Terminal Accuracy Research Articles

Reinforcement-Learning-Based Robust Guidance for Asteroid Approaching

This paper presents a reinforcement-learning (RL)-based robust low-thrust guidance method for asteroid approaching under process uncertainties. Markov decision processes with stochastic dynamics are formulated for RL. To overcome the problem of low terminal accuracy in RL-based transfer trajectory design, robust zero-effort-miss/zero-effort-velocity (R-ZEM/ZEV) guidance is proposed. Originally, an eigenvalue-related term is defined according to the stability conditions of the ZEM/ZEV feedback system and chosen as the learning parameter, which can significantly improve the robustness of the agent to process uncertainties under the low-thrust magnitude constraint. Moreover, the navigation performance of the asteroid approaching is modeled via the Fisher information matrix and incorporated in the reward function design, which enables optimizing the optical observation performance together with the propellant cost. Thereafter, the proximal policy optimization is adopted to train an RL agent that can efficiently deal with the uncertainties. The effectiveness and efficiency of the proposed method are validated through simulations of a low-thrust spacecraft approaching the asteroid Bennu. The promising results indicate that the proposed method can not only deal with various uncertainties efficiently and autonomously but can also guarantee high terminal accuracy.

Uncertainty-resilient constrained rendezvous trajectory optimization via stochastic feedback control and unscented transformation

This paper proposes an innovative approach for constrained rendezvous trajectory optimization (CRTO) using stochastic optimal feedback control and unscented transform (UT) uncertainty quantification. The method overcomes limitations of traditional deterministic CRTO solutions that suffer from uncontrolled terminal state error growth and severely deteriorated path constraint satisfaction when initial state uncertainty, dynamics uncertainty, and navigation uncertainty are considered. The approach involves constructing a stochastic optimal feedback control (SOFC) problem with chance constraints and introducing linear feedback control to regulate both the mean and variance of terminal state errors. UT is employed to approximately quantify the state errors and their propagation, transforming the SOFC problem into an unconstrained deterministic optimization (UDO) problem. Differential dynamic programming (DDP) is then used to solve the UDO problem. The obtained stochastic optimal solution provides a robust rendezvous trajectory and a corresponding explicit closed-loop guidance law, improving terminal accuracy and path constraint satisfaction in the presence of various considered uncertainties. The influence of different term weights in the objective function on terminal accuracy and path constraint satisfaction is also studied. The effectiveness of the proposed approach is verified through Monte Carlo simulation, demonstrating the robustness of the closed-loop control strategy. The results highlight the potential of the method in enhancing terminal accuracy and path constraint satisfaction in uncertain rendezvous scenarios.

Characterization of the mIF4G Domains in the RNA Surveillance Protein Upf2p.

Thirty percent of all mutations causing human disease generate mRNAs with premature termination codons (PTCs). Recognition and degradation of these PTC-containing mRNAs is carried out by the mechanism known as nonsense-mediated mRNA decay (NMD). Upf2 is a scaffold protein known to be a central component of the NMD surveillance pathway. It harbors three middle domains of eukaryotic initiation factor 4G (mIF4G-1, mIF4G-2, mIF4G-3) in its N-terminal region that are potentially important in regulating the surveillance pathway. In this study, we defined regions within the mIF4G-1 and mIF4G-2 that are required for proper function of Upf2p in NMD and translation termination in Saccharomyces cerevisiae. In addition, we narrowed down the activity of these regions to an aspartic acid (D59) in mIF4G-1 that is important for NMD activity and translation termination accuracy. Taken together, these studies suggest that inherently charged residues within mIF4G-1 of Upf2p play a role in the regulation of the NMD surveillance mechanism in S. cerevisiae.

A Real-Time and Optimal Hypersonic Entry Guidance Method Using Inverse Reinforcement Learning

The mission of hypersonic vehicles faces the problem of highly nonlinear dynamics and complex environments, which presents challenges to the intelligent level and real-time performance of onboard guidance algorithms. In this paper, inverse reinforcement learning is used to address the hypersonic entry guidance problem. The state-control sample pairs and state-rewards sample pairs obtained by interacting with hypersonic entry dynamics are used to train the neural network by applying the distributed proximal policy optimization method. To overcome the sparse reward problem in the hypersonic entry problem, a novel reward function combined with a sophisticated discriminator network is designed to generate dense optimal rewards continuously, which is the main contribution of this paper. The optimized guidance methodology can achieve good terminal accuracy and high success rates with a small number of trajectories as datasets while satisfying heating rate, overload, and dynamic pressure constraints. The proposed guidance method is employed for two typical hypersonic entry vehicles (Common Aero Vehicle-Hypersonic and Reusable Launch Vehicle) to demonstrate the feasibility and potential. Numerical simulation results validate the real-time performance and optimality of the proposed method and indicate its suitability for onboard applications in the hypersonic entry flight.

