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the claim
Precision landing of rocket fairings is difficult due to unmodeled wind gusts and parachute glide uncertainties
the verdict
INSUFFICIENT LEANING
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the weight of evidence
3 sources for · 0 against

Peer-reviewed literature notes that autonomous parafoil systems and returning rocket stages face low landing accuracy and path planning challenges due to wind disturbances and environmental factors, though specific data on rocket fairings combined with parachute glide uncertainties is only partially covered.

Evidence for · 3
2022 · cited by 3
Parafoil is an important novel method to realize the precise recovery of sub-stage booster of rocket. In this paper, a parafoil optimal path planning algorithm based on longicorn algorithm is proposed to solve the problems that the parafoil is easily affected by wind field and the error of landing point is large in the recovery of sub-stage booster of rocket. Firstly, according to the dynamics and kinematics equations of the parafoil and a rocket sub-stage combined system, a 6-degree-of-freedom model of the system was established to analyze the effects of different downward deviation on the forward velocity, vertical velocity and the trajectory planning of the parafoil during the homing process of the rocket sub-stage. On this basis, the number of circling turns, radius and azimuth of the cutting-high section of the combination of the parafoil and the sub-stage booster were taken as the optimal parameters, and the optimal path planning was carried out by using the longicorn algorithm. Finally, a homing path with comprehensive consideration of energy and the accuracy of the landing point was obtained. The simulation results show that the piecewise optimal flight path planning algorithm based on longicorn algorithm proposed in this paper has fast convergence speed and high precision of flight track landing point. 2022 年 2 月 第 40 卷第 1 期 西 北 工 业 大 学 学 报 Journal of Northwestern Polytechnical University Feb. Vol.40 2022 No.1 https: / / doi.org / 10.1051 / jnwpu / 20224010062 收稿日期:2021⁃05⁃20 基金项目:国家自然科学基金(61771399) 与陕西省自然科学基础研究计划(2020JM⁃123) 资助 作者简介:邢小军(1976—) ,西北工业大学副教授,主要从事飞行控制、导航理论及应用、计算智能理论及应用等研究。 e⁃mail:xxiaojun@ nwpu.edu.cn 面向火箭子级精确回收的翼伞最优 航迹规划算法研究 邢小军, 韩逸尘, 樊国政, 陈梦萍, 李丰浩 ( 西北工业大学 自动化学院, 陕西 西安  710072) 摘  要:翼伞是实现运载火箭子级精确回收的一种新的重要手段,针对翼伞在火箭子级回收中易受风 场影响、落点误差大的问题,提出了一种基于天牛群算法的翼伞最优航迹规划算法。 根据翼伞和某型 火箭一子级组合体的动力学和运动学方程建立六自由度模型,并分析火箭一子级归航过程中不同转 弯下偏量对前向速度、垂直速度及翼伞航迹规划的影响。 在此基础上,将翼伞一子级组合体盘旋削高 段的盘旋圈数、盘旋半径和方位角作为寻优参数,应用天牛群算法对组合体进行最优航迹规划,将平 均风的影响转换为目标点的飘移,最终获得一条综合考虑能量以及落点精确度的归航航迹。 仿真结 果表明,所提出的基于天牛群算法的火箭一子级翼伞回收分段最优航迹规划算法收敛速度快,航迹落 点精度高。 关  键  词:航迹规划;翼伞;火箭一子级;天牛群算法 中图分类号:V249.31      文献标志码:A      文章编号:1000⁃2758(2022)01⁃0062⁃07     当前,运载火箭子级的无损精确回收及可重复 使用已经成为国际航天领域的研究热点。 