A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer
Differential dynamic programming algorithm for discrete time orbit transfer optimization
Gershwin, S. B.↗
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A discrete-time differential dynamic programming algorithm with application to optimal orbit transfer
Discrete time differential dynamic programming algorithm with application to optimal orbit transfer
Gershwin, S. B.↗
A near optimal guidance algorithm for aero-assisted orbit transfer
The paper presents a near optimal guidance algorithm for aero-assited orbit plane change, based on minimizing the energy loss during the atmospheric portion of the maneuver. The guidance algorithm makes use of recent results obtained from energy state approximations and singular perturbation analysis of optimal heading change for a hypersonic gliding vehicle. This earlier work ignored the terminal constraint on altitude needed to insure that the vehicle exits that atmosphere. Thus, the resulting guidance algorithm was only appropriate for maneuvering reentry vehicle guidance. In the context of singular perturbation theory, a constraint on final altitude gives rise to a difficult terminal boundary layer problem, which cannot be solved in closed form. This paper will demonstrate the near optimality of a predictive/corrective guidance algorithm for the terminal maneuver. Comparisons are made to numerically optimized trajectories for a range or orbit plane angles.
Calise, Anthony J.↗
Low-thrust orbit transfer optimization with refined Q-law and multi-objective genetic algorithm
An optimization method for low-thrust orbit transfers around a central body is developed using the Q-law and a multi-objective genetic algorithm. in the hybrid method, the Q-law generates candidate orbit transfers, and the multi-objective genetic algorithm optimizes the Q-law control parameters in order to simultaneously minimize both the consumed propellant mass and flight time of the orbit tranfer. This paper addresses the problem of finding optimal orbit transfers for low-thrust spacecraft.
low-thrust orbit transfer↗
Predicting Spacecraft Trajectories by the WeavEncke Method
A combination of methods is proposed of predicting spacecraft trajectories that possibly include multiple maneuvers and/or perturbing accelerations, with greater speed, accuracy, and repeatability than were heretofore achievable. The combination is denoted the WeavEncke method because it is based on unpublished studies by Jonathan Weaver of the orbit-prediction formulation of the noted astronomer Johann Franz Encke. Weaver evaluated a number of alternatives that arise within that formulation, arriving at an orbit-predicting algorithm optimized for complex trajectory operations. In the WeavEncke method, Encke's method of prediction of perturbed orbits is enhanced by application of modern numerical methods. Among these methods are efficient Kepler s-equation time-of-flight solutions and self-starting numerical integration with time as the independent variable. Self-starting numerical integration satisfies the requirements for accuracy, reproducibility, and efficiency (and, hence, speed). Self-starting numerical integration also supports fully analytic regulation of integration step sizes, thereby further increasing speed while maintaining accuracy.
Weaver, Jonathan K.↗
An Evolutionary Optimization System for Spacecraft Design
Spacecraft design optimization is a domian that can benefit from the application of optimization algorithms such as genetic algorithms. In this paper, we describe DEVO, an evolutionary optimization system that addresses these issues and provides a tool that can be applied to a number of real-world spacecraft design applications. We describe two current applications of DEVO: physical design if a Mars Microprobe Soil Penetrator, and system configuration optimization for a Neptune Orbiter.
Orbiter optimization algorithms↗
Evaluation of an optimal guidance algorithm for aero-assisted orbit transfer
A detailed evaluation is performed of a guidance algorithm for aeroassisted orbit transfer that was developed earlier based on the method of matched asymptotic expansions. It is shown that, by exploiting the structure of the matched asymptotic expansion solution procedure, the original problem which requires the solution of a set of 20 implicit algebraic equations can be reduced to a problem of six implicit equations in six unknowns. The main contribution here is that it was possible to obtain a solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the matched asymptotic expansion problem to obtain the feedback controls.
Melamed, N.↗
A real-time guidance algorithm for aerospace plane optimal ascent to low earth orbit
Problems of onboard trajectory optimization and synthesis of suitable guidance laws for ascent to low Earth orbit of an air-breathing, single-stage-to-orbit vehicle are addressed. A multimode propulsion system is assumed which incorporates turbojet, ramjet, Scramjet, and rocket engines. An algorithm for generating fuel-optimal climb profiles is presented. This algorithm results from the application of the minimum principle to a low-order dynamic model that includes angle-of-attack effects and the normal component of thrust. Maximum dynamic pressure and maximum aerodynamic heating rate constraints are considered. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. A nonlinear transformation technique is employed to derived a feedback controller for tracking the computed trajectory. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.
