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remove duplicate script
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Atsushi Sakai
@@ -1,303 +0,0 @@
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"""
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Dubins path planner sample code
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author Atsushi Sakai (@Atsushi_twi)
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"""
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import math
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import matplotlib.pyplot as plt
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import numpy as np
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def mod2pi(theta):
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return theta - 2.0 * math.pi * math.floor(theta / 2.0 / math.pi)
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def pi_2_pi(angle):
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return (angle + math.pi) % (2 * math.pi) - math.pi
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def LSL(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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tmp0 = d + sa - sb
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mode = ["L", "S", "L"]
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p_squared = 2 + (d * d) - (2 * c_ab) + (2 * d * (sa - sb))
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if p_squared < 0:
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return None, None, None, mode
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tmp1 = math.atan2((cb - ca), tmp0)
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t = mod2pi(-alpha + tmp1)
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p = math.sqrt(p_squared)
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q = mod2pi(beta - tmp1)
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# print(np.rad2deg(t), p, np.rad2deg(q))
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return t, p, q, mode
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def RSR(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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tmp0 = d - sa + sb
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mode = ["R", "S", "R"]
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p_squared = 2 + (d * d) - (2 * c_ab) + (2 * d * (sb - sa))
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if p_squared < 0:
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return None, None, None, mode
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tmp1 = math.atan2((ca - cb), tmp0)
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t = mod2pi(alpha - tmp1)
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p = math.sqrt(p_squared)
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q = mod2pi(-beta + tmp1)
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return t, p, q, mode
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def LSR(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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p_squared = -2 + (d * d) + (2 * c_ab) + (2 * d * (sa + sb))
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mode = ["L", "S", "R"]
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if p_squared < 0:
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return None, None, None, mode
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p = math.sqrt(p_squared)
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tmp2 = math.atan2((-ca - cb), (d + sa + sb)) - math.atan2(-2.0, p)
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t = mod2pi(-alpha + tmp2)
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q = mod2pi(-mod2pi(beta) + tmp2)
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return t, p, q, mode
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def RSL(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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p_squared = (d * d) - 2 + (2 * c_ab) - (2 * d * (sa + sb))
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mode = ["R", "S", "L"]
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if p_squared < 0:
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return None, None, None, mode
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p = math.sqrt(p_squared)
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tmp2 = math.atan2((ca + cb), (d - sa - sb)) - math.atan2(2.0, p)
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t = mod2pi(alpha - tmp2)
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q = mod2pi(beta - tmp2)
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return t, p, q, mode
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def RLR(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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mode = ["R", "L", "R"]
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tmp_rlr = (6.0 - d * d + 2.0 * c_ab + 2.0 * d * (sa - sb)) / 8.0
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if abs(tmp_rlr) > 1.0:
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return None, None, None, mode
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p = mod2pi(2 * math.pi - math.acos(tmp_rlr))
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t = mod2pi(alpha - math.atan2(ca - cb, d - sa + sb) + mod2pi(p / 2.0))
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q = mod2pi(alpha - beta - t + mod2pi(p))
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return t, p, q, mode
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def LRL(alpha, beta, d):
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sa = math.sin(alpha)
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sb = math.sin(beta)
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ca = math.cos(alpha)
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cb = math.cos(beta)
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c_ab = math.cos(alpha - beta)
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mode = ["L", "R", "L"]
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tmp_lrl = (6. - d * d + 2 * c_ab + 2 * d * (- sa + sb)) / 8.
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if abs(tmp_lrl) > 1:
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return None, None, None, mode
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p = mod2pi(2 * math.pi - math.acos(tmp_lrl))
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t = mod2pi(-alpha - math.atan2(ca - cb, d + sa - sb) + p / 2.)
