ix ** 2 for ix in x]) sumy2 = sum([iy ** 2 for iy in y]) sumxy = sum([ix * iy for (ix, iy) in zip(x, y)]) F = np.array([[sumx2, sumxy, sumx], [sumxy, sumy2, sumy], [sumx, sumy, len(x)]]) G = np.array([[-sum([ix ** 3 + ix * iy ** 2 for (ix, iy) in zip(x, y)])], [-sum([ix ** 2 * iy + iy ** 3 for (ix, iy) in zip(x, y)])], [-sum([ix ** 2 + iy ** 2 for (ix, iy) in zip(x, y)])]]) T = np.linalg.inv(F).dot(G) cxe = float(T[0] / -2) cye = float(T[1] / -2) re = math.sqrt(cxe**2 + cye**2 - T[2]) error = sum([np.hypot(cxe - ix, cye - iy) - re for (ix, iy) in zip(x, y)]) return (cxe, cye, re, error)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/circle_fitting/circle_fitting.py#L17-L49

def circle_fitting(x, y): sumx = sum(x) sumy = sum(y) sumx2 = sum([ix ** 2 for ix in x]) sumy2 = sum([iy ** 2 for iy in y]) sumxy = sum([ix * iy for (ix, iy) in zip(x, y)]) F = np.array([[sumx2, sumxy, sumx], [sumxy, sumy2, sumy], [sumx, sumy, len(x)]]) G = np.array([[-sum([ix ** 3 + ix * iy ** 2 for (ix, iy) in zip(x, y)])], [-sum([ix ** 2 * iy + iy ** 3 for (ix, iy) in zip(x, y)])], [-sum([ix ** 2 + iy ** 2 for (ix, iy) in zip(x, y)])]]) T = np.linalg.inv(F).dot(G) cxe = float(T[0] / -2) cye = float(T[1] / -2) re = math.sqrt(cxe**2 + cye**2 - T[2]) error = sum([np.hypot(cxe - ix, cye - iy) - re for (ix, iy) in zip(x, y)]) return (cxe, cye, re, error)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/circle_fitting/circle_fitting.py

get_sample_points

(cx, cy, cr, angle_reso)

return rx, ry

def get_sample_points(cx, cy, cr, angle_reso): x, y, angle, r = [], [], [], [] # points sampling for theta in np.arange(0.0, 2.0 * math.pi, angle_reso): nx = cx + cr * math.cos(theta) ny = cy + cr * math.sin(theta) nangle = math.atan2(ny, nx) nr = math.hypot(nx, ny) * random.uniform(0.95, 1.05) x.append(nx) y.append(ny) angle.append(nangle) r.append(nr) # ray casting filter rx, ry = ray_casting_filter(x, y, angle, r, angle_reso) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/circle_fitting/circle_fitting.py#L52-L70

def get_sample_points(cx, cy, cr, angle_reso): x, y, angle, r = [], [], [], [] # points sampling for theta in np.arange(0.0, 2.0 * math.pi, angle_reso): nx = cx + cr * math.cos(theta) ny = cy + cr * math.sin(theta) nangle = math.atan2(ny, nx) nr = math.hypot(nx, ny) * random.uniform(0.95, 1.05) x.append(nx) y.append(ny) angle.append(nangle) r.append(nr) # ray casting filter rx, ry = ray_casting_filter(x, y, angle, r, angle_reso) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/circle_fitting/circle_fitting.py

ray_casting_filter

(xl, yl, thetal, rangel, angle_reso)

return rx, ry

def ray_casting_filter(xl, yl, thetal, rangel, angle_reso): rx, ry = [], [] rangedb = [float("inf") for _ in range( int(math.floor((math.pi * 2.0) / angle_reso)) + 1)] for i, _ in enumerate(thetal): angleid = math.floor(thetal[i] / angle_reso) if rangedb[angleid] > rangel[i]: rangedb[angleid] = rangel[i] for i, _ in enumerate(rangedb): t = i * angle_reso if rangedb[i] != float("inf"): rx.append(rangedb[i] * math.cos(t)) ry.append(rangedb[i] * math.sin(t)) return rx, ry

