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Keywords = parafoil

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29 pages, 54656 KB  
Article
Nonlinear Multibody Dynamics of a Powered Parafoil Vehicle Using Kane’s Equations: Directional Asymmetry and Dutch-Roll
by Wenying Zeng, Weiliang He, Chuang Du, Yujian Du, Mengqun Liu and Yi Feng
Aerospace 2026, 13(9), 784; https://doi.org/10.3390/aerospace13090784 - 30 Aug 2026
Viewed by 161
Abstract
Directional asymmetry and Dutch-roll are critical phenomena observed during powered parafoil vehicle (PPV) flight tests, complicating stable flight and leading to obvious lateral–directional biases in autopilot tracking. However, existing PPV models typically neglect propeller counter-torque (PCT), resulting in limited research on directional asymmetry. [...] Read more.
Directional asymmetry and Dutch-roll are critical phenomena observed during powered parafoil vehicle (PPV) flight tests, complicating stable flight and leading to obvious lateral–directional biases in autopilot tracking. However, existing PPV models typically neglect propeller counter-torque (PCT), resulting in limited research on directional asymmetry. Moreover, conventional Newton–Euler formulations require explicit treatment of internal constraint forces, complicating analytical linearization and local stability analysis. To address these issues, first, this paper develops a nonlinear 9-degree-of-freedom (9-DOF) PPV model using Kane’s equations with quasi-velocities. This multibody dynamic model provides a compact and structurally consistent basis for linearization and stability analysis. Subsequently, the mechanism analysis shows that PCT shifts the coupled roll–yaw equilibrium and is the primary physical source of the observed directional asymmetry. In addition, the Dutch-roll mode is identified as the dominant oscillatory mode governing the lateral–directional stability of the PPV. The modal analysis further indicates that increasing thrust and directional control inputs reduce the Dutch-roll damping ratio. On this basis, a damping-ratio-based flight envelope is constructed. Furthermore, numerical simulations and flight-test comparisons demonstrate that the proposed model captures the principal PPV dynamic responses. The simulation results also support the mechanism analysis of directional asymmetry and the Dutch-roll. Full article
(This article belongs to the Section Aeronautics)
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29 pages, 14085 KB  
Article
Dynamic Trajectory Planning for Autonomous Parafoil Homing Under Wind Disturbances
by Luqi Yan, Yanguo Song, Huanjin Wang, Zhiwei Shi and Yilei Song
Aerospace 2026, 13(3), 276; https://doi.org/10.3390/aerospace13030276 - 15 Mar 2026
Viewed by 775
Abstract
The parafoil is highly susceptible to deviations from its reference trajectory under wind disturbances. Given its constrained longitudinal control authority, it has limited capability to correct these deviations and regain the intended glide path. To overcome this limitation, we propose a dynamic planning [...] Read more.
The parafoil is highly susceptible to deviations from its reference trajectory under wind disturbances. Given its constrained longitudinal control authority, it has limited capability to correct these deviations and regain the intended glide path. To overcome this limitation, we propose a dynamic planning framework based on a layered homing strategy. The airdrop mission trajectory is initially designed as a traditional multi-segment path. To approximate non-uniform glide characteristics under wind disturbances, this planning problem incorporates a predicted wind model as an external input. Node parameters of the segmented trajectory are then solved using an improved grey wolf optimizer (IGWO). By tracking this reference trajectory, the parafoil is guided into the proximity of the target. To ensure landing precision, the terminal phase is formulated and discretized using an adaptive pseudo-spectral method (APSM). The online planner computes a real-time trajectory to account for actual motion characteristics. This dynamic replanning (DRP) compensates for deviations caused by model mismatches and external disturbances. The proposed homing method is statistically verified via extensive Monte Carlo simulations under different wind conditions. Finally, the airdrop experiment is conducted to validate the DRP method. Full article
(This article belongs to the Section Aeronautics)
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17 pages, 1718 KB  
Perspective
Augmenting Offshore Wind-Farm Yield with Tethered Kites
by Karl Zammit, Luke Jurgen Briffa, Jean-Paul Mollicone and Tonio Sant
Energies 2026, 19(3), 668; https://doi.org/10.3390/en19030668 - 27 Jan 2026
Viewed by 683
Abstract
Offshore wind-farm performance remains constrained by persistent wake deficits and turbulence that compound across intra-farm, intra-cluster, and inter-cluster scales, particularly under atmospheric neutral–stable stratification. A concept is advanced whereby offshore wind-farm yield may be augmented by pairing conventional horizontal-axis wind turbines (HAWTs) with [...] Read more.
