Introduction to Multicopter Design and Control


➤  Reference Books

  • [1] Quan Quan. Introduction to Multicopter Design and Control. Springer, Singapore, 2017. [京东]
  • [2] Quan Quan, Xunhua Dai, Shuai Wang. Multicopter Design and Control Practice: A Series Experiments Based on MATLAB and Pixhawk. Springer, Singapore, 2020. [京东]

➤  Online course (Chinese)


➤  Experimental Course

Chinese Version:
English Version:


        This course is about multicopter design, dynamical model, state estimation, control and decision. It has two salient features: fundamental and systematic.
(1) Fundamental.
        The most of contents related to multicopters are self-contained, aiming to make this course be understood by students with an undergraduate knowledge. For such a purpose, the components are introduced starting from their functions and key parameters. The design starts from the principle, while the modeling from the theoretical mechanics. The state estimation starts from the measurement principle of sensors and filters. Before talking about the control, the stability and controllability are introduced in advance. Most of the given methods are also basic and practical.
(2) Systematic.
        This course aims to give a complete picture of multicopter system rather than a single method or technique. For an undergraduate student, many knowledge has be learned, such as math, aerodynamics, electric circuit, motor, filtering theory, control theory and software, which corresponds to many courses. This course is expected to combine them together. It is expected to help the students to have the feeling of linking theory with practice.  

Textbook: [Google book] [Springer]   ,   PPTs [Download]   ,   PPTs(pptx)[Download]Code:3jc7

Lesson 01 Introduction

Download:   [Lesson 01] ,   [第一讲],  

    Commonly-used small aircraft (less than 20kg or 25kg) can be classified into fixed-wing aircraft, helicopters and multicopters, among which multicopters are most popular so far. Before 2010, fixed-wing aircraft and helicopters took overwhelming dominance in the field of both aerial photography and model aircraft sports. However, in the following years, due to the ease-of-use, the multicopter became a new star. During this period, since the autopilot and the other components were sold separately, multicopters were often only assembled by some professional personnels. Moreover, the parameters had to be tuned in accordance with the payload. At the end of 2012, DJI (Da-Jiang Innovations Science and Technology Co., Ltd.) released an all-in-one solution which is the ready-to-fly Phantom quadcopter. Users could pilot it in a short time. Moreover, DJI’s Phantom only cost about one thousand dollars. It was a huge saving in comparison with some commercial multicopters, then such as MD4-200 or MD4-1000 from Microdrones GmbH in Germany. Since the Phantom quadcopter reduced the difficulty and cost of aerial photography, its market share expanded rapidly and took dominance soon after. In the following two years, there are a lot of media released about multicopters in terms of technologies, products, applications and investigations. Today, multicopters have consolidated its dominance in the market of small aircraft. The speed they occupy the market is similar to that of the mobile internet defeating the traditional internet, or the smart mobile phones defeating the traditional mobile phones. The development of multicopters is becoming increasingly popular because of several factors, i.e., stories of success, the advancement in related technologies, the promotion of open source autopilots, participation of talented professionals, popularization of multicopters, continual capital investment, and preferential policy support. This lesson aims to answer the question as below:

Why do people choose small multicopters eventually?

    The answer to this question involves the introduction to multicopters, the performance evaluation of small aircraft, and the brief history of multicopters.

Lesson 02 Basic Composition

Download: [Lesson 02] ,   [第二讲]

    The compositions of multicopter systems are both simple yet complex. The compositions are thought to be simple because a multicopter system is generally composed of several well-modularized components such as the airframe, propulsion system, command and control system, etc. These components for a multicopter can be described as the organs for a human, where the airframe corresponds to the body, carrying other hardware; the propulsion system would be the feet and hands powered by the heart and blood vessels, providing power for the multicopter; the command and control system would be the sense organs and brain, controlling the propulsion system to achieve tasks. On the other hand, the compositions are also complex, because each component is not independent, and they are connected and constrained with others in a very complex way. Though there are countless combinations for a multicopter, only a few of them can really work. If designers are unaware of the principle of components and assemble multicopters blindly, then the assembled multicopters may have poor performance, or even could not work at all. Therefore, it is necessary to know the basic principle of each component and their relationship. This lesson aims to answer the question as below:

What are the basic compositions of a multicopter system?

