Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Online parameter estimation for the Crazyflie quadcopter through an EM algorithm

Yanhua Zhao

TL;DR

This work models a quadcopter as a stochastic dynamical system and applies an online EM framework to estimate mass and inertia from flight data. State estimation via an Extended Kalman Filter, aided by a Rauch-Tung-Striebel smoother, provides the latent variables for the EM updates, while a linear-quadratic Gaussian controller governs trajectory tracking. The study compares offline and online parameter learning using three sensor configurations, showing online EM remains robust but typically yields broader parameter convergence ranges than offline. The results demonstrate the method’s viability for adapting dynamics during flight, with implications for improved autonomy and resilience in real-world quadrotor operations. Future work includes validating on a real platform and exploring enhancements to reduce estimation bias under partial observability.

Abstract

Drones are becoming more and more popular nowadays. They are small in size, low in cost, and reliable in operation. They contain a variety of sensors and can perform a variety of flight tasks, reaching places that are difficult or inaccessible for humans. Earthquakes damage a lot of infrastructure, making it impossible for rescuers to reach some areas. But drones can help. Many amateur and professional photographers like to use drones for aerial photography. Drones play a non-negligible role in agriculture and transportation too. Drones can be used to spray pesticides, and they can also transport supplies. A quadcopter is a four-rotor drone and has been studied in this paper. In this paper, random noise is added to the quadcopter system and its effects on the drone system are studied. An extended Kalman filter has been used to estimate the state based on noisy observations from the sensor. Based on a SDE system, a linear quadratic Gaussian controller has been implemented. The expectation maximization algorithm has been applied for parameter estimation of the quadcopter. The results of offline parameter estimation and online parameter estimation are presented. The results show that the online parameter estimation has a slightly larger range of convergence values than the offline parameter estimation.

Online parameter estimation for the Crazyflie quadcopter through an EM algorithm

TL;DR

This work models a quadcopter as a stochastic dynamical system and applies an online EM framework to estimate mass and inertia from flight data. State estimation via an Extended Kalman Filter, aided by a Rauch-Tung-Striebel smoother, provides the latent variables for the EM updates, while a linear-quadratic Gaussian controller governs trajectory tracking. The study compares offline and online parameter learning using three sensor configurations, showing online EM remains robust but typically yields broader parameter convergence ranges than offline. The results demonstrate the method’s viability for adapting dynamics during flight, with implications for improved autonomy and resilience in real-world quadrotor operations. Future work includes validating on a real platform and exploring enhancements to reduce estimation bias under partial observability.

Abstract

Drones are becoming more and more popular nowadays. They are small in size, low in cost, and reliable in operation. They contain a variety of sensors and can perform a variety of flight tasks, reaching places that are difficult or inaccessible for humans. Earthquakes damage a lot of infrastructure, making it impossible for rescuers to reach some areas. But drones can help. Many amateur and professional photographers like to use drones for aerial photography. Drones play a non-negligible role in agriculture and transportation too. Drones can be used to spray pesticides, and they can also transport supplies. A quadcopter is a four-rotor drone and has been studied in this paper. In this paper, random noise is added to the quadcopter system and its effects on the drone system are studied. An extended Kalman filter has been used to estimate the state based on noisy observations from the sensor. Based on a SDE system, a linear quadratic Gaussian controller has been implemented. The expectation maximization algorithm has been applied for parameter estimation of the quadcopter. The results of offline parameter estimation and online parameter estimation are presented. The results show that the online parameter estimation has a slightly larger range of convergence values than the offline parameter estimation.
Paper Structure (50 sections, 124 equations, 37 figures, 5 tables)

This paper contains 50 sections, 124 equations, 37 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Applications of drones
  3. Advantanges and challenges
  4. Outline
  5. Background
  6. Hidden Markov model
  7. State space models
  8. Differential flatness
  9. Sensor
  10. Sensor A
  11. Sensor B
  12. Sensor C
  13. State space model for extended Kalman filter
  14. Expectation maximization algorithm
  15. Dynamics
  16. ...and 35 more sections

Figures (37)

  • Figure 1: Hidden Markov model
  • Figure 2: Quadcopter model with the used coordinate systems
  • Figure 3: True state from quadcopter
  • Figure 4: Estimated state from EKF
  • Figure 5: Error between eatimated state and true state
  • ...and 32 more figures