Offshore wind-farm performance remains constrained by persistent wake deficits and turbulence that compound across intra-farm, intra-cluster, and inter-cluster scales, particularly under atmospheric neutral–stable stratification. A concept is advanced whereby offshore wind-farm yield may be augmented by pairing conventional horizontal-axis wind turbines (HAWTs) with lighter-than-air parafoil systems that entrain higher-momentum air and re-energise wakes, complementing yaw/induction-based wake control and enabling higher array energy density. A concise synthesis of wake physics and associated challenges motivates opportunities for active momentum re-injection, while a review of kite technologies frames design choices for lift generation and spatial keeping. Stability and control, spanning static and dynamic behaviours, tether dynamics, and response to extreme meteorological conditions, are identified as key challenges. System-integration pathways are outlined, including alignment and mounting options relative to turbine rows and prevailing shear. A staged validation programme is proposed, combining high-fidelity numerical simulation with wave-tank testing of coupled mooring–tether dynamics and wind-tunnel experiments on scaled arrays. Evaluation metrics emphasise net energy gain, fatigue loading, availability, and Levelized Cost of Energy (LCOE). The paper concludes with research directions and recommendations to guide standards and investment, and with a quantitative assessment of the techno-economic significance of kite–HAWT integration at scale. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
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19 pages, 3823 KB  
Article
Full Process Dynamics and HIL Simulation of Precise Airdrop System
by Wen Zou, Zhanxin Cui, Jiaoyan Li and Qingbin Zhang
Electronics 2025, 14(21), 4285; https://doi.org/10.3390/electronics14214285 - 31 Oct 2025
Viewed by 1432
Abstract
Amid intensifying competition in airdrop equipment development, there is a growing demand for large-load, high-precision, maneuverable, and low-cost airdrop systems. However, Precision Aerial Delivery Systems (PADS) exhibit structural complexity and immature dynamics theory for flexible-body parachute/parafoil systems. Flight testing proves prohibitively expensive, while [...] Read more.
Amid intensifying competition in airdrop equipment development, there is a growing demand for large-load, high-precision, maneuverable, and low-cost airdrop systems. However, Precision Aerial Delivery Systems (PADS) exhibit structural complexity and immature dynamics theory for flexible-body parachute/parafoil systems. Flight testing proves prohibitively expensive, while random environmental interference hinders data consistency. To address these challenges, this paper integrates navigation control systems and actuators with dynamics models through a Hardware-in-the-Loop (HIL) simulation system for comprehensive performance evaluation. Full article
(This article belongs to the Special Issue Digital Intelligence Technology and Applications, 2nd Edition)
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22 pages, 1725 KB  
Article
Stochastic Model Predictive Control for Parafoil System via Markov-Based Multi-Scenario Optimization
by Qi Feng, Qingbin Zhang, Zhiwei Feng, Jianquan Ge, Qingquan Chen, Linhong Li and Yujiao Huang
Aerospace 2025, 12(9), 810; https://doi.org/10.3390/aerospace12090810 - 8 Sep 2025
Viewed by 1301
Abstract
As an essential technology for precision airdrop missions, parafoil systems have gained widespread adoption in military and civilian applications due to their superior glide performance and maneuverability compared to conventional parachutes. Addressing the trajectory-tracking control challenges of the parafoil system under significant wind [...] Read more.