Calise, A. J.↗
Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers
This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.
Goodson, Troy D.↗
Design and Optimization of Low-thrust Orbit Transfers Using Q-law and Evolutionary Algorithms
Future space missions will depend more on low-thrust propulsion (such as ion engines) thanks to its high specific impulse. Yet, the design of low-thrust trajectories is complex and challenging. Third-body perturbations often dominate the thrust, and a significant change to the orbit requires a long duration of thrust. In order to guide the early design phases, we have developed an efficient and efficacious method to obtain approximate propellant and flight-time requirements (i.e., the Pareto front) for orbit transfers. A search for the Pareto-optimal trajectories is done in two levels: optimal thrust angles and locations are determined by Q-law, while the Q-law is optimized with two evolutionary algorithms: a genetic algorithm and a simulated-annealing-related algorithm. The examples considered are several types of orbit transfers around the Earth and the asteroid Vesta.
low-thrust orbit transfer↗
An algorithm for Liapunov stability analysis of complex nonlinear systems with application to the Orbiting Astronomical Observatory
Optimal quadratic Liapunov function generating algorithm for estimating domain of equilibrium attraction of nonlinear star tracker attitude control systems for OAO stability
Chomas, A.↗
Towards the Development of a Global, Satellite-based, Terrestrial Snow Mission Planning Tool
A global, satellite-based, terrestrial snow mission planning tool is proposed to help inform experimental mission design with relevance to snow depth and snow water equivalent (SWE). The idea leverages the capabilities of NASAs Land Information System (LIS) and the Tradespace Analysis Tool for Constellations (TAT C) to harness the information content of Earth science mission data across a suite of hypothetical sensor designs, orbital configurations, data assimilation algorithms, and optimization and uncertainty techniques, including cost estimates and risk assessments of each hypothetical orbital configuration.One objective the proposed observing system simulation experiment (OSSE) is to assess the complementary or perhaps contradictory information content derived from the simultaneous collection of passive microwave (radiometer), active microwave (radar), and LIDAR observations from space-based platforms. The integrated system will enable a true end-to-end OSSE that can help quantify the value of observations based on their utility towards both scientific research and applications as well as to better guide future mission design. Science and mission planning questions addressed as part of this concept include:1. What observational records are needed (in space and time) to maximize terrestrial snow experimental utility?2. How might observations be coordinated (in space and time) to maximize utility? 3. What is the additional utility associated with an additional observation?4. How can future mission costs being minimized while ensuring Science requirements are fulfilled?
Mission Design↗
An adaptive guidance algorithm for an aerodynamically assisted orbital plane change maneuver
Using analysis results from the post trajectory optimization program, an adaptive guidance algorithm is developed to compensate for density, aerodynamic and thrust perturbations during an atmospheric orbital plane change maneuver. The maneuver offers increased mission flexibility along with potential fuel savings for future reentry vehicles. Although designed to guide a proposed NASA Entry Research Vehicle, the algorithm is sufficiently generic for a range of future entry vehicles. The plane change analysis provides insight suggesting a straight-forward algorithm based on an optimized nominal command profile. Bank angle, angle of attack, and engine thrust level, ignition and cutoff times are modulated to adjust the vehicle's trajectory to achieve the desired end-conditions. A performance evaluation of the scheme demonstrates a capability to guide to within 0.05 degrees of the desired plane change and five nautical miles of the desired apogee altitude while maintaining heating constraints. The algorithm is tested under off-nominal conditions of + or -30% density biases, two density profile models, + or -15% aerodynamic uncertainty, and a 33% thrust loss and for various combinations of these conditions.
