Iterative Guidance Research Articles

Onboard Burn Targeting and Guidance of NASA Human Flight Vehicles

The mission requirements of crewed space vehicles flown by NASA drove the development of new techniques for burn targeting and guidance for ascent, rendezvous, lunar landing, and deorbit. The Saturn V Iterative Guidance Mode used an approximately optimal steering law that could adjust the trajectory to compensate for performance issues while meeting trajectory constraints at propulsion-system cutoff. Hypersurface targeting provided constraints for the Saturn V Trans-Lunar Injection burn. E Guidance, in quadratic- and linear-acceleration forms, provided closed-loop descent and ascent guidance for the Apollo Lunar Module. The Space Shuttle’s Powered Explicit Guidance algorithm was more flexible than Apollo-era guidance algorithms, and it had better convergence characteristics, enabling it to support challenging abort profiles. The Space Launch System has built on the heritage of the Space Shuttle’s guidance algorithm. The Orion spacecraft’s Two-Level Targeter enables onboard, autonomous targeting of an entire mission profile subject to three-body dynamics in cislunar space. Orion uses Shuttle-derived guidance as the basis for an orbit-guidance package with more capability than guidance algorithms of previous vehicles.

Adaptive closed-loop maneuver planning for low-thrust spacecraft using reinforcement learning

Autonomy is an increasingly essential component of future space missions, and new technologies are necessary to accommodate off-nominal occurrences onboard that may pose risks to mission success. Identifying a suitable maneuver plan for onboard, low-thrust mission applications in cislunar space remains challenging, particularly in the case of unanticipated events. This investigation addresses this challenge by demonstrating artificial neural networks as promising tools for accurately estimating startup solutions for a conventional targeting-based iterative guidance and control algorithm. This blended approach produces a robust ‘hybrid’ architecture that simultaneously benefits from the computational simplicity of neural networks and the robustness of differential corrections to satisfy mission requirements. In this paradigm, a multiple shooting scheme is incorporated directly into a reinforcement learning process, tasking the resulting neural network controller with convergence basin identification for trajectory recovery. Rapid low-thrust maneuver planning is demonstrated in a ‘runaway’ spacecraft scenario, where deviation over time from a planned near rectilinear halo orbit path renders stationkeeping ineffective and demands an alternative approach to determine an effective recovery plan. The proposed Neural Network-Initialized Targeting (NNIT) algorithm significantly extends the recovery window compared to a crossing-control orbit maintenance approach and exhibits promising results in identifying both the timing and control components for low-thrust maneuver plans.

Building an Academic Infrastructure for Rigorous Testing of Online Platforms to Support Family Caregivers

AbstractBackgroundWith COVID‐19, online opportunities to support families living with dementia are becoming increasingly important. However, academic institutions are typically not prepared to develop and test online platforms. We present a case study to describe steps for creating an infrastructure to test an online platform, WeCareAdvisor (WCA). WCA provides caregivers disease education and tailored strategies to manage dementia‐related behavioral symptoms using the DICE Approach. WCA was previously tested in a small, randomized trial demonstrating positive caregiver outcomes. To advance its evidence‐base, WCA is being tested in a NIA‐funded Stage III efficacy trial with a national sample of 326 caregivers.MethodTo test WCA, an infrastructure in the academic institution had to be created to address HIPAA compliance, privacy considerations, integrate user and developer input, and support rigorous trial methodologies. Through key informant interviews and literature reviews, we established a six‐step process: 1) Identifying and engaging key stakeholders (legal, Information Technology offices, research team, software company); 2) Creating software development agreement with stakeholder input; 3) Detailing scope of work and an oversight structure of software company, 4) Developing formal agreements with the software company, 5) Conducting security assessments with university IT offices; and 6) Establishing formal vendor status of the software company. This also necessitated new roles and responsibilities of research team members.ResultThe six‐step process was labor intensive, transpired over 12 months, and involved over 15 iterative meetings with investigators, project staff, and stakeholders. Careful coordination of stakeholders to provide practical and iterative guidance at each of the six steps was essential. Deliberations resulted in app store access, URLs and domains, and compliance and privacy statements reviewed and approved by various university offices, and then launching WCA on app stores for access by study participants.ConclusionResearchers and academic institutions have varying levels of understanding and readiness to engage in infrastructure development to rigorously test online platforms. Our approach resulted in an effective infrastructure for testing WCA which can be used by other researchers. Development of an infrastructure requires new skills for investigators, engaging multiple stakeholders, appropriately budgeting for this activity, and allocating sufficient start‐up time.

