Adaptive control for uncrewed aerial vehicles based on communication information optimization in complex environments

The attitude control for the UAV

In contrast to various other UAV types, quadrotor UAVs boast a host of advantages, notably their compact structure, operational versatility, and a diminished threat to both nearby personnel and equipment. However, they also exhibit distinctive traits such as underactuation, strong coupling, nonlinearity, and susceptibility to external disturbances. As a result, the investigation into control algorithms for quadrotor UAVs has garnered substantial attention from scholars worldwide. Commencing with the classical PID control method, researchers have introduced a spectrum of advanced control algorithms, each aimed at enhancing system stability and robustness. In the initial phases of quadrotor UAV research, the PID controller devised by Salih & Moghavvemi (2010) was pivotal in achieving control over positional attitude. An appealing feature of this approach is its freedom from necessitating the development of a dynamic model or precise UAV parameters. To enhance control efficacy, PID is frequently amalgamated and refined in conjunction with advanced control algorithms. Efe (2011) innovatively designed a PID controller and harnessed neural networks to mitigate perturbations, resulting in stable control over UAV position and attitude. Chowdhary, Wu & Cutler (2012) introduced an adaptive control algorithm with online learning capabilities, which obviates the need for laborious PID parameter adjustments. This approach capitalizes on historical and real-time data to expedite system error convergence without continuous excitation. To ascertain the tracking capabilities of quadrotor UAVs under significant perturbations, Das, Lewis & Subbarao (2009) devised a backstepping controller augmented with an integral term. Experimental findings substantiate the controller’s capacity to eliminate steady-state errors and bolster overall robustness. Furthermore, Mohd-Basri, Husain & Danapalasingam (2015) employed a radial basis function to estimate uncertain perturbations and designed an adaptive backstepping controller capable of robust performance in the presence of unknown disturbances. Du, Zhu & Wen (2017) employed the backstepping technique for UAV formation control, resolving the finite-time convergence of error states to the origin through the application of chi-square system theory and Lyapunov stability theory. Ma, Qin & Salsbury (2014) conducted a comprehensive analysis and design of the flight controller, leveraging Model Predictive Control (MPC) to suppress active interference in attitude control. Alexis et al. (2016) devised robust MPC controllers for two distinct rotor UAV architectures, optimizing the performance metric while integrating model dynamics and input state constraints, thereby minimizing deviations in the presence of severe disturbances. Model Predictive Control, in particular, finds application in UAV trajectory planning. Sun et al. (2018) proposed an MPC-based trajectory planning method for effective obstacle avoidance when suspending a payload from a quadcopter UAV. They formulated a cost function considering load swing angle and obstacle-UAV distance to generate an optimal trajectory that satisfies the prescribed requirements.

Deep learning based UAV optimization research

Guo et al. (2019) employed the DQN algorithm for path planning of UAV lift-off platforms, aiming to maximize data transfer rates. However, this algorithm is solely applicable to tasks with discrete action spaces and is plagued by the issue of overvaluing the value function, which can skew the learning of path planning strategies by intelligent agents. In response, Wang et al. (2019) harnessed the Double DQN algorithm (Wang et al., 2019) to optimize the flight trajectory of UAV platforms, with the objective of maximizing the downlink rate while ensuring coverage of all ground-based users. The Double DQN algorithm mitigates the problem of overestimation inherent in the DQN value function, although it still falls short in its applicability to tasks with continuous action spaces. In contrast, Liu et al. (2015) leveraged the DDPG algorithm to successfully implement deep reinforcement learning in continuous action space for path planning tasks.

Furthermore, as deep learning continues to exert a profound influence on research in the field, researchers have increasingly optimized UAV image data for surveillance and target studies. UAV aerial images are predominantly available in the form of visible light and infrared imagery, yet there remains a scarcity of public datasets for visible light, and infrared datasets are even rarer. Notable among the visible light UAV image datasets are VisDrone (Ullah et al., 2019) and UAVDT (Hourani, Kandeepan & Lardner, 2014). Given the distinctive characteristics of target clustering within UAV images, Yi, Wang & Meng (2013) devised a multi-stage cluster detection network, ClusDet, building upon the R-CNN enhancement algorithm. ClusDet leverages region clustering, slice detection, and scale adaptation to enhance the operational speed and the detection rate of small targets within high-resolution UAV imagery. Duan et al. (2019) introduced the CenterNet approach, which conceptualizes positioning as a task of center point detection and its offset. It employs predicted foci for regression to extract the actual position information from the offset parameters of the center regression. This method markedly bolsters the detection rate of small targets, although it does introduce higher resolution output, thereby affecting inference latency.

