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Qitong Zou, , Haiyan Hu
Journal of Guidance, Control, and Dynamics pp 1-11; https://doi.org/10.2514/1.g006114

Abstract:
This paper describes a novel time-delayed control scheme for suppressing the body-freedom flutter of a flexible flying-wing drone and verifies its robustness. The simple formulation and strong robustness of the proposed control scheme are of particular interest. The procedure of designing the proposed delayed controller includes the following three steps. First, the displacement and velocity signals from the wingtip are taken as the input signals to delayed feedback, and the ailerons are used as the control inputs. The proportional gain, derivative gain, and specific value of a time delay are taken as control parameters. Second, the proportional and derivative gains are determined by checking the stable region for various time delays. Finally, a single time delay is determined according to both the critical stability condition and the stability margins. The stability and robustness of the closed-loop system are analyzed in time domain and frequency domain. The numerical results demonstrate that the flutter boundary of the flexible flying-wing drone can be expanded by up to 35% while retaining strong robustness via the proposed delayed controller.
Zvonimir Stojanovski,
Journal of Guidance, Control, and Dynamics pp 1-13; https://doi.org/10.2514/1.g006109

Abstract:
This paper introduces a new extension of the unscented Kalman filter with asymmetric sample points and weights chosen to match third- and fourth-order moments in addition to the mean and covariance. Explicit solutions are obtained for sample points and weights, making their evaluation efficient and robust, and rigorous constraints are derived for their applicability. The use of the new filter is demonstrated with three dynamic systems (an aircraft coordinated turn model, a rotating rigid body, and a projectile with drag), and filter performance is compared with that of the conventional unscented Kalman filter and conjugate unscented transform filters. The new filter is found to be more robust in most cases where the initial distribution, process noise, and measurement noise have a high kurtosis, in that it does not generate extreme outliers in the estimation error. Also, execution times for the new filter are found to be only slightly longer than for the conventional unscented Kalman filter and significantly shorter than for the conjugate unscented transform filters.
Kaushik Prabhu, Manoranjan Majji, Kyle T. Alfriend
Journal of Guidance, Control, and Dynamics pp 1-13; https://doi.org/10.2514/1.g006088

Abstract:
A statistical orbit determination approach that minimizes the sum of absolute errors incurred by the vector measurements is developed. An iterative linear program is derived for the differential corrections associated with the best estimated epoch state to minimize the sum of the absolute errors. It is shown that in the presence of redundant measurements, the minimum one-norm solution rejects outlier measurements. An estimate of the variance of the estimated epoch state is also derived. The epoch state and associated covariance estimates are verified using Monte Carlo simulations for representative orbit determination examples.
Syed Aseem Ul Islam, Tam W. Nguyen, Ilya V. Kolmanovsky, Dennis S. Bernstein
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1732-1758; https://doi.org/10.2514/1.g005778

Abstract:
Unlike fixed-gain robust control, which trades off performance with modeling uncertainty, direct adaptive control uses partial modeling information for online tuning. The present paper combines retrospective cost adaptive control (RCAC), a direct adaptive control technique for sampled-data systems, with online system identification based on recursive least squares (RLS) with variable-rate forgetting (VRF). The combination of RCAC and RLS-VRF constitutes data-driven RCAC (DDRCAC), where the online system identification is used to construct the target model, which defines the retrospective performance variable. This paper investigates the ability of RLS-VRF to provide the modeling information needed for the target model, especially non-minimum-phase (NMP) zeros. DDRCAC is applied to single-input, single-output and multiple-input, multiple-output numerical examples with unknown NMP zeros, as well as several flight control problems, namely, unknown transition from minimum phase to NMP lateral dynamics, flexible modes, flutter, and nonlinear planar missile dynamics.
Madhusudan Vijayakumar,
Journal of Guidance, Control, and Dynamics pp 1-18; https://doi.org/10.2514/1.g006182

