The equivalence and approximation of optimal control problems.
Discontinuities occurring in closed loop optimal control problems when using maximum principle
TIME OPTIMAL CONTROL↗
SEARCH · Search NASA
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Dynamic programming and Pontryagin's maximum principle
Dynamic programming and Pontryagin maximum principle
DYNAMIC PROGRAMMING↗
Guidance and Control Algorithms for the Mars Entry, Descent and Landing Systems Analysis
The purpose of the Mars Entry, Descent and Landing Systems Analysis (EDL-SA) study was to identify feasible technologies that will enable human exploration of Mars, specifically to deliver large payloads to the Martian surface. This paper focuses on the methods used to guide and control two of the contending technologies, a mid- lift-to-drag (L/D) rigid aeroshell and a hypersonic inflatable aerodynamic decelerator (HIAD), through the entry portion of the trajectory. The Program to Optimize Simulated Trajectories II (POST2) is used to simulate and analyze the trajectories of the contending technologies and guidance and control algorithms. Three guidance algorithms are discussed in this paper: EDL theoretical guidance, Numerical Predictor-Corrector (NPC) guidance and Analytical Predictor-Corrector (APC) guidance. EDL-SA also considered two forms of control: bank angle control, similar to that used by Apollo and the Space Shuttle, and a center-of-gravity (CG) offset control. This paper presents the performance comparison of these guidance algorithms and summarizes the results as they impact the technology recommendations for future study.
Davis, Jody L.↗
Safe Onboard Guidance and Control Under Probabilistic Uncertainty
An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time.
Blackmore, Lars James↗
Benchmarking the Collocation Stand-Alone Library and Toolkit (CSALT)
This paper describes the processes and results of Verification and Validation (V&V) efforts for the Collocation Stand Alone Library and Toolkit (CSALT). We describe the test program and environments, the tools used for independent test data, and comparison results. The V&V effort employs classical problems with known analytic solutions, solutions from other available software tools, and comparisons to benchmarking data available in the public literature. Presenting all test results are beyond the scope of a single paper. Here we present high-level test results for a broad range of problems, and detailed comparisons for selected problems.
optimal control↗
Sensitivity of the Asteroid Redirect Robotic Mission (ARRM) to Launch Date and Asteroid Stay Time
National Aeronautics and Space Administrations (NASAs) proposed Asteroid Redirect Mission (ARM) is being designed to robotically capture and then redirect an asteroidal boulder mass into a stable orbit in the vicinity of the moon, where astronauts would be able to visit and study it. The current reference trajectory for the robotic portion, ARRM, assumes a launch on a Delta IV H in the end of the calendar year 2021, with a return for astronaut operations in cislunar space in 2026. The current baseline design allocates 245 days of stay time at the asteroid for operations and boulder collection. This paper outlines analysis completed by the ARRM mission design team to understand the sensitivity of the reference trajectory to launch date and asteroid stay time.
trajectory analysis↗
Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming
A new method is described for the determination of optimal spacecraft trajectories in an inverse-square field using finite, fixed thrust. The method employs a recently developed optimization technique which uses a piecewise polynomial representation for the state and controls, and collocation, thus converting the optimal control problem into a nonlinear programming problem, which is solved numerically. This technique has been modified to provide efficient handling of those portions of the trajectory which can be determined analytically, i.e., the coast arcs. Among the problems that have been solved using this method are optimal rendezvous and transfer (including multirevolution cases) and optimal multiburn orbit insertion from hyperbolic approach.
Enright, Paul J.↗
Dynamic Optimization of the Operational Trajectory of a Supercritical Pulverized Coal-Fired Boiler under Load-Following with Consideration of Boiler Health
Reynolds, K., E. Hedrick, B. Omell, S.E. Zitney, D. Bhattacharyya, "Dynamic Optimization of the Operational Trajectory of a Supercritical Pulverized Coal-Fired Boiler under Load-Following with Consideration of Boiler Health," AIChE 2021 Annual Meeting, Boston, MA, November 7-11 (2021).
