Warning

This repository is no longer maintained. All models have been integrated into crazyflow, its successor, and can be imported from there as before. Please use crazyflow for new projects.

$$ \huge \displaystyle \dot{x} = f(x,u) $$

---

Physics-based and data-driven quadrotor dynamics models for estimation, control, and simulation.

Overview

drone-models provides quadrotor dynamics as pure Python functions, from full physics-based implementations to lightweight data-driven approximations. All models support NumPy, JAX, and any Array API backend, plus CasADi symbolic variants for optimization-based control. Pre-fitted parameters are included for several Crazyflie platforms.

Available models — ranging from high-fidelity to lightweight:

Model	Description
first_principles	Full rigid-body physics with optional rotor dynamics and aerodynamic drag
so_rpy_rotor_drag	Data-driven, attitude as roll/pitch/yaw, with rotor dynamics and drag
so_rpy_rotor	Data-driven, attitude as roll/pitch/yaw, with rotor dynamics
so_rpy	Lightest data-driven model, attitude as roll/pitch/yaw, no rotor dynamics

Pre-fitted configurations for Crazyflie 2.x (brushed) and Crazyflie 2.1 Brushless: cf2x_L250, cf2x_P250, cf2x_T350, cf21B_500

Installation

pip install drone-models

For system identification (fitting parameters from your own flight data):

pip install "drone-models[sysid]"

Note: drone_models must be imported before SciPy to enable Array API support. If you encounter a RuntimeError, either import drone_models first or set export SCIPY_ARRAY_API=1 in your shell.

Usage

Basic

Bind parameters to a drone configuration with parametrize, then call the model with state and command arrays:

import numpy as np
from drone_models import parametrize
from drone_models.first_principles import dynamics

model = parametrize(dynamics, drone_model="cf2x_L250")

pos     = np.zeros(3)
quat    = np.array([0., 0., 0., 1.])   # xyzw, identity
vel     = np.zeros(3)
ang_vel = np.zeros(3)
rotor_vel = np.ones(4) * 12_000.        # current motor RPMs
cmd     = np.full(4, 15_000.)           # commanded motor RPMs

pos_dot, quat_dot, vel_dot, ang_vel_dot, rotor_vel_dot = model(
    pos, quat, vel, ang_vel, cmd, rotor_vel
)

The model returns continuous-time state derivatives $\dot{x} = f(x, u)$. Integrate with any ODE solver (e.g. scipy.integrate.solve_ivp) to simulate forward in time.

Switching backends

Pass any Array API-compatible array and the output type follows automatically — no code changes needed:

import jax.numpy as jnp
from drone_models import parametrize
from drone_models.first_principles import dynamics

model = parametrize(dynamics, drone_model="cf2x_L250", xp=jnp)
# Pass jax arrays — get jax arrays back

Arbitrary leading batch dimensions work out of the box: stack states for a thousand drones and evaluate them in one call.

Symbolic models (CasADi)

Every model exposes a symbolic_dynamics function returning CasADi MX expressions, for use in MPC, trajectory optimization, or estimation:

from drone_models import parametrize
from drone_models.first_principles import symbolic_dynamics

sym_model = parametrize(symbolic_dynamics, drone_model="cf2x_L250")

Development

Clone and install with pixi:

git clone https://github.com/learnsyslab/drone-models.git
cd drone-models
pixi install

Run tests:

pixi run -e tests tests

Citation

@misc{schuck2026crazyflow,
      title={Crazyflow: An Accurate, GPU-Accelerated, Differentiable Drone Simulator in JAX}, 
      author={Martin Schuck and Marcel P. Rath and Yufei Hua and AbhisheK Goudar and SiQi Zhou and Angela P. Schoellig},
      year={2026},
      eprint={2606.01478},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2606.01478}, 
}