Abstract:
A robust finite Fourier series (R-FFS) approach is developed for fast generation of Earth–moon trajectories using continuous low thrust. Each component of the position vector is approximated using a finite Fourier series as a function of time; these approximations are then used to design a trajectory that satisfies the equations of motion and the constraints, at discrete points, as well as the problem boundary conditions. The R-FFS method leverages the three-body problem characteristics to achieve all the required plane change without the use of propulsion. The trajectory is divided into phases: escape, intermediate, and capture. The escape phase is further divided into segments. The phase of the trajectory near the L1 Lagrange point is designed first and is always a thrust-free phase. This thrust-free phase is optimized to achieve the required plane change, enabling planar trajectories in the other phases. The initial guess needed by the solver, in the escape and capture phases, is generated using an analytic approximation developed in this paper. The numerical results show that the R-FFS can generate three-dimensional transfers to high lunar orbits, low lunar orbits, and halo orbits, while meeting constraints on the maximum thrust level of the engine.
Yuta Takahashi, Hiraku Sakamoto, Shin-Ichiro Sakai
Journal of Guidance, Control, and Dynamics pp 1-16; https://doi.org/10.2514/1.g005873

Abstract:
Electromagnetic formation flight (EMFF) uses the electromagnetic force to control the relative positions of multiple satellites without using conventional fuel-based propulsion. To compensate for the electromagnetic torque generated alongside the electromagnetic force, in most previous studies, all satellites were assumed to have reaction wheels (RWs) besides electromagnetic coils. However, the RW-loaded angular momentum becomes nonuniformly distributed among the satellites, because the electromagnetic torque usually differs between satellites. Without a proper control scheme, this deviation increases over time, and the RWs become saturated quickly, preventing the attitudes of the satellites from being controlled. In this study, a new controller is proposed that enables the electromagnetic force and torque to be controlled simultaneously. The EMFF kinematics derived from the conservation of angular momentum are used for the controller design. This controller can control n satellites without saturating the RWs, and only one set of RWs is required among all satellites. The combination of the proposed controller with a simple unloading control exclusive to the chief satellite results in the elimination of the accumulation of angular momentum in the entire system. The effectiveness of the proposed controller is demonstrated through numerical simulations of the formation maintenance and formation reconfiguration of a five-satellite system.
Journal of Guidance, Control, and Dynamics pp 1-19; https://doi.org/10.2514/1.g005970

Abstract:
Any space trajectories are subject to state uncertainty due to imperfect state knowledge, random disturbances, and partially known dynamical environments. Ideally, such uncertainty and associated risks must be properly quantified and taken into account in the process of trajectory design, ensuring a sufficiently low risk of causing hazardous events. To bridge the gap between the ideal goal and current practice in mission design, this paper extends Lawden’s primer vector theory and develops a solution method to solve the problem of low-thrust trajectory optimization under state uncertainty. The new primer vector, termed stochastic primer vector, provides an analytical open-loop optimal control law that respects a probabilistic path constraint with a user-specified confidence level (chance constraint). A numerical aspect of the indirect method is also extended by introducing a smoothing approach across constraint corner discontinuities, enabling efficient solution methods for constrained optimal control problems. The validity and effectiveness of the theoretical development are demonstrated with two numerical examples, which clarify the behavior of chance-constrained optimal low-thrust trajectories and confirm through Monte Carlo simulations that the designed trajectories indeed satisfy the imposed constraints under uncertainty with the prescribed confidence level.
, Mark J. S. Lopez
Journal of Guidance, Control, and Dynamics pp 1-13; https://doi.org/10.2514/1.g006044

Abstract:
This paper describes a frequency-domain method for the identification of multi-input control equivalent turbulence input models. Such models can be identified from flight data gathered in specific turbulent environments, such as behind a ship or near a rooftop vertiport, and used to accurately simulate an aircraft’s response to turbulence. Identification of control equivalent turbulence input models has previously been done in the frequency domain for single-input/single-output applications or using a two-step time- and frequency-domain approach for multi-input/multi-output applications. In this paper, the frequency-domain approach is extended to account for the possible correlation between the measured control inputs and aircraft states (when flight data are collected closed loop) and to handle multi-input/multi-output applications. Several simulation examples are provided that demonstrate that known turbulence models can be accurately identified, for both open- and closed-loop simulations. The results validate the multi-input control equivalent turbulence input model frequency-domain identification approach proposed in this paper.
, Zhi Jun Lim, Sameer Alam, Narendra Pratap Singh
Journal of Guidance, Control, and Dynamics pp 1-12; https://doi.org/10.2514/1.g005802

