🚀 Drone Simulation

This project is a simple simulation of vertical drone control using PID controller written in Rust + Bevy. The drone attempts to maintain or reach a target altitude by controlling its thrust in real-time.

📐 Mathematical Model

In Bevy: vertical axis is Y, and we ignore air resistance for simplicity.

🚁 Translational Motion (Vertical)

Equation of Motion

$$ \sum F = m \cdot a $$

In Y direction:

$$ \sum F_y = T - m \cdot g = m \cdot a_y $$

Therefore,

$$ T = m \cdot (g + a_y) $$

🔁 Rotational Motion (Pitch, Roll, Yaw)

We use Newton's second law for rotation:

$$ \sum \tau = I \cdot \alpha $$

Where:

$$ \tau = torque $$

$$ I = moment \space of \space inertia $$

$$ \alpha = angular \space acceleration $$

Pitch (X axis):

$$ \tau_x = I_x \cdot \alpha_x $$

Roll (Z axis):

$$ \tau_z = I_z \cdot \alpha_z $$

Yaw (Y axis):

$$ \tau_y = I_y \cdot \alpha_y $$

🎯 PID Controller:

$$ \text{output}(t) = K_p \cdot e(t) + K_i \cdot \int e(t) dt + K_d \cdot \frac{de(t)}{dt} $$

Where:

Symbol	Meaning
e(t)	Error = Target - Current Altitude
K_p	Proportional gain
K_i	Integral gain
K_d	Derivative gain

🎲 Ziegler–Nichols Method

Control Type	K_p	K_i	K_d
P	0.50K_u	—	—
PI	0.45K_u	0.54K_u / T_u	—
PID	0.60K_u	1.2K_u / T_u	3K_uT_u / 40

🎮 Manual Control

You can override the system by pressing:

• P → Toggle Start Engine on/off
• Space → Increase Altitude (go up)
• Left Ctrl → Decrease Altitude (go down)
• W → Pitch Down (tilt forward)
• S → Pitch Up (tilt backward)
• A → Roll Left (tilt left)
• D → Roll Right (tilt right)
• Q → Yaw Left (rotate left)
• E → Yaw Right (rotate right)
• R → Reset Target Altitude to 0 (Only works when engine is off)
• Esc → Exit the simulation