A deep reinforcement learning-based approach to onboard trajectory generation for hypersonic vehicles

AbstractAn onboard three-dimensional (3D) trajectory generation approach based on the reinforcement learning (RL) algorithm and deep neural network (DNN) is proposed for hypersonic vehicles in glide phase. Multiple trajectory samples are generated offline through the convex optimisation method. The deep learning (DL) is employed to pre-train the DNN for initialising the actor network and accelerating the RL process. Based on the offline deep policy deterministic actor-critic algorithm, a flight target-oriented reward function with path constraints is designed. The actor network is optimised by the end-to-end RL and policy gradients of the critic network until the reward function converges to the maximum. The actor network is considered as the onboard trajectory generator to compute optimal control values online based on the real-time motion states. The simulation results show that the single-step online planning time meets the real-time requirements of onboard trajectory generation. The significant improvement in terminal accuracy of the online trajectory and the better generalisation under biased initial states for hypersonic vehicles in glide phase is observed.

Terminal Adaptive Guidance for Autonomous Hypersonic Strike Weapons via Reinforcement Metalearning

An adaptive guidance system suitable for the terminal phase trajectory of a hypersonic strike weapon is optimized using reinforcement meta learning. The guidance system maps observations directly to commanded bank angle, angle of attack, and sideslip angle rates. Importantly, the observations are directly measurable from radar seeker outputs with minimal processing. The optimization framework implements a shaping reward that minimizes the line-of-sight rotation rate, with a terminal reward given if the agent satisfies path constraints and meets terminal accuracy and speed criteria. This paper shows that the guidance system can adapt to off-nominal flight conditions, including perturbation of aerodynamic coefficient parameters, actuator failure scenarios, sensor scale factor errors, and actuator lag, while satisfying heating rate, dynamic pressure, and load path constraints, as well as a minimum impact speed constraint. This paper demonstrates precision strike capability against a maneuvering ground target and the ability to divert to a new target, the latter being important to maximize strike effectiveness for a group of hypersonic strike weapons. Moreover, this paper demonstrates a threat evasion strategy against interceptors with limited midcourse correction capability, where the hypersonic strike weapon implements multiple diverts to alternate targets, with the last divert to the actual target.

Identification of sensor location and link flow reconstruction using turn ratio and flow sensors in an arterial network

In this article, a quadratic programming problem is considered to identify all link flows in an arterial network when there are unmeasured link flows. A graphical method is provided to determine the minimum number of measurements and sensor locations required to obtain a fully observable model. It is shown that this method is also valid for the augmented graph with turn ratio measurements. If the minimum measurements required are met, a fully determined network can be obtained. If there is not enough measurement, a bound on the magnitude of the resulting inaccuracy in terms of vehicle kilometers traveled (VKT) can be calculated by the proposed linear programming method. The model is that of a queueing network; the parameters describe network geometry, saturation flow rates, turning ratios, timing plan and link flows. Three case studies are conducted to validate this approach. The first two cases are to calculate all missing flows by using a few numbers of measurements and minimum number of measurements required, respectively. Upper and lower bounds in terms of VKT are also calculated for these cases. Third case is to obtain a fully determined network with the minimum number of flow measurements when turn ratio sensors are included. Real measurements are collected from a network in Mugla including 55 links and 16 intersections. Vissim simulator is used to analyze the accuracy of the link flow calculations obtained from the proposed method. The results show that the proposed programming method can calculate the missing flows with a high accuracy and short computation time.

Making video tutorials to help St. Francis of Assisi Parish in practicing the Dolo-dolo motive Ordinarium

In regular masses, the ordinarium song consisting of Kyrie, Gloria, Sanctus, and Agnus Dei with Dolo-dolo motif is the most frequently sung. However, in reality, mistakes often happened when singing this ordinarium song, including inaccuracies in terms of accent and rhythm that do not characterize as the Dolo-dolo motif. This Community Service activity aims to help the parishioners of St. Fransiskus Assisi at BTN-Kupang City to sing the ordinarium song with the Dolo-dolo motif properly and correctly through producing tutorials. Making tutorials began with studying the ordinarium song with the Dolo-dolo motif by Matheus Weruin. Based on the results of the study, the team then made a video tutorial on how to sing the ordinarium song in a good and correct Dolo-dolo motif, starting from how to read the notation to reading the lyrics/poems. As meant to make it easier for people to learn the material provided. The most important matter emphasized in each tutorial is the accent and rhythm of the Dolo-dolo motif of each song. Based on the results from trials in small choir groups and evaluation with partners, using the video tutorial that has been made, the group was able to sing the ordinarium song with the Dolo-dolo motif properly and correctly for each type of sound or combined sound. The video was distributed to choir teams in the parish to be rehearsed and sung in celebration of the mass.