Abstract:
Approach and landing accidents have resulted in a significant number of hull losses worldwide. Technologies (e.g., instrument landing system) and procedures (e.g., stabilized approach criteria) have been developed to reduce the risks. This paper proposes a data-driven method to learn and interpret flight’s approach and landing parameters to facilitate comprehensible and actionable insights into flight dynamics. Specifically, two variants of tunnel Gaussian process (TGP) models are developed to elucidate aircraft’s approach and landing dynamics using advanced surface movement guidance and control system (A-SMGCS) data, which then indicates the stability of flight. TGP hybridizes the strengths of sparse variational Gaussian process and polar Gaussian process to learn from a large amount of data in cylindrical coordinates. This paper examines TGP qualitatively and quantitatively by synthesizing three complex trajectory datasets and compared TGP against existing methods on trajectory learning. Empirically, TGP demonstrates superior modeling performance. When applied to operational A-SMGCS data, TGP provides the generative probabilistic description of landing dynamics and interpretable tunnel views of approach and landing parameters. These probabilistic tunnel models can facilitate the analysis of procedure adherence and augment existing aircrew and air traffic controller’ displays during the approach and landing procedures, enabling necessary corrective actions.
Xiangyu Li, Daniel J. Scheeres, Dong Qiao
Journal of Guidance, Control, and Dynamics pp 1-17; https://doi.org/10.2514/1.g006016

Abstract:
This paper investigates a novel method to increase the accuracy of ballistic deployment by controlling the spin rate of the lander, assuming that the lander is spherical. The concept of the bouncing return trajectory is proposed, which takes off and lands at the same point on the asteroid surface. The spin rate of a spherical lander is controlled before each impact to change its postimpact velocity so that it can be driven into the bouncing return trajectory and remains in the vicinity of its original landing site until it finally rests on the surface. First, the properties of bouncing return trajectories are investigated based on a spherical model. Based on the contact dynamics, the analytical solution of the required spin rate to change velocity is derived. Next, candidate deployment trajectories of the proposed method are studied under different asteroid parameters. Finally, the feasibility and robustness of the method are verified using a model of the asteroid Bennu. It is found that the proposed deployment method can achieve a precise landing if the surface environment is ascertained and largely reduce the landing dispersion under an uncertain environment. This paper provides a novel idea for future asteroid lander deployment and surface exploration missions.
Shiyu Chen, Hexi Baoyin
Journal of Guidance, Control, and Dynamics pp 1-10; https://doi.org/10.2514/1.g005827

Abstract:
It is essential when planning multitarget missions to rapidly and accurately estimate the velocity increments of target-to-target transfers. An analytical method is proposed to estimate the optimal velocity increment of a multirevolution impulsive transfer, taking account of the J2 perturbation. First, for a phasing problem where the differences in semimajor axis, inclination, ascending node, and argument of latitude at the termination of the transfer are eliminated, two linear equations derived from the first-order necessary conditions are solved to determine the normal components of the impulses. Then, the radial and tangential components of the impulses are determined by solving another two linear equations, thereby eliminating the difference in the eccentricity vector. In a classical debris removal scenario, the proposed method shows better accuracy than previous analytical methods and even a method based on a deep neural network. The computational efficiency of the method is also much higher than that of the existing semi-analytical method. In addition, the estimated transfer process is in good agreement with the exact one in some cases, and so the method shows potential for preliminary designs of impulsive trajectories.
Eugene A. Morelli
Journal of Guidance, Control, and Dynamics pp 1-11; https://doi.org/10.2514/1.g006072

Abstract:
Flight test maneuvers and dynamic modeling techniques were developed for determining aircraft moments of inertia from flight test data. Full nonlinear rigid-body rotational equations of motion were used in the analysis, with aerodynamic moment dependencies modeled by linear expansions in the aircraft states and controls. Aerodynamic parameters were estimated simultaneously with inertia parameters using equation-error modeling applied to flight test data from maneuvers designed specifically for this problem. The approach was demonstrated using a nonlinear F-16 simulation, then applied to a remotely piloted subscale aircraft flight test. Errors in the aircraft moment of inertia parameters determined from simulated F-16 flight test data were less than 6% compared to the true values in the simulation. Flight test results for the subscale aircraft were within 6% of ground-test values obtained using the same aircraft.
, Zhengliang Lu, Wenhe Liao,
Journal of Guidance, Control, and Dynamics pp 1-15; https://doi.org/10.2514/1.g006141