Temporal knowledge graphs reasoning with iterative guidance by temporal logical rules

Reasoning is essential for the development of large temporal knowledge graphs, which aim to infer new facts based on existing ones. Recent temporal knowledge graph reasoning methods mainly embed timestamps into low-dimensional spaces. These methods focus on entity reasoning, which cannot obtain the specific reasoning paths. More importantly, they ignore the logic and explanation of reasoning paths in temporal knowledge graphs (TKGs). To overcome this limitation, we propose a novel Temporal Logical reasoning Model, denoted as TLmod. This model represents a reasoning process that works through iterative guidance by temporal logical rules. More importantly, we propose two principles of temporal logical rules and define five types of temporal logical rules. Meanwhile, considering the diversity of temporal logical rules, we propose a pruning strategy for obtaining them and calculating the confidence score by combining traversing and random selection. Experimental results show that our model outperforms most metrics compared to prior state-of-the-art baselines across two benchmarks. In addition, analysis of the ablation experiment reveals the validity and importance of temporal logical rules in TKGs.

An Iterative Guidance and Navigation Algorithm for Orbit Rendezvous of Cooperating CubeSats

Modern space missions often require satellites to perform guidance, navigation, and control tasks autonomously. Despite their limited resources, small satellites are also involved in this trend, as in-orbit rendezvous and docking maneuvers and formation flying have become common requirements in their operational scenarios. A critical aspect of these tasks is that these algorithms are very much intertwined with each other, although they are often designed completely independently of one another. This paper describes the design and simulation of a guidance and relative navigation architecture for the rendezvous of two cooperating CubeSats. The integration of the two algorithms provides robustness to the solution, by simulating realistic levels of noise and uncertainty in the guidance law implementation. The proposed guidance law is derived based on the linearized equations of orbital motion, written in terms of spherical coordinates. The trajectory is iteratively corrected at a fixed time step, so that errors from the navigation and the initial orbital condition can be recovered. The navigation algorithm processes the bearing and range measurements from a camera and an intersatellite link through an unscented filter to provide the information required from the guidance law. A Monte Carlo campaign based on a 3-DOF simulation demonstrates the effectiveness of the proposed solution.

Online trajectory optimization and guidance algorithm for space interceptors with nonlinear terminal constraints via convex programming

PurposeIn this paper, an online convex optimization method for the exoatmospheric ascent trajectory of space interceptors is proposed. The purpose of this paper is to transform the original trajectory optimization problem into a sequence of convex optimization subproblems.Design/methodology/approachFor convenience in calculating accuracy and efficiency, the complex nonlinear terminal orbital elements constraints are converted into several quadratic equality constraints, which can be better computed by a two-step correction method during the iteration. First, the nonconvex thrust magnitude constraint is convexified by the lossless convexification technique. Then, discretization and successive linearization are introduced to transform the original problem into a sequence of one convex optimization subproblem, considering different flight phases. Parameters of trust-region and penalty are also applied to improve the computation performance. To correct the deviation in real time, the iterative guidance method is applied before orbit injection.FindingsNumerical experiments show that the algorithm proposed in this paper has good convergence and accuracy. The successive progress can converge in a few steps and 3–4 s of CPU time. Even under engine failure or mission change, the algorithm can yield satisfactory results.Practical implicationsThe convex optimization method presented in this paper is expected to generate a reliable optimal trajectory rapidly in different situations and has great potential for onboard applications of space interceptors.Originality/valueThe originality of this paper lies in the proposed online trajectory optimization method and guidance algorithm of the space inceptors, especially for onboard applications in emergency situations.

