Performing rendezvous and proximity operations (RPO) is an important part of the life cycle of many satellite missions. Although several methods have been proposed to develop guidance solutions for RPO problems, they are all based on a nominal description of the dynamical system. In practice, however, various uncertainties must be managed. For example, un-managed uncertainty in the mean motion or orbital velocity can have a large impact on the final position and velocity of the satellite. To obtain a robust guidance solution for such RPO problems and reduce the requirements on feedback, we employ unscented trajectory optimization which uses the unscented transformation as a means to minimize the variance about the terminal target. We show that the standard ( 2n+1 ) unscented transform may not adequately capture the maneuver statistics, prompting the use of higher-order ( 4n+1 ) unscented transformations for improving the reliability of uncertain RPO guidance solutions.

Parameter uncertainties pose significant challenges to implementing open-loop optimal control solutions in practical systems. Trajectory optimization methods that explicitly address the effects of such variations should be used. In this paper, we illustrate that desensitized optimal trajectory should be designed in a closed-loop set up. Moreover, concurrently optimizing the guidance trajectory as well as the fixed feedback gain(s) is advantageous. We show that this 'one-shot' trajectory desensitization method can be applied using the sensitivity function-based approach or unscented trajectory optimization to improve robustness against parameter variations.

In a nutshell, unscented trajectory optimization is the generation of optimal trajectories through the use of an unscented transform. Although unscented trajectory optimization was introduced by the authors about a decade ago, it is reintroduced in this paper as a special instantiation of tychastic optimal control theory. Tychastic optimal control theory (from Tyche, the Greek goddess of chance) avoids the use of a Brownian motion and the resulting Ito calculus even though it uses random variables across the entire spectrum of a problem formulation. This approach circumvents the enormous technical and numerical challenges associated with stochastic trajectory optimization. Furthermore, it is shown how a tychastic optimal control problem that involves nonlinear transformations of the expectation operator can be quickly instantiated using the unscented transform. These nonlinear transformations are particularly useful in managing trajectory dispersions, be they associated with path constraints or targeted values of final-time conditions. This paper also presents a systematic and rapid process for formulating and computing the most desirable tychastic trajectory using the unscented transform. Numerical examples are used to illustrate how unscented trajectory optimization may be used for risk reduction and mission recovery caused by uncertainties and failures.

Model uncertainties and external disturbances present significant challenges in implementing open-loop optimal control solutions for practical systems. Thus, trajectory optimization should be done for the closed-loop plant. In this paper, we illustrate that while it is straightforward to design the nominal optimal input trajectory for a closed-loop system by reinterpreting the control variable, the overall sensitivity reduction remains defined by the loop transmission. However, the cost of feedback can be reduced by designing an alternative input trajectory that is optimized over the plant uncertainties. This is achieved by using unscented trajectory optimization to guide the feedback system. We show that this new approach can enhance the robustness of a practical system without requiring higher-gain feedback control.

The aerothermal load on an aerospace vehicle is one of the most critical conditions during hypersonic flight. To maximize performance, a typical hypersonic vehicle rides the maximum allowable value of the heating-rate constraint during a portion of its flight. Because atmospheric density has high uncertainty, guiding a hypersonic vehicle along a deterministic optimal trajectory will violate the maximum heating-rate limit with an unacceptable probability. To address this problem, we pose the maximum heating rate on the vehicle as a chance constraint in a tychastic trajectory optimization problem (from Tyche, the Greek goddess of chance). To generate a tractable problem formulation, the chance constraint is mapped to a constraint on a deviation measure of the heating rate. The resulting tychastic problem is transcribed to a constrained unscented trajectory optimization problem and solved by a guess-free, spectral algorithm. The validity of the entire approach is independently verified via a Monte Carlo analysis. Sample numerical results demonstrate how risk can be reduced from unsafe (i.e., 70% risk) to safe (i.e., near 0% risk) operations.

Attitude guidance can improve the efficiency of rotational maneuvers and is designed to work in concert with existing attitude control systems. This paper describes the approach and how attitude guidance (specifically minimum-time maneuvering) can be modeled to support initial system design and science feasibility studies through to detailed analysis for flight. Attitude guidance can be leveraged in a variety of ways to reduce the cost of rotating from 'A' to 'B', such as improving the overall slew efficiency of flagship observatories like the James Webb Space Telescope or the Roman Space Telescope. Attitude guidance can be implemented via Hamiltonian programming as part of a mission operations ground process. Autonomy for event-driven architectures is also conceivable with present-day flight processors by using neural networks to autogenerate attitude guidance commands on orbit.