运载火箭 子级回收的方式主要分为带翼飞回、垂直反推以及 伞降回收 3 种。 其中伞降回收方式主要有降落伞回 收和翼伞回收 2 种[1] 。 相比于降落伞,翼伞具有出 色的滑翔性以及可操纵性,是实现火箭子级回收的 重要手段。 这其中如何规划合理的翼伞回收航迹以 实现子级的落点准确对保障地面人员的生命、财产 安全及航天器的安全回收尤为重要。 基于翼伞进行火箭一子级回收主要采用径向归 航、锥形归航和非比例控制等归航方式[2⁃3] ,但这些 归航方式存在如下问题:①翼伞操纵比较频繁,难以 实现逆风着陆;②接近目标点时容易造成翼伞频繁 控制,消耗能量过多;③实现复杂,且归航精度较低。 当前,分段 归 航 策 略 成 为 翼 伞 航 迹 设 计 的 主 要 方 式[4] 。 国内外学者对分段归航做了很多研究,如文 献[5⁃6] 将最优控制与分段归航相结合,并且进行了 仿真验证。 文献[ 7⁃8] 研究了翼伞的最优控制归航 方案,在分段归航的基础上考虑了地形威胁和风场 的影响,将航迹寻优问题转换成参数寻优问题,应用 粒子群算法实现了最优航迹规划等。 但上述研究未考虑翼伞不同转弯下偏量对火箭 子级速度的影响,且未将分段归航的盘旋削高圈数 作为规划目标,易导致翼伞控制机构能量过度消耗。 此外,粒子群算法计算耗时、迭代缓慢会降低航迹规 划效率。 为此,本文针对某固体运载火箭一子级翼 伞回收,主要研究翼伞不同转弯下偏量对一子级速 度及航迹的影响,并提出一种基于天牛群算法的低 能耗、高效率的翼伞一子级航迹规划算法。 1  火箭一子级翼伞组合体建模 在翼伞航迹规划中可将翼伞和火箭一子级组合 体视为刚体,为更方便地分析翼伞运动对一子级及 组合体姿态和航迹的影响,本节首先根据火箭一子 级和翼伞的动力学和运动学方程建立组合体的六自 第 1 期 邢小军,等:面向火箭子级精确回收的翼伞最优航迹规划算法研究 由度模型,并分析翼伞在不同转弯半径下对组合体 速度的影响。 1.1  假设条件 为简化分析,对翼伞建模做如下理想化假设: 1) 翼伞完全打开充满气后,展开形状为固定的 对称形( 除去存在下拉量的情况) ; 2) 伞衣质心与压心重合, 位置在弦上距前缘 1 / 4。 1.2  运动学和动力学方程 表 1 列出了某型火箭一子级翼伞组合体的主要 气动系数,其他参数请参考文献[9] 中的具体数据。 表 1  火箭一子级翼伞组合体气动系数 CL0 CLα CLδα CD0 CDα CDδα 0.457 9 0.034 4 0.328 1 0.069 4 0.000 6 0.127 5 翼伞一子级组合体运动学方程为 ̇x ̇y ̇z é ëê ê ê ê ù ûú ú ú ú = Bd p u v w é ëê ê ê ê ù ûú ú ú ú (1) 式中: [ x,y,z] 表示大地坐标系内火箭一子级翼伞 组合体的位置坐标;[ u,v,w] 分别为机体坐标系三 轴方向上速度分量;Bd p 表示为机体坐标系到大地坐 标系的转换矩阵,其表达式为 Bd p = cosθcosψ sinθcosψsinφ - sinψcosφ sinθcosψcosφ + sinψsinφ cosθsinψ sinθsinψsinφ + cosψcosφ sinθsinψcosφ - cosψsinφ - sinθ cosθsinφ cosθcosφ é ëê ê ê ê ù ûú ú ú ú (2) 式中, φ,θ,ψ 分别表示组合体的滚转角、 俯仰角和 偏航角。 翼伞一子级组合体的动力学方程为 ̇u ̇v ̇w é ëê ê ê ê ù ûú ú ú ú = rv - qw pw - ru qu - pv é ëê ê ê ê ù ûú ú ú ú + 1 mp + mb ( FA + FW) (3) 式中: FA 为气动力在组合体三轴上的分量;FW 为重 力在机体坐标系上的分量; [ p,q,r] 为机体坐标系 中组合体的角速度;mp 为翼伞的质量;mb 为一子级 的质量。 火箭一子级翼伞组合体的角运动方程为 ̇p ̇q ̇r é ëê ê ê ê ù ûú ú ú ú = I - 1 T MA - 0 - r q r 0 - p - q p 0 é ëê ê ê ê ù ûú ú ú ú IT p q r é ëê ê ê ê ù ûú ú ú ú æ èç ç ç ö ø÷ ÷ ÷(4) 式中: [ ̇p, ̇q,̇r] 为机体坐标系中组合体角速度的变 化率;IT 为组合体相对于刚体质心的转动惯量矩阵; MA 为组合体总的气动力矩。 火箭一子级翼伞组合体的欧拉角变化率与机体 坐标系的 3 个角速度分量之间的关系式可以写为 ̇φ ̇θ ̇ψ é ëê ê ê ê ù ûú ú ú ú = 1 sinφtanθ cosφtanθ 0 cosφ - sinφ 0 sinφ / cosθ cosφ / cosθ é ëê ê ê ê ù ûú ú ú ú p q r é ëê ê ê ê ù ûú ú ú ú (5) 2  基于天牛群算法分段最优航迹规划 火箭一子级翼伞组合体的航迹反映了组合体质 点的运动轨迹,航迹规划采用分阶段设计方式,可体 现出火箭一子级翼伞组合体的位置及航向角变化。 因此,本文首先通过火箭一子级翼伞组合体六自由 度模型分析翼伞不同转弯下偏量对组合体速度及航 迹的影响,并在航迹规划中予以考虑。 此外,为降低 翼伞航迹规划的复杂度,进一步将六自由度模型简 化为质点模型。 2.1  质点模型 在风场方向水平、大小已知的情况下,取大地坐 标系,水平风向为 x 轴方向,按照右手准则确定 y 轴 方向,z 轴为垂直于地面向上,则火箭一子级翼伞组 合体的模型可以简化为 ̇x = vl·cosψ + vwind,x ̇y = vl·sinψ + vwind,y ̇z = vz ̇ψ = δa ì î íï ï ïï ï ï (6) 式中: vl 表示火箭一子级翼伞组合体的水平飞行速 度;vz 表示火箭一子级翼伞组合体的垂直下降速度; vwind,x 表示水平风速在 x 轴的投影;vwind,y 表示为水平 风速在 y 轴的投影;ψ, ̇ψ 分别为火箭一子级翼伞组 合体的转弯角度、 转弯角速度;δ a 表示火箭一子级 36 西  北  工  业  大  学  学  报 第 40 卷 翼伞组合体转弯下偏量,它可改变火箭一子级翼伞 组合体的滚转角,根据受力平衡及几何运动关系可 以得出滚转角与火箭一子级翼伞组合体的转弯角速 度正相关, 滚 转 角 和 转 弯 下 偏 量 存 在 一 一 对 应 关 系[7] ,因此定义火箭一子级翼伞组合体转弯下偏量 数值上等于转弯角速度。 