Abstract:
This paper investigates a formation control technique for low-Earth-orbit nanosatellites based on the differential aerodynamic drag and lift. An innovative method of using only the yaw angle deviation, instead of the three-axis attitude rotation, is proposed to simultaneously control the in-plane and out-of-plane relative motions. This method can be used for the formation control of the Earth-pointing satellite. A control scheme consisting of four steps is designed considering complex input constraints. In this scheme, two control inputs are defined based on the predicted atmospheric density, and the explicit expressions of their time-varying feasible regions are analyzed. To obtain the yaw angle of each nanosatellite, a yaw angle solution algorithm based on the grid interpolation method is designed with online solving nonlinear optimization avoided. A dynamic surface control algorithm based on the hyperbolic tangent function and a linear model predictive control algorithm are, respectively, used to limit two control inputs within their feasible regions. In addition, a nonlinear finite-time disturbance observer is used to track the total system disturbance. Numerical simulations are carried out for along-track and circular formations, in which the uncertainties of aerodynamic forces, the attitude dynamics, and the unknown perturbation are taken into account.
Adam Vigneron, Simon Delchambre, Tobias Ziegler, Walter Fichter
Journal of Guidance, Control, and Dynamics pp 1-12; https://doi.org/10.2514/1.g005948

Abstract:
The use of low-bandwidth attitude controllers is a standard solution for spacecraft facing tight frequency-domain requirements for attitude-stable payloads and platforms. However, such controllers have difficulty responding to transients both planned and unexpected. This paper introduces a novel method of controller re-initialization to counteract a transient in progress. This method, the eigenmode initialization, pursues time-optimal performance for a given controller and plant by attempting to suppress the slow eigenmodes of the closed-loop system; the dynamics that remain are a function of the remaining eigenmodes. The derivation of this method from first principles is presented alongside analytical solutions for the ideal response and specific examples for which postinitialization transients decay 5, 7, and 30 times faster than their uninitialized counterparts. The method is extended to account for actuator bias and bound the actual response in the presence of estimation error. Finally, the method is validated through the high-fidelity simulation of a critical mode transition within the attitude control system of a legacy Airbus satellite, demonstrating the eigenmode initialization’s simple and effective implementation despite considerable nonlinearities in the sensor and actuator models employed.
Fernando Gámez Losada, Jeannette Heiligers
Journal of Guidance, Control, and Dynamics pp 1-17; https://doi.org/10.2514/1.g005955

Abstract:
In this paper, a new family of solar-sail periodic orbits with adequate properties for polar observation of the Earth and moon is developed under the simplified but nonautonomous dynamics of the solar-sail augmented Earth–moon circular restricted three-body problem. The novel orbits, termed “distant-circular orbits,” are found through differential correction and continuation and employ a simple sun-facing steering law for the solar sail. A basic coverage analysis shows that one of the distant-circular orbits is capable of providing continuous coverage of both the Earth’s and lunar north (or south) poles with just a single sailcraft at a minimum elevation angle of 14 deg and an average range of six Earth–moon distances. Moreover, simple transfer trajectories between orbits of the family are found, so that the sailcraft can switch between observing the northern and southern latitudes of the Earth and moon during a single mission. Subsequently, using multiple-shooting differential correction, all results are migrated to a higher-fidelity dynamic framework that considers, among others, the eccentricity of the moon’s orbit. The perturbations cause the periodicity of the orbits to break, turning them into seemingly quasi-periodic orbits, but it is shown that the coverage capabilities are maintained. Finally, an active control strategy is developed to counteract part of the perturbing effects such that, by appropriately steering the sail, the apparent quasi-periodicity of the orbits is enhanced and the deviation from the unperturbed orbits is reduced.
Gleb Merkulov, Martin Weiss, Tal Shima
Journal of Guidance, Control, and Dynamics pp 1-14; https://doi.org/10.2514/1.g006190

Abstract:
A guidance law for intercepting a stationary target is derived based on solving the minimum effort optimal control problem with fixed terminal time and a quadratic approximation of the kinematic equations. It is proven that this optimal control problem has, in general, a unique solution. Based on this solution, a guidance law is proposed that is shown to be implementable based on typically available sensor data, using a semi-analytic procedure. Numerical simulations show that the solution based on the quadratic kinematics approximation matches closely the solution based on the original nonlinear kinematics that can only be obtained by numerical optimization.
Dzung Tran, David Casbeer, Eloy Garcia, Isaac E. Weintraub, Dejan Milutinović
Journal of Guidance, Control, and Dynamics pp 1-8; https://doi.org/10.2514/1.g005925