As an essential technology for precision airdrop missions, parafoil systems have gained widespread adoption in military and civilian applications due to their superior glide performance and maneuverability compared to conventional parachutes. Addressing the trajectory-tracking control challenges of the parafoil system under significant wind disturbances, characterized by wind uncertainty and system underactuation, this paper proposes a stochastic model predictive control (SMPC) framework based on Markov-based multi-scenario optimization. Traditional deterministic model predictive control (MPC) methods often exhibit excessive conservatism due to reliance on worst-case assumptions and fail to capture the time-varying nature of real-world wind fields. To address these limitations, a high-fidelity dynamic model is developed to accurately characterize aerodynamic coupling effects, overcoming the oversimplifications of conventional three-degree-of-freedom point-mass models. Leveraging Markov state transitions, multiple wind-disturbance scenarios are dynamically generated, effectively overcoming the limitations of independent and identically distributed hypotheses in modeling realistic wind variations. A probabilistic constraint-reconstruction strategy combined with a rolling time-domain covariance update mechanism mitigates uncertainties and enables cooperative optimization of inner-loop attitude stabilization and outer-loop trajectory tracking. The simulation results demonstrate that the SMPC framework achieves superior comprehensive performance compared to deterministic MPC, evidenced by significant reductions in maximum position error, average position error, and control effort variation rate, along with a 94% tracking success rate. By balancing robustness, tracking precision, and computational efficiency, the method provides a theoretical foundation and a promising simulation-validated solution for airdrop missions. Full article
(This article belongs to the Special Issue Advances in Landing Systems Engineering)
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40 pages, 18755 KB  
Article
Autonomous Parafoil Flaring Control System for eVTOL Aircraft
by Stephen Doran, Toufik Souanef and James F. Whidborne
Aerospace 2025, 12(2), 145; https://doi.org/10.3390/aerospace12020145 - 14 Feb 2025
Cited by 1 | Viewed by 3837
Abstract
Reducing landing kinetic energy during emergency landings is critical for minimising occupant injury in eVTOL aircraft. This study presents the development of an autonomous parafoil control system for impact point targeting and flare control. A model predictive controller for a six-degree-of-freedom parafoil and [...] Read more.
Reducing landing kinetic energy during emergency landings is critical for minimising occupant injury in eVTOL aircraft. This study presents the development of an autonomous parafoil control system for impact point targeting and flare control. A model predictive controller for a six-degree-of-freedom parafoil and eVTOL payload model was designed incorporating an inner-loop flare controller for descent speed-based flare height adjustments and an outer-loop nonlinear model predictive control (MPC) to minimize line-of-sight error. Two guidance methods were explored: a standard fixed impact point approach and an adaptive method that adjusts the target point dynamically to account for horizontal travel during flaring. The standard method outperformed the uncontrolled system in 79.64% of cases, while the adaptive method achieved success in 40.73% of scenarios, with both methods maintaining vertical landing velocities below 8 m/s in all tested cases. Controller performance degraded under higher wind speeds and large control derivative variations, with the adaptive method position error attributed to flare distance estimation inaccuracies. Full article
(This article belongs to the Special Issue Challenges and Innovations in Aircraft Flight Control)
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28 pages, 16178 KB  
Article
A High-Feasibility Real-Time Trajectory-Planning Method for Parafoils Based on a Flexible Dynamic Model
by Jiaming Yu, Hao Sun, Qinglin Sun, Mingwei Sun and Zengqiang Chen
Mathematics 2024, 12(24), 3913; https://doi.org/10.3390/math12243913 - 11 Dec 2024
Cited by 1 | Viewed by 2315
Abstract
Effective trajectory planning is critical for achieving precise autonomous navigation and safe landing of parafoil delivery systems. However, current parafoil trajectory planning still faces challenges in ensuring consistency between actual system behavior and algorithmic real-time performance. Due to the strong fluid–structure interaction (FSI) [...] Read more.
Effective trajectory planning is critical for achieving precise autonomous navigation and safe landing of parafoil delivery systems. However, current parafoil trajectory planning still faces challenges in ensuring consistency between actual system behavior and algorithmic real-time performance. Due to the strong fluid–structure interaction (FSI) between the flexible canopy and airflow, traditional dynamic models based on point mass and rigid-body assumptions often lack aerodynamic accuracy. These models produce planned trajectories in simulation environments that are inconsistent with the actual system’s behavior and cannot directly provide an effective reference for airdrop experiments. Additionally, traditional planning methods require a significant amount of time to calculate complex dynamic models and generate fixed trajectories in advance. These methods not only fail to provide usable results in a short period of time, but also cannot prevent the accumulation of tracking errors by adjusting the target trajectory in real time. To address these issues, this paper proposes a flexible 8-degree-of-freedom (8-DOF) dynamic model based on the FSI method, utilizing the actual aerodynamic parameters of the canopy to achieve improved consistency with the behavior of the actual system. The Soft Actor–Critic (SAC) algorithm is then employed to achieve real-time trajectory planning for parafoil airdrop systems, addressing the real-time planning performance limitations of traditional algorithms. The airdrop experiments validate that the simulation trajectories generated using this model demonstrate higher consistency with actual flight trajectories, providing more accurate references for pre-flight trajectory optimization. Moreover, the proposed method enables real-time trajectory planning and dynamically adjusts target trajectories based on the current position and attitude of the parafoil, effectively mitigating the accumulation of errors. Full article
(This article belongs to the Special Issue Applied Mathematical Modeling and Intelligent Algorithms)
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25 pages, 8268 KB  
Article
Simulation Training System for Parafoil Motion Controller Based on Actor–Critic RL Approach
by Xi He, Jingnan Liu, Jing Zhao, Ronghua Xu, Qi Liu, Jincheng Wan and Gang Yu
Actuators 2024, 13(8), 280; https://doi.org/10.3390/act13080280 - 25 Jul 2024
Cited by 2 | Viewed by 2130
Abstract
The unique ram air aerodynamic shape and control rope pulling course of the parafoil system make it difficult to realize its precise control. At present, the commonly used control methods of the parafoil system include proportional–integral–derivative (PID) control, model predictive control, and adaptive [...] Read more.