    This lesson consists of three parts, namely the airframe, propulsion system, and command and control system. The component of each part will be introduced from the corresponding function, working principle and key parameter, etc.

Lesson 03 Airframe Design

Download: [Lesson 03] ,   [第三讲]

    When given a multicopter, its configuration and structure come into our sight first, including the shape and size of the airframe, the choice of motors and propellers and the distribution of the battery and the payload. All these designs not only influence the multicopter performance, but also help customers distinguish between different brands of multicopters. Compared with the configuration design, structural design to reduce vibration and noise is more important, especially for multicopters flying over residential areas. Considerable vibration will degrade the normal operation of a multicopter, consume more energy, accelerate component aging, and reduce the quality of aerial photography. Similarly, considerable noise will affect the nearby residents’ life and make the multicopters not suitable for detective works. This lesson aims to answer the question below:

What should be taken into consideration when designing the airframe of a multicopter?

    The answer to this question mainly involves three aspects including configuration design, anti-vibration design, and noise reduction.

Lesson 04 Modeling and Evaluation of Propulsion System

Download: [Lesson 04] ,   [第四讲] [实验一. 多旋翼飞行器动力系统设计实验]

     To design a multicopter, first of all, a designer has to select proper components to assemble a multicopter to meet the performance requirements, such as hover endurance, system efficiency, maximum payload, maximum pitch angle and maximum flight distance. Multicopter performance is mainly determined by the chosen propulsion systems, consisting of propellers, brushless Direct Current (DC) motors, Electronic Speed Controllers (ESCs) and the batteries. Different components will lead to different flight performance in a very complex way. For instance, it seems that increasing the capacity of the battery can increase endurance, but it also increases the weight and power. Thus the endurance of flight would probably even be decreased sometimes. As far as we know, in practice, many designers used to evaluate the performance of a multicopter through their experience or repeated experiments, which is an inefficient and costly process. Moreover, the optimal choice of components related to the performance requirements remains a problem, which is hard to solve by experiments and experience. This lesson aims to answer the question below:

How to evaluate the flight performance of a multicopter?

     To answer this question, a practical modeling method is proposed for the propulsion system of multicopters to evaluate a series of performance indices. For a practical purpose, only technical specifications of components offered by manufacturers are required as the input to the models. Testing examples are finally given to demonstrate the effectiveness of the proposed method. Furthermore, a website is established which can provide users with the performance evaluation mentioned in this lesson.

Lesson 05 Coordinate System and Attitude Representation

Download: [Lesson 05] ,   [第五讲]

     In order to describe the attitude and position of a multicopter, it is necessary to establish appropriate coordinate frames. Coordinate frames are helpful to establish the relationship among dynamic variables. Thus facilitating calculation. This lesson regards the multicopter as a rigid body whose attitude in space mainly describes the rotation between the Aircraft-Body Coordinate Frame (ABCF) and the Earth-Fixed Coordinate Frame (EFCF). There are many methods to represent the attitude. Each method has its advantages and disadvantages. This lesson will present the Euler angles, rotation matrix and quaternions as well as the relationship between the corresponding attitude rate and the body’s angular velocity. Different attitude representation methods correspond to different modeling methods, which are closely related to filtering methods and control methods in the following lessons. Deep understanding of the coordinate frames and attitude representation is helpful to understand the motions of a multicopter and then to design filters and controllers. This lesson aims to answer the question below:

What are the three attitude representation methods and the relationship between their derivatives and the aircraft body’s angular velocity?

     This lesson will start with the establishment of coordinate frames and give further details about the attitude representation as well as its derivation.