Midcourse Iterative Guidance Method for the Impact Time and Angle Control of Two-Pulse Interceptors

To address the need for flexible energy management and impact angle control in the midcourse guidance of modern long-range antiballistic interceptors, an impact time and angle guidance law is designed for the exoatmospheric midcourse flight of antiballistic interceptors, which covers two pulse sections and two coast sections. The problem is described as an optimal control model with discontinuities in the system equations at interior points, and an iterative guidance method is used to efficiently solve the two-point boundary value problem. Simulation results demonstrate the effectiveness of the proposed guidance law; the obtained miss distance accuracy has an order of magnitude of 1 m, and the impact angle accuracy has a 1° order of magnitude while the angle can be achieved.

Surrogate-Based Optimization Design for Air-Launched Vehicle Using Iterative Terminal Guidance

In recent years, the penetration of low-cost air-launched vehicles for nano/micro satellites has significantly increased worldwide. Conceptual design and overall parameters optimization of the air-launched vehicle has become an exigent task. In the present research, a modified surrogate-based sequential approximate optimization (SAO) framework with multidisciplinary simulation is proposed for overall design and parameters optimization of a solid air-launched vehicle system. In order to reduce the large computation costs of time-consuming simulation, a local density-based radial basis function is applied to build the surrogate model. In addition, an improved particle swarm algorithm with adaptive control parameters is proposed to ensure the efficiency and reliability of the optimization method. According to the LauncherOne air-launched vehicle, the overall optimization design problem aims to improve payload capacity with the same lift-off mass. Reasonable constraints are imposed to ensure the orbit injection accuracy and stability of the launch vehicle. The influences of the vehicle configuration, optimization method, and terminal guidance are considered and compared for eight different cases. Finally, the effect on the speed of optimization convergence of employing a terminal guidance module is investigated. The payload capability of the optimized configurations increased by 27.52% and 23.35%, respectively. The final estimated results and analysis show the significant efficiency of the proposed method. These results emphasize the ability of SAO to optimize the parameters of an air-launched vehicle at a lower computation cost.

Iterative Guidance Algorithm for Lunar Soft Landing

A closed-form explicit guidance algorithm for the deceleration, attitude adjustment and final landing phases before lunar probe soft landing is presented in this paper. Guidance with a variable-thrust engine is extended from the iterative guidance mode (IGM) to satisfy the terminal velocity, position, and attitude constraints. The closed form expression, obtained by integrating the acceleration and shutdown time, is analysed to obtain an explicit ex-pression for the velocity and position requirements and vertical touchdown of the spacecraft toward a designated landing site with high terminal accuracy. The influence of the attitude constraint on the motion equation is analysed to calculate the attitude, which is the physical control variable for the guidance loop. The variable thrust IGM formulation ensures the least switch of the thrust magnitude profile based on the analysis result of the residual flight altitude. The simulation results demonstrate that the proposed multi-constrained iterative guidance method can help accomplish an accurate lunar soft landing and that employed the algorithm is simple and easy to implement in engineering practice.

Orbit-Injection Strategy and Trajectory-Planning Method of the Launch Vehicle under Power Failure Conditions

Aiming at the problem of autonomous decision making and trajectory planning (ADMTP) for launch vehicles under power failure conditions, the target degradation order strategy (TDOS) and the trajectory online planning method were studied in this paper. Firstly, the influence of power failure on the orbit-injection process was analyzed. Secondly, the TDOS was proposed according to the mission attribute, failure mode, and multi-payload combination. Then, an online planning method based on the adaptive target update iterative guidance method (ATU-IGM) and radial basis neural network (RBFNN) was proposed, where the ATU-IGM adopted the basic TDOS criterion for generating optimal orbit-injection samples and online guidance instructions, and the RBFNN was used for orbit-injection samples training and online generation of orbital missions. Finally, the comparative simulation analysis was performed under multi-failure conditions. The results showed that the TDOS proposed in this paper could meet the requirements of the mission decision making under different failures, target orbit types, orbit-injection methods, and payload compositions. The online trajectory-planning capability deviation was less than 5%, and the mission decision-making and trajectory-planning time were less than 10 ms. This study provides theoretical support for autonomous decision making and planning of space launch missions.