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/circle_fitting/circle_fitting.py#L73-L90

def ray_casting_filter(xl, yl, thetal, rangel, angle_reso): rx, ry = [], [] rangedb = [float("inf") for _ in range( int(math.floor((math.pi * 2.0) / angle_reso)) + 1)] for i, _ in enumerate(thetal): angleid = math.floor(thetal[i] / angle_reso) if rangedb[angleid] > rangel[i]: rangedb[angleid] = rangel[i] for i, _ in enumerate(rangedb): t = i * angle_reso if rangedb[i] != float("inf"): rx.append(rangedb[i] * math.cos(t)) ry.append(rangedb[i] * math.sin(t)) return rx, ry

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/circle_fitting/circle_fitting.py

plot_circle

(x, y, size, color="-b")

def plot_circle(x, y, size, color="-b"): # pragma: no cover deg = list(range(0, 360, 5)) deg.append(0) xl = [x + size * math.cos(np.deg2rad(d)) for d in deg] yl = [y + size * math.sin(np.deg2rad(d)) for d in deg] plt.plot(xl, yl, color)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/circle_fitting/circle_fitting.py#L93-L98

def plot_circle(x, y, size, color="-b"): # pragma: no cover deg = list(range(0, 360, 5)) deg.append(0) xl = [x + size * math.cos(np.deg2rad(d)) for d in deg] yl = [y + size * math.sin(np.deg2rad(d)) for d in deg] plt.plot(xl, yl, color)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Mapping/circle_fitting/circle_fitting.py

main

()

def main(): # simulation parameters simtime = 15.0 # simulation time dt = 1.0 # time tick cx = -2.0 # initial x position of obstacle cy = -8.0 # initial y position of obstacle cr = 1.0 # obstacle radious theta = np.deg2rad(30.0) # obstacle moving direction angle_reso = np.deg2rad(3.0) # sensor angle resolution time = 0.0 while time <= simtime: time += dt cx += math.cos(theta) cy += math.cos(theta) x, y = get_sample_points(cx, cy, cr, angle_reso) ex, ey, er, error = circle_fitting(x, y) print("Error:", error) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.axis("equal") plt.plot(0.0, 0.0, "*r") plot_circle(cx, cy, cr) plt.plot(x, y, "xr") plot_circle(ex, ey, er, "-r") plt.pause(dt) print("Done")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Mapping/circle_fitting/circle_fitting.py#L101-L137

def main(): # simulation parameters simtime = 15.0 # simulation time dt = 1.0 # time tick cx = -2.0 # initial x position of obstacle cy = -8.0 # initial y position of obstacle cr = 1.0 # obstacle radious theta = np.deg2rad(30.0) # obstacle moving direction angle_reso = np.deg2rad(3.0) # sensor angle resolution time = 0.0 while time <= simtime: time += dt cx += math.cos(theta) cy += math.cos(theta) x, y = get_sample_points(cx, cy, cr, angle_reso) ex, ey, er, error = circle_fitting(x, y) print("Error:", error) if show_animation: # pragma: no cover plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.axis("equal") plt.plot(0.0, 0.0, "*r") plot_circle(cx, cy, cr) plt.plot(x, y, "xr") plot_circle(ex, ey, er, "-r") plt.pause(dt) print("Done")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

calc_input

()

return u

def calc_input(): v = 1.0 # [m/s] yawrate = 0.1 # [rad/s] u = np.array([[v], [yawrate]]) return u

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L37-L41

def calc_input(): v = 1.0 # [m/s] yawrate = 0.1 # [rad/s] u = np.array([[v], [yawrate]]) return u

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

observation

(xTrue, xd, u)

return xTrue, z, xd, ud

def observation(xTrue, xd, u): xTrue = motion_model(xTrue, u) # add noise to gps x-y z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1) # add noise to input ud = u + INPUT_NOISE @ np.random.randn(2, 1) xd = motion_model(xd, ud) return xTrue, z, xd, ud

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L44-L55

def observation(xTrue, xd, u): xTrue = motion_model(xTrue, u) # add noise to gps x-y z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1) # add noise to input ud = u + INPUT_NOISE @ np.random.randn(2, 1) xd = motion_model(xd, ud) return xTrue, z, xd, ud