2.2  航迹分阶段设计 基于分段归航方案[10] ,航迹分为飞行段、盘旋 削高段和雀降段[11] ,图 1 为分段归航航迹示意图。 图 1  分段归航航迹示意图 其中 BC 段为飞行段, DE 段为盘旋削高段, FG 段为雀降段,AB、CD、EF 段为圆弧过渡段,β 1,β 2 分 别表示圆弧过渡段弧度;β 3 表示盘旋阶段的圆弧段 弧度;β 4 为盘旋 削 高 段 和 雀 降 段 之 间 的 过 渡 段 弧 度,是盘旋削高段末尾速度方向和逆风方向的夹角, 可通过调整 β 4 确保雀降段能够逆风着陆。 显然,根 据图 1 可以很容易得出各段航迹的几何关系。 本文翼伞航迹规划的目标是确定盘旋削高段和 雀降段切入点的最优坐标,以保证组合体在雀降段 能够逆风着陆于目标点,同时能量消耗尽可能低。 由于不同的盘旋半径对应不同的前向速度和垂直速 度,盘旋阶段的盘旋半径表达式为 Rep = vl δa = vl ̇ψ (7) 式中, vl 是关于 ̇ψ 的方程式。 根据上述分析,设置航 迹规划算法寻优的 3 个未知量分别为盘旋阶段的转 弯下偏量 ̇ψ、盘旋阶段切入点相对于落点的方位角 θ ep 以及盘旋阶段的整圆周圈数 k。 再以能量消耗最小以及落点偏差最小为优化目 标,首先构造如(8) 式所示的函数 F1 = Rmin( β1 + β2 + β4) fmin + Repβ3 + 2kπ·Rep f +   DBC f0 + ( Rep - 2Rmin) Rep f0 - z0 F2 = ∫ t f t0 δ2 adt ì î íï ï ï ïï ï ï ï (8) 式中: f0 为组合体稳定滑翔状态下的滑翔比;fmin 为 组合体最小转弯半径时的滑翔比;f 为组合体盘旋削 高阶段时的滑翔比;2kπ·Rep 为盘旋阶段过程中盘 旋段整圆周的水平距离;z0 为翼伞开始工作时一子 级高度。 F1 为组合体着陆时的偏差,即设计的一子 级航迹的垂直海拔高度与不同阶段下各水平飞行距 离通过滑翔比转化成的高度总和之差的绝对值。 DBC 为 BC 段的直线长度。 取最终目标函数为 F = min{ k1F1 + k2F2} (9)     本节中设定 F1 的权重系数为 0.8,F2 的权重系 数为 0.2。 2.3  天牛群算法 本文采用天牛群算法[12⁃13] 对(9) 式所示的目标 函数
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rails:sufficiency:partial_only:for=0+3p:against=0+0p | v55:multi_partial_one_side:lean=lean_partial:for:one_sided

More for · 2
2025 · cited by 1
Abstract Low landing accuracy of autonomous parafoil systems under wind disturbances remains a significant challenge in precision airdrop operations. To address this, there is a critical need for homing control systems with enhanced robustness and adaptability to cope with an uncertain environment. This study proposes a novel control framework that integrates the T-Approach guidance strategy with nonlinear model predictive control (NMPC) for path point correction and trajectory optimization. A nonlinear dynamic model is developed to accurately capture the system behaviour, and an adaptive tracking controller with real-time predictive correction is designed. Compared to traditional J-Approach methods, the T-Approach strategy demonstrates significantly improved wind disturbance rejection and landing accuracy under both steady and shear wind conditions. In 10,000 Monte Carlo simulations with randomized turbulent wind, the proposed approach reduces the 90% circular error probable (CEP90) by 24.4 meters, lowers energy consumption by 11%, and increases the likelihood of maintaining an upwind landing angle deviation within 1° by 43.5%. These results confirm the effectiveness of the proposed method in improving both energy efficiency and disturbance robustness, providing a reliable solution for autonomous parafoil landings in uncertain wind conditions.
2023 · cited by 0