The unique ram air aerodynamic shape and control rope pulling course of the parafoil system make it difficult to realize its precise control. At present, the commonly used control methods of the parafoil system include proportional–integral–derivative (PID) control, model predictive control, and adaptive control. The control precision of PID control and model predictive control is low, while the adaptive control has the problems of complexity and high cost. This study proposes a new method to improve the control precision of the parafoil system by establishing a parafoil motion simulation training system that trains the neural network controllers based on actor–critic reinforcement learning (RL). Simulation results verify the feasibility of the proposed parafoil motion-control-simulation training system. Furthermore, the test results of the real flight experiment based on the motion controller trained by the proximal policy optimization (PPO) algorithm are presented, which are close to the simulation results. Full article
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15 pages, 28225 KB  
Article
Simulation and Analysis of Aerodynamic Characteristics during Parafoil Canopy Curving Process and Application by LBM
by Yi Wang and Chunxin Yang
Aerospace 2024, 11(2), 118; https://doi.org/10.3390/aerospace11020118 - 28 Jan 2024
Cited by 6 | Viewed by 3093
Abstract
A parafoil is a crucial aerodynamic deceleration device used in the field of airdrop. The overall objective of this paper is to study the aerodynamic characteristics of the curving process of the canopy using the lattice Boltzmann method, to verify it with the [...] Read more.
A parafoil is a crucial aerodynamic deceleration device used in the field of airdrop. The overall objective of this paper is to study the aerodynamic characteristics of the curving process of the canopy using the lattice Boltzmann method, to verify it with the experimental results, and to analyze the stalling phenomenon using the finite volume method(FVM). Simulations were conducted to analyze the aerodynamic curves of four−stage models of canopies, examining the flow field characteristics. Additionally, the influence of air chamber structures is also analyzed. The reasons for differences in the aerodynamic characteristics are discussed based on the results obtained. The reliability of utilizing the lattice Boltzmann method for aerodynamic simulations is demonstrated. Overall, the lift coefficient of models II/III/IV was increased by 30.97% compared with model I, which proved the effectiveness of the air chamber structure and curving process. Notably, different curved canopies showed significantly improved lift and drag aerodynamic characteristics to varying extents, highlighting their robustness. Also, it was observed that air chamber partitions exerted a greater influence compared to perforation. Through validation and analysis, it was determined the accuracy of the LBM improved up to 10.9% with respect to the FVM. These findings provide a valuable reference for parafoil experiments and simulation research. Full article
(This article belongs to the Section Aeronautics)
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19 pages, 6576 KB  
Article
Intelligent Trajectory Tracking Linear Active Disturbance Rejection Control of a Powered Parafoil Based on Twin Delayed Deep Deterministic Policy Gradient Algorithm Optimization
by Yuemin Zheng, Zelin Fei, Jin Tao, Qinglin Sun, Hao Sun, Zengqiang Chen and Mingwei Sun
Appl. Sci. 2023, 13(23), 12555; https://doi.org/10.3390/app132312555 - 21 Nov 2023
Cited by 6 | Viewed by 2685
Abstract
Powered parafoils, known for their impressive load-bearing capacity and extended endurance, have garnered significant interest. However, the parafoil system is a highly complex nonlinear system. It primarily relies on the steering gear to change flight direction and utilizes a thrust motor for climbing. [...] Read more.
