OPTIMUM TWO-IMPULSE ORBITAL TRANSFER AND RENDEZVOUS BETWEEN INCLINED ELLIPTICAL ORBITS
Spacecraft rendezvous trajectory between two elliptical orbits is determined by optimization of the two impulse orbital transfer
ORBITAL TRANSFER↗
SEARCH · Engineering Papers
Results for “Trajectory Optimization”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Fast Earth-Mars Roundtrip Trajectories to Reduce Health and Safety Risks for Crewed Missions
The extended mission duration of a crewed Mars mission compounds integrated risks to crew health and safety. Shortening mission duration would therefore have a direct impact on reducing many human health and performance risk factors. This paper describes trajectory feasibility analyses performed to examine trajectory options for a fast crewed mission to Mars. Studies were conducted to examine options with short overall mission durations (≤ 400-day roundtrip) and options that focus on minimizing astronaut time in deep space, while allowing for longer Mars surface stays. Trade studies were performed to determine ∆v requirements for a range of launch dates, Mars orbit periods, Mars stay times, and Earth-to-Mars flight time maxima. The implications of a Venus gravity assist are also described. The analyses presented here build on and specifically aim to optimize and address key concerns of assumptions made in previously published studies of fast crewed Mars missions.
Mars↗
Poincare: A Multi-Body, Multi-System Trajectory Design Tool
Poincare is a modular trajectory design tool based on a catalog of three-body science orbits and a differential corrector to compute connecting transfer arcs between orbits in multibody systems. Poincare attempts to offer a unified approach, i.e.,an“all-in-one”integrated search within one interface and setup in MONTE (JPL’s signature astrodynamic computing platform.) The Science Orbit Design Tool facilitates rapid and well-informed decisions regarding the selection of periodic orbits for a particular mission and enables the simultaneous study of various orbit alternatives. The Reference Trajectory Design Tool allows the user to calculate optimal transfer paths from a departure orbit to a science orbit via dynamical systems structures (invariant manifolds and Poincare maps), resulting in an end-to-end reference trajectory.
Senent, Juan↗
Development of Complexity Science and Technology Tools for NextGen Airspace Research and Applications
The objective of this research by NextGen AeroSciences, LLC is twofold: 1) to deliver an initial "toolbox" of algorithms, agent-based structures, and method descriptions for introducing trajectory agency as a methodology for simulating and analyzing airspace states, including bulk properties of large numbers of heterogeneous 4D aircraft trajectories in a test airspace -- while maintaining or increasing system safety; and 2) to use these tools in a test airspace to identify possible phase transition structure to predict when an airspace will approach the limits of its capacity. These 4D trajectories continuously replan their paths in the presence of noise and uncertainty while optimizing performance measures and performing conflict detection and resolution. In this approach, trajectories are represented as extended objects endowed with pseudopotential, maintaining time and fuel-efficient paths by bending just enough to accommodate separation while remaining inside of performance envelopes. This trajectory-centric approach differs from previous aircraft-centric distributed approaches to deconfliction. The results of this project are the following: 1) we delivered a toolbox of algorithms, agent-based structures and method descriptions as pseudocode; and 2) we corroborated the existence of phase transition structure in simulation with the addition of "early warning" detected prior to "full" airspace. This research suggests that airspace "fullness" can be anticipated and remedied before the airspace becomes unsafe.
Holmes, Bruce J.↗
The separation computation of arcs for optimal flight paths with state variable inequality constraints.
Maximum trajectory for glider entering earth atmosphere at supercircular velocity, subject to maximum altitude constraint
Bryson, A. E., Jr.↗
Some applications of mathematical optimization to automatic landing systems
Algorithms applied to vertical trajectory control system
Kinnon, D. M.↗
VIPRE: A Tool Aiding the Design for Entry Probe Missions
Exploring planetary atmospheres uncovers important information for how our solar system formed and evolved. While remote sensing is extensively used, some crucial observations require in-situ measurements by an atmospheric probe. Given their scientific importance, probe missions to Saturn, Uranus and Neptune are considered for the coming decades. In anticipation of future probe missions, the software tool VIPRE was developed as proof-of-concept to facilitate selection of probe entry locations. Currently, there is no analytical way to identify which interplanetary trajectory from thousands of feasible launch opportunities is optimal for a considered mission concept. The search and decision process for that solution is complex and relies on the intuition of mission designers, who focus on a subset of trajectories to make the trade space manageable. The idea of VIPRE is to (1) generate a multi-dimensional data cube showing relevant engineering and science parameters simultaneously for thousands of trajectories, and (2) visualize the data for all entry sites over the body's envelope. VIPRE lays the foundation to make the data available for browsing in a 3-D visualization to identify the best family of solutions for a given mission. The paper introduces the validated and verified core algorithms of VIPRE, published on GitHub. VIPRE serves as a basic framework to be used and extended for different purposes. The paper presents the motivation for the development and algorithms. It explains the computation and data visualization strategy, and gives a list of suggested functionalities to extend and further develop VIPRE to fully leverage its potential.
