# Helical trajectory generation using frenet frame

8 visualizaciones (últimos 30 días)
Drishya Dinesh el 8 de Abr. de 2021
Respondida: Vaibhav el 28 de Mayo de 2024
How to generate a helical trajectory using frenet frame? Position vector given as [x y z]^T=[[500sin(0.01t) 500cos(0.01t) −2t−20000]^T initial position is ζ (0) = [−300 0 −19800]^T initial line velocity is υ(0) =[5 0 0]^T, the initial attitude is γ (0) = [0, 0, 0]^T How to convert this data to frenet frame and find attitude coordinates and then plot a helical trajectory
##### 0 comentariosMostrar -2 comentarios más antiguosOcultar -2 comentarios más antiguos

Iniciar sesión para comentar.

### Respuestas (1)

Vaibhav el 28 de Mayo de 2024
Hi Dhishya
To generate the helical trajector using frenet frame. We first define the helical trajectory using the given position vector. Then, we calculate the velocity and acceleration to derive the Frenet frame vectors (Tangent, Normal, Binormal). Finally, we can plot the trajectory and the Frenet frame vectors for visualization.
Here is the code for your reference:
% Define the trajectory
t = linspace(0, 20000, 10000);
x = 500*sin(0.01*t);
y = 500*cos(0.01*t);
z = -2*t - 20000;
% Calculate derivatives for velocity and acceleration
% Calculate Frenet frame vectors
T = [dx; dy; dz];
T_norm = sqrt(dx.^2 + dy.^2 + dz.^2);
T_unit = T ./ T_norm;
N = [dTx; dTy; dTz];
N_norm = sqrt(dTx.^2 + dTy.^2 + dTz.^2);
N_unit = N ./ N_norm;
B = cross(T, N);
B_norm = sqrt(B(1,:).^2 + B(2,:).^2 + B(3,:).^2);
B_unit = B ./ B_norm;
% Plot the trajectory and Frenet frame vectors
figure;
plot3(x, y, z, 'LineWidth', 2);
hold on;
quiver3(x(1:100:end), y(1:100:end), z(1:100:end), T_unit(1,1:100:end), T_unit(2,1:100:end), T_unit(3,1:100:end), 'r');
quiver3(x(1:100:end), y(1:100:end), z(1:100:end), N_unit(1,1:100:end), N_unit(2,1:100:end), N_unit(3,1:100:end), 'g');
quiver3(x(1:100:end), y(1:100:end), z(1:100:end), B_unit(1,1:100:end), B_unit(2,1:100:end), B_unit(3,1:100:end), 'b');
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Helical Trajectory with Frenet Frame');
legend('Trajectory', 'Tangent', 'Normal', 'Binormal');
grid on;
axis equal;
Hope it helps!
##### 0 comentariosMostrar -2 comentarios más antiguosOcultar -2 comentarios más antiguos

Iniciar sesión para comentar.

### Categorías

Más información sobre Mathematics and Optimization en Help Center y File Exchange.

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by