Limit sets in global multiobjective optimization

ABSTRACT Inspired by the recently introduced branch-and-bound method for continuous multiobjective optimization problems from G. Eichfelder, P. Kirst, L. Meng, O. Stein [A general branch-and-bound framework for continuous global multiobjective optimization. J Glob Optim. 2021;80:195–227], we study for a general class of branch-and-bound methods in which sense the generated terminal enclosure and the terminal provisional nondominated set approximate the nondominated set when the termination accuracy is driven to zero. Our convergence analysis of the enclosures relies on constructions from the above paper, but is self-contained and also covers the mixed-integer case. The analysis for the provisional nondominated set is based on general convergence properties of the epsilon-nondominated set, and hence it is also applicable to other algorithms which generate such points. Furthermore, we discuss post-processing steps for the terminal enclosure and provide numerical illustrations for the cases of two and three objective functions.

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.

Geometric Error Propagation Model-Based Accuracy Synthesis and Its Application to a 1T2R Parallel Manipulator

Abstract To meet the increasing requirements for precision hybrid machine tools, this paper presents a geometric error propagation model-based accuracy synthesis method for parallel manipulators (PMs) with one translational and two rotational (1T2R) motion abilities. A unified geometric error propagation model of a family of 1T2R PMs is established with the first-order kinematic perturbation method. A set of geometric error propagation intensity indexes is formulated to describe the geometric error propagation characteristics in a quantitative manner. The equivalent effects of specified terminal accuracy are derived to directly determine the allowable values of all geometric source errors. Based on these, a computation algorithm is summarized for designating a tolerance allocation scheme to meet the specified terminal accuracy of a 1T2R PM. To demonstrate the accuracy synthesis method, a novel 1T2R PM with a 2UPR-1RPS (“R,” revolute joint; “U,” universal joint; “S,” spherical joint; “P,” prismatic actuated joint) topology is taken as an example to allocate geometric tolerances under the specified terminal accuracy. Following the tolerance allocation scheme, a laboratory prototype of the exemplary PM is fabricated and further experimentally measured. The measured kinematic results indicate that the prototype possesses an acceptable position error smaller than 0.15 mm, verifying the feasibility of the proposed accuracy synthesis method. Hence, the proposed method can be applied as a forward tolerance design tool to reduce the design iterations and development risks of low-mobility parallel robots.

Fast convex optimization of vehicle trajectories based on improved trust domain

The re-entry process of lift vehicles faces a variety of complex constraints and path limitations, so fast and accurate trajectory optimization for them is an important topic. This paper proposes a fast trajectory generation method based on improved sequential convex optimization, which simplifies the equations of motion with energy as the independent variable, takes the sine and cosine function of the bank angle as the control variable, and convexities multiple constraints to obtain a computational model that satisfies the optimization conditions. On this basis, the "jitter" phenomenon, which is easy to occur in the optimization process, is improved, and the method of variable trust domain and weight function is proposed to reduce the jump problem in the iterative process, and also to improve the terminal accuracy requirement. Finally, numerical simulations show that the algorithm can efficiently and rapidly solve the re-entry trajectory optimization problem under the inclusion of no-fly zone.

Segmented guidance law for single moving mass controlled reentry vehicle with multiple constraints

This paper addresses the problem of low guidance accuracy when the traditional guidance method is adopted on the single moving mass controlled reentry vehicle (SMMCRV) with multiple constraints. More specifically, the range and the velocity cannot be controlled accurately by the single bank angle. To solve the aforementioned problems, the segmented guidance law is employed for the reentry phase to achieve the goal of considerable range adjustment and meeting multiple constraints, which consists of the reference trajectory planning & tracking method and the modified rolling guidance law, making full use of the range adjustment capability of the high-altitude phase and the deceleration capacity of the low-altitude phase. For the high-altitude phase, it is difficult to guarantee the precise control of the velocity and range with the bank angle. Therefore, the varying-weight trajectory planning method and adaptive trajectory tracking method considering the combination between tracking errors are employed. In addition, to decrease the influence caused by the lateral motion and the multiple changing rolling direction, the lateral logic and improved B-spline fitting method are also proposed. For the low-altitude phase, the lateral deviation is counteracted by the high speed rotation. Considering the influence on the stability of the SMMCRV caused by the too high rotation, the nonlinear error angle command is designed and the finite-time guidance law is proposed to obtain the high guidance accuracy. Compared with the traditional method, lower terminal velocity dispersion, higher terminal accuracy and lower rotation speed can be obtained, which can be also demonstrated by the numerical simulation.