From the preceding research, a notable gap emerges in the focus on UAV control optimization. While existing studies predominantly emphasize attitude optimization by enhancing classical controllers, there is a distinct lack of attention to optimizing other critical facets of UAV functionality, including path planning and target detection. Deep learning techniques, renowned for their feature extraction capabilities from unknown data, play a pivotal role in addressing this gap. This study strategically addresses the underexplored realm of UAV parameter optimization and attitude control. By leveraging deep learning methodologies, we not only achieve optimal position control but also elevate UAV control to its zenith by introducing additional information. This highlights a crucial area of consideration and underscores the need for a comprehensive exploration of various dimensions in UAV optimization research.

PID control

The proportional-integral-derivative (PID) controller represents a prevalent feedback control mechanism extensively applied in the field of control engineering. Its primary objective is to adjust the system’s output to closely match a desired reference value. The PID controller comprises three integral components: the proportional (P), integral (I), and differential (D) parts, each with distinct roles in managing the error’s magnitude, its accumulation, and the rate of change, respectively (Houthooft et al., 2017). These components are computed as demonstrated in Eqs. (1) through (3):

(1)${\displaystyle \mathrm{P}\left(\mathrm{t}\right)={\mathrm{K}}_{\mathrm{p}}\cdot \mathrm{e}\left(\mathrm{t}\right)}$ (2)${\displaystyle \mathrm{I}\left(\mathrm{t}\right)={\mathrm{K}}_{\mathrm{i}}\cdot {\int }_0^{\mathrm{t}}\mathrm{e}\left(\tau \right)\mathrm{d}\tau }$ (3)${\displaystyle \mathrm{D}\left(\mathrm{t}\right)={\mathrm{K}}_{\mathrm{d}}\cdot \frac{\mathrm{de}\left(\mathrm{t}\right)}{\mathrm{dt}}}$

where P(t) is the output of the proportional part. K_p is the proportional gain, and K_i is the integral gain, and K_d is the differential gain, and these three gains are used to regulate the corresponding output section respectively. e(t) is the error at the current moment, usually defined as the difference between the desired value and the actual value. $\mathrm{e}\left(\mathrm{t}\right)=\mathrm{r}\left(\mathrm{t}\right)-\mathrm{y}\left(\mathrm{t}\right),{\int }_0^{\mathrm{t}}\mathrm{e}\left(\tau \right)\mathrm{d}\tau$ is the integral of the error, and $\frac{\mathrm{de}\left(\mathrm{t}\right)}{\mathrm{dt}}$ denotes the rate of change of the error over time. PID control can be effectively employed to stabilize the attitude of a vehicle, encompassing pitch, roll, and yaw. By continuously assessing the disparity between the vehicle’s attitude angle and the desired reference, the PID controller can finely modulate the control of rudder surfaces or motor outputs, ensuring that the vehicle maintains the desired attitude. This process involves the optimal integration of error by considering various types of errors over different time intervals. These preliminary control algorithms prove highly rational and essential for real-time UAV control, establishing a solid foundation for the precise management of UAV flight dynamics.

Bi-LSTM networks

Long short-term memory (LSTM) stands as a variant of recurrent neural networks (RNNs) explicitly engineered to address the longstanding challenge of managing long-term dependencies in RNNs. LSTM excels particularly in the domain of handling sequential data. Distinguished from conventional RNNs, the LSTM unit primarily optimizes data for long-term control by means of the “forgetting the gate” mechanism, the implementation of which is delineated in Eq. (4) (Johnson & Moradi, 2005; Shi, Wang & Zhao, 2022): (4)${\displaystyle {\mathrm{f}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{f}}\cdot \left[{\mathrm{h}}_{\mathrm{t}-1},{\mathrm{x}}_{\mathrm{t}}\right]+{\mathrm{b}}_{\mathrm{f}}\right)}$

