polynomials.py

import numpy as np


class QuinticPolynomial(object):
    """
    五次多项试，用于求解多项是的微分和导数
    """

    def __init__(self, xs, vxs, axs, xe, vxe, axe, T):
        self.xs = xs
        self.vxs = vxs
        self.axs = axs
        self.xe = xe
        self.vxe = vxe
        self.axe = axe

        self.a0 = xs
        self.a1 = vxs
        self.a2 = axs / 2.0

        A = np.array([[T**3, T**4, T**5],
                      [3 * T ** 2, 4 * T ** 3, 5 * T ** 4],
                      [6 * T, 12 * T ** 2, 20 * T ** 3]])
        b = np.array([xe - self.a0 - self.a1 * T - self.a2 * T**2,
                      vxe - self.a1 - 2 * self.a2 * T,
                      axe - 2 * self.a2])
        x = np.linalg.solve(A, b)

        self.a3 = x[0]
        self.a4 = x[1]
        self.a5 = x[2]

    def calc_point(self, t):
        """
        return the t state based on QuinticPolynomial theory
        """
        xt = self.a0 + self.a1 * t + self.a2 * t**2 + \
            self.a3 * t**3 + self.a4 * t**4 + self.a5 * t**5
        return xt

    # below are all derivatives (一阶导数，二阶导数...)
    def calc_first_derivative(self, t):
        xt = self.a1 + 2 * self.a2 * t + \
            3 * self.a3 * t**2 + 4 * self.a4 * t**3 + 5 * self.a5 * t**4
        return xt

    def calc_second_derivative(self, t):
        xt = 2 * self.a2 + 6 * self.a3 * t + 12 * self.a4 * t**2 + 20 * self.a5 * t**3
        return xt

    def calc_third_derivative(self, t):
        xt = 6 * self.a3 + 24 * self.a4 * t + 60 * self.a5 * t**2
        return xt


class QuarticPolynomial(object):
    """
    四次多项式
    """

    def __init__(self, xs, vxs, axs, vxe, axe, T):
        self.xs = xs
        self.vxs = vxs
        self.axs = axs
        self.vxe = vxe
        self.axe = axe

        self.a0 = xs
        self.a1 = vxs
        self.a2 = axs / 2.0

        A = np.array([[3 * T ** 2, 4 * T ** 3],
                      [6 * T, 12 * T ** 2]])
        b = np.array([vxe - self.a1 - 2 * self.a2 * T,
                      axe - 2 * self.a2])
        x = np.linalg.solve(A, b)
        self.a3 = x[0]
        self.a4 = x[1]

    def calc_point(self, t):
        xt = self.a0 + self.a1 * t + self.a2 * t**2 + \
            self.a3 * t**3 + self.a4 * t**4
        return xt

    def calc_first_derivative(self, t):
        xt = self.a1 + 2 * self.a2 * t + \
            3 * self.a3 * t**2 + 4 * self.a4 * t**3
        return xt

    def calc_second_derivative(self, t):
        xt = 2 * self.a2 + 6 * self.a3 * t + 12 * self.a4 * t**2
        return xt

    def calc_third_derivative(self, t):
        xt = 6 * self.a3 + 24 * self.a4 * t
        return xt