Ice Giants↗
Lunar Browser trajectory tool
The Lunar Browser is a tool developed at NASA Ames Research Center for building, processing, and analyzing a database of lunar transfer trajectory solutions. Examples of intended uses include design trades for lunar missions and preliminary assessments of key parameters such as launch opportunities, delta-v and propulsion budgets, communication windows, eclipse durations, and lunar landing windows. The Lunar Browser tool is in the development phase and it is already producing results in its current form to address various NASA program requirements, proposals, and mission trajectories. The tool has also been used for research analysis in trajectory design, including a first publication regarding its application to the CLPS and Artemis programs. In particular, the results included transfers to lunar frozen orbits. Future work include the generation of more trajectories to expand the existing database and the optimization of the results.
Lunar Browser trajectory tool↗
A randomized sketching trust-region secant method for low-memory dynamic optimization
The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.
dynamic optimization↗
Dynamics and control of DNA sequence amplification
DNA amplification is the process of replication of a specified DNA sequence in vitro through time-dependent manipulation of its external environment. A theoretical framework for determination of the optimal dynamic operating conditions of DNA amplification reactions, for any specified amplification objective, is presented based on first-principles biophysical modeling and control theory. Amplification of DNA is formulated as a problem in control theory with optimal solutions that can differ considerably from strategies typically used in practice. Using the Polymerase Chain Reaction as an example, sequence-dependent biophysical models for DNA amplification are cast as control systems, wherein the dynamics of the reaction are controlled by a manipulated input variable. Using these control systems, we demonstrate that there exists an optimal temperature cycling strategy for geometric amplification of any DNA sequence and formulate optimal control problems that can be used to derive the optimal temperature profile. Strategies for the optimal synthesis of the DNA amplification control trajectory are proposed. Analogous methods can be used to formulate control problems for more advanced amplification objectives corresponding to the design of new types of DNA amplification reactions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A Linear Analysis for the Flight Path Control of the Cassini Grand Finale Orbits
Cassini’s Grand Finale Mission begins after the last targeted Titan flyby on April 22, 2017 and ends with a series of 22 ballistic orbits each passing within a few thousand kilometers of the cloud tops of Saturn, ultimately impacting the planet on September 15, 2017. Despite the ballistic nature of the trajectory, the absence of targeted maneuvers throughout the final orbits causes position uncertainties to grow exponentially with time, posing a significant difficulty for the science sequence planning team. Thus, a strategy that incorporates trajectory correction maneuvers was developed to significantly reduce dispersions from the reference path and maintain dispersions below 250 km (1- ). In this paper, the linear method used to determine the optimal number and location of the maneuvers to control the trajectory, along with the corresponding targets, is detailed. A nonlinear Monte Carlo trajectory dispersion tool served as a testbed to validate the linear analysis results. Based on orbit determination covariance sampling with Monte Carlo simulations, the linear approach allowed the Cassini maneuver analysts to run thousands of maneuver combinations in little time, eventually finding an optimal strategy with three statistical maneuvers ( V99 < 1.5 m/s) to adequately control most of the trajectory.
Vaquero, Mar↗
An Optimal Initial Guess Generator for Entry Interface Targeters
If a pure numerical iterative approach is used, targeting entry interface (EI) conditions for nominal and abort return trajectories or for correction maneuvers can be computationally expensive. This paper describes an algorithm to obtain an optimal impulsive maneuver that generates a trajectory satisfying a set of EI targets: inequality constraints on longitude, latitude and azimuth and a fixed flight-path angle. Most of the calculations require no iterations, making it suitable for real-time applications or large trade studies. This algorithm has been used to generate initial guesses for abort trajectories during Earth-Moon transfers.
Senent, Juan S.↗
Optimal low-thrust takeoff from an orbit about an oblate planet
Future space missions to the outer planets may depend upon the use of low-thrust propulsion systems. As these planets are decidedly oblate, the question of the effect of that oblateness on a low-thrust trajectory is of some interest. In this paper the problem of optimal energy increase is attacked under the assumption that the coefficients for the second zonal harmonic, and the nondimensional thrust acceleration are the same order of magnitude. By means of a two-variable asymptotic expansion technique, a near optimal control program is generated and the first-order uniformly valid approximation for the corresponding trajectory is obtained. Tangential thrust is shown to be a good near-optimal thrust program even in the presence of oblateness effects. The optimal control program is found to be oscillatory and quite similar to the optimal control for energy increase in an inverse square gravitational field.