Powered parafoils, known for their impressive load-bearing capacity and extended endurance, have garnered significant interest. However, the parafoil system is a highly complex nonlinear system. It primarily relies on the steering gear to change flight direction and utilizes a thrust motor for climbing. However, achieving precise trajectory tracking control presents a challenge due to the interdependence of direction and altitude control. Furthermore, underactuation and wind disturbances bring additional difficulties for trajectory tracking control. Consequently, realizing trajectory tracking control for powered parafoils holds immense significance. In this paper, we propose a trajectory tracking method based on Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm-optimized Linear Active Disturbance Rejection Control (LADRC). Our method addresses the underactuation issue by incorporating a guiding law while utilizing two LADRC methods to achieve decoupling and compensate for disturbances. Moreover, we employ the TD3 algorithm to dynamically adjust controller parameters, thus enhancing the controller performance. The simulation results demonstrate the effectiveness of our proposed method as a trajectory tracking control approach. Additionally, since the control process is not reliant on system-specific models, our method can also provide guidance for trajectory tracking control in other aircraft. Full article
(This article belongs to the Special Issue Disruptive Trends in Automation Technology)
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22 pages, 3906 KB  
Article
Optimal Path Planning and Tracking Control Methods for Parafoil
by Zhihan Li and Ying Nan
Appl. Sci. 2023, 13(14), 8115; https://doi.org/10.3390/app13148115 - 12 Jul 2023
Cited by 10 | Viewed by 3406
Abstract
Due to the problems of flexible parafoil systems that are susceptible to complex disturbances, such as external wind fields and being difficult to control, it is necessary to study the path planning and tracking control methods of parafoil under complex conditions. In this [...] Read more.
Due to the problems of flexible parafoil systems that are susceptible to complex disturbances, such as external wind fields and being difficult to control, it is necessary to study the path planning and tracking control methods of parafoil under complex conditions. In this paper, the particle model and dynamic model of the parafoil system are established, and the path planning method based on the original natural (ON) principle coupled with meteorological interference, terrain avoidance, and other environmental models is studied. Sliding mode control is introduced into the path tracking control of the parafoil system, and tracking errors of the parafoil position and velocity are taken as the design criteria for the sliding mode surface. The control law of the sliding mode controller is derived. Through simulation comparison with other path planning and tracking control methods, the methods designed in this paper can reflect better path planning and tracking performance. The methods designed in this paper can effectively suppress the impact of external disturbances, improve accuracy, and enhance robustness. Full article
(This article belongs to the Section Aerospace Science and Engineering)
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15 pages, 4034 KB  
Article
Predefined-Time Heading Control for a 9-DOF Parafoil Recovery System Subject to Internal Relative Motions
by Yiming Guo, Jianguo Yan, Xiaojun Xing, Xiwei Wu and Lingwei Li
Aerospace 2023, 10(4), 348; https://doi.org/10.3390/aerospace10040348 - 3 Apr 2023
Cited by 2 | Viewed by 3137
Abstract
This paper addresses the challenging problem of predefined-time heading control of a parafoil recovery system (PRS) with internal relative motions and external disturbance. On the basis of the PRS described by a 9-degree-of-freedom model, a simplification and equivalent model is first derived, which [...] Read more.
This paper addresses the challenging problem of predefined-time heading control of a parafoil recovery system (PRS) with internal relative motions and external disturbance. On the basis of the PRS described by a 9-degree-of-freedom model, a simplification and equivalent model is first derived, which is convenient to design control law. Then, a predefined-time disturbance observer is provided to estimate the lumped disturbance caused by internal relative motions and apparent mass. With the application of the disturbance estimation, a predefined-time heading controller is developed for the PRS. The control system is proven to be predefined-time stable by Lyapunov theory. Simulation results illustrate that the proposed method has better control performance than finite-time and PID controllers. Full article
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18 pages, 4083 KB  
Article
An Aero-Structural Model for Ram-Air Kite Simulations
by Paul Thedens and Roland Schmehl
Energies 2023, 16(6), 2603; https://doi.org/10.3390/en16062603 - 9 Mar 2023
Cited by 13 | Viewed by 5467
Abstract
Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around [...] Read more.