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q = mod2pi(mod2pi(beta) - alpha - t + mod2pi(p))
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return t, p, q, mode
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def dubins_path_planning_from_origin(ex, ey, eyaw, c):
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# nomalize
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dx = ex
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dy = ey
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D = math.sqrt(dx ** 2.0 + dy ** 2.0)
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d = D / c
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# print(dx, dy, D, d)
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theta = mod2pi(math.atan2(dy, dx))
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alpha = mod2pi(- theta)
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beta = mod2pi(eyaw - theta)
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# print(theta, alpha, beta, d)
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planners = [LSL, RSR, LSR, RSL, RLR, LRL]
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bcost = float("inf")
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bt, bp, bq, bmode = None, None, None, None
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for planner in planners:
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t, p, q, mode = planner(alpha, beta, d)
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if t is None:
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# print("".join(mode) + " cannot generate path")
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continue
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cost = (abs(t) + abs(p) + abs(q))
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if bcost > cost:
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bt, bp, bq, bmode = t, p, q, mode
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bcost = cost
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# print(bmode)
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px, py, pyaw = generate_course([bt, bp, bq], bmode, c)
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return px, py, pyaw, bmode, bcost
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def dubins_path_planning(sx, sy, syaw, ex, ey, eyaw, c):
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"""
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Dubins path plannner
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input:
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sx x position of start point [m]
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sy y position of start point [m]
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syaw yaw angle of start point [rad]
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ex x position of end point [m]
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ey y position of end point [m]
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eyaw yaw angle of end point [rad]
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c curvature [1/m]
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output:
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px
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py
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pyaw
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mode
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"""
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ex = ex - sx
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ey = ey - sy
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lex = math.cos(syaw) * ex + math.sin(syaw) * ey
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ley = - math.sin(syaw) * ex + math.cos(syaw) * ey
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leyaw = eyaw - syaw
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lpx, lpy, lpyaw, mode, clen = dubins_path_planning_from_origin(
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lex, ley, leyaw, c)
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px = [math.cos(-syaw) * x + math.sin(-syaw)
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* y + sx for x, y in zip(lpx, lpy)]
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py = [- math.sin(-syaw) * x + math.cos(-syaw)
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* y + sy for x, y in zip(lpx, lpy)]
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pyaw = [pi_2_pi(iyaw + syaw) for iyaw in lpyaw]
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# print(syaw)
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# pyaw = lpyaw
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# plt.plot(pyaw, "-r")
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# plt.plot(lpyaw, "-b")
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# plt.plot(eyaw, "*r")
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# plt.plot(syaw, "*b")
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# plt.show()
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return px, py, pyaw, mode, clen
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def generate_course(length, mode, c):
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px = [0.0]
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py = [0.0]
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pyaw = [0.0]
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for m, l in zip(mode, length):
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pd = 0.0
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if m == "S":
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d = 1.0 / c
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else: # turning couse
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d = np.deg2rad(3.0)
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while pd < abs(l - d):
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# print(pd, l)
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px.append(px[-1] + d * c * math.cos(pyaw[-1]))
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py.append(py[-1] + d * c * math.sin(pyaw[-1]))
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if m == "L": # left turn
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pyaw.append(pyaw[-1] + d)
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elif m == "S": # Straight
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pyaw.append(pyaw[-1])
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elif m == "R": # right turn
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pyaw.append(pyaw[-1] - d)
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pd += d
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d = l - pd
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px.append(px[-1] + d * c * math.cos(pyaw[-1]))
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py.append(py[-1] + d * c * math.sin(pyaw[-1]))
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if m == "L": # left turn
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pyaw.append(pyaw[-1] + d)
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elif m == "S": # Straight
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pyaw.append(pyaw[-1])
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elif m == "R": # right turn
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pyaw.append(pyaw[-1] - d)
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pd += d
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return px, py, pyaw
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def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"): # pragma: no cover
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"""
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Plot arrow
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"""
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if not isinstance(x, float):
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for (ix, iy, iyaw) in zip(x, y, yaw):
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plot_arrow(ix, iy, iyaw)
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else:
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plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
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fc=fc, ec=ec, head_width=width, head_length=width)
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plt.plot(x, y)
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if __name__ == '__main__':
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print("Dubins path planner sample start!!")
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start_x = 1.0 # [m]
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start_y = 1.0 # [m]
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start_yaw = np.deg2rad(45.0) # [rad]
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end_x = -3.0 # [m]
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end_y = -3.0 # [m]
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end_yaw = np.deg2rad(-45.0) # [rad]
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curvature = 1.0
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px, py, pyaw, mode, clen = dubins_path_planning(start_x, start_y, start_yaw,
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end_x, end_y, end_yaw, curvature)
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plt.plot(px, py, label="final course " + "".join(mode))
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# plotting
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plot_arrow(start_x, start_y, start_yaw)
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plot_arrow(end_x, end_y, end_yaw)
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# for (ix, iy, iyaw) in zip(px, py, pyaw):
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# plot_arrow(ix, iy, iyaw, fc="b")
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plt.legend()
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plt.grid(True)
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plt.axis("equal")
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plt.show()
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