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

motion_model

(x, u)

return x

def motion_model(x, u): F = np.array([[1.0, 0, 0, 0], [0, 1.0, 0, 0], [0, 0, 1.0, 0], [0, 0, 0, 0]]) B = np.array([[DT * math.cos(x[2, 0]), 0], [DT * math.sin(x[2, 0]), 0], [0.0, DT], [1.0, 0.0]]) x = F @ x + B @ u return x

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L58-L71

def motion_model(x, u): F = np.array([[1.0, 0, 0, 0], [0, 1.0, 0, 0], [0, 0, 1.0, 0], [0, 0, 0, 0]]) B = np.array([[DT * math.cos(x[2, 0]), 0], [DT * math.sin(x[2, 0]), 0], [0.0, DT], [1.0, 0.0]]) x = F @ x + B @ u return x

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

observation_model

(x)

return z

def observation_model(x): H = np.array([ [1, 0, 0, 0], [0, 1, 0, 0] ]) z = H @ x return z

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L74-L82

def observation_model(x): H = np.array([ [1, 0, 0, 0], [0, 1, 0, 0] ]) z = H @ x return z

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

jacob_f

(x, u)

return jF

Jacobian of Motion Model motion model x_{t+1} = x_t+v*dt*cos(yaw) y_{t+1} = y_t+v*dt*sin(yaw) yaw_{t+1} = yaw_t+omega*dt v_{t+1} = v{t} so dx/dyaw = -v*dt*sin(yaw) dx/dv = dt*cos(yaw) dy/dyaw = v*dt*cos(yaw) dy/dv = dt*sin(yaw)

Jacobian of Motion Model

def jacob_f(x, u): """ Jacobian of Motion Model motion model x_{t+1} = x_t+v*dt*cos(yaw) y_{t+1} = y_t+v*dt*sin(yaw) yaw_{t+1} = yaw_t+omega*dt v_{t+1} = v{t} so dx/dyaw = -v*dt*sin(yaw) dx/dv = dt*cos(yaw) dy/dyaw = v*dt*cos(yaw) dy/dv = dt*sin(yaw) """ yaw = x[2, 0] v = u[0, 0] jF = np.array([ [1.0, 0.0, -DT * v * math.sin(yaw), DT * math.cos(yaw)], [0.0, 1.0, DT * v * math.cos(yaw), DT * math.sin(yaw)], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]) return jF

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L85-L108

def jacob_f(x, u): yaw = x[2, 0] v = u[0, 0] jF = np.array([ [1.0, 0.0, -DT * v * math.sin(yaw), DT * math.cos(yaw)], [0.0, 1.0, DT * v * math.cos(yaw), DT * math.sin(yaw)], [0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 1.0]]) return jF

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

jacob_h

()

return jH

def jacob_h(): # Jacobian of Observation Model jH = np.array([ [1, 0, 0, 0], [0, 1, 0, 0] ]) return jH

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L111-L118

def jacob_h(): # Jacobian of Observation Model jH = np.array([ [1, 0, 0, 0], [0, 1, 0, 0] ]) return jH

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

ekf_estimation

(xEst, PEst, z, u)

return xEst, PEst

def ekf_estimation(xEst, PEst, z, u): # Predict xPred = motion_model(xEst, u) jF = jacob_f(xEst, u) PPred = jF @ PEst @ jF.T + Q # Update jH = jacob_h() zPred = observation_model(xPred) y = z - zPred S = jH @ PPred @ jH.T + R K = PPred @ jH.T @ np.linalg.inv(S) xEst = xPred + K @ y PEst = (np.eye(len(xEst)) - K @ jH) @ PPred return xEst, PEst

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L121-L135

def ekf_estimation(xEst, PEst, z, u): # Predict xPred = motion_model(xEst, u) jF = jacob_f(xEst, u) PPred = jF @ PEst @ jF.T + Q # Update jH = jacob_h() zPred = observation_model(xPred) y = z - zPred S = jH @ PPred @ jH.T + R K = PPred @ jH.T @ np.linalg.inv(S) xEst = xPred + K @ y PEst = (np.eye(len(xEst)) - K @ jH) @ PPred return xEst, PEst