Similar to parafoils, ram-air kites are flexible membrane wings inflated by the apparent wind and supported by a bridle line system. A major challenge in estimating the performance of these wings using a computer model is the strong coupling between the airflow around the wing and the deformation of the membrane structure. In this paper, we introduce a staggered coupling scheme combining a structural finite element solver using a dynamic relaxation technique with a potential flow solver. The developed method proved numerically stable for determining the equilibrium shape of the wing under aerodynamic load and is thus suitable for performance measurement and load estimation. The method was validated with flight data provided by SkySails Power. Measured forces on the tether and steering belt of the robotic kite control pod showed good resemblance with the simulation results. As expected for a potential flow solver, the kite’s glide ratio was overestimated by 10–15%, and the measured tether elevation angle in a neutral flight scenario matched the simulations within 2 degrees. Based on the obtained results, it can be concluded that the proposed aero-structural model can be used for initial designs of ram-air kites with application to airborne wind energy. Full article
(This article belongs to the Special Issue Airborne Wind Energy Systems)
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16 pages, 7572 KB  
Article
Numerical Investigations of Precise Wind Field in Main Landing Area during the Landing Phase of “Shen Zhou” Series Spacecraft Mission
by Yilei Song, Guolin Ma, Linlin Tian, Ning Zhao and Xiyun Lu
Aerospace 2023, 10(1), 37; https://doi.org/10.3390/aerospace10010037 - 1 Jan 2023
Cited by 4 | Viewed by 2419
Abstract
Wind is one of the main factors raising errors in the spacecraft’s landing phase. As a result, an accurate description of incoming wind conditions is supposed to be a prerequisite for reliable parafoil trajectory planning. This work utilizes the Weather Research Forecast (WRF) [...] Read more.
Wind is one of the main factors raising errors in the spacecraft’s landing phase. As a result, an accurate description of incoming wind conditions is supposed to be a prerequisite for reliable parafoil trajectory planning. This work utilizes the Weather Research Forecast (WRF) model system with efficient parameterization schemes to reproduce the wind field in the main landing area during the landing phase of the “Shen Zhou” series spacecraft mission. In comparison with observational data from several cases, it is validated that the WRF model has the potential to give an accurate imitation of wind behaviors and is expected to be an alternative technique for costly and time-consuming experimental undertakings. Based on the numerical results, a linear model is proposed in the current work, which is applicable to the altitude range, specifically for parafoil trajectory planning. It is validated by comparisons with observational wind properties from radio-sounding stations. In addition, a sixth-order polynomial model is introduced for comparison as well. The results show that the current proposed model has both the characteristics of a simple form and good accuracy. It shows overall better consistency with observational data than the sixth-order polynomial model. Full article
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18 pages, 3903 KB  
Article
Deep-Reinforcement-Learning-Based Active Disturbance Rejection Control for Lateral Path Following of Parafoil System
by Yuemin Zheng, Jin Tao, Qinglin Sun, Hao Sun, Zengqiang Chen, Mingwei Sun and Feng Duan
Sustainability 2023, 15(1), 435; https://doi.org/10.3390/su15010435 - 27 Dec 2022
Cited by 12 | Viewed by 3819
Abstract
The path-following control of the parafoil system is essential for executing missions, such as accurate homing and delivery. In this paper, the lateral path-following control of the parafoil system is studied. First, considering the relative motion between the parafoil canopy and the payload, [...] Read more.
The path-following control of the parafoil system is essential for executing missions, such as accurate homing and delivery. In this paper, the lateral path-following control of the parafoil system is studied. First, considering the relative motion between the parafoil canopy and the payload, an eight-degree-of-freedom (DOF) model of the parafoil system is constructed. Then, a guidance law containing the position deviation and heading angle deviation is proposed. Moreover, a linear active disturbance rejection controller (LADRC) is designed based on the guidance law to allow the parafoil system to track the desired path under internal unmodeled dynamics or external environmental disturbances. For the adaptive tuning of the controller parameters, a deep Q-network (DQN) is applied to the LADRC-based path-following control system, and the controller parameters can be adjusted in real time according to the system’s states. Finally, the effectiveness of the proposed method is applied to a parafoil system following circular and straight paths in an environment with wind disturbances. The simulation results show that the proposed method is an effective means to realize the lateral path-following control of the parafoil system, and it can also promote the development of intelligent controllers. Full article
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