Blissit, J. A.↗
Orbit design and optimization based on global telecommunication performance metrics
The orbit selection of telecommunications orbiters is one of the critical design processes and should be guided by global telecom performance metrics and mission-specific constraints. In order to aid the orbit selection, we have coupled the Telecom Orbit Analysis and Simulation Tool (TOAST) with genetic optimization algorithms. As a demonstration, we have applied the developed tool to select an optimal orbit for general Mars telecommunications orbiters with the constraint of being a frozen orbit. While a typical optimization goal is to minimize tele-communications down time, several relevant performance metrics are examined: 1) area-weighted average gap time, 2) global maximum of local maximum gap time, 3) global maximum of local minimum gap time. Optimal solutions are found with each of the metrics. Common and different features among the optimal solutions as well as the advantage and disadvantage of each metric are presented. The optimal solutions are compared with several candidate orbits that were considered during the development of Mars Telecommunications Orbiter.
genetic algorithms↗
Optimal control of satellite attitude acquisition by a random search algorithm on a hybrid computer.
Random search algorithm for nonlinear orbital transfer problems applied to optimal control of satellite attitude acquisition
Brocker, D. H.↗
Communication-Aware Orbit Design for Small Spacecraft Swarms around Small Bodies
Exploration of small Solar System bodies has traditionally been performed by single monolithic spacecraft carrying a number of science instruments. However, science instruments typically cannot be operated simultaneously due to the instrument requirements including optimal viewing angle, surface illumination, altitude and ground resolution, power, and data constraints. This observation has motivated interest in multi-spacecraft architectures where a swarm of small spacecraft, each carrying a single science instrument, studies a small body after being deployed by a carrier spacecraft, which then collects data from the vehicles and relays it to Earth. Such architectures hold promise to yield significant improvements in mission efficiency, increases in data quality, and shorter mission duration. A key difficulty in the design of such missions is the selection of orbits for the small spacecraft, which must satisfy not only instrument requirements, but also strict inter-spacecraft communication and on-board storage constraints. To address this, in this paper, we present a novel computationally-efficient optimization algorithm for \emph{communication-aware design} of the orbits of a small spacecraft swarm orbiting a small body. The proposed approach captures constraints including instrument requirements, inter-spacecraft communication bandwidths, and on-board memory usage, and it can accommodate highly irregular gravity field models and surface geometries. We propose an efficient algorithm for optimization of instrument observations and inter-spacecraft communications; we then leverage the differentiable nature of the proposed algorithm to accelerate a gradient-based global search algorithm. Numerical simulations of a six-spacecraft swarm studying 433 Eros show that the proposed approach successfully identifies high-quality orbits, and significantly outperform communication-agnostic optimization techniques, resulting in a 10% increase in scientific returns and a 30% increase in the quality of the collected data.
Rahmani, Amir↗
An optimized rotation-axis model-following controller for STS orbiter attitude maneuvers
This paper describes a new controller for automatic attitude maneuvers of the Space Shuttle Orbiter. The controller incorporates a new solution algorithm for partially linearized, fuel-optimal maneuvers for RCS jet controlled spacecraft. These solutions provide model trajectories and jet commands that are easily tracked using a feed-forward, feedback controller structure. The result is a substantial performance improvement over the current Orbiter attitude maneuver controller. The paper discusses optimal maneuvers for this type of vehicle, giving detail of the solution algorithm. Closed-loop controller design and implementation is discussed. Detailed performance results are presented.
Redding, D. C.↗
Towards the Development of a Global, Satellite-Based, Terrestrial Snow Mission Planning Tool
A global, satellite-based, terrestrial snow mission planning tool is proposed to help inform experimental mission design with relevance to snow depth and snow water equivalent (SWE). The idea leverages the capabilities of NASA's Land Information System (LIS) and the Tradespace Analysis Tool for Constellations (TAT-C) to harness the information content of Earth science mission data across a suite of hypothetical sensor designs, orbital configurations, data assimilation algorithms, and optimization and uncertainty techniques, including cost estimates and risk assessments of each hypothetical permutation. One objective of the proposed observing system simulation experiment (OSSE) is to assess the complementary or perhaps contradictory information content derived from the simultaneous collection of passive microwave (radiometer), active microwave (radar), and LIDAR observations from space-based platforms. The integrated system will enable a true end-to-end OSSE that can help quantify the value of observations based on their utility towards both scientific research and applications as well as to better guide future mission design. Science and mission planning questions addressed as part of this concept include: What observational records are needed (in space and time) to maximize terrestrial snow experimental utility? How might observations be coordinated (in space and time) to maximize this utility? What is the additional utility associated with an additional observation? How can future mission costs be minimized while ensuring Science requirements are fulfilled?
Mission Desig↗