Peng Zhao, Heinz Erzberger, Yongming Liu
Journal of Guidance, Control, and Dynamics pp 1-19; https://doi.org/10.2514/1.g005825

Abstract:
A new method for efficient trajectory planning to resolve potential conflicts among multiple aircraft is proposed. A brief review of aircraft trajectory planning and conflict resolution methods is given first. Next, a new method is proposed that is based on a probabilistic conflict risk map using the predicted probability of conflict with the intention information of the intruders. The risk-map-based method allows the path planning algorithm to simultaneously account for many uncertainties affecting safety, such as positioning error, wind variability, and human errors. Following this, A* algorithm is used to find the cost-minimized trajectory for a single aircraft by considering all other aircraft as intruders. Search heuristic method is implemented to iterate the A* algorithm for all aircraft to optimize the trajectory planning. Convergence and computation efficiency of the proposed method are investigated in detail. Numerical examples are used to illustrate the effectiveness of the proposed method under several important scenarios for air traffic control, such as wind effects, non-cooperative aircraft, minimum disturbance of pilots, and deconflict with flight intent information. Several conclusions are drawn based on the proposed method.
Wei Dong, Chunyan Wang, Jianan Wang,
Journal of Guidance, Control, and Dynamics pp 1-15; https://doi.org/10.2514/1.g005971

Abstract:
In this paper, a distributed three-dimensional (3D) nonsingular cooperative guidance law is designed for multiple missiles with different seeker’s field-of-view (FOV) constraints to achieve salvo attack against a stationary target. The guidance law is derived from an extended biased proportional navigation guidance (PNG). The PNG is augmented by a cooperative guidance term to ensure that times-to-go of the missile group reach consensus in a fixed time before interception. Two auxiliary functions are included into the biased guidance term to guarantee nonsingularity of the guidance law and meet the FOV constraints. The proposed design does not require guidance law switching that is used in some existing biased or multistage guidance designs, which allows for a smooth guidance command. A feasible impact time set is given for the cooperative mission when applying the proposed guidance law. The nonsingularity, FOV constraint satisfaction, and closed-loop stability of the proposed guidance law are theoretically analyzed and proved. Moreover, the criteria for selecting all guidance parameters are provided to facilitate the guidance design. Finally, numerical simulations with comparative studies are conducted to verify the effectiveness of the proposed guidance law and demonstrate the advantages over existing cooperative guidance laws.
, Yusuke Oki, Yuichi Tsuda
Journal of Guidance, Control, and Dynamics pp 1-23; https://doi.org/10.2514/1.g005564

Abstract:
The orbital motion of spacecraft around asteroids is strongly disturbed primarily because of solar radiation pressure (SRP) and higher-order gravitational forces. To achieve stable orbits in such an environment, the implementation of frozen orbits is a promising approach. This research derives semi-analytical solutions of frozen orbits subject to SRP and zonal gravity up to the fourth order based on singly averaged Lagrange planetary equations. Moreover, the stability of frozen orbits is characterized analytically by introducing linearized variational equations, revealing the complex eigenstructures of the proposed frozen orbits. These analytical theories identify several different types of stable frozen orbits, which are further validated via high-fidelity numerical simulations. Consequently, this paper demonstrates the feasibility and intriguing dynamic characteristics of frozen orbits around asteroids.
Hugo Fournier, Paolo Massioni, Minh Tu Pham, Laurent Bako, Robin Vernay, Michele Colombo
Journal of Guidance, Control, and Dynamics pp 1-15; https://doi.org/10.2514/1.g006084

Abstract:
This work concerns the problem of gust load alleviation of a flexible aircraft by focusing on Airbus’s XRF1 aircraft concept, with a fully actuated wing. The aircraft is equipped with a lidar sensor, which measures the wind velocity ahead of it, together with standard sensors. Based on the available measurements, controllers are then designed by H∞ and μ syntheses, with emphasis put on the multiple-input multiple-output robustness in order to reduce a selected set of loads due to the wind, hence potentially saving mass in the aircraft design. A state-space model of the flexible aircraft is obtained by means of an aeroelastic computation and system identification from frequency data. The controllers’ performance is evaluated through their capability to reduce shear force, bending, and torsion moments on different locations of the aircraft in response to different types of discrete gusts and continuous turbulence; the constraints of the sensors and the actuators are taken into account. The gain in performance due to the use of lidar is assessed, and a tradeoff is discussed concerning the optimal measurement distance. Finally, the closed-loop robustness is assessed by simulations where different types of uncertainties are applied to the system.
David Löbl, , Martin Weiss, Tal Shima
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1638-1648; https://doi.org/10.2514/1.g004425