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

plot_covariance_ellipse

(xEst, PEst)

def plot_covariance_ellipse(xEst, PEst): # pragma: no cover Pxy = PEst[0:2, 0:2] eigval, eigvec = np.linalg.eig(Pxy) if eigval[0] >= eigval[1]: bigind = 0 smallind = 1 else: bigind = 1 smallind = 0 t = np.arange(0, 2 * math.pi + 0.1, 0.1) a = math.sqrt(eigval[bigind]) b = math.sqrt(eigval[smallind]) x = [a * math.cos(it) for it in t] y = [b * math.sin(it) for it in t] angle = math.atan2(eigvec[1, bigind], eigvec[0, bigind]) fx = rot_mat_2d(angle) @ (np.array([x, y])) px = np.array(fx[0, :] + xEst[0, 0]).flatten() py = np.array(fx[1, :] + xEst[1, 0]).flatten() plt.plot(px, py, "--r")

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L138-L158

def plot_covariance_ellipse(xEst, PEst): # pragma: no cover Pxy = PEst[0:2, 0:2] eigval, eigvec = np.linalg.eig(Pxy) if eigval[0] >= eigval[1]: bigind = 0 smallind = 1 else: bigind = 1 smallind = 0 t = np.arange(0, 2 * math.pi + 0.1, 0.1) a = math.sqrt(eigval[bigind]) b = math.sqrt(eigval[smallind]) x = [a * math.cos(it) for it in t] y = [b * math.sin(it) for it in t] angle = math.atan2(eigvec[1, bigind], eigvec[0, bigind]) fx = rot_mat_2d(angle) @ (np.array([x, y])) px = np.array(fx[0, :] + xEst[0, 0]).flatten() py = np.array(fx[1, :] + xEst[1, 0]).flatten() plt.plot(px, py, "--r")

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/extended_kalman_filter/extended_kalman_filter.py

main

()

def main(): print(__file__ + " start!!") time = 0.0 # State Vector [x y yaw v]' xEst = np.zeros((4, 1)) xTrue = np.zeros((4, 1)) PEst = np.eye(4) xDR = np.zeros((4, 1)) # Dead reckoning # history hxEst = xEst hxTrue = xTrue hxDR = xTrue hz = np.zeros((2, 1)) while SIM_TIME >= time: time += DT u = calc_input() xTrue, z, xDR, ud = observation(xTrue, xDR, u) xEst, PEst = ekf_estimation(xEst, PEst, z, ud) # store data history hxEst = np.hstack((hxEst, xEst)) hxDR = np.hstack((hxDR, xDR)) hxTrue = np.hstack((hxTrue, xTrue)) hz = np.hstack((hz, z)) if show_animation: plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.plot(hz[0, :], hz[1, :], ".g") plt.plot(hxTrue[0, :].flatten(), hxTrue[1, :].flatten(), "-b") plt.plot(hxDR[0, :].flatten(), hxDR[1, :].flatten(), "-k") plt.plot(hxEst[0, :].flatten(), hxEst[1, :].flatten(), "-r") plot_covariance_ellipse(xEst, PEst) plt.axis("equal") plt.grid(True) plt.pause(0.001)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/extended_kalman_filter/extended_kalman_filter.py#L161-L208

def main(): print(__file__ + " start!!") time = 0.0 # State Vector [x y yaw v]' xEst = np.zeros((4, 1)) xTrue = np.zeros((4, 1)) PEst = np.eye(4) xDR = np.zeros((4, 1)) # Dead reckoning # history hxEst = xEst hxTrue = xTrue hxDR = xTrue hz = np.zeros((2, 1)) while SIM_TIME >= time: time += DT u = calc_input() xTrue, z, xDR, ud = observation(xTrue, xDR, u) xEst, PEst = ekf_estimation(xEst, PEst, z, ud) # store data history hxEst = np.hstack((hxEst, xEst)) hxDR = np.hstack((hxDR, xDR)) hxTrue = np.hstack((hxTrue, xTrue)) hz = np.hstack((hz, z)) if show_animation: plt.cla() # for stopping simulation with the esc key. plt.gcf().canvas.mpl_connect('key_release_event', lambda event: [exit(0) if event.key == 'escape' else None]) plt.plot(hz[0, :], hz[1, :], ".g") plt.plot(hxTrue[0, :].flatten(), hxTrue[1, :].flatten(), "-b") plt.plot(hxDR[0, :].flatten(), hxDR[1, :].flatten(), "-k") plt.plot(hxEst[0, :].flatten(), hxEst[1, :].flatten(), "-r") plot_covariance_ellipse(xEst, PEst) plt.axis("equal") plt.grid(True) plt.pause(0.001)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

