Unmanned Aerial Systems: Theoretical Foundation and Applications

By Anis Koubaa

Unmanned Aerial Systems: Theoretical Foundation and Applications presents some of the latest innovative approaches to drones from the point-of-view of dynamic modeling, system analysis, optimization, control, communications, 3D-mapping, search and rescue, surveillance, farmland and construction monitoring, and more. With the emergence of low-cost UAS, a vast array of research works in academia and products in the industrial sectors have evolved. The book covers the safe operation of UAS, including, but not limited to, fundamental design, mission and path planning, control theory, computer vision, artificial intelligence, applications requirements, and more.

This book provides a unique reference of the state-of-the-art research and development of unmanned aerial systems, making it an essential resource for researchers, instructors and practitioners.

• Covers some of the most innovative approaches to drones
• Provides the latest state-of-the-art research and development surrounding unmanned aerial systems
• Presents a comprehensive reference on unmanned aerial systems, with a focus on cutting-edge technologies and recent research trends in the area

• Language: English
• Publisher: Academic Press
• Release date: Jan 21, 2021
• ISBN: 9780128202777

Book preview

team.

Chapter 1: Evolutionary aerial robotics: the human way of learning

Fendy Santosoa,b; Matthew A. Garratta; Sreenatha G. Anavattia; Jiefei Wanga    aSchool of Engineering and Information Technology, UNSW Canberra, Canberra, ACT, Australia

bDefence and Systems Institute (DASI); Science, Technology, Engineering, and Mathematics (STEM) of the University of South Australia - UniSA STEM, Adelaide, SA, Australia

Abstract

Robotic aircraft are often required to operate in harsh environments (e.g., underground mining, cluttered environments, and battlefields). In this chapter, we discuss an adaptive (evolving) fuzzy system that has the ability to learn and to configure itself based on the human way of learning, which is also somewhat akin to the principles of natural evolution. We will be looking at the capability of an evolving Takagi-Sugeno (ETS) fuzzy algorithm to learn-from-scratch in order to adapt the challenging dynamics of autonomous systems in real-time. The ETS system can also work in unknown environments, where there is no expert knowledge. While we focus on the implementation of the ETS system to identify the behavior of a fast-dynamical system as in the case of the low altitude hovering of our Tarot hexacopter drone by performing an online ETS-based data driven modelling (online system identification) technique, we also conduct a preliminary study to highlight the efficacy of the ETS autopilot under computer simulations.

Keywords

Evolutionary TS fuzzy systems; Learning-from-scratch; Aerial robotics; Online system identification

Acknowledgements

This research was supported by the Defence Science and Technology (DST) Group Australia through the DST Competitive Evaluation Research Agreement (CERA) program. The title of the project was CERA 259: Feasibility Testing for Adaptive Flight Control of a Dragonfly Inspired Micro Air Vehicle. In particular, we would like to thank Dr Jia Kok from the DST Group, who has worked with us to develop the program objectives.

1.1 Introduction

Unmanned aerial vehicles (UAVs), also known as drones, have been playing significant roles in modern society in both military and civilian domains. There have been multiple applications of robotic aircraft in harsh and challenging environments, namely, aircraft inspection (Santoso et al., 2016b), bridge assessment (Obradovic et al., 2019), building examination (Raja and Pang, 2016), border protection (Abushahma et al., 2019), forest monitoring (Thomazella et al., 2018), agriculture observation (Murugan et al., 2017), biodiversity monitoring (Bagaram et al., 2018), law enforcement as well as surveillance (Singh et al., 2018) and cinematography (Mademlis et al., 2018).

To date, there have been numerous research papers discussing the efficacy of model-based control systems for stabilizing the dynamics of robotic aircraft. For instance, (Maithripala and Berg, 2014), (Jiang et al., 2019) developed a feedback linearization technique while (Kang and Hedrick, 2009) employed model predictive control for UAVs. Meanwhile, (Poksawat et al., 2018) employed gain scheduling control. Although the proposed control systems seem to be promising, in the absence of high-fidelity mathematical models, those approaches may nonetheless be impractical. In real life, accurate mathematical models are not always available. In fact, in every modeling task, the presence of uncertainties is inevitable, even for the most trivial systems, limiting the effectiveness of model-based control systems.