Abstract:
This paper proposes a novel concept for automatic docking of a boom-receptacle aerial refueling system adequate for civil aerial transportation. The receiving aircraft is assumed to keep straight and steady flight, and the docking maneuver is performed exclusively by the tanker and its boom system. As opposed to the conventional approach, the docking maneuver consists in a coordinated and guided motion of the tanker and the boom arm that is simultaneous with the extension of the nozzle tip. To achieve this, a cooperative guidance algorithm is derived in a systematic manner. The first step is to reduce the docking problem to a planar kinematic guidance problem. Subsequently, the cooperative guidance law algorithm is derived and applied to generate commands for the inner-loop controllers of the tanker aircraft and the boom. The ability to achieve successful docking is demonstrated using numerical simulations, and advantages of this concept are highlighted using a comparison with a baseline controller that uses separated control of the tanker and the boom in a sequential manner.
Hongyan Li, Jiang Wang, Shaoming He, Chang-Hun Lee
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1663-1676; https://doi.org/10.2514/1.g005868

Abstract:
This paper investigates the problem of impact-angle-constrained guidance law design against maneuvering target with large initial heading error. The guidance problem is first formulated in the range domain by leveraging a relative reference frame. Based on optimal control theory and optimal error dynamics, the proposed guidance law is derived analytically without using any linearization assumptions. The approximate closed-form solution and exact numerical solution are presented to analyze the characteristics and physical meaning of the proposed guidance law. The key feature of the proposed guidance law lies in its simple implementation and exact nonlinear nature. Hence, the tolerable initial heading error of the proposed approach is larger than that of conventional linear optimal guidance laws. Numerical simulations are conducted to support the analytical findings.
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1578-1592; https://doi.org/10.2514/1.g005519

Abstract:
This paper presents a novel method for nonlinear uncertainty propagation and estimation in orbital dynamics. The proposed technique relies on a Taylor series expansion of the integral flow to model the dynamics around the reference solution and introduces an approximation of the high-order variational equations that reduces the complexity of evaluating the series. In particular, the high-order state-transition tensors (STTs) are approximated by capturing the dominant secular terms. Simple expressions to compute them are provided. The approximation stems from confining the Lyapunov instability of the motion to the time domain. The result is a time-explicit approximation of the STTs that can be used to predict the evolution of the uncertainty distribution accounting for nonlinear effects with minimal overhead. Finally, a high-order version of the extended Kalman filter is developed by implementing the approximation of the nonlinear terms of the Taylor series into an estimation scheme. The performance of the algorithm is evaluated with several practical examples.
Simon Shuster, David Geller, Matthew Harris
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1593-1606; https://doi.org/10.2514/1.g005698

Abstract:
This paper presents an analytic solution for a three-impulse maneuver sequence that reconfigures safety ellipses. Safety ellipses are relative motion trajectories that do not require thrusting to ensure a high probability of short-term collision avoidance. Primer vector theory is used to derive analytic expressions that relate the necessary conditions for optimality to properties of the initial and final safety ellipses. The primer vector analysis is validated numerically using convex optimization and Monte Carlo methods. A general passive safety parameter for relative motion trajectories in near-circular orbits is also introduced. It is shown that for practical safety ellipse reconfiguration scenarios, the maneuver sequence generates optimal transfer trajectories that also remain passively safe.
Tao Fu, Yue Wang
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1607-1620; https://doi.org/10.2514/1.g005832