Lesson 06 Dynamic Model and Parameter Measurement

Download: [Lesson 06] ,   [第六讲] ,   [Ch6 Data] [实验二. 多旋翼飞行器动态模型建立实验] [实验二源代码]

     On the basis of the coordinate frames and attitude representations in Lesson 5, forces on a multicopter will be taken into account and dynamic models for filtering and control will be established. The forces and moments can change the acceleration and angular acceleration directly and further influence the velocity and angular velocity. This influence is related to most parameters of a multicopter. Furthermore, the velocity and angular velocity can change the position and the attitude of the multicopter. This influence is independent of parameters of the multicopter. For example, the position is calculated through the velocity without requiring the parameters of the multicopter. As pointed out in Lesson 1, multicopters are different from fixed-wing aircraft or single rotor blade helicopters. The differences appear mainly in its special dynamic model and control effectiveness model. A traditional multicopter has four independent control inputs: thrust, pitching moment, rolling moment and yawing moment. The thrust is always perpendicular to the multicopter fuselage plane. Moreover, propellers of the multicopter can generate thrust to lift the multicopter directly. Therefore, the multicopter is simple and flexible in terms of the control allocation. Deep understanding of the multicopter dynamic model helps to understand its motion and further to design filters and controllers. This lesson aims to answer the questions below:

How is the multicopter dynamic model established and how are the model parameters measured?

     The answer to these questions involves the multicopter control model, multicopter aerodynamic drag model, and multicopter model parameter measurement. The multicopter control model is mainly used for the control in the following lessons. It is also used for the state estimation. The multicopter aerodynamic drag model is mainly used for the state estimation. The last part of this lesson provides methods to measure the model parameters mentioned before.

Lesson 07 Sensor Calibration and Measurement Model

Download: [Lesson 07] ,   [第七讲] ,   [Ch7 Data][实验三. 多旋翼飞行器传感器标定实验] [实验三源代码]

     There are many sensors mounted in a multicopter, such as the three-axis accelerometer, three-axis gyroscope, three-axis magnetometer, ultrasonic range finder, 2D laser range finder, Global Positioning System (GPS) receiver and camera. These sensors in a multicopter are like sensory organs of a human being. A multicopter can obtain its position and attitude with these sensors. However, these sensors based on Micro-Electro-Mechanical System (MEMS) are inaccurate. For example, the devices on the circuit board can affect the measurement of a magnetometer. So it is impossible to obtain an accurate orientation, not to mention making flight reliably control. On the other hand, unsteady take-off of multicopters can also be related to uncalibrated sensors. Uncalibrated sensors could make multicopters unstable once they take off. Thus, the calibration should be performed as the key step of manufacturing. Some calibration methods that do not need any additional equipment are introduced. This lesson aims to answer the question below:

How are sensors calibrated and what are the measurement models?

     The answer to this question involves fundamental principles, calibration methods, and measurement models of sensors.

Lesson 08 Observability and Kalman Filter

Download: [Lesson 08] ,   [第八讲] [实验四. 多旋翼飞行器滤波器设计] [实验四源代码]

     The state of a multicopter may not be measured directly by existing sensors. For example, since the speed of a multicopter is very low, its accurate value is difficult to be measured directly through speed sensors, like Pitot tubes or a Global Positioning System (GPS) receiver. For such a purpose, a question that arises is what kind of sensor or the combination of sensors is necessary to estimate a given state. For example, given sensors such as an accelerometer, a GPS receiver and a monocular camera, which sensor can give stable estimate for the speed of a multicopter? This involves the observability of a system. Observability is a measure for how well a system can be observed, i.e., to determine the initial states by measuring the outputs. Formally, a system is observable if, from the sequence of outputs and control vectors, the current state can be uniquely determined in a finite time interval. The concept of the observability can also be extended to the social survey. In the era of big data, huge reliable, easy-to-access and local data can be collected online. Based on these data, the question is whether a local index related to the society can be observed online. If so, it will not only avoid false statistics, but also can save much labor and a lot of resources. Back to the topic of this lesson, after guaranteeing the observability, an observer design, such as the Kalman filter design, will make sense. This lesson aims to answer the questions below:

What is the observability and how is a Kalman filter derived?

