A = [1 t0 t0^2 t0^3 t0^4 t0^5;
0 1 2*t0 3*t0^2 4*t0^3 5*t0^4;
0 0 2 6*t0 12*t0^2 20*t0^3;
1 t1 t1^2 t1^3 t1^4 t1^5;
0 1 2*t1 3*t1^2 4*t1^3 5*t1^4;
0 0 2 6*t1 12*t1^2 20*t1^3]
A =
1 1 1 1 1 1
0 1 2 3 4 5
0 0 2 6 12 20
1 2 4 8 16 32
0 1 4 12 32 80
0 0 2 12 48 160
x = A\B
x =
46.0000
-171.0000
258.0000
-185.5000
64.0000
-8.5000
t = linspace(t0, t1, 10001);
y = x(1) + x(2)*t + x(3)*t.^2 + x(4)*t.^3 + x(5)*t.^4 + x(6)*t.^5;
dy = gradient(y)./gradient(t);
ddy = gradient(dy)./gradient(t);
tiledlayout(3, 1, 'TileSpacing', 'compact')
plot(t, y, 'linewidth', 1.5, 'color', '#cc3232'), grid on
ylabel({'$\theta$ / rad'}, 'interpreter', 'latex', 'fontsize', 12)
title('Quintic Polynomial Trajectories', 'fontsize', 12)
plot(t, dy, 'linewidth', 1.5, 'color', '#e6b415'), grid on
ylabel({'$\dot{\theta}$ / (rad/s)'}, 'interpreter', 'latex', 'fontsize', 12)
plot(t, ddy, 'linewidth', 1.5, 'color', '#2dc937'), grid on
ylabel({'$\ddot{\theta}$ / (rad/s$^2$)'}, 'interpreter', 'latex', 'fontsize', 12)
xlabel({'$t$ / s'}, 'interpreter', 'latex', 'fontsize', 12)
