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116 lines
2.5 KiB
Python
116 lines
2.5 KiB
Python
"""
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Quinitc Polynomials Planner
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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 matplotlib.pyplot as plt
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import math
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class quinic_polynomial:
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def __init__(self, xs, vxs, axs, xe, vxe, axe, T):
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self.xs = xs
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self.vxs = vxs
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self.axs = axs
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self.xe = xe
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self.vxe = vxe
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self.axe = axe
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self.a0 = xs
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self.a1 = vxs
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self.a2 = axs / 2.0
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A = np.array([[T**3, T**4, T**5],
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[3 * T ** 2, 4 * T ** 3, 5 * T ** 4],
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[6 * T, 12 * T ** 2, 20 * T ** 3]])
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# print(A)
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b = np.array([xe - self.a0 - self.a1 * T - self.a2 * T**2,
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vxe - self.a1 - 2 * self.a2 * T,
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axe - 2 * self.a2])
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x = np.linalg.solve(A, b)
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# print(x)
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self.a3 = x[0]
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self.a4 = x[1]
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self.a5 = x[2]
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def calc_point(self, t):
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xt = self.a0 + self.a1 * t + self.a2 * t**2 + \
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self.a3 * t**3 + self.a4 * t**4 + self.a5 * t**5
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return xt
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def quinic_polynomials_planner(sx, sy, syaw, sv, sa, gx, gy, gyaw, gv, ga):
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vxs = sv * math.cos(syaw)
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vys = sv * math.sin(syaw)
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vxg = gv * math.cos(gyaw)
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vyg = gv * math.sin(gyaw)
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axs = sa * math.cos(syaw)
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ays = sa * math.sin(syaw)
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axg = ga * math.cos(gyaw)
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ayg = ga * math.sin(gyaw)
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T = 10.0
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dt = 0.1
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xqp = quinic_polynomial(sx, vxs, axs, gx, vxg, axg, T)
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yqp = quinic_polynomial(sy, vys, ays, gy, vyg, ayg, T)
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rx, ry = [], []
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for t in np.arange(0.0, T + dt, dt):
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rx.append(xqp.calc_point(t))
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ry.append(yqp.calc_point(t))
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return rx, ry
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def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
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u"""
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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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def main():
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print(__file__ + " start!!")
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sx = 10.0
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sy = 10.0
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syaw = math.radians(10.0)
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sv = 10.0 # [m/s]
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sa = 0.0
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gx = 30.0
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gy = -10.0
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gyaw = math.radians(20.0)
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gv = 1.0 # [m/s]
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ga = 0.0
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rx, ry = quinic_polynomials_planner(
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sx, sy, syaw, sv, sa, gx, gy, gyaw, gv, ga)
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plt.plot(rx, ry, "-r")
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plot_arrow(sx, sy, syaw)
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plot_arrow(gx, gy, gyaw)
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plt.grid(True)
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plt.axis("equal")
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plt.show()
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if __name__ == '__main__':
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main()
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