where W_f is the weight matrix. h_t−1 is the hidden state of the previous time step. x_t is the input of the current time step. The hidden state can then be calculated by Eq. (5), (5)${\displaystyle {\mathrm{h}}_{\mathrm{t}}={\mathrm{o}}_{\mathrm{t}}\cdot tanh\left({\mathrm{C}}_{\mathrm{t}}\right)}$

where Ct is the state of the cell at t. It is related to the computation of the forgetting gate, which can be calculated by Eq. (6): (6)${\displaystyle {\mathrm{C}}_{\mathrm{t}}={\mathrm{f}}_{\mathrm{t}}\cdot {\mathrm{C}}_{\mathrm{t}-1}+{\mathrm{i}}_{\mathrm{t}}\cdot tanh\left({\mathrm{W}}_{\mathrm{c}}\cdot \left[{\mathrm{h}}_{\mathrm{t}-1},{\mathrm{x}}_{\mathrm{t}}\right]+{\mathrm{b}}_{\mathrm{c}}\right)}$

After completing the above calculation of the relevant state quantities, the output of each cell can be obtained: (7)${\displaystyle {\mathrm{o}}_{\mathrm{t}}=\sigma \left({\mathrm{W}}_{\mathrm{o}}\cdot \left[{\mathrm{h}}_{\mathrm{t}-1},{\mathrm{x}}_{\mathrm{t}}\right]+{\mathrm{b}}_{\mathrm{o}}\right)}$

The comprehensive overview of the LSTM standalone cell is depicted in Fig. 1, where we also introduce and elucidate the BI-LSTM method. Recognizing the significance of integrating information from different time periods into the position update process during position optimization, this article advocates the utilization of the BI-LSTM method for in-depth analysis.

BI-LSTM represents an extension of LSTM that enhances the model’s ability to consider not only historical data but also anticipate future information when handling sequential data. In the standard LSTM, input sequence information is processed from left to right, while BI-LSTM processes both left-to-right and right-to-left data. This approach equips the model to grasp the entire sequence comprehensively, enabling it to assimilate not only past data but also make predictions regarding future information. The computational procedures for BI-LSTM are elucidated in Eqs. (8) through (9):

(8)${\displaystyle \overrightarrow{{\mathrm{h}}_{\mathrm{t}}}=\overrightarrow{\text{LSTM}}\left({\mathrm{x}}_{\mathrm{t}},{\mathrm{h}}_{\mathrm{t}-1}\right)=\sigma \left(\mathrm{W}\cdot \left[{\mathrm{h}}_{\mathrm{t}-1},{\mathrm{x}}_{\mathrm{t}}\right]+\mathrm{b}\right)}$ (9)${\displaystyle \stackrel{⃖}{{\mathrm{h}}_{\mathrm{t}}}=\stackrel{⃖}{\text{LSTM}}\left({\mathrm{x}}_{\mathrm{t}},\stackrel{⃖}{{\mathrm{h}}_{\mathrm{t}+1}}\right)=\sigma \left(\mathrm{W}\cdot \left[\stackrel{⃖}{{\mathrm{h}}_{\mathrm{t}+1}},{\mathrm{x}}_{\mathrm{t}}\right]+\mathrm{b}\right)}$

where h_t is the time step t of the hidden state, and $\overrightarrow{{\mathrm{h}}_{\mathrm{t}}}$ is the output of forward LSTM, and $\stackrel{⃖}{{\mathrm{h}}_{\mathrm{t}}}$ is the output of the inverse LSTM,the two merged outputs in the sequence process is shown in Fig. 1 (Shi, Wang & Zhao, 2022).

Attention mechanism based network as well as parameter control

To facilitate a more comprehensive analysis of the correlation within positional data and to achieve optimal positional control, this study enhances the attention mechanism within the framework of the Bi-LSTM network. The attention mechanism is a fundamental concept in deep learning that empowers a neural network model to assign varying attention weights to distinct segments of input when processing sequential data. This refinement enables more effective processing of critical information. Typically, attention mechanism consists of three main components: query (Q), key (K), and value (V) (Lei et al., 2023). Q is a vector utilized to pinpoint the location or the information that requires attention, serving as the foundation for calculating the attention weights, typically derived from the preceding layer of the model. K represents the characteristics of the source data, while V corresponds to the value associated with the key. The operational flow of the attention mechanism is elucidated in Fig. 2 (Lei et al., 2023).