Powered-Coast-Powered Guidance Reconfiguration Method of Launch Vehicle with Thrust Drop Fault

This paper describes the study of a powered-coast-powered guidance reconfiguration (PCPGR) method used to solve the autonomous rescue problem for the mission profile of a launch vehicle with a coasting phase when the thrust drop fault occurs in the first powered phase (FPP) of the final stage. We first described the constraints of the final stage and the construction of the PCP guidance problem. Then we evaluated the adaptability of the guidance reconfiguration (GR) offline with numerical optimization by adjusting the constraints of the FPP, the coast phase, and the second powered phase. To determine the fault state set where the rocket can enter the prescribed target orbit through the GR initiate, we proposed a Newton method-based rapid replanning method of the transfer orbit that transforms the complex multi-flight phase trajectory planning problem into a feasible transfer orbit search problem to produce a fast solution onboard. Combined with the adaptive adjustment of the coasting time and the iterative guidance mode, we realized the autonomous online rescue of the payload. The simulation results showed that the proposed method achieved a reliable and rapid solution and improved a launch vehicle’s adaptability to a thrust drop fault.

Instantaneous Impact Point Guidance with Coast Arcs for Solid Rockets

This paper proposed an analytical iterative guidance method with the desired instantaneous impact point constraint for solid rockets in “burn-coast-burn” trajectory mode. Solid rocket motors expect to remove the thrust termination mechanism to increase the structural strength and launch reliability, which induce new difficulties and challenges to the guidance problems. In terms of the “Hohmann transfer” principle, a pointing algorithm is deduced in depth to establish the theoretical relations among the ignition time, the required velocity vector, and the orbital element constraints and provides the analytical expression of the ignition time. Then, an analytic solution of the required velocity vector is derived based on orthogonal and nonorthogonal velocity vectors, and a complete guidance logic is used to solve the target orbit elements satisfying the desired instantaneous impact point. Finally, the application of the developed theoretical algorithm in this paper is conducted using a two-stage solid rocket. The proposed guidance method is verified by Monte Carlo simulations, and the testing results demonstrate the adaptability, strong robustness, and excellent performance for different desired impact point missions.

Novel methods for noisy 3D point cloud based object recognition

3D point cloud based object recognition becomes increasingly important in the last few years, as the widely use of point cloud over the low-cost 3D sensors have developed rapidly. However, the obtained 3D point cloud is inevitably contaminated with noise due to physical and environmental factors, which has a negative impact on recognition task. To address this problem, a complete object recognition framework for 3D noisy point cloud is presented into which a pre-processing step of filtering is integrated for the first time. In the filtering phase, our two proposed approaches, named Guided 3D Point Cloud Filter (G3DF) and Iterative Guidance Normal Filter (IGNF), are taken into account to produce high-quality point cloud model. Then, on the basis of advantages of local-based and global-based descriptors, a new type of feature descriptor, called Local-to-Global Histogram (LGH), is proposed, which contains Local Viewpoint Feature Histogram (LVFH) and Local Ensemble of Shape Function (LESF). Experimental results show that the comprehensive classification performance yielded by using proposed filters and descriptors is competitive compared to other state-of-the-art combinations. In particularly, the composition of G3DF and LVFH is more suited for real-time applications.

Autonomous mission reconstruction during the ascending flight of launch vehicles under typical propulsion system failures

In recent years, Chinese Long March (LM) launchers have experienced several launch failures, most of which occurred in their propulsion systems, and this paper studies Autonomous Mission Reconstruction (AMRC) technology to alleviate losses due to these failures. The status of the techniques related to AMRC, including trajectory and mission planning, guidance methods, and fault tolerant technologies, are reviewed, and their features are compared, which reflect the challenges faced by AMRC technology. After a brief introduction about the failure modes of engines that can occur during flight, and the fundamentals of trajectory planning and joint optimization of the target orbit and flight path, an AMRC algorithm is proposed for geostationary transfer orbit launch missions. The algorithm evaluates the residual performance onboard, and plans new objectives and corresponding flight path by iterative guidance mode or segmented state triggered optimization methods in real-time. Three failure scenarios that have occurred during previous LM missions are simulated to check the robustness of the algorithm: imminent explosion risk of the boosters’ engines, thrust drop during the first stage of flight, and being unable to start the engine during the second stage. The payloads would fall from space according to the current design under these conditions, but they were saved with the AMRC algorithm in the simulations, which allowed the rocket to get into the target orbit as intended or the payloads were deployed in other orbits without crashing. Although spaceflight can be very unforgiving, the AMRC algorithm has the potential to avoid the total loss of a launch mission when faced with these kinds of typical failures.

