233 lines
5.4 KiB
Python
233 lines
5.4 KiB
Python
"""
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Cubic spline planner
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Author: Atsushi Sakai(@Atsushi_twi)
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"""
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import math
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import numpy as np
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import bisect
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class Spline:
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"""
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Cubic Spline class
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"""
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def __init__(self, x, y):
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self.b, self.c, self.d, self.w = [], [], [], []
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self.x = x
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self.y = y
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self.nx = len(x) # dimension of x
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h = np.diff(x)
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# calc coefficient c
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self.a = [iy for iy in y]
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# calc coefficient c
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A = self.__calc_A(h)
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B = self.__calc_B(h)
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self.c = np.linalg.solve(A, B)
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# print(self.c1)
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# calc spline coefficient b and d
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for i in range(self.nx - 1):
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self.d.append((self.c[i + 1] - self.c[i]) / (3.0 * h[i]))
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tb = (self.a[i + 1] - self.a[i]) / h[i] - h[i] * \
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(self.c[i + 1] + 2.0 * self.c[i]) / 3.0
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self.b.append(tb)
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def calc(self, t):
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"""
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Calc position
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if t is outside of the input x, return None
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"""
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if t < self.x[0]:
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return None
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elif t > self.x[-1]:
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return None
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i = self.__search_index(t)
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dx = t - self.x[i]
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result = self.a[i] + self.b[i] * dx + \
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self.c[i] * dx ** 2.0 + self.d[i] * dx ** 3.0
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return result
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def calcd(self, t):
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"""
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Calc first derivative
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if t is outside of the input x, return None
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"""
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if t < self.x[0]:
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return None
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elif t > self.x[-1]:
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return None
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i = self.__search_index(t)
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dx = t - self.x[i]
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result = self.b[i] + 2.0 * self.c[i] * dx + 3.0 * self.d[i] * dx ** 2.0
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return result
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def calcdd(self, t):
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"""
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Calc second derivative
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"""
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if t < self.x[0]:
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return None
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elif t > self.x[-1]:
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return None
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i = self.__search_index(t)
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dx = t - self.x[i]
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result = 2.0 * self.c[i] + 6.0 * self.d[i] * dx
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return result
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def __search_index(self, x):
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"""
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search data segment index
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"""
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return bisect.bisect(self.x, x) - 1
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def __calc_A(self, h):
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"""
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calc matrix A for spline coefficient c
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"""
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A = np.zeros((self.nx, self.nx))
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A[0, 0] = 1.0
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for i in range(self.nx - 1):
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if i != (self.nx - 2):
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A[i + 1, i + 1] = 2.0 * (h[i] + h[i + 1])
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A[i + 1, i] = h[i]
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A[i, i + 1] = h[i]
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A[0, 1] = 0.0
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A[self.nx - 1, self.nx - 2] = 0.0
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A[self.nx - 1, self.nx - 1] = 1.0
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# print(A)
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return A
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def __calc_B(self, h):
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"""
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calc matrix B for spline coefficient c
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"""
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B = np.zeros(self.nx)
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for i in range(self.nx - 2):
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B[i + 1] = 3.0 * (self.a[i + 2] - self.a[i + 1]) / \
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h[i + 1] - 3.0 * (self.a[i + 1] - self.a[i]) / h[i]
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return B
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class Spline2D:
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"""
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2D Cubic Spline class
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"""
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def __init__(self, x, y):
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self.s = self.__calc_s(x, y)
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self.sx = Spline(self.s, x)
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self.sy = Spline(self.s, y)
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def __calc_s(self, x, y):
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dx = np.diff(x)
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dy = np.diff(y)
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self.ds = [math.sqrt(idx ** 2 + idy ** 2)
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for (idx, idy) in zip(dx, dy)]
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s = [0]
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s.extend(np.cumsum(self.ds))
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return s
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def calc_position(self, s):
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"""
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calc position
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"""
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x = self.sx.calc(s)
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y = self.sy.calc(s)
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return x, y
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def calc_curvature(self, s):
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"""
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calc curvature
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"""
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dx = self.sx.calcd(s)
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ddx = self.sx.calcdd(s)
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dy = self.sy.calcd(s)
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ddy = self.sy.calcdd(s)
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k = (ddy * dx - ddx * dy) / ((dx ** 2 + dy ** 2)**(3 / 2))
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return k
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def calc_yaw(self, s):
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"""
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calc yaw
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"""
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dx = self.sx.calcd(s)
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dy = self.sy.calcd(s)
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yaw = math.atan2(dy, dx)
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return yaw
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def calc_spline_course(x, y, ds=0.1):
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sp = Spline2D(x, y)
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s = list(np.arange(0, sp.s[-1], ds))
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rx, ry, ryaw, rk = [], [], [], []
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for i_s in s:
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ix, iy = sp.calc_position(i_s)
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rx.append(ix)
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ry.append(iy)
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ryaw.append(sp.calc_yaw(i_s))
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rk.append(sp.calc_curvature(i_s))
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return rx, ry, ryaw, rk, s
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def main():
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print("Spline 2D test")
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import matplotlib.pyplot as plt
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x = [-2.5, 0.0, 2.5, 5.0, 7.5, 3.0, -1.0]
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y = [0.7, -6, 5, 6.5, 0.0, 5.0, -2.0]
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ds = 0.1 # [m] distance of each intepolated points
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sp = Spline2D(x, y)
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s = np.arange(0, sp.s[-1], ds)
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rx, ry, ryaw, rk = [], [], [], []
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for i_s in s:
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ix, iy = sp.calc_position(i_s)
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rx.append(ix)
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ry.append(iy)
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ryaw.append(sp.calc_yaw(i_s))
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rk.append(sp.calc_curvature(i_s))
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plt.subplots(1)
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plt.plot(x, y, "xb", label="input")
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plt.plot(rx, ry, "-r", label="spline")
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plt.grid(True)
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plt.axis("equal")
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plt.xlabel("x[m]")
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plt.ylabel("y[m]")
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plt.legend()
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plt.subplots(1)
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plt.plot(s, [np.rad2deg(iyaw) for iyaw in ryaw], "-r", label="yaw")
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plt.grid(True)
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plt.legend()
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plt.xlabel("line length[m]")
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plt.ylabel("yaw angle[deg]")
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plt.subplots(1)
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plt.plot(s, rk, "-r", label="curvature")
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plt.grid(True)
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plt.legend()
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plt.xlabel("line length[m]")
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plt.ylabel("curvature [1/m]")
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plt.show()
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if __name__ == '__main__':
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main() |