cubature_kalman_filter

(x_est, p_est, z)

return x_upd, p_upd

def cubature_kalman_filter(x_est, p_est, z): x_pred, p_pred = cubature_prediction(x_est, p_est) x_upd, p_upd = cubature_update(x_pred, p_pred, z) return x_upd, p_upd

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L88-L91

def cubature_kalman_filter(x_est, p_est, z): x_pred, p_pred = cubature_prediction(x_est, p_est) x_upd, p_upd = cubature_update(x_pred, p_pred, z) return x_upd, p_upd

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

f

(x)

return x

Motion Model References: http://fusion.isif.org/proceedings/fusion08CD/papers/1569107835.pdf https://github.com/balzer82/Kalman

Motion Model References: http://fusion.isif.org/proceedings/fusion08CD/papers/1569107835.pdf https://github.com/balzer82/Kalman

def f(x): """ Motion Model References: http://fusion.isif.org/proceedings/fusion08CD/papers/1569107835.pdf https://github.com/balzer82/Kalman """ x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4] * dt + x[2]) - np.sin(x[2])) x[1] = x[1] + (x[3]/x[4]) * (- np.cos(x[4] * dt + x[2]) + np.cos(x[2])) x[2] = x[2] + x[4] * dt x[3] = x[3] x[4] = x[4] return x

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L94-L106

def f(x): x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4] * dt + x[2]) - np.sin(x[2])) x[1] = x[1] + (x[3]/x[4]) * (- np.cos(x[4] * dt + x[2]) + np.cos(x[2])) x[2] = x[2] + x[4] * dt x[3] = x[3] x[4] = x[4] return x

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

h

(x)

return x

Measurement Model

Measurement Model

def h(x): """Measurement Model""" x = hx @ x return x

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L109-L112

def h(x): x = hx @ x return x

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

sigma

(x, p)

return SP, W

Unscented Transform with Cubature Rule Generate 2n Sigma Points to represent the nonlinear motion Assign Weights to each Sigma Point, Wi = 1/2n Cubature Rule - Special Case of Unscented Transform W0 = 0, no extra tuning parameters, no negative weights

Unscented Transform with Cubature Rule Generate 2n Sigma Points to represent the nonlinear motion Assign Weights to each Sigma Point, Wi = 1/2n Cubature Rule - Special Case of Unscented Transform W0 = 0, no extra tuning parameters, no negative weights

def sigma(x, p): """ Unscented Transform with Cubature Rule Generate 2n Sigma Points to represent the nonlinear motion Assign Weights to each Sigma Point, Wi = 1/2n Cubature Rule - Special Case of Unscented Transform W0 = 0, no extra tuning parameters, no negative weights """ n = np.shape(x)[0] SP = np.zeros((n, 2*n)) W = np.zeros((1, 2*n)) for i in range(n): SD = sqrtm(p) SP[:, i] = (x + (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten() SP[:, i+n] = (x - (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten() W[:, i] = 1/(2*n) W[:, i+n] = W[:, i] return SP, W

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L115-L132

def sigma(x, p): n = np.shape(x)[0] SP = np.zeros((n, 2*n)) W = np.zeros((1, 2*n)) for i in range(n): SD = sqrtm(p) SP[:, i] = (x + (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten() SP[:, i+n] = (x - (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten() W[:, i] = 1/(2*n) W[:, i+n] = W[:, i] return SP, W

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

cubature_prediction

(x_pred, p_pred)

return x_pred, p_pred

def cubature_prediction(x_pred, p_pred): n = np.shape(x_pred)[0] [SP, W] = sigma(x_pred, p_pred) x_pred = np.zeros((n, 1)) p_pred = q for i in range(2*n): x_pred = x_pred + (f(SP[:, i]).reshape((n, 1)) * W[0, i]) for i in range(2*n): p_step = (f(SP[:, i]).reshape((n, 1)) - x_pred) p_pred = p_pred + (p_step @ p_step.T * W[0, i]) return x_pred, p_pred

