usv_LOS_path_tracking/CubicPathGenerator at main · YT-USV-Platform/usv_LOS_path_tracking · GitHub

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import numpy as np
import matplotlib.pyplot as plt


class FossenCubicSpline():

    def __init__(self,x,y):

        self.Wpx = x
        self.Wpy = y
        self.N   = len(self.Wpx)


    def Spline_generator(self,xstart,xfinal,ystart,yfinal):

        N = len(self.Wpx)-1 # Toplam Denklem Sayısı

        th = list(range(0,(N+1)))  # theta values along the path

        c1 = [3*th[0]**2,2*th[0],1,0]

        c2 = [3*th[N]**2,2*th[N],1,0]

        ## Y vector generation accorting  to number of waypoint

        # xstart = self.Wpx[0]
        # xfinal = self.Wpx[-1]

        # ystart = self.Wpy[0]
        # yfinal = self.Wpy[-1]


        # y_x = np.zeros((4*N,1))
        # y_y = np.zeros((4*N,1))

        y_x = [xstart,self.Wpx[0]]
        y_y = [ystart,self.Wpy[0]]

        ## Generate A Matrix

        for k in range(1,N):

            y_x.extend([self.Wpx[k],self.Wpx[k],0,0])
            y_y.extend([self.Wpy[k],self.Wpy[k],0,0])

        y_x.extend([self.Wpx[N],xfinal])
        y_y.extend([self.Wpy[N],yfinal])

        A = np.zeros((4*N,4*N))
        A[0,0:4] = c1
        A[1,0:4] = np.array([th[0]**3,th[0]**2,th[0],1])
        A[4*N-1,(4*(N-1)):4*N] = c2
        A[(4*N-1)-1,(4*(N-1)):4*N] = [th[N]**3,th[N]**2,th[N],1]


        for j in range(1,N):

            row = 4*(j-1)+2
            col = 4*(j)

            A[row,col-4:col] = [th[j]**3,th[j]**2,th[j],1]
            A[row+1,col:col+4] = [th[j]**3,th[j]**2,th[j],1]

            A[row+2,col-4:col] = [-3*th[j]**2,-2*th[j],-1,0]
            A[row+2,col:col+4] = [3*th[j]**2,2*th[j],1,0]

            A[row+3,col-4:col] = [-6*th[j],-2,0,0]
            A[row+3,col:col+4] = [6*th[j],2,0,0]

        x_x = np.matmul(np.linalg.inv(A),y_x)
        x_y = np.matmul(np.linalg.inv(A),y_y)

        self.Acoeff = np.zeros((N,4))
        self.Bcoeff = np.zeros((N,4))
        self.x_theta_one=np.zeros((N,4))
        self.y_theta_one=np.zeros((N,4))
        self.x_theta_two=np.zeros((N,4))
        self.y_theta_two=np.zeros((N,4))
        self.x_theta_three=np.zeros((N,4))
        self.y_theta_three=np.zeros((N,4))


        for m in range(0,N):

            self.Acoeff[m,:] = x_x[4*m:4*m+4]
            self.Bcoeff[m,:] = x_y[4*m:4*m+4]
            self.x_theta_one[m,:] = [0,3*self.Acoeff[m,0],2*self.Acoeff[m,1],self.Acoeff[m,2]]
            self.y_theta_one[m,:] = [0,3*self.Bcoeff[m,0],2*self.Bcoeff[m,1],self.Bcoeff[m,2]]
            self.x_theta_two[m,:] = [0,0,6*self.Acoeff[m,0],2*self.Acoeff[m,1]]
            self.y_theta_two[m,:] = [0,0,6*self.Bcoeff[m,0],2*self.Bcoeff[m,1]]
            self.x_theta_three[m,:] = [0,0,0,6*self.Acoeff[m,0]]
            self.y_theta_three[m,:] = [0,0,0,self.Bcoeff[m,0]]

        table_x = [self.Acoeff,self.x_theta_one,self.x_theta_two,self.x_theta_three]

        table_y = [self.Bcoeff,self.y_theta_one,self.y_theta_two,self.y_theta_three]

        return table_x ,table_y

    def curve_plot(self):


        plt.plot(self.Wpx,self.Wpy,'go')


        for i in range(0,self.N-1):

            th = np.linspace(i,i+1)
            plt.plot(np.polyval(self.Acoeff[i,:],th),np.polyval(self.Bcoeff[i,:],th))
            plt.xlabel('X Position')
            plt.ylabel('Y Position')


        plt.show()

        for i in range(0,self.N-1):

            th = np.linspace(i,i+1)
            plt.plot(th,np.polyval(self.x_theta_one[i,:],th))
            plt.xlabel('Way Points ')
            plt.ylabel('First Derivative of X')
        plt.show()


        for i in range(0,self.N-1):

            th = np.linspace(i,i+1)
            plt.plot(th,np.polyval(self.x_theta_two[i,:],th))
            plt.xlabel('Way Points ')
            plt.ylabel('Second Derivative of Y')
        plt.show()


if __name__ == '__main__':
    x = [0, 200, 400, 700, 1000]
    y = [0, 600, 500, 400, 1200]
    cubic = FossenCubicSpline(x,y)
    X,Y=cubic.Spline_generator(10,0,190,0)
    cubic.curve_plot()