On the other hand, recent technological developments in artificial intelligence have simplified the design procedures of traditional model-based control systems as researchers can now develop robust model-free control systems that have an ability to learn (Santoso et al., 2017) and (Santoso et al., 2018b). In fact, there are multiple computational intelligence approaches in the literature with their unique capabilities, such as, genetic algorithms (Jamshidi et al., 2003), particle swarm optimization techniques (Seo et al., 2006), which are known for their ability to optimize complex mathematical functions (derivative-free optimization approaches), neural networks, which are known for their deep learning feature (Zhang and Ge, 2009), incremental metacognitive scaffolding (Pratama et al., 2015), and fuzzy inference systems, which are known for their knowledge-based nature (Santoso et al., 2018a), (Al-Mahturi et al., 2018a) or adaptive fuzzy systems (Al-Mahturi et al., 2019a), (Al-Mahturi et al., 2019b), (Santoso et al., 2016a), (Al-Mahturi et al., 2018b), and also (Al-Mahturi et al., 2019c).

Addressing the aforementioned, we advocate the concept of an evolutionary fuzzy system, originally introduced in (Angelov and Filev, 2004), to facilitate learning-from-scratch in aerial robotics. To achieve this mission, we have built a Tarot hexacopter drone from scratch (see Fig 1.1). The system employs the Intel Edison computer as its on-board processing system. The drone also employs the MAVLink (Micro Air Vehicle communication) to connect with the PixHawk2 Flight Controller Unit (FCU) and the flight stack. The hexacopter can carry up to 10 kg take-off load. We will be using our Tarot hexacopter to validate the human way of learning concept applied in ETS to learn the behavior of an unmanned hexacopter. In addition, we will also conduct a preliminary study to investigate the efficacy of the ETS autopilot system to regulate the vertical dynamics of our hexacopter under numerical simulations.

Figure 1.1 Our Tarot hexacopter hovers at a reasonably low altitude. This makes the system prone to the exposure of severe ground effects, causing large uncertainties in the closed loop control system.

Thus, the contribution of this chapter is mainly in practical domain as we intend to study the efficacy of the evolutionary Takagi–Sugeno (TS) fuzzy system (ETS) algorithm based on the real-time experimental data. We will attack this problem statement from two different angles. Firstly, from the point-of-view of online data-driven modeling (system identification), that is, to describe the challenging dynamic behaviors of a hexacopter UAV in the face of severe ground effects and secondly from the perspective of a biomimetic adaptive flight control system in aerial robotics in the form of preliminary computer simulations.

The rest of this chapter is organized as follows. While Section 1.2 discusses nonlinear aerodynamic models for a typical multirotor aircraft, Section 1.3 depicts the concept of biomimetic learning systems applied in our system. Section 1.4 describes the hardware configuration of our system. Section 1.5 highlights the efficacy of the ETS system to capture the dynamics of a hexacopter UAV under severe ground effects, i.e., to perform an online system identification task. Moreover, Section 1.6 delineates our initial study regarding the performance of the ETS controller to regulate the vertical dynamics of a hexacopter vehicle, while Section 1.7 concludes this chapter.

1.2 Nonlinear aerodynamic modeling of a multirotor aircraft

represent the angular velocities of the drone.

1.2.1 Rotor thrust model

We employ the Glauert induced flow model in (velocities (see Fig. 1.2).

Figure 1.2 Glauert's assumed aerodynamic flow model ( Glauert, 1926). Please note that Vt and Vn denote the tangential and the normal velocities while V∞ highlights the free stream velocity.

within a radius or azimuth, we can use the blade element theory to derive the mathematical expression for the thrust T , and the advanced ratio μ (see (Seddon and Newman, 2011), (Glauert, 1926) for a complete mathematical derivation of the rotor thrust model) as follows:

(1.1)

where Ω is the rotational speed of the blade, ρ is the density of air, a . Assuming we employ N ), the total thrust is given by the summation of each single thrust component.