Three-dimensional low-order finite-time integrated guidance and control design with side-window constraint

The infrared seeker has usually been mounted to the side of the hypersonic vehicle's head to reduce the performance degradation caused by the severe aerodynamic heating. In this way, the rotational dynamics of the flight vehicle and the line-of-sight (LOS) need to satisfy a particular constraint so that the target can be located in the seeker's field-of-view (FOV) during the whole engagement. Consequently, the coupling between the centroid dynamic and the rotational dynamic is more significant. To deal with the side-window constraint and the aforementioned significant coupling, the novel vehicle-target relative motion model in the body-LOS coordinate system is introduced to describe the guidance problem accurately. Combined with the dynamics of body angular rates and the fact that the derivative of angular rates appears in the proposed relative motion model, a novel three-dimensional (3D) low-order integrated guidance and control (IGC) design model is obtained. Furthermore, the IGC design with a side-window constraint can be converted to an output constraint problem of a low-order nonlinear system. Meanwhile, the desired reference trajectories of the FOV angles are designed to meet the asymmetric FOV constraint and the terminal accuracy requirement, simultaneously. Based on the asymmetric barrier Lyapunov function (BLF), finite-time stability theory and the modified dynamic surface technique, a novel 3D low-order adaptive finite-time IGC scheme with side-window constraint is proposed in this paper. The finite-time stability of the closed-loop system is proven, and the side-window constraint would never be violated using Lyapunov theory. Finally, the effectiveness and robustness of the newly proposed IGC algorithm are demonstrated by means of numerical simulations.

Kinematic Calibration of Cable-Driven Parallel Robots Considering the Pulley Kinematics

Pulleys used in cable-driven parallel robots (CDPRs) introduce a time-varying geometry that adds significant complexity to the CDPR's kinematic model. The proximal point-to-point method brings significant model error and makes it difficult to achieve high accuracy for CDPRs, especially when the CDPR's scale is small. To solve this problem, this paper establishes the kinematics of CDPRs considering pulley mechanisms and further develops the error model as well as the kinematic calibration method for CDPRs. Firstly, the kinematic characteristics of the pulley mechanisms are analyzed, and the complete kinematic model of CDPRs is established. Then, the error modeling method considering pulley kinematics is established, and the error identification matrix is derived. Based on these results, the kinematic calibration method for CDPRs considering the pulley kinematics is established, including the calibration process and measurement pose selection. Finally, the proposed methods are verified via both simulations and experiments by taking the translational TBot CDPR as an example. The terminal accuracy of the TBot-600 CDPR is improved by 30% with the proposed methods considering the kinematics of pulleys.

A minimal-error-model based two-step kinematic calibration methodology for redundantly actuated parallel manipulators: An application to a 3-DOF spindle head

Zero offsets and geometric source errors will significantly degrade the kinematic accuracy of redundantly actuated parallel manipulators (RAPMs). To relieve the influences of these factors, this paper presents a minimal-error-model based two-step kinematic calibration methodology for this type of parallel manipulators. A novel 3-DOF spindle head with a 2UPR&2RPS topology is taken as an example to demonstrate the kinematic calibration methodology. The proposed kinematic calibration methodology includes three critical steps: (1) a set of general principles is proposed to eliminate redundant geometric source errors in the manipulator to derive a minimal error model that includes the least number of geometric source errors; (2) a sensitivity analysis is carried out using the Monte-Carlo simulation to reveal the relative impact of geometric source errors on the terminal accuracy; (3) a hierarchical identification strategy composed of a coarse identification and a fine identification is proposed, based on which a two-step calibration methodology is constructed. Finally, a set of calibration experiments is performed to verify the effectiveness of the proposed calibration methodology.

С. В. Бахрушин в Институте Красной профессуры: Лекции по истории народов Сибири. 1936 г.