Abstract:
Orbiting the primary of a binary asteroid system is extremely challenging due to the perturbative effects of the primary’s nonspherical gravity and the secondary’s close-proximity third-body gravity. In this work, the stability of perturbed Keplerian orbits around the primary is investigated from the point of view of the long-term eccentricity oscillation. Numerical investigations indicate that the eccentricity undergoes a large-amplitude oscillation, caused by the secular perturbation of the secondary’s gravity and may cause impact. A two-degree-of-freedom dynamic model is established, based on the doubly averaged, semi-analytical orbital dynamics incorporating effects of the primary’s oblateness and the secondary’s nonspherical third-body gravity. The oscillation of eccentricity, including its phase and amplitude, and its dependence on initial orbital geometry, is investigated through the phase space structure. The results can reveal the origin of the instability, predict stable and unstable regions in the space of orbital elements, and determine the initial orbital geometry that can ensure the secular stability. The binary asteroid system 2003 YT1 is used as an example to present our verifications and analyses, and the results can also be applied to other binary asteroid systems and even planetary systems with the central body’s oblateness and the third-body gravity dominating the perturbative environments.
, Tigran Mkhoyan, Iren Mkhoyan,
Journal of Guidance, Control, and Dynamics, Volume 44, pp 1649-1662; https://doi.org/10.2514/1.g005870

Abstract:
This paper deals with the simultaneous gust and maneuver load alleviation problem of a seamless active morphing wing. The incremental nonlinear dynamic inversion with quadratic programming control allocation and virtual shape functions (denoted as INDI-QP-V) is proposed to fulfill this goal. The designed control allocator provides an optimal solution while satisfying actuator position constraints, rate constraints, and relative position constraints. Virtual shape functions ensure the smoothness of the morphing wing at every moment. In the presence of model uncertainties, external disturbances, and control allocation errors, the closed-loop stability is guaranteed in the Lyapunov sense. Wind tunnel tests demonstrate that INDI-QP-V can make the seamless wing morph actively to resist “1-cos” gusts and modify the spanwise lift distribution at the same time. The wing root shear force and bending moment have been alleviated by more than 44% despite unexpected actuator fault and nonlinear backlash. Moreover, during the experiment, all the input constraints were satisfied, the wing shape was smooth all the time, and the control law was executed in real time. Furthermore, as compared with the linear quadratic Gaussian control, the hardware implementation of INDI-QP-V is easier; the robust performance of INDI-QP-V is also superior.
, Tigran Mkhoyan,
Journal of Guidance, Control, and Dynamics pp 1-19; https://doi.org/10.2514/1.g005921

Abstract:
This paper proposes a nonlinear control architecture for flexible aircraft simultaneous trajectory tracking and load alleviation. By exploiting the control redundancy, the gust and maneuver loads are alleviated without degrading the rigid-body command tracking performance. The proposed control architecture contains four cascaded loops: position control, flight path control, attitude control, and optimal multi-objective wing control. Because the position kinematics are not influenced by model uncertainties, the nonlinear dynamic inversion control is applied. On the contrary, the flight path dynamics are perturbed by both model uncertainties and atmospheric disturbances; thus the incremental sliding mode control is adopted. Lyapunov-based analyses show that this method can simultaneously reduce the model dependency and the minimum possible gains of conventional sliding mode control methods. Moreover, the attitude dynamics are in the strict-feedback form; thus the incremental backstepping sliding mode control is implemented. Furthermore, a novel load reference generator is designed to distinguish the necessary loads for performing maneuvers from the excessive loads. The load references are realized by the inner-loop optimal wing controller, whereas the excessive loads are naturalized by flaps without influencing the outer-loop tracking performance. The merits of the proposed control architecture are verified by trajectory tracking tasks in spatial von Kármán turbulence fields.
Gunner S. Fritsch, Kyle J. DeMars
Journal of Guidance, Control, and Dynamics pp 1-14; https://doi.org/10.2514/1.g005965

Abstract:
Because of limitations in onboard computing, spaceflight navigation has long been relegated to estimation processes that promote computational efficiency over increased model accuracy. Such is the case with fault tolerance methods, where residual editing is the most common practice to screen out erroneous sensor data. This work investigates an alternative approach, where sensor returns classified as faulty are not simply rejected, but are accounted for within the measurement model of the sensor, ultimately leading to a filter with intrinsic fault resistance in lieu of supplementary extensions like residual editing. Several different faulty measurement models are examined by comparing the proposed filter to a baseline filter outfitted with residual editing, where analysis is performed to test relative performance, robustness, and approximation ability of the proposed filter. The proposed approach not only outperforms residual editing, but is also found to be exceptionally robust to both unknown and approximated faulty measurement distributions.
Ignace Ransquin, Denis-Gabriel Caprace, Matthieu Duponcheel, Philippe Chatelain
Journal of Guidance, Control, and Dynamics pp 1-19; https://doi.org/10.2514/1.g006028