Meanwhile, the mean induced velocity can be expressed using the Glauert model as follows (Glauert, 1926):

(1.2)

is the Glauert hypothetical velocity in forward flight and A is the area of the rotor disc. The flow pattern can be described using two conditions, namely, (i) hovering flight, where , the same equation for the predicted elliptically loaded wings, which can be regarded as a force distribution on wings with an elliptical form pattern in the direction of an aerofoil to achieve the least induced drag.

Rearranging (1.2), we finally arrive at:

(1.3)

, the two nonlinear equations in .

1.2.2 Rotor torque calculation

The yawing torque N with respect to the angular velocity Ω as follows:

(1.4)

, which is related to the power required to deal with the drag profile of the blades, which can be mathematically expressed as follows:

(1.5)

(1.6)

is a correction factor due to the tip loss effects, nonuniform induced velocity, etc.; κ is the climbing speed of the rotor. Consequently, the resulting total power due to (1.4)–(1.6) can be expressed as follows:

In this study, we neglect the aerodynamic effects of the vortex ring in rapid descent.

1.2.3 Rigid body dynamics

:

(1.7)

where m is the velocity of the vehicle, where I presents the inertial (Earth) frame of reference. Using the product rule, the equation in (1.7) can be expressed as follows:

(1.8)

presents the position of the drone

Under conventional mass distribution assumption, one can employ Newton's second law of motion to derive the general mathematical relationship between forces and moments in 3D space. Considering the relation between the body axis system B and the inertial (earth) axis system I, we finally arrive at:

(1.9)

is the angular velocity of the system. Eq. (1.8) is clearly vectorial and hence it involves changes in both magnitude and direction.

Considering (1.9), the derivation of the rigid body translational dynamics can be obtained in (Nelson, 1998) and also discussed in (Santoso et al., 2019a):

(1.10)

where m denotes the rotational rates. From (1.10), it is apparent that the translational dynamics of an aircraft can be described by those three ordinary differential equations, which are coupled and nonlinear.

, the equations for the rotational motion can be obtained in a similar fashion:

(1.11)

Likewise, the relationship between the inertial (earth) frame of reference and the body axis reference transforms (1.11) into:

(1.12)

Meanwhile, the moment equations from (1.12), describing the rotational dynamics of a rigid body, which were initially derived in (Nelson, 1998) and they were also recalled in (Santoso et al., 2019a), are given as follows:

(1.13)

expresses the product of inertia.

We employ the quaternion system to store the attitudes of our drone while constantly updating them using the quaternions. This technique will remove the need to use the trigonometric functions, which would be required when integrating the Euler angle differential equations. Thus, we have the following matrix equation:

(1.14)

denotes the rate of the attitude of the aircraft.

Meanwhile, the rotational matrix B , where B is the matrix of rotation given as follows:

where

1.2.4 Ground effects

When a rotorcraft vehicle flies at sufficiently low altitude (i.e., less than three times of the radius of the blades), ground effects become significant (Seddon and Newman, 2011). The reason is because the continuity of the airflow pattern is altered or disturbed by the ground obstruction. This leads to decreased downwash velocity, induced by the rotor, triggering a cushioning effect. As a result, the vertical lift will increase given the same control input and power setting. Ground effect introduces substantial nonlinearity into the system. The adverse cushioning effects can be regarded as continuous stochastic disturbances during flight. Accordingly, the relationship between thrust and control input can be altered by up to 50%, increasing the nonlinearity of the system dynamics (Garratt and Anavatti, 2012) (see Fig. 1.3). Please also refer to (Santoso et al., 2019b) for an application of fuzzy system identifier to model the ground effects during a low altitude hovering flight of an unmanned helicopter.

Figure 1.3 Airflow patterns: (a) Out of Ground effect (OGE) occurs when an aircraft flies at a reasonably high altitude, (b) In Ground Effect (IGE) when an aircraft flies at a very low altitude (very near) to the ground. This phenomenon is also experienced by a rotorcraft vehicle.

1.3 The architecture of the ETS learning system: a biomimetic identification and control system

1.3.1 The human way of learning

We all constantly learn through our sensory systems and update our knowledge accordingly. Our sensory systems (sight, smell, taste, sound, touch) gather all information before passing it to our central nervous system (comprised of the brain and the spinal cord), whose main role is to convert the selected sensory inputs into information that is transmitted to the rest of our body (e.g., through motor neurons). Our level of attention to our sensory system plays an important role in absorbing and processing new information.