The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Nevertheless, these techniques are well-adapted to the control system design of single-input single-output systems, such as for example a reusable rocket using a ESA GNC Conference Papers Repository ESA GNC Conference Papers Repository Go back to search form. Title: Robust Control Design via Structured H-infinity for the Atmospheric Re-entry of Reusable Launchers Authors: Alice De Oliveira, Michèle Lavagna Presented at: Sopot 2023 DOI: 10.5270/esa-gnc-icatt-2023-191 Full paper: Open paper Abstract: The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Moreover, model uncertainties are not accurately considered in the design process, developed only with nominal conditions and stability margin requirements. For all these reasons, it results in an extensive (both in terms of time and cost) Verification and Validation campaign with many iterations and Monte-Carlo analyses to assess the performance and robustness of the control system. To overcome these drawbacks, the H-infinity family of methods, introduced a few years ago [8], This paper studies the synthesis of a robust control system via structured H-infinity for the RLV atmospheric re-entry problem. First, the nonlinear 6-Degree-of-Freedom (6-DoF) RLV re-entry dynamics are simplified into a linear model and then linearised along a reference trajectory to get the nominal LFT of the system, then augmented with parametric uncertainties. The model covers the atmospheric re-entry and vertical landing of a first-stage rocket equipped with a TVC system and steerable planar fins. The controllers are built at different points of the re-entry trajectory, using the structured H-infinity framework through PID-like structures. This study lies within the ASCenSIon (Advancing Space Access Capabilities - Reusability and Multiple Satellite Injection) project, an innovative training network funded within H2020. References: [1] L. Blackmore, “Autonomous Precision Landing of Space Rockets”, The Bridge on Frontiers of Engineering, Vol. 4, No. 46, pp. 15–20 (2016). [2] M. Wall, “Wow! SpaceX Lands Orbital Rocket Successfully in Historic First”, SPACE.com (2015). Retrieval Date: 20-Jan-2022. URL: https://www.space.com/31420-spacex-rocket-landing-success.html [3] Rocket Lab (2017). “Rocket Lab Electron 'Its a Test' flight successfully makes it to space”. Retrieval Date: 20-Jan-2022.
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  1. Research on parafoil optimal flight path planning algorithm for precise recovery of sub-stage booster of rocketpeer-reviewedno side taken
  2. Robust Control Design via Structured H-infinity for the Atmospheric Re-entry of Reusable Launcherspeer-reviewedno side taken
  3. T-approach-integrated nonlinear MPC for parafoil landing under wind uncertaintiespeer-reviewedno side taken
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