Abstract:
In a fuel-efficient extended formation flight of commercial airplanes, the aerodynamic benefits depend on one’s ability to surf wake vortices. This paper presents a wake vortex detection scheme based on the exploitation of the aircraft flight dynamics measurements that effectively enables wake surfing. The study focuses on a two-aircraft formation where the follower senses, successfully locates, and tracks the wake produced by the leader over time. The proposed approach relies on an ensemble Kalman filter that propagates a surrogate model of the formation. The model output is here corrected within the estimator through a comparison with measurements of the full six-degree-of-freedom dynamics of the follower, as well as geometric characteristics of the leader. This essentially waives the need for dedicated hardware devices and only requires episodic communication between the leader and the follower. The efficiency of the novel detection strategy is demonstrated using reference data obtained from large-eddy simulations. It is found that the chosen combination of estimator and dynamics measurements is sufficient to detect the position of the impacting wake as long as the dynamics are accurately reproduced by the surrogate model. Additionally, it is shown that a lack of observability hinders the concurrent estimation of the wake position and strength in the presence of uncertainty. Finally, a simulation case evaluates the fuel savings that an active tracking strategy of the optimal relative positioning provides compared with a wake-independent positioning.
Journal of Guidance, Control, and Dynamics pp 1-11; https://doi.org/10.2514/1.g005891

Abstract:
A Gaussian mixture orbit determination filter is developed using a state vector that consists of equinoctial-like osculating elements. This new filter seeks to reduce the number of Gaussian mixture elements that are needed in order to accurately model the Bayesian posterior distributions that apply to the angles-only orbit determination problem. The modified version of the equinoctial elements replaces the elements h and k, whose sum squared is bounded by 1. The two replacement elements are unbounded, and h and k can be determined from them. This modification allows the orbit determination filter to operate in an unbounded state space. The new state requires the development of a corresponding mixand covariance upper bound due to the particular type of Gaussian mixture filter that is implemented. The upper bound is used in a mixture resampling algorithm in a way which ensures that extended Kalman filter calculations will be sufficiently accurate for each mixand’s computations. The resulting filter is able to reduce the required number of mixands from 5000 to 500 for angles-only orbit determination of a geosynchronous spacecraft.
Rafael M. Bertolin, , Guilherme C. Barbosa, Juliano A. Paulino,
Journal of Guidance, Control, and Dynamics pp 1-19; https://doi.org/10.2514/1.g005783

Abstract:
There are many challenges related to the design and operation of flexible aircraft. Flight control law design for improving handling qualities is one of them because the major problem in the design of controllers then concerns aeroservoelastic stability. To deal with this difficulty, methodologies for flight control law design considering the aeroelastic dynamics of the aircraft are being pursued. In this paper, a static output-feedback-based stability augmentation system is proposed and designed to improve the handling qualities and the structural dynamics decoupling of a flexible aircraft. The design is based on the projective control technique, which allows preserving in the closed-loop system the eigenstructure of certain modes of interest whose dynamic characteristics stem from an optimal state feedback solution. An experimental prototype of a flexible aircraft that mimics a high-altitude long-endurance airplane, called X-HALE, is considered in the case studies. Robustness analysis based on classical and disk-based stability margins, and nonlinear simulations of gusts and turbulent flight conditions evaluated and confirmed the effectiveness of the proposed controller.
Samer Shaghoury, Miroslav Krstić, Kevin Wise
Journal of Guidance, Control, and Dynamics pp 1-11; https://doi.org/10.2514/1.g005573

Abstract:
Extensive effort in controller design of aircraft systems is invested ensuring safe, stable behavior in spite of large parametric uncertainties. Particular attention is placed on anomalous flight conditions harbored by the atmosphere, especially icing. This paper presents a regulation trigger-based adaptive controller to cope with the impact of ice on the aircraft equations of motion and to control the aircraft pitch to the commanded angle. For a pitch model of an aircraft system with the impact of icing, the design of a stabilizing certainty-equivalence controller using backstepping is first given, and it is succeeded by the introduction of a regulation-triggered batch least-squares identifier. A theorem is incorporated that guarantees that 1) pitch angle and pitch rate converge to the setpoint asymptotically, and 2) parameter estimates end after a finite number of switches. Finally, simulation results of an aircraft experiencing icing demonstrate the effectiveness of the identifier, with the trajectory of the iced system using the proposed identifier closely following that of the nominal system.
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