The information is filtered, regulated, and integrated into our short-term memory in the prefrontal cortex area (see Fig. 1.4). Only those memories, which are considered worthy of our conscious attention will be stored in the long-term period. Although the hippocampus, which is the most important area of the brain, responsible for maintaining our long-term memory, the information is also encoded and distributed in various places in the cortex.

Figure 1.4 An illustration of the human memory system. This public domain image is due to the National Institute for Aging, National Institutes of Health, The United States Department of Health and Human Services.

Our short-term (working) memory links and comprehends prior knowledge and previous experience while establishing meaningful connections with new information; our long-term memory keeps ideas, thoughts, feelings, etc., before connecting it to the working memory to make sense of it, so that we can recognize a certain pattern, establish a relationship among information, and consider new knowledge. On a daily basis, our brain establishes connections between our short-term and long-term memories so that our ideas can be expanded. In fact, our brain works around the clock, irrespective of the level of our consciousness. The processes of combining and consolidating daily events occur during sleep. Interested reader may refer to (Greenleaf and Wells-Papanek, 2005) to gain more insight.

In the sense of bio-inspired computing, this phenomenon can be elaborated as follows. First, we would like to introduce a certain index, called ‘the level of worthiness,’ which gives an indication about the importance of a certain piece of information. This index will be used as a benchmark on whether or not new information should be kept and how long that new knowledge should be retained. New important knowledge will be assigned a higher worthiness index while less relevant information will be assigned a lower value of worthiness. The higher the index, the longer the information tends to be kept in the memory. Meanwhile, insignificant information will be discarded immediately.

As time progresses, the existing old knowledge may be becoming less relevant, and as such the index will be decreasing over time. Meanwhile, the existing less important knowledge may become progressively more important in the future, and hence its index of worthiness may be steadily increasing. Thus, every bit of information will constantly compete to retain its place in our brain based on this criterion, indicating an ongoing optimization process in our cognitive system.

As the process constantly evolves, only the most important and relevant knowledge will be kept, recalled, and updated. The less relevant knowledge will be slowly forgotten as our old memory fades away. This principle is also highly relevant to the concept of natural evolution, where only the fittest and the strongest individuals will eventually survive – the stronger individuals constantly replace their weaker counterparts. Likewise, as part of its optimization process, the ETS system also filters information based on its effectiveness. Eventually, only information that is relevant and useful for the system will be stored, constantly used, and updated.

1.3.2 The evolutionary Takagi–Sugeno fuzzy systems

As a part of our framework, we recall the general block diagram of fuzzy systems as given in Fig. 1.5. There are at least three main processes in the system, namely, the fuzzification procedure, the inference engine process, and the defuzzification task. While fuzzification is the process of converting crisp input values into fuzzy values, that is, to determine the level of fuzziness of the input variables as reflected by the degree of the fuzzy membership functions, the defuzzification process is the opposite process, that is, a set of procedures to compute the real values (crisp outputs) from the overall fuzzy sets. Thus, it is now possible to employ an inference system in the form of "If-Then" fuzzy linguistic rules as the main source of knowledge (Zhang, 2010).

Figure 1.5 General block diagram of fuzzy systems, showing the three major steps, namely, the fuzzification, the inference engine (rule-based system), and the defuzzification tasks ( Santoso et al., 2017).

While there are at least two major fuzzy structures, namely, the Mamdani and the TS fuzzy systems; in this chapter, we will focus on the latter. We will employ a class of the evolving TS fuzzy systems, known as the evolutionary TS fuzzy systems (ETSs) as in (Angelov and Filev, 2004), for identification and control in aerial robotics. Mimicking the human way of learning, the term evolutionary refers to the online optimization process of both the structural and the parametric models of the acquired fuzzy system.

As we learn every day, we are continuously bombarded by millions of pieces of new information. To select only the necessary and appropriate information, our brain acts as a filter. Knowledge that is relevant will be kept and constantly updated for the purpose of future use. Irrelevant knowledge will be kept for short-term only or else will be immediately removed. Hence, as discussed, the survival of the most relevant knowledge mimics the nature of the optimization process, that is, only the most relevant and useful knowledge will eventually survive.