     The answer to these questions involves the concept of observability and its criteria for the system like the continuous-time linear system, discrete-time linear system and continuous- time nonlinear system. Furthermore, the classical Kalman filter is derivated in details, and its extensions, multirate Kalman filter, Extended Kalman filter (EKF), and Implicit Extended Kalman filter (IEKF) are introduction.

Lesson 09 State Estimation

Download: [Lesson 09] ,   [第九讲] ,   [Ch9 Data]

     The state estimation is very important as it is the base for control and decision-making. Sensors of multicopters are like sensory organs of a human being, which can provide the necessary information. In order to reduce the cost of a multicopter, cheap sensors with poor precision are often used. With such kinds of sensors, some information such as acceleration, angular velocity and absolute position can be directly measured but subject to a lot of noise. Some information such as velocity, attitude angles, and obstacle position may not be measured by sensors directly, and requires to be estimated. Moreover, information measured by sensors is redundant. For instance, an accelerometer and a GPS receiver both contain information related to the position. Therefore, it is necessary to improve the accuracy and robustness of state estimation by fusing the redundant information of the sensors. This lesson aims to answer the question below:

How is the information from the multiple sensors fused?

     The answer to this question involves the attitude estimation, position estimation, velocity estimation and obstacle estimation.

Lesson 10 Stability and Controllability

Download: [Lesson 10] ,   [第十讲] ,   [Ch10 Data]

     Stability and controllability are the basic properties of a dynamical system. Since a multicopter without control feedback is unstable, an autopilot is required to guarantee its stability and further make the multicopter hover automatically without any need for an external intervention. However, if a multicopter is uncontrollable at an equilibrium state, then no controller exists to stabilize it at the equilibrium state. Unlike general systems, the control inputs of multicopters are often constrained because of the fact that the thrust provided by each propeller is unidirectional. This will lead to a special controllability, called positive controllability. Without controllability, any controller, including the fault-tolerant controller, would not help. The controllability is to answer the question: whether a multicopter can be controlled or not. However, multicopter design contains far more than merely the controllability issue. For such a purpose, the Degree of Controllability (DoC) is further introduced to quantify the degree to which a process can be controlled. For the same system subject to different control constraints, the DoC will be different. The DoC can help in choosing a fault-tolerant control strategy or evaluating a multicopter design in the sense of the controllability in presence of wind. This lesson will answer the questions below:

Why is a multicopter dynamical system unstable and how is the DoC of a multicopter?

     In order to answer these questions, this lesson includes the definition of stability, stability criteria, basic concepts of controllability, and controllability of multicopters.

Lesson 11 Low-level Flight Control

Download: [Lesson 11] ,   [第十一讲] [实验五. 旋翼飞行器姿态控制器设计] [实验五源代码]

     Control is an enabling technology, the essence of which is the feedback. Unstable multicopters can become stable with the help of feedback control. However, it is not enough to be just stable. A good control performance is also required, such as fast response, no overshoot and robustness against uncertainties. Therefore, effective control strategy is very important. In practice, traditional Proportional-Integral-Derivative (PID) control laws can tackle most problems for multicopters. Thus, this lesson mainly introduces PID control schemes in the position and attitude control. Moreover, in terms of different attitude representations, attitude control methods based on Euler angles and rotation matrix are presented, respectively. Different control methods exhibit their own advantages. This lesson aims to answer the question below:

How is a multicopter controlled by motors to achieve a desired position?

     This lesson consists of six parts, namely the framework of low-level flight control, model simplification, position control, attitude control, control allocation and motor control. The effectiveness of these control algorithms is illustrated by comprehensive simulations.

Lesson 12 Position Control Based on Semi-Autonomous Autopilot

Download: [Lesson 12] ,   [第十二讲] [实验六. 旋翼飞行器位置控制器设计] [实验六源代码]

     Remote pilots often control multicopters based on Semi-Autonomous Autopilots (SAAs) to accomplish some specified tasks, such as crop-dusting and inspection of power lines. During the process, most remote pilots do not know the flight control law in the autopilots. But, it is not an obstacle for them to accomplish these tasks. In fact, it is difficult for most people to design an autopilot starting from the motor control. On the other hand, many groups or companies have designed some open source SAAs or offered SAAs with Software Development Kits (SDK). Please refer to Tables 1.3 in Lesson 1. Therefore, it is useful to develop special applications based on existing SAAs directly. Not only can it avoid the trouble of modifying the low-level source code of autopilots, but also it can utilize commercial reliable autopilots to achieve targets. This will simplify the complete design. This lesson aims to answer the question as below:

How is a multicopter controlled based on the SAA to track a given target position?