Lunar Reconnaissance Orbiter (LRO) was launched in 2009 to study and map the Moon and is now completing its fifth extended science mission. The LRO (see Figure 1 ) hosts a payload of seven different scientific instruments. The Cosmic Ray Telescope for the Effects of Radiation instrument has characterized the lunar radiation environment and allowed scientists to determine potential impacts to astronauts and other life. The Diviner Lunar Radiometer Experiment (DLRE) has identified cold traps where ice could reside and mapped global thermophysical and mineralogical properties by measuring surface and subsurface temperatures. The Lyman Alpha Mapping Project has found evidence of exposed ice in south polar cold traps as well as global diurnal variations in hydration. The Lunar Exploration Neutron Detector has been used to create high-resolution maps of lunar hydrogen distribution and gather information about the neutron component of the lunar radiation environment. The Lunar Reconnaissance Orbiter Camera (LROC) is a system of three cameras [one wide-angle camera and two narrow-angle cameras (NACs)] mounted on the LRO that capture high-resolution black-and-white images and moderate resolution multispectral (seven-color band) images of the lunar surface. These images can be used, for example, to learn new details about the history of lunar volcanism or the present-day flux of impactors. The Miniature Radio Frequency (Mini-RF) instrument is an advanced synthetic aperture radar (SAR) that can probe surface and subsurface coherent rock contents to identify the polarization signature of ice in cold traps. The Lunar Orbiter Laser Altimeter (LOLA) has been used to generate a high-resolution, 3D map of the Moon that serves as the most accurate geodetic framework available for co-locating LRO (and other lunar) data. The data produced by the LRO continue to revolutionize our scientific understanding of the Moon, and are essential to planning NASA’s future human and robotic lunar missions.

Attitude guidance is a concept for implementing performance enhancing rotational maneuvers that uses a conventional closed-loop attitude control system to track an optimized maneuver trajectory. Minimum-time attitude guidance is presently being used for executing fast occultation avoidance maneuvers on NASA’s Lunar Reconnaissance Orbiter (LRO). A challenge in operationalizing the idea is related to the limited size of the spacecraft’s command buffer, which was not designed with maneuver tracking in mind. In this paper, we propose an interpolating pre-filter built on B-splines that can be used on board to process downsampled maneuver commands (to save buffer space) and provide attitude control inputs at the servo-rate. The approach is validated using a high-fidelity simulation of the LRO developed at NASA’s Goddard Space Flight Center.

No AccessEngineering NotesConnections Between Proportional Navigation and Terminal Velocity Maximization GuidanceIn-Soo Jeon, Mark Karpenko and Jin-Ik LeeIn-Soo JeonAgency for Defense Development, Daejeon 34186, Republic of Korea, Mark KarpenkoNaval Postgraduate School, Monterey, California 93943 and Jin-Ik LeeAgency for Defense Development, Daejeon 34186, Republic of KoreaPublished Online:20 Oct 2019https://doi.org/10.2514/1.G004672SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] Imado F., Kuroda T. and Miwa S., "Optimal Midcourse Guidance for Medium-Range Air-to-Air Missiles," Journal of Guidance, Control, and Dynamics, Vol. 13, No. 4, 1990, pp. 603–608. https://doi.org/10.2514/3.25376 LinkGoogle Scholar[2] Benson D. A., Huntington G. T., Thorvaldsen T. P. and Rao A. 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I., "Analysis on Optimality of Proportional Navigation with Time-Varying Velocity," Journal of the Korean Society for Aeronautical and Space Sciences, Vol. 37, No. 10, 2009, pp. 998–1001 (in Korean). https://doi.org/10.5139/JKSAS.2009.37.10.998 CrossrefGoogle Scholar Previous article Next article FiguresReferencesRelatedDetailsCited byClosed-Form Impact-Angle-Control Guidance of Nose-Dive Missiles for Maximum Terminal Speed9 April 2021 | International Journal of Aeronautical and Space Sciences, Vol. 22, No. 6Learning prediction-correction guidance for impact time controlAerospace Science and Technology, Vol. 119Nonlinear Model Predictive Control and Collision-Cone-Based Missile Guidance AlgorithmDiganta Bhattacharjee, Animesh Chakravarthy and Kamesh Subbarao21 May 2021 | Journal of Guidance, Control, and Dynamics, Vol. 44, No. 8Near-Optimal Midcourse Guidance for Velocity Maximization with Constrained Arrival AngleHongyan Li, Shaoming He, Jiang Wang, Hyo-Sang Shin and Antonios Tsourdos18 October 2020 | Journal of Guidance, Control, and Dynamics, Vol. 44, No. 1Event-Trigger based Adaptive-Robust Guidance Strategy with Input SaturationNonlinear Model Predictive Control based Missile Guidance for Target InterceptionDiganta Bhattacharjee, Animesh Chakravarthy and Kamesh Subbarao5 January 2020 What's Popular Volume 43, Number 2February 2020 CrossmarkInformationCopyright © 2019 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAir NavigationBallistic MissileControl TheoryGuidance, Navigation, and Control SystemsHoming GuidanceMissile Guidance and ControlMissile Systems, Dynamics and TechnologyMissilesNavigational GuidanceOptimal Control Theory KeywordsTerminal VelocityProportional NavigationAerodynamic DragGuidance LawsTransversality ConditionHoming GuidanceClosed LoopNumerical OptimizationCommand MissileHoming MissilePDF Received22 July 2019Accepted18 September 2019Published online20 October 2019