A joint guidance-enhanced perceptual encoder and atrous separable pyramid-convolutions for image inpainting

Satisfactory image inpainting requires visually-exquisite details and semantically-plausible structures, where encoder-decoder networks have shown their potentials but bear undesired local and global inconsistencies, such as blurry textures. To address this issue, we incorporate a perception operation in the encoder, which extracts features from known areas of the input image, to improve textured details in missing areas. We also propose an iterative guidance loss for the perception operation to guide perceptual encoding features approaching to ground-truth encoding features. The guidance-enhanced perceptual encoding features are transferred to the decoder through skip connections, mutually reinforcing the entire encoder–decoder performance. Since the inpainting task involves different levels of feature representations, we further apply atrous separable parallel-convolutions (i.e., atrous separable pyramid-convolutions or ASPC) with different receptive fields in the last guidance-enhanced perceptual encoding feature, which is used to learn high-level semantic features with multi-scale information. Experiments on public databases show that the proposed method achieves promising results in terms of visual details and semantic structures.

Autonomous trajectory planning for launch vehicle under thrust drop failure

An online autonomous rescue strategy and the algorithm for launch vehicle are studied in the case of a thrust drop during ascending flight. First, an iterative guidance method and numerical integration are used to evaluate the remaining carrying capacity. When the target orbit is unreachable, but the lowest safe orbit could be met, an optimal rescue orbit (ORO) needs to be solved. Using the geocentric angle estimation, orbit coordinate system transformation, and convexification, the maximum-height circular orbit in the orbit plane determined by states at failure time, is found under the constraint of geocentric angle. Then, an optimal circular orbit (OCO) relaxing the above constraint is solved by the adaptive collocation method (ACM) using the former solution as initial values. Finally, a decision whether to adjust other orbital elements by comparing the height between OCO and target orbit is made. The algorithm gives priority to the orbit height, optimizes the ORO based on the objective function weights, and makes full use of the advantages of geocentric angle estimation: simplifying the terminal constraints, making the convex optimization achieve good convergence, and improving the effectiveness of the ACM under reasonable initial guess. The simulation results show that the proposed strategy and algorithm are adaptable and, convergent for onboard application.

Geometry and time updaters-based arbitrary-yaw iterative explicit guidance for fixed-thrust boost back of vertical take-off/vertical landing reusable launch vehicles

The typical return flight profile of vertical take-off/vertical landing (VTVL) reusable launch vehicles (RLVs) mainly comprises flip maneuver phase, boost back phase, grid fins deploy phase, among which the boost back phase plays a determinant role in accurate landing of reusable launch vehicles. In order to achieve pinpoint terminal precision in the boost back phase, a geometry and time updaters-based arbitrary-yaw iterative explicit guidance method is presented in this paper. By adopting an analytic motion predictor and abandoning small yaw angle hypothesis, the arbitrary-yaw iterative guidance law is formulated to deal with large yaw guidance problem caused by initial deviations and long-time flight. To compensate for the guidance errors due to the ignorance of terminal position constraint in the baseline guidance, a geometry updater is developed to update the target based on analytical geometry relationship. Furthermore, considering that the terminal target continuously moves following the earth, the time updater is designed to determine the candidate virtual orbit according to the estimated time-to-go. Simulations under various nominal flight trajectories and different initial deviations as well as the Monte Carlo simulation are carried out. Results illustrate that the proposed guidance algorithm performs well, showing high precision, strong adaptability and robustness.

