Simulating a 3D Quadcopter from Scratch
This article discusses the simulation of a 3D quadcopter from scratch, building on previous work in 2D. It covers the derivation of equations of motion, the use of quaternions for representing attitude, and the integration of these concepts into a Python simulation. The article aims to provide a comprehensive understanding of quadcopter dynamics and simulation techniques.
- ▪The simulation involves deriving equations of motion for a 3D quadcopter using both world and body frames.
- ▪Quaternions are introduced as a method for representing the quadcopter's attitude, offering advantages over traditional methods.
- ▪The article provides a detailed explanation of the rigid-body equations of motion necessary for simulating the quadcopter's behavior.
Opening excerpt (first ~120 words) tap to expand
Simulating a 3D quadcopter from scratch Apr 11, 2026 This post is the second post in our series on quadcopter simulation. If you want the simpler planar version first, the previous post derives and simulates the same ideas in 2D, but this post is fully standalone. Today, we simulate a three-dimensional quadcopter. We will derive the equations of motion, transform them into state-space form, and finally simulate the system in Python. Along the way, we introduce quaternions and quaternion derivatives. Problem setup and coordinates The free-body diagram for the quadcopter is shown below. We use a right-hand coordinate frame with the \(z\) axis for altitude. The axes \(\{x, y, z\}\) are constant over time and form the world frame. This frame of reference is inertial (does not accelerate).
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Home.
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