mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
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195 lines
4.9 KiB
Python
195 lines
4.9 KiB
Python
"""
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Graph SLAM example
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author: Atsushi Sakai (@Atsushi_twi)
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"""
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import numpy as np
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import math
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import copy
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import matplotlib.pyplot as plt
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# EKF state covariance
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Cx = np.diag([0.5, 0.5, math.radians(30.0)])**2
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# Simulation parameter
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Qsim = np.diag([0.2, math.radians(1.0)])**2
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Rsim = np.diag([1.0, math.radians(10.0)])**2
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DT = 0.1 # time tick [s]
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SIM_TIME = 50.0 # simulation time [s]
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MAX_RANGE = 20.0 # maximum observation range
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M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
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STATE_SIZE = 3 # State size [x,y,yaw]
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LM_SIZE = 2 # LM srate size [x,y]
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MAX_ITR = 20
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show_animation = True
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def graph_based_slam(xEst, PEst, u, z, hxDR, hz):
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x_opt = copy.deepcopy(hxDR)
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for itr in range(20):
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# pos_edges = []
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# # このfor文では、HalfEdgeからグラフの辺を作っていきます。
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# for i in range(len(actual_landmarks.positions)): # ランドマークごとにHalfEdgeからEdgeを作る
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# es = list(filter(lambda e: e.landmark_id == i, obs_edges)) # 同じランドマークIDを持つHalfEdgeの抽出
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# ps = list(itertools.combinations(es,2)) # esの要素のペアを全通り作る
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# for p in ps:
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# pos_edges.append(Edge(p[0],p[1])) # エッジを登録
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n = len(hz) * 3
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H = np.zeros((n, n))
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b = np.zeros((n, 1))
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# for e in pos_edges:
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# e.addInfo(matH,vecb)
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# H[0:3, 0:3] += np.identity(3) * 10000 # to fix origin
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H += np.identity(n) * 10000 # to fix origin
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dx = - np.linalg.inv(H).dot(b)
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# print(dx)
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for i in range(len(hz)):
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x_opt[0, i] += dx[i * 3, 0]
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x_opt[1, i] += dx[i * 3 + 1, 0]
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x_opt[2, i] += dx[i * 3 + 2, 0]
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# # HalfEdgeに登録してある推定値も更新
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# for e in obs_edges:
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# e.update(robot.guess_poses)
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diff = dx.T.dot(dx)
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print("iteration: %d, diff: %f" % (itr + 1, diff))
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if dx[0, 0] < 1.0e-5:
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break
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return x_opt, None
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def calc_input():
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v = 1.0 # [m/s]
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yawrate = 0.1 # [rad/s]
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u = np.matrix([v, yawrate]).T
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return u
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def observation(xTrue, xd, u, RFID):
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xTrue = motion_model(xTrue, u)
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# add noise to gps x-y
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z = np.matrix(np.zeros((0, 3)))
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for i in range(len(RFID[:, 0])):
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dx = RFID[i, 0] - xTrue[0, 0]
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dy = RFID[i, 1] - xTrue[1, 0]
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d = math.sqrt(dx**2 + dy**2)
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angle = pi_2_pi(math.atan2(dy, dx))
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if d <= MAX_RANGE:
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dn = d + np.random.randn() * Qsim[0, 0] # add noise
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anglen = angle + np.random.randn() * Qsim[1, 1] # add noise
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zi = np.matrix([dn, anglen, i])
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z = np.vstack((z, zi))
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# add noise to input
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ud1 = u[0, 0] + np.random.randn() * Rsim[0, 0]
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ud2 = u[1, 0] + np.random.randn() * Rsim[1, 1]
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ud = np.matrix([ud1, ud2]).T
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xd = motion_model(xd, ud)
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return xTrue, z, xd, ud
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def motion_model(x, u):
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F = np.matrix([[1.0, 0, 0],
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[0, 1.0, 0],
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[0, 0, 1.0]])
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B = np.matrix([[DT * math.cos(x[2, 0]), 0],
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[DT * math.sin(x[2, 0]), 0],
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[0.0, DT]])
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x = F * x + B * u
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return x
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def pi_2_pi(angle):
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while(angle > math.pi):
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angle = angle - 2.0 * math.pi
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while(angle < -math.pi):
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angle = angle + 2.0 * math.pi
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return angle
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def main():
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print(__file__ + " start!!")
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time = 0.0
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# RFID positions [x, y]
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RFID = np.array([[10.0, -2.0],
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[15.0, 10.0],
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[3.0, 15.0],
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[-5.0, 20.0]])
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# State Vector [x y yaw v]'
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xEst = np.matrix(np.zeros((STATE_SIZE, 1)))
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xTrue = np.matrix(np.zeros((STATE_SIZE, 1)))
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PEst = np.eye(STATE_SIZE)
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xDR = np.matrix(np.zeros((STATE_SIZE, 1))) # Dead reckoning
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# history
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hxTrue = xTrue
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hxDR = xTrue
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hz = []
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while SIM_TIME >= time:
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time += DT
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u = calc_input()
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xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
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hxDR = np.hstack((hxDR, xDR))
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hz.append(z)
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x_opt, PEst = graph_based_slam(xEst, PEst, ud, z, hxDR, hz)
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# store data history
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hxTrue = np.hstack((hxTrue, xTrue))
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if show_animation:
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plt.cla()
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plt.plot(RFID[:, 0], RFID[:, 1], "*k")
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plt.plot(xEst[0], xEst[1], ".r")
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plt.plot(np.array(hxTrue[0, :]).flatten(),
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np.array(hxTrue[1, :]).flatten(), "-b")
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plt.plot(np.array(hxDR[0, :]).flatten(),
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np.array(hxDR[1, :]).flatten(), "-k")
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plt.plot(np.array(x_opt[0, :]).flatten(),
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np.array(x_opt[1, :]).flatten(), "-r")
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plt.axis("equal")
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plt.grid(True)
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plt.pause(0.001)
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if __name__ == '__main__':
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main()
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