The entire learning process in the ETS algorithm can be performed without human intervention. As new data come in, the algorithm constructs knowledge (adding new knowledge and updating old rules while removing unnecessary [unused] knowledge). In terms of the fuzzy structure, we employ a TS type fuzzy system (Takagi and Sugeno, 1985) due to its suitability and efficiency for online computation, in addition to having a compact structure. The learning process can start either from scratch or from a certain defined rule. We employ Gaussian-like fuzzy sets (Angelov and Filev, 2004):

(1.15)

where the spread of the antecedent and the zone of the influence of the ipresents the focal point of the ith rule antecedent, and R indicates the number of fuzzy rules. The effectiveness of each fuzzy rule is given by the firing strength, representing the degree to which a certain rule matches the input signal.

The final output of our TS fuzzy model can be computed as follows:

(1.16)

indicates the normalized firing strength of the ihighlights the output of the idenotes the weight of the i, and the spread r of the consequents.

Leveraging the concept of subtractive clustering, also known as mountain clustering (highlights the potential of the kpresents the radius of the neighborhood given by a positive constant r.

. This way, our fuzzy rules can be constantly modified or updated based on the potential of a new data point relative to the potential of the existing focal points. The system adds a new rule to satisfy the condition in (1.17), that is, IF AND the new data point closer to the old center, THEN , see: (Angelov and Filev, 2004)

(1.17)

indicates the shortest of the distance.

Subsequently, the algorithm performs recursive calculation of a new center and the parameters of the consequent functions by employing the recursive least square (RLS) technique (1.18) and (1.19). Meanwhile, the local parameters are computed using the weighted RLS, see: (Angelov and Filev, 2004)

(1.18)

where

(1.19)

, where Ω is a constant.

The last step is to determine the output of the system for the subsequent time step by means of the following online prediction in (1.20), (1.21), and (1.22) (see: (Angelov and Filev, 2004)):

(1.20)

is calculated using the following Kalman filter procedure:

(1.21)

while

(1.22)

.

Employing the cluster potential, instead of using distance, the system is more informative and more compact (Angelov and Filev, 2004). This is because when making a decision to change the parameters associated to a rule or to change the rule base structure, the spatial information and its history are fully taken into account. Interested readers are recommended to refer to (Angelov and Filev, 2004) and (Santoso et al., 2020) for a theoretical reference and a typical practical application, respectively.

1.4 Hardware configuration

As an experimental platform, we used the Tarot 680-Pro hexacopter aircraft, which was built from a kit as shown in Fig. 1.1. The aircraft has a maximum take-off weight of 10 kg and a maximum flight duration of around 15 minutes. We executed our control algorithm on an onboard microprocessor which was interfaced to a Pixhawk 2 Flight Control Unit (FCU). The Pixhawk generates the low level signals to all six rotors based on the pitch, roll, yaw, and thrust commands sent from the onboard microprocessor.

When it comes to the onboard microprocessors, we employed the Intel Edison system due to its compact size, low power consumption, and compatibility with the PixHawk2 FCU. The Intel Edison is a dual-core Intel Atom 500 MHz x86 microprocessor with 1 GB of DRR400 memory and 4GB of EMMC onboard memory, equipped with WiFi. We interfaced our Intel Edison to the Pixhawk 2 FCU using the MAVLink protocol. The system communicates via an asynchronous serial connection at 921,600 Baud under the MAVROS protocol, which is an extendable communication node for the Robot Operating System (ROS) with a proxy for ground station control (see Fig. 1.6).

Figure 1.6 The architecture of our hardware system, showing the communication protocols, used to connect the avionics components. While GCS stands for ground control station, FCU indicates flight control unit.

Allowing the ground station to send and receive the state and control data from the FCU, we employed ROSBAG, where the published ROS TOPICS was stored. Data transfer was performed via a WiFi network, linking the ground station computer with the aircraft. The ground station utilized the Ubilinux operating system, ROS, and MAVROS. Via the SBUS protocol, the radio control receiver communicated to the PixHawk processor at 100 kBaud. The system could handle up to 18 servo channels, encoded with 11 bits/channel. The system also employed the QGroundControl software, supported by a user-friendly graphical user interface, to connect with the FCU firmware.