Attention mechanism is mainly to calculate the attention score, which is shown in Eq. (10): (10)${\displaystyle \text{Attention Scores}=Q\ast KT}$ where Q is the query vector and K is the transpose of the key vector. After completing the establishment of the attention mechanism, the overall network model established is presented as follows:

Within the constructed model, the initial input consists of processed UAV position data, which subsequently undergoes processing via a two-layer BI-LSTM network in Fig. 3. This phase entails the data’s feature extraction through truth-value comparisons. Ultimately, the final step integrates the Attention mechanism to yield the optimized position output.

Datasets

The wireless signal strength of uncrewed aerial vehicles (UAVs) is contingent upon a multitude of factors, including transmission power (Wang, Huang & Zhu, 2016), path loss (Jang & Lee, 2003), antenna gain (Phillips, Sicker & Grunwald, 2012), and reception sensitivity (Klein & Degnan, 1974). Within this context, transmission power determines the power level of the signal dispatched by the UAV, path loss quantifies the reduction in signal power due to distance and environmental influences during signal propagation, antenna gain characterizes the performance of a wireless communication antenna concerning an ideal point source antenna, and reception sensitivity denotes the minimum signal power level that the receiving device can detect and decode.

This article computes the signal strength by taking these four factors into account, as demonstrated in Eq. (11) (Liu et al., 2015). (11)${\displaystyle \text{Received Power}=\text{Transmit Power-Path Loss +Antenna Gain-Free Space Loss}.}$ In this equation Path Loss denotes the path loss, Antenna Gain denotes the antenna gain, and Free Space Loss can be calculated by the free space propagation equation: (12)${\displaystyle FSL\left(dB\right)=20\cdot lg\left(\frac{4\pi d}{\lambda }\right)}$

where FSL denotes free space loss, d is distance and λ is wavelength, this equation considers the relationship between wavelength and distance of the propagating signal.

In the current research on UAV attitudes, the data primarily originates from video image data captured during target monitoring, as exemplified by datasets such as the UAV123 Dataset (Zhang et al., 2019) and VisDrone Dataset (Mueller, Smith & Ghanem, 2016). Nonetheless, these datasets may not fully suffice to meet the study’s requirements. Additionally, when examining communication relationships, publicly available datasets may also fall short of the requirements. To address this, this study draws inspiration from Han, Hu & Zhou (2019), which employed an optical verification system to establish a relevant data model. The data collection primarily centers on three types of attitude information of the UAV, namely yaw, pitch, and roll, while also recording communication strength data throughout the entire course of UAV motion. This data serves as the foundation for subsequent model training. In the initial phase of test validation, the PID method, as discussed in Section ‘PID control’, is employed to realize UAV control and collect pertinent data. Subsequently, in offline simulations, neural network methods are employed to validate attitude and perform data analysis.

Experiment details

To evaluate the proposed model, the index for the method comparison in this article including the RMSE, MAE, MdAE, MdAPE, which is shown as follows (Han, Hu & Zhou, 2019).

(13)${\displaystyle \text{RMSE}=\sqrt{\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}{\left({\text{Actual}}_{\mathrm{i}}-{\text{Predicted}}_{\mathrm{i}}\right)}^2}}$ (14)${\displaystyle \mathrm{MAE}=\frac{1}{\mathrm{n}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\mid {\text{Actual}}_{\mathrm{i}}-{\text{Predicted}}_{\mathrm{i}}\mid }$ (15)${\displaystyle \text{MdAE}=\text{median}\left(\mid {\text{Actual}}_{\mathrm{i}}-{\text{Predicted}}_{\mathrm{i}}\mid \right).}$ In the above equations, median denotes the median, Actuali denotes the first i observation, P_i denotes the first observed value, In addition to these three indexes, we also evaluated the model using the Median Absolute Percentage Error (MdAPE), which is calculated as follows. (16)${\displaystyle \text{MdAPE}=\text{median}\left(\frac{\mid {\text{Actual}}_{\mathrm{i}}-{\text{Predicted}}_{\mathrm{i}}\mid }{{\text{Actual}}_{\mathrm{i}}}\times 100\right).}$