     To answer this question, this lesson mainly includes: problem formulation, system identification and controller design.

Lesson 13 Mission Decision-Making

Download: [Lesson 13] ,   [第十三讲][实验七. 多旋翼飞行器半自主模式飞行设计实验] [实验七源代码]

     A Flight Control System (FCS) or an autopilot includes not only a low-level flight control system as introduced in Lesson 11, but also a high-level decision-making module. The former just aims at solving the problem—“how to fly to a desired position”, while the latter mainly aims at solving the problem—“how to determine the desired position”. The decision-making process mainly includes the mission decision-making and failsafe. This lesson only considers the mission decision-making, aiming to provide a sequence of discrete-time desired waypoints or continuous-time desired trajectories in real time for a multicopter to follow. Currently, the majority of multicopter products and open source autopilots support two control manners, namely Fully-Autonomous Control (FAC) and Semi-Autonomous Control (SAC). For each control manner, the mission decision-making has different functions. This lesson aims to answer the question below:

What are the mission decision-making mechanisms under the FAC and SAC manners, respectively?

     In order to clearly explain the mission decision-making mechanism, this lesson describes the FAC manner and SAC manner. Then, the mission planning and path planning methods will be introduced, where the path following and obstacle avoidance are considered. Finally, the SAC manner, the Radio Control (RC) and Automatic Control (AC) are introduced. Furthermore, a switching logic between the RC and AC is summarized and analyzed.

Lesson 14 Health Evaluation and Failsafe

Download: [Lesson 14] ,   [第十四讲] ,   [Ch14 Data] [实验八. 多旋翼失效保护逻辑设计实验] [实验八源代码]

     For multicopters, failures cannot be avoided, including communication breakdown, sensor failure and propulsion system anomaly, etc. These failures may abort missions, crash multicopters, and moreover, injure or even kill people. In order to guarantee safety, multicopter’s decision-making module should prevent or mitigate unsafe consequences of system’s failures. For such a purpose, some flight modes are defined and switched to according to the health evaluation results of each component. Concretely, if there are safety risks in the key components of a multicopter before taking off, then the previously arranged flight mission needs to be aborted. Furthermore, if there is an anomaly or a fault in the key components of a multicopter during the flight, then the multicopter should return home or land immediately. This lesson mainly considers the safety issue of the multicopters, and aims to answer the questions below:

What kind of events are involved in safety issue? How are these events dealt with?

     The answer to these questions involves an introduction to potential safety issues, some health evaluation methods, failsafe suggestions and a failsafe decision-making case.

Lesson 15 Outlook

Download: [Lesson 15] ,   [第十五讲]

     Since multicopters entered the consumer market, the related companies have emerged like bamboo shoots after a spring rain, and scholars have also flocked. The largest market of multicopters remains the aerial photography area, which has been firmly occupied by a few well-known companies. The remaining markets seem relatively small or have a higher entering threshold. In recent years, there exists a dispute on the multicopter market whether it is a “Red Ocean” or a “Blue Ocean”? There is diminishing interest in academia because most of the fundamental problems, such as stabilizing or tracking, seem to have been solved. Therefore, everyone seems to be standing at a crossroads. This lesson aims to answer the question below:

Where will multicopters go?

     The answer to this question involves the related technology development, innovation direction, risk analysis, opportunities and challenges. Contents in this lesson are the revision and extension of a magazine paper in Chinese published by the author.


Download: [All English PPT] ,   [所有中文PPT打包下载] ,   [中文PPT合集打印版]

Please refer to the textbook: Quan, Quan. Introduction to Multicopter Design and Control. Springer, 2017. ISBN: 978-981-10-3382-7. (It will be available soon, please visit