1.5 ETS-based multi-input, multi-output data-driven modeling: nonlinear system identification

Originated by Zadeh in 1956, system identification is known as a process of deriving a mathematical model of a particular system from a set of input–output data taken from measurements. Considering the importance of online system identification in many engineering fields, we will first investigate the efficacy of the ETS algorithm to predict the challenging dynamics of low altitude hovering of a hexacopter unmanned aerial vehicle.

Mimicking the human way of learning, in this section, we discuss the ability of the ETS algorithm to model the challenging nonlinear aerodynamics of a hexacopter aircraft under severe ground effects. We will derive the multi-input, multi-output (MIMO) fuzzy model of the drone, describing the relationship of the attitude (inner) loop among the control signals of the roll, the pitch, and the yaw loops with respect to the rates of the roll, pitch, and yaw angles.

We employed a black box identification technique and as such we relied on a set of experimental I/O data to simultaneously derive the MIMO nonlinear dynamics of our hexacopter aircraft in its three inner control loops. To do so, we first manually controlled the aircraft by an experienced human pilot, holding a hand-held transmitter. The flight data were recorded by the onboard computer. We varied the input signal from low frequencies (less than 1 Hz) to high counterparts in order to capture the overall dynamics of our system.

Referring to the general block diagram of system identification (, which will be used as an important learning parameter to constantly update our fuzzy model. As seen in Fig. 1.8a, our hexacopter was deliberately flown at a reasonably low altitude (⩽40 cm), making the ground effects significant. This significantly alters the dynamics of the systems when climbing and descending while introducing more uncertainties to the system. From Fig. 1.8, it is clear that our hexacopter performed random motions in 3D space as expected in system identification in order to capture the whole dynamics of the system.

Figure 1.7 , ∀ k  ⩾ 0 as a means of updating our identified fuzzy model ( Santoso et al., 2019a).

Figure 1.8 Multi-input, multi-output data-driven modeling (online system identification) for the altitude and attitude dynamics of our Tarot hexacopter unmanned aerial vehicle. (a) 3D flight trajectory of the drone. The attitude dynamics of the system, during the identification process, consisting of the (b) Roll angle (deg), (c) Pitch angle (deg), and (d) Yaw angle (deg).

Meanwhile, the input control signals, regulating the attitudes (the roll, the pitch, and the yaw angles) of our hexacopter are depicted in Fig. 1.9. Those three variables will become the input variables in our online system identification process. Given the input control variables, the rotational velocities of our hexacopter aircraft are given in Fig. 1.10. It is clear that the ETS system can predict the angular velocities of our hexacopter drone at a reasonably good accuracy. The number of fuzzy rules, as seen in Fig. 1.10d, evolved from 1 to about 11. Given the complexity of our UAV system, this figure is completely reasonable. Moreover, in Fig. 1.11, we show the adaptation process of some consequent parameters in our TS fuzzy systems.

Figure 1.9 Control signals applied during the flight test to identify the model of the system. (a) The roll loop control signal, (b) The pitch loop control signal, (c) The yaw loop control signal.

Figure 1.10 Predicted vs. actual values of the (a) Roll rate, (b) Pitch rate, (c) Yaw rate, in addition to (c) the cluster potentials of the system, and (d) the number of fuzzy rules applied in the system as the fuzzy system evolved.

Figure 1.11 The evolving process of the consequent parameters of our TS fuzzy system identifier as given by θ i  = [ θ 0 θ 1 θ 2 θ 3 θ 4 ...] ∀ i . The fuzzy system constantly adjusts its parameters in an attempt to learn the dynamics of a hovering hexacopter drone to minimize the error signal.