Based on the established evaluation indexes and combined with the overall network model established in the ‘Research method’ section for model training and evaluation, the overall algorithmic is as follows:

The method comparison

Drawing from the dataset and related data that have been established, this article conducted practical tests. During the model validation process, we also engaged in a comparative analysis of various methods, using the established dataset for this purpose. The comparison encompassed several commonly used methods in the realm of UAV posture study, including PID, ADRC (Willmott & Matsuura, 2005), as well as classic machine learning methods like BPNN, SVM, and LSTM, along with more established deep learning methods such as CNN, to assess their performance and suitability. BPNN is an artificial neural network based on backpropagation algorithm, mainly used for regression tasks. Its characteristics include strong nonlinear modeling ability, suitable for fitting complex relationships, but requiring a large amount of data for training and easy overfitting. The application of SVM in regression is based on the support vector regression (SVR) model, which constructs an optimal hyperplane to fit the data. Its characteristics include effectively handling complex relationships in high-dimensional spaces, having good robustness against outliers, but may face significant computational challenges when dealing with large-scale data.

Experiment results and analysis

In this article, our primary focus centers on the assessment of three key indicators: yaw, pitch, and roll. The outcomes of our analysis are visually presented in Figs. 4–6 and are detailed in Tables 1–3.

Upon evaluating the yaw indicators, it is evident that the proposed method excels across all four indicators. Particularly noteworthy is its remarkable performance in terms of root mean square error (RMSE), which surpasses the performance of traditional machine learning methods and individual CNN feature extraction methods. This underscores the pivotal role played by the double-layer BI-LSTM in both feature extraction and model optimization. Furthermore, the favorable results for MdAEr and MdAPE underscore the comprehensive performance advantage offered by this method. Yaw, being a challenging and error-prone aspect of inertial navigation and UAV control, has yielded highly satisfactory control outcomes.

As those three indicators are very important for the control estimation, we made a fine analysis about that. In the comparison of the data pertaining to pitch and roll, as depicted in Figs. 5 and 6, it is discernible that their indicators are notably lower than those for yaw. All indicators attest to robust prediction performance. A thorough analysis of the three indicators—yaw, pitch, and roll—reveals that the employed method exhibits superior pose optimization capabilities, with lower errors compared to actual values collected by optical systems. This substantiates the method’s efficacy in optimizing pose. Among these indicators, it is apparent that yaw exhibits the largest error, primarily due to the sensor’s susceptibility to strong geomagnetic interference and substantial signal fluctuations, necessitating more comprehensive error correction. In the performance analysis of the aforementioned methods, it becomes evident that the PID method yields moderate performance across all three indicators, indicating its suitability for preliminary control during the early stages of this experiment.

Furthermore, this article incorporates the FSL information introduced at the outset of this chapter into the pose optimization process. By introducing communication information, the model’s phenotype can be somewhat enhanced. To better validate the effectiveness of this additional information, the article conducts optimization function tests on the model with and without this information, with results displayed in Fig. 7.

As Fig. 7 illustrates, the overall estimation value in this study exhibits a more pronounced improvement after the addition of communication information. Consequently, in future UAV position control, introducing more communication information will enhance the effectiveness of position optimization.

Regarding the deep model, the data input size exerts a discernible impact on its performance. In this article, subsequent to conducting comparisons of multiple methods, we also executed batch size comparison experiments for the proposed method across various datasets. The results are presented in Fig. 8.

In our experimentation involving diverse batch sizes, a comprehensive analysis was conducted across a spectrum of batch sizes, including 2, 4, 8, and up to 64, with corresponding boxplots constructed to provide a visual representation of the results. The findings, as depicted in Fig. 8, reveal a remarkable consistency in the model’s performance across the range of batch sizes, showcasing minimal deviation. This robust behavior under varying batch sizes is a noteworthy observation, highlighting the model’s stability and adaptability to different input scales. Furthermore, the ATT-Bi-LSTM model consistently outperforms alternative models, demonstrating its superior optimization performance across the entire batch size spectrum. The model’s ability to maintain high-quality results across different batch sizes underscores its reliability and efficacy, reinforcing its suitability for diverse scenarios and datasets.