Jacobson, R. A.↗
Interplanetary Trajectory Design for the Asteroid Robotic Redirect Mission Alternate Approach Trade Study
This paper presents mission performance analysis methods and results for the Asteroid Robotic Redirect Mission (ARRM) option to capture a free standing boulder on the surface of a 100 m or larger NEA. It details the optimization and design of heliocentric low-thrust trajectories to asteroid targets for the ARRM solar electric propulsion spacecraft. Extensive searches were conducted to determine asteroid targets with large pick-up mass potential and potential observation opportunities. Interplanetary trajectory approximations were developed in method based tools for Itokawa, Bennu, 1999 JU3, and 2008 EV5 and were validated by end-to-end integrated trajectories.
Merrill, Raymond Gabriel↗
Fast model-based scenario optimization in NSTX-U enabled by analytic gradient computation
Model-based optimization offers a systematic approach to advanced scenario planning. In this case, the feedforward-control inputs (actuator trajectories) that are needed to attain and sustain a desired scenario are obtained by solving a nonlinear constrained optimization problem. This class of problems generally minimize a cost function that measures the difference between desired and actual plasma states. Several numerical optimization algorithms, such as sequential quadratic programming, require repeated calculation of the cost function gradients with respect to the input trajectories. Calculating these gradients numerically can be computationally intensive, increasing the time needed to solve the feedforward-control optimization problem. Here, this work introduces a method to analytically calculate these cost function gradients from the current profile evolution model. This can significantly reduce the computational time and allow for fast feedforward-control optimization, which would eventually enable optimal scenario planning between discharges. The performance of the feedforward optimizer with analytical gradients is compared to a traditional optimization algorithm based on numerical gradients for different NSTX-U scenarios. The plasma dynamics in the optimization algorithm are simulated using the Control Oriented Transport SIMulator (COTSIM). Results of the work show that analytical gradients consistently reduce the computation time while achieving trajectories that are comparable to those obtained by traditional optimization algorithms based on numerical gradients.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations
Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.
Chaotic dynamical systems↗
POINT: Partially Observable Imitation Network for Traffic Signal Control
Smart traffic signals bring together transportation infrastructure and advance technologies to improve the mobility and efficiency of urban transportation network. Adaptive traffic signal control studies can be categorized into modeling-based approaches and learning-based approaches. In order to take advantages of these two systems, this study developed an offline-online combined Partial Observable Imitation Network for Traffic signal control (POINT). In the offline system, the traffic signal timing optimization problem was formulated as a Mixed Integer Nonlinear Programming (MINLP) given complete traffic information, i.e., second-by-second speeds and locations of all vehicles. Furthermore, the objective of MINLP is to minimize total travel delays considering individual vehicle trajectories under Connected Vehicle (CV) environment. The calculated optimal solutions under various traffic conditions were considered as the ”expert” decisions. In the online system, an imitation neural network model was developed to learn the ”expert” signal plans generated from offline system. Given partial observable traffic conditions in real time, e.g., the aggregate-level of traffic volume, the POINT model can compute the signal timing parameters in the online system. The numerical results demonstrated that the proposed method outperformed other state-of-the-art signal control method under high and unbalanced traffic demand levels in terms of reducing travel delays and queue length.
33 ADVANCED PROPULSION SYSTEMS↗
Mission-Maps For Outbound Cislunar Transfer Trajectories
This study quantifies the robustness and sensitivity of an outbound cislunar trajectory for a lunar lander in the form of mission-maps, or topological maps that allows either a computer program or mission designer to intuitively optimize the placement of critical outbound correction burns from the derived sensitivity data. The non-linear multi-body dynamics are applied to generate an outbound cislunar reference profile used by a linear covariance analysis (LinCov) tool to compute the expected Δv and trajectory dispersions due to the initial state uncertainty, sensor errors, maneuver execution errors, and disturbance accelerations along the outbound cislunar profile. The rapid performance analysis capabilities of LinCov are complimented with parallel processing techniques to evaluate hundreds and thousands of different translational burn locations, placements, and targeting constraints to identify the combination that minimizes the total Δv usage (nominal plus 3σ Δv) and trajectory dispersions at lunar orbit insertion. This study utilizes a generalized reference targeting algorithm to quickly assess the integrated closed-loop GN&C system performance due to different targeting configurations and constraints. The resulting mission maps provide an intuitive insight to ascertain each trajectory correction maneuver’s (TCM) sensitivity to different burn times along an outbound cislunar trajectory and quickly identify desirable engineering tradeoffs when performing analysis on the number and placement of these burns that nominally zero. Multiple mission maps are generated for a variety of different performance parameters that allow engineers to visually identify optimal solutions for trajectory correction maneuver placements, the number of correction burns, and the targeting constraints for each burn.
GN&C↗