On-line orbit planning and guidance for advanced upper stage

Purpose This paper aims to investigate the problem of on-line orbit planning and guidance for an advanced upper stage. Design/methodology/approach The double impulse optimal transfer orbit is planned by the Lambert algorithm and the improved particle swarm optimization (IPSO) method, which can reduce the total velocity increment of the transfer orbit. More specially, a simplified formula is developed to obtain the working time of the main engine for two phases of flight based on the theorem of impulse. Subsequently, the true anomalies of the start position and the end position for both two phases are planned by the Newton iterative algorithm and the Kepler equation. Finally, the first phase of flight is guided by a novel iterative guidance (NIG) law based on the true anomaly update with respect to the geometrical relationship. Also, a completely analytical powered explicit guidance (APEG) law is presented to realize orbital injection for the second phase of flight. Findings Simulations including Monte Carlo and three typical orbit transfer missions are carried out to demonstrate the efficiency of the proposed scheme. Originality/value A novel on-line orbit planning algorithm is developed based on the Lambert problem, IPSO optimization method and Newton iterative algorithm. The NIG and APEG are presented to realize the designed transfer orbit for the first and second phases of flight. Both two guidance laws achieve higher orbit injection accuracies than traditional guidance laws.

Energy-level structure ofSn3+ions

Laser-produced Sn plasma sources are used to generate extreme ultraviolet (EUV) light in state-of-the-art nanolithography. An ultraviolet and optical spectrum is measured from a droplet-based laser-produced Sn plasma, with a spectrograph covering the range 200 - 800 nm. This spectrum contains hundreds of spectral lines from lowly charged tin ions Sn$^{1+}$ - Sn$^{4+}$ of which a major fraction was hitherto unidentified. We present and identify a selected class of lines belonging to the quasi-one-electron, Ag-like ([Kr]$4d^{10} nl$ electronic configuration), Sn$^{3+}$ ion, linking the optical lines to a specific charge state by means of a masking technique. These line identifications are made with iterative guidance from COWAN code calculations. Of the 53 lines attributed to Sn$^{3+}$, some 20 were identified from previously known energy levels, and 33 lines are used to determine previously unknown level energies of 13 electronic configurations, i.e., $ 7p $, $ (7,8)d $, $ (5,6)f $, $ (6-8)g $, $ (6-8)h $, $ (7,8)i $. The consistency of the level energy determination is verified by the quantum-defect scaling procedure. The ionization limit of Sn$^{3+}$ is confirmed and refined to 328908.4 cm$^{-1}$ with an uncertainty of 2.1 cm$^{-1}$. The relativistic Fock space coupled cluster (FSCC) calculation of the measured level energies are generally in good agreement with experiment, but fail to reproduce the anomalous behavior of the $5d$ $^2$D and $nf$ $^2$F terms. By combining the strengths of FSCC, COWAN code calculations, and configuration interaction many-body perturbation theory (CI+MBPT), this behavior is shown to arise from interactions with doubly-excited configurations.

Knowledge Graph Embedding With Iterative Guidance From Soft Rules

Embedding knowledge graphs (KGs) into continuous vector spaces is a focus of current research. Combining such an embedding model with logic rules has recently attracted increasing attention. Most previous attempts made a one-time injection of logic rules, ignoring the interactive nature between embedding learning and logical inference. And they focused only on hard rules, which always hold with no exception and usually require extensive manual effort to create or validate. In this paper, we propose Rule-Guided Embedding (RUGE), a novel paradigm of KG embedding with iterative guidance from soft rules. RUGE enables an embedding model to learn simultaneously from 1) labeled triples that have been directly observed in a given KG, 2) unlabeled triples whose labels are going to be predicted iteratively, and 3) soft rules with various confidence levels extracted automatically from the KG. In the learning process, RUGE iteratively queries rules to obtain soft labels for unlabeled triples, and integrates such newly labeled triples to update the embedding model. Through this iterative procedure, knowledge embodied in logic rules may be better transferred into the learned embeddings. We evaluate RUGE in link prediction on Freebase and YAGO. Experimental results show that: 1) with rule knowledge injected iteratively, RUGE achieves significant and consistent improvements over state-of-the-art baselines; and 2) despite their uncertainties, automatically extracted soft rules are highly beneficial to KG embedding, even those with moderate confidence levels. The code and data used for this paper can be obtained from https://github.com/iieir-km/RUGE.