As new data came in, our fuzzy system evolved over the time in terms of its structure as indicated by the number of fuzzy rules and its parameters in Fig. 1.11. Since we flew our drone at reasonably low altitude (<40 cm) from the surface, ground effect was inevitably severe. Adding this into account, our fuzzy model has incorporated large uncertainties. Since the airflow pattern was altered, the drone experienced increased lift and reduced aerodynamic drag. In the sense of our hexacopter, this enabled the system to achieve extra power during hovering. Thus, given the complexity of the process, it may not be practical to accurately capture this challenging phenomenon using traditional modeling techniques (i.e. linear system identification).

By means of an evolving TS fuzzy system, we will demonstrate our technical contribution to model the dynamics of a nonlinear uncertain dynamical system in the form of a low altitude hovering of a hexacopter aerial robot, faced by large uncertainties (e.g. due to significant ground effects). As discussed, ground effects can substantially alter the lift characteristics of the system by 50%. This will clearly introduce large uncertainties to the closed loop control system.

In what follows, we will also conduct a preliminary study to investigate the efficacy of the ETS algorithm to regulate the challenging dynamics of our Tarot hexacopter aerial vehicle in its vertical control loop.

1.6 The evolutionary Takagi–Sugeno flight control system: a preliminary study

Given the duality between system identification and control, we are also interested in studying the efficacy of the ETS algorithm in regulating (stabilizing) the challenging dynamics of our Tarot hexacopter drone. Accordingly, we conduct computer simulations to highlight the effectiveness of the ETS algorithm in the vertical loop of our hexacopter drone. This investigation serves as our preliminary result in this topic.

, where T denotes the sampling period and k indicates the discrete time duration applied in our autopilot system. In the sense of feedback control system, the role of the ETS autopilot is to minimize the tracking error so that the actual controlled variables can be stabilized (the steady state values will approach the desired values) within a finite amount of time.

(see , a new fuzzy rule will be added to the system. This simulation demonstrates the learning capability of the ETS system to accommodate the uncertain flight dynamics of our hexacopter. As can be seen in our preliminary study, the closed loop ETS control system performs reasonably well in the vertical loop, as indicated by its reasonably small tracking error. The learning process of the controller as evidenced by the cluster potential and the modification of the fuzzy rules can be highlighted in Fig. 1.12b and c.

Figure 1.12 (a) Computer simulation of the sine wave trajectory tracking of the ETS autopilot in the vertical loop. (b) Cluster potential with respect to its upper bound P max and its lower bound P min . (c) The number of rule replacements in time as the system evolved.

1.7 Conclusion

Facilitating learning-from-scratch in aerial robotics, we have demonstrated the efficacy of the ETS system to identify the challenging dynamics of a low altitude hovering of our Tarot hexacopter drone under severe ground effects. The prediction error is reasonably small despite the uncertain dynamics of the system.

When it comes to our preliminary study on the efficacy of the ETS autopilot system, it is clear that the ETS autopilot can perform reasonably well to achieve a stable and responsive system within a reasonably short period of time. This approach clearly addresses the drawback of model-based control systems while extending the benefits of knowledge-based fuzzy systems. Since high-fidelity mathematical models, required by model-based control systems, are not always available in practice, intelligent control systems can provide more realistic solutions due to their ability to efficiently learn as in the case of the ETS system.

Given the flexibility of the ETS algorithm to learn the dynamics of nonlinear uncertain systems while tracking their parameter variations, the ETS autopilot system can offer a high-level of robustness in the face of uncertainties. Addressing the limitation of traditional (gradient-based) optimization techniques, requiring the presence of continuous and differentiable signals, the learning outcome of the ETS system is more powerful and practical since it can deal with nondifferentiable, complex, and noisy signals.

Overall, the acquired fuzzy model is relatively simple and practical – in both system identification and control tasks. The control system only employs less than five membership functions in each control loop, making it very beneficial for real-time implementation, especially for small robotic platforms, where the systems are often faced by limited computational capability. The efficacy of the ETS control system is further enhanced by the nature of fuzzy systems, which are also more intuitive compared to traditional model-based control approaches, making them more appropriate for average drone operators.

For future work, we will conduct a more rigorous comparative study regarding the possibility of implementing the ETS autopilot in real-time. Given the promising outcomes in our preliminary study, we are planning to implement the ETS autopilot in all control loops of our Tarot hexacopter and further investigate its efficacy in real-time flight tests.

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