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L135-L145

def cubature_prediction(x_pred, p_pred): n = np.shape(x_pred)[0] [SP, W] = sigma(x_pred, p_pred) x_pred = np.zeros((n, 1)) p_pred = q for i in range(2*n): x_pred = x_pred + (f(SP[:, i]).reshape((n, 1)) * W[0, i]) for i in range(2*n): p_step = (f(SP[:, i]).reshape((n, 1)) - x_pred) p_pred = p_pred + (p_step @ p_step.T * W[0, i]) return x_pred, p_pred

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

cubature_update

(x_pred, p_pred, z)

return x_pred, p_pred

def cubature_update(x_pred, p_pred, z): n = np.shape(x_pred)[0] m = np.shape(z)[0] [SP, W] = sigma(x_pred, p_pred) y_k = np.zeros((m, 1)) P_xy = np.zeros((n, m)) s = r for i in range(2*n): y_k = y_k + (h(SP[:, i]).reshape((m, 1)) * W[0, i]) for i in range(2*n): p_step = (h(SP[:, i]).reshape((m, 1)) - y_k) P_xy = P_xy + ((SP[:, i]).reshape((n, 1)) - x_pred) @ p_step.T * W[0, i] s = s + p_step @ p_step.T * W[0, i] x_pred = x_pred + P_xy @ np.linalg.pinv(s) @ (z - y_k) p_pred = p_pred - P_xy @ np.linalg.pinv(s) @ P_xy.T return x_pred, p_pred

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L148-L164

def cubature_update(x_pred, p_pred, z): n = np.shape(x_pred)[0] m = np.shape(z)[0] [SP, W] = sigma(x_pred, p_pred) y_k = np.zeros((m, 1)) P_xy = np.zeros((n, m)) s = r for i in range(2*n): y_k = y_k + (h(SP[:, i]).reshape((m, 1)) * W[0, i]) for i in range(2*n): p_step = (h(SP[:, i]).reshape((m, 1)) - y_k) P_xy = P_xy + ((SP[:, i]).reshape((n, 1)) - x_pred) @ p_step.T * W[0, i] s = s + p_step @ p_step.T * W[0, i] x_pred = x_pred + P_xy @ np.linalg.pinv(s) @ (z - y_k) p_pred = p_pred - P_xy @ np.linalg.pinv(s) @ P_xy.T return x_pred, p_pred

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

generate_measurement

(x_true)

return z

def generate_measurement(x_true): gz = hx @ x_true z = gz + z_noise @ np.random.randn(4, 1) return z

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L167-L170

def generate_measurement(x_true): gz = hx @ x_true z = gz + z_noise @ np.random.randn(4, 1) return z

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

plot_animation

(i, x_true_cat, x_est_cat, z)

def plot_animation(i, x_true_cat, x_est_cat, z): if i == 0: plt.plot(x_true_cat[0], x_true_cat[1], '.r') plt.plot(x_est_cat[0], x_est_cat[1], '.b') else: plt.plot(x_true_cat[0:, 0], x_true_cat[0:, 1], 'r') plt.plot(x_est_cat[0:, 0], x_est_cat[0:, 1], 'b') plt.plot(z[0], z[1], '+g') plt.grid(True) plt.pause(0.001)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L173-L182

def plot_animation(i, x_true_cat, x_est_cat, z): if i == 0: plt.plot(x_true_cat[0], x_true_cat[1], '.r') plt.plot(x_est_cat[0], x_est_cat[1], '.b') else: plt.plot(x_true_cat[0:, 0], x_true_cat[0:, 1], 'r') plt.plot(x_est_cat[0:, 0], x_est_cat[0:, 1], 'b') plt.plot(z[0], z[1], '+g') plt.grid(True) plt.pause(0.001)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

plot_ellipse

(x_est, p_est)

def plot_ellipse(x_est, p_est): phi = np.linspace(0, 2 * math.pi, 100) p_ellipse = np.array( [[p_est[0, 0], p_est[0, 1]], [p_est[1, 0], p_est[1, 1]]]) x0 = 3 * sqrtm(p_ellipse) xy_1 = np.array([]) xy_2 = np.array([]) for i in range(100): arr = np.array([[math.sin(phi[i])], [math.cos(phi[i])]]) arr = x0 @ arr xy_1 = np.hstack([xy_1, arr[0]]) xy_2 = np.hstack([xy_2, arr[1]]) plt.plot(xy_1 + x_est[0], xy_2 + x_est[1], 'r') plt.pause(0.00001)