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.

An uninhabited aerial vehicle (UAV) equipped with an electro-optical payload is tasked to collect over a set of discrete regions of interest. By considering the discrete regions to be obstacles that must be engaged, rather than avoided, a new mathematical technique emerges. To frame the anti-obstacle-avoidance problem, we use Kronecker indicator functions to localize the totality of constraints associated with the discrete regions. A rich class of payoff functionals can be defined using nonsmooth constructs. We show that the integrated sensor planning, scheduling and UAV maneuvering problem can be framed under a single unified mathematical framework. The price for this unification is nonsmooth calculus. The practical viability of the new problem formulation is demonstrated by solving a sample problem using DIDO © - a guess-free, advanced MATLAB ® optimal control toolbox for solving dynamic optimization problems.

An off-target look angle control guidance law for nonmaneuvering moving targets is proposed. Unlike impact angle control guidance laws whose angle requirement is defined on the target, the proposed guidance law controls a look angle on a virtual circle centered on the moving target in the horizontal plane. A closed-form solution is derived using optimal control theory for a nonlinear problem formulation. The resulting guidance law can be expressed as a version of biased proportional navigation. It is shown how the new off-target look angle control can be applied in midcourse guidance problems to handover to terminal homing. The scenarios described include generating a collision course condition at a designated distance from a moving target, circling over a moving target, and attaining a desired look angle on the circle for a fixed target.

This paper describes a new operational capability for fast attitude maneuvering that is being developed for the Lunar Reconnaissance Orbiter (LRO). The LRO hosts seven scientific instruments. For some instruments, it is necessary to perform large off-nadir slews to collect scientific data. The accessibility of off-nadir science targets has been limited by slew rates and/or occultation, thermal and power constraints along the standard slew path. The new fast maneuver (FastMan) algorithm employs a slew path that autonomously avoids constraint violations while simultaneously minimizing the slew time. The FastMan algorithm will open regions of observation that were not previously feasible and improve the overall science return for LRO’s extended mission. The design of an example fast maneuver for LRO’s Lunar Orbiter Laser Altimeter that reduces the slew time by nearly 40% is presented. Pre-flight, ground-test, end-to-end tests are also presented to demonstrate the readiness of FastMan. This pioneering work is extensible and has potential to improve the science data collection return of other NASA spacecraft, especially those observatories in extended mission phases where new applications are proposed to expand their utility.

This paper presents a computational optimal control problem formulation for solving optimal gain programs for pure proportional navigation (PPN). The influence of 3 degree-of-freedom (DOF) missile flight dynamics is considered explicitly. The development provides an approach for exploring the optimality of conventional fixed-gain missile guidance laws (that consider missile kinematics only) and for extending the performance of conventional PPN. Algebraic constraint equations are utilized to sidestep computational challenges associated with the engagement equations. Furthermore, the navigation gain may be box-constrained to ensure that the solution retains sufficient control authority against an uncertain engagement. The results show that a fixed navigation gain is not acceleration optimal when 3-DOF missile flight dynamics are considered and that implementing an optimal gain program can be utilized to improve impact angles and/or acceleration margins as compared to fixed-gain PPN.

Closed-loop attitude steering is a concept for implementing an attitude trajectory by using a conventional quaternion error feedback controller to track the time-varying attitude reference, rather than to simply regulate to a desired orientation. This is done by sampling the reference input and executing the maneuver as a sequence of closely spaced regulating commands that are read out from the spacecraft's command buffer. The idea has been employed in practice to perform zero-propellant maneuvers on the International Space Station and minimum-time maneuvers on NASA's TRACE space telescope as well as NASA's Lunar Reconnaissance Orbiter (LRO). A challenge for operational implementation of the idea is the limited capacity of a space vehicle's command storage buffer, which is normally not designed with attitude tracking in mind. One approach to mitigate the problem is to downsample-and-hold the attitude commands so that the attitude control system (ACS) regulates to a series of waypoints. This article explores the waypoint following dynamics of a quaternion error feedback control law for such an approach. It is shown that downsample-and-hold induces a ripple between downsamples that causes the satellite angular rate to significantly overshoot the desired limit. Analysis in the z-domain is carried out in order to understand the phenomenon. An interpolating Chebyshev-type filter is proposed that allows the desired attitude trajectory to alternatively be encoded in terms of a small set of filter coefficients. Using the interpolating filter, the continuous-time reference trajectory can be reconstructed and issued at the ACS rate but with significantly reduced memory requirements. The ACS of the LRO is used as an example to illustrate the behavior of a practical ACS.