The publication is to introduce into scientific use two lectures read by the historian Sergei V. Bakhrushin to his students at the Institute of Red professors in 1936. The published document thematically falls within the field of history and ethnography of Siberia. Bakhrushin’s contribution to this scholarship was significant: he provided a holistic view on the development of Siberia in the 16th–17th centuries and on situation of the peoples inhabiting it; and introduced into scientific use a rich body of archival documents. Thus, any unpublished materials from his heritage are of great interest, particularly, data on his work in the higher school. The document illustrates his manner of presenting historical material and his style of communication with his audience. Bakhrushin began lecturing to the “red professors” after his exile under the Academic Trial. In contrast to his published works and lectures, the document, being a written reproduction of oral speech, includes some errors and inaccuracies. The lectures are important for understanding historical geography and history of the indigenous peoples of Siberia. However, topical contribution of these lectures is greater: they reveal the foundations of the Marxist concept of colonization and economic development of Siberia, which turned into an interesting synthesis of Marxism and national concept of the Russian colonization of the 17th century. The document has been found in the Russian State Historical Archive (GARF). It is being published according to the modern rules of spelling and punctuation, but some errors and inaccuracies in the historical terms and toponyms are preserved and corrected in footnotes. Сommentary preceding the publication of the document is of particular importance, as it brings the source up to date and characterizes the specifics of dialogue in the communist institute in the mid-1930s.

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

This paper proposes a novel hybrid algorithm called Fractional-order Particle Swarm optimization Gravitational Search Algorithm (FPSOGSA) and applies it to the trajectory planning of the hypersonic lifting reentry flight vehicles. The proposed method is used to calculate the control profiles to achieve the two objectives, namely a smoother trajectory and enforcement of the path constraints with terminal accuracy. The smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide (QEG) scheme. The aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement scheme. The maximum heating rate path constraint is enforced through the angle of attack parameterization. The Common Aero Vehicle (CAV) flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization (PSO) method and the standard Gravitational Search Algorithm (GSA). The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.

Predictable real-time constraints reveal anticipatory strategies of coupled planning in a sequential pick and place task.

Planning a sequence of two motor elements is much more than concatenating two independent movements. However, very little is known about the cognitive strategies that are used to perform fluent sequences for intentional object manipulation. In this series of studies, the participants' task was to reach for and pick to place a wooden cylinder to set it on a place pad of three different diameters, which served to modify terminal accuracy constraints. Participants were required to perform the sequences (1) at their preferred speed or (2) as fast as possible. Action kinematics were recorded with the Qualisys motion-capture system in order to implement a real-time protocol to get participants to engage in a true interactive relation. Results revealed that with low internal constraints (at preferred speed), low coupling between the two elements of the motor sequence was observed, suggesting a step-by-step planning strategy. Under high constraints (at fastest speed), an important terminal accuracy effect back propagated to modify early kinematic parameters of the first element, suggesting strong coupling of the parameters in an encapsulated planning strategy. In Studies 2 and 3, we further manipulated instructions and timing constraints to confirm the importance of time and predictability of external information for coupled planning. These findings overall sustain the hypothesis that coupled planning can take place in a pick and place task when anticipatory strategies are possible. This mode of action planning may be the key reason why motor intention can be read through the observation of micro variations in body kinematics.

A robust hybrid nonlinear guidance law for intercepting a non-cooperative maneuvering target

ABSTRACTThis paper has proposed a new robust hybrid nonlinear guidance law, which accounts for a missile’s terminal line-of-sight (LOS) angle constraint, in order to intercept a non-cooperative maneuvering target. The proposed hybrid nonlinear guidance strategy consists of two phases; in the first phase, a guidance law named PIGL is derived from prescribed performance control and the inertial delay control method. In PIGL, a revised prescribed performance function is put forward, and a prescribed performance controller with unknown uncertainties is then derived. The controller smoothly drives both the LOS angle and its rate to a predesigned small region under unknown uncertainties that are induced by target’s maneuvers within a fixed time. Then, a guidance law named SIGL is activated, which is derived from sliding mode control and inertial delay control. By driving the desired sliding mode variable to zero within a finite time, the SIGL guidance law is able to achieve high terminal interception accuracy. The robustness of both of the proposed sub-guidance laws has been proved explicitly in this paper. The hybrid guidance law has the advantage of a tunable convergence rate of the LOS angle and the rate of the LOS angle at the beginning period, by which an excessive large initial maneuver can be avoided. Meanwhile, the hybrid guidance law also has the advantage of lower sensitivity to errors in the estimation of the time-to-go.