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L185-L198

def plot_ellipse(x_est, p_est): phi = np.linspace(0, 2 * math.pi, 100) p_ellipse = np.array( [[p_est[0, 0], p_est[0, 1]], [p_est[1, 0], p_est[1, 1]]]) x0 = 3 * sqrtm(p_ellipse) xy_1 = np.array([]) xy_2 = np.array([]) for i in range(100): arr = np.array([[math.sin(phi[i])], [math.cos(phi[i])]]) arr = x0 @ arr xy_1 = np.hstack([xy_1, arr[0]]) xy_2 = np.hstack([xy_2, arr[1]]) plt.plot(xy_1 + x_est[0], xy_2 + x_est[1], 'r') plt.pause(0.00001)

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

plot_final

(x_true_cat, x_est_cat, z_cat)

def plot_final(x_true_cat, x_est_cat, z_cat): fig = plt.figure() subplot = fig.add_subplot(111) subplot.plot(x_true_cat[0:, 0], x_true_cat[0:, 1], 'r', label='True Position') subplot.plot(x_est_cat[0:, 0], x_est_cat[0:, 1], 'b', label='Estimated Position') subplot.plot(z_cat[0:, 0], z_cat[0:, 1], '+g', label='Noisy Measurements') subplot.set_xlabel('x [m]') subplot.set_ylabel('y [m]') subplot.set_title('Cubature Kalman Filter - CTRV Model') subplot.legend(loc='upper left', shadow=True, fontsize='large') plt.grid(True) plt.show()

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L201-L214

def plot_final(x_true_cat, x_est_cat, z_cat): fig = plt.figure() subplot = fig.add_subplot(111) subplot.plot(x_true_cat[0:, 0], x_true_cat[0:, 1], 'r', label='True Position') subplot.plot(x_est_cat[0:, 0], x_est_cat[0:, 1], 'b', label='Estimated Position') subplot.plot(z_cat[0:, 0], z_cat[0:, 1], '+g', label='Noisy Measurements') subplot.set_xlabel('x [m]') subplot.set_ylabel('y [m]') subplot.set_title('Cubature Kalman Filter - CTRV Model') subplot.legend(loc='upper left', shadow=True, fontsize='large') plt.grid(True) plt.show()

AtsushiSakai/PythonRobotics

15ab19688b2f6c03ee91a853f1f8cc9def84d162

Localization/cubature_kalman_filter/cubature_kalman_filter.py

main

()

def main(): print(__file__ + " start!!") x_est = x_0 p_est = p_0 x_true = x_0 x_true_cat = np.array([x_0[0, 0], x_0[1, 0]]) x_est_cat = np.array([x_0[0, 0], x_0[1, 0]]) z_cat = np.array([x_0[0, 0], x_0[1, 0]]) for i in range(N): x_true = f(x_true) z = generate_measurement(x_true) if i == (N - 1) and show_final == 1: show_final_flag = 1 else: show_final_flag = 0 if show_animation == 1: plot_animation(i, x_true_cat, x_est_cat, z) if show_ellipse == 1: plot_ellipse(x_est[0:2], p_est) if show_final_flag == 1: plot_final(x_true_cat, x_est_cat, z_cat) x_est, p_est = cubature_kalman_filter(x_est, p_est, z) x_true_cat = np.vstack((x_true_cat, x_true[0:2].T)) x_est_cat = np.vstack((x_est_cat, x_est[0:2].T)) z_cat = np.vstack((z_cat, z[0:2].T)) print('CKF Over')

https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/cubature_kalman_filter/cubature_kalman_filter.py#L217-L242