Attitude control system failures are often mission ending even when the mission payload remains operational. In this paper, the concept of unscented guidance is applied to accurately reorient a reaction wheel satellite in the absence of feedback. It is shown that it is possible for a properly designed open-loop maneuver to achieve terminal attitude errors that are comparable with closed-loop control in the presence of uncertainty in the satellite inertia tensor. Following the open-loop maneuver, control can be handed over to a fine pointing control mode that uses other sensors, such as a fine guidance sensor or a star tracker to close the loop for science acquisition. The approach presented here enables large angle attitude control to be recovered so that operations may be continued, even in the event of a total rate gyroscope failure.

The agility of a rigid-body spacecraft can be expressed in terms of a geometric, three-dimensional, solid called the agilitoid. Originally developed as a means for explaining the concept of "hidden agility" made visible through the use of optimal control techniques, a modified agilitoid called an agility envelope is presented here that is compatible with conventional eigenaxis maneuvers. This paper demonstrates how the agility envelope can be applied to size an attitude control system (ACS) and/or assess the capability of an existing design. Analysis of the James Webb Space Telescope (JWST) ACS shows that the agility envelope accurately predicts the true capability of the ACS: a 90 deg maneuver can actually be completed 15% faster than the conventional back-of-the-envelope slew-sizing equations suggest. The utility of the agility envelope is further illustrated by showing how an alternative control allocation scheme can reduce the JWST torque and momentum requirements by 40%. The otherwise hidden agility can be recovered to enhance the slew performance of the JWST or allow the reaction wheel array to be reduced from six to five wheels, while meeting existing maneuver requirements. The agility envelope allows such design trades to be studied without the need to perform detailed simulations of the attitude control system.

A dynamic optimization problem is employed to aid operators of large-scale satellite constellations with automated mission planning and data collection. Traditional techniques focus on graph-theoretic ideas that use heuristics to simplify the problem. The solution presented in this paper is formulated as a dynamic optimization problem that scales linearly as the number of satellites and ground stations increases. The problem formulation is implemented with the DIDO(C) pseudospectral optimal control solver to produce deconflicted ground antenna slew trajectories as a function of parameters and constraints used commonly by satellite operators. In this paper, one such factor, space-to-ground link margin, is used for the proof of concept. Other parameters can include mission priority, asset availability, and onboard spacecraft health. The specific problem solved here is to optimally slew ground-based antennas between multiple satellites that are simultaneously in view of one or more earth stations. The approach is tested using orbiting CubeSats and the Mobile CubeSat Command and Control (MC3) network.

Spacecraft agility is limited by the maximum torque that reaction wheels can provide. Therefore, a reaction wheel array is typically configured to maximize the inscribed sphere of the reaction wheel torque envelope. Agility is then determined by dividing the spherical torque by the maximum principal inertia. This industry standard approach can severely underestimate the true capability of an attitude control system. An agility envelope considers the reaction wheel torque envelope along with the spacecraft inertia tensor. The agility envelope can therefore be used as a means to quantify the conservatism associated with the standard approach in order to improve slew performance of a conventional attitude control system without the need for larger, more costly hardware or new control algorithms. This paper, presents a simple approach for constructing the agility envelope of a reaction wheel attitude control system. The agility envelope is applied to determine design curves for limits on angular acceleration and rate for maneuver design and for finding the reaction wheel skew angles that maximize agility for a given spacecraft configuration. A surprising result is the observation that maximizing the inscribed sphere of the reaction wheel torque envelope does not, in general, optimize agility.

This paper examines the effectiveness of reducing the energy consumption of a reaction-wheel array over the course of a slewing maneuver by steering the attitude of the spacecraft, in situations where it is not possible to command the reaction wheel torque directly. To explore this avenue, a set of constrained nonlinear non-smooth L1 optimal-control problems are formulated and solved. It is demonstrated that energy consumption, dissipative losses, and peak-power load, of the reaction-wheel array can each be reduced substantially, by controlling the input to the attitude control system through attitude steering, thereby avoiding software modifications to flight software.