Reynolds, Katherine↗
Calculation of free fall trajectories based on numerical optimization techniques
The development of a means of computing free-fall (nonthrusting) trajectories from one specified point in the solar system to another specified point in the solar system in a given amount of time was studied. The problem is that of solving a two-point boundary value problem for which the initial slope is unknown. Two standard methods of attack exist for solving two-point boundary value problems. The first method is known as the initial value or shooting method. The second method of attack for two-point boundary value problems is to approximate the nonlinear differential equations by an appropriate linearized set. Parts of both boundary value problem solution techniques described above are used. A complete velocity history is guessed such that the corresponding position history satisfies the given boundary conditions at the appropriate times. An iterative procedure is then followed until the last guessed velocity history and the velocity history obtained from integrating the acceleration history agree to some specified tolerance everywhere along the trajectory.
Source record↗
Flight Envelope Assessment of SmallSat Aerocapture Trajectories at Venus and Mars
Aerocapture is an increasingly studied orbit insertion concept for small satellite (SmallSat) missions beyond low Earth orbit (LEO). Compared to fully propulsive methods, aerocapture reduces the orbit-insertion propellant mass by approaching on a hyperbolic path and using the planetary atmosphere to reduce the vehicle’s velocity such that the final target orbit is achieved. This allows for an increase in payload mass delivered to orbit and a reduction in launch-to-orbit time. To analyze the feasibility at Venus and Mars, aerocapture flight envelope analysis is conducted by assessing the guidable trajectory space during atmospheric flight given entry conditions, vehicle properties, target parameters, and planet-dependent trajectory dispersions. The Program to Optimize Simulated Trajectories II (POST2) is used to simulate both ballistic and lifting aerocapture trajectories with SmallSat-compatible aeroshell designs. The entry flight path angle is optimized to achieve a final target orbit for lift up/down and max/min control configurations. When plotted, the resulting area between the steep and shallow trajectories forms a flight envelope with planet-dependent ±3σ atmospheric, aerodynamic, and delivery state dispersion profiles applied. The results presented in this paper show that SmallSat aerocapture is feasible for lifting aeroshell designs at Mars and Venus as well as ballistic vehicle designs at Mars.
Jack A. Joshi↗
A review of some exact solutions to the planar equations of motion of a thrusting spacecraft
With the complexities in computing optimal low thrust trajectories, easily-computed, good sub-optimal trajectories provide both a practical alternative for mission designers and a starting point for optimisation. The present paper collects in one place for easy reference and comparison several exact solutions that have been obtained in the literature over the last few decades: the logarithmic spiral, Pinkham's variant thereof, Forbes spiral, the exponential sinusoid, the case of constant radial thrust, Markopoulos's Keplerian thrust arcs, Lawden's spiral, and the analogous Bishop and Azimov spiral.
low-thrust trajectories electric propulsion solar ↗
Optimization and gamma/theta guidance of flight trajectories in a windshear
Guidance schemes for near-optimum performance in wind shear are examined. The presence of a downdraft is assumed in addition to the horizontal shear. The takeoff problem is considered with reference to flight in a vertical plane. Trajectories for optimum performance in a wind shear are determined for different wind shear models and intensities. Methods of optimal control theory are used together with the dual sequential gradient-restoration algorithm for optimal control problems. Guidance schemes for near-optimum performance in a wind shear are developed, starting from optimal trajectories. These are gamma guidance, based on either the absolute of the relative path inclination, and theta guidance, based on the pitch attitude angle. These schemes are evaluated through numerical experiments in order to determine whether the resulting trajectories are sufficiently close to optimum and to compare these trajectories with those arising from alternative guidance schemes.
Miele, A.↗
Optimal velocity prediction for fuel economy improvement of connected vehicles
With the advancement of vehicle-to-vehicle and vehicle-to-infrastructure technologies, more and more real-time information regarding traffic and transportation system will be available to vehicles. This paper presents the development of a novel algorithm that uses available velocity bounds and powertrain information to generate an optimal velocity trajectory over a prediction horizon. When utilised by a vehicle, this optimal velocity trajectory reduces fuel consumption. The objective of this optimisation problem is to reduce dynamic losses, required tractive force, and completing trip distance with a given travel time. Sequential quadratic programming method is employed for this nonlinearly constrained optimisation problem. When applied to a GM Volt-2, the generated velocity trajectory saves fuel compared to a real-world drive cycle. The simulation results confirm the fuel consumption reduction with the rule-based mode selection and the energy management strategy of a GM Volt 2 model in Autonomie.
33 ADVANCED PROPULSION SYSTEMS↗
Minimum noise impact aircraft trajectories
Numerical optimization is used to compute the optimum flight paths, based upon a parametric form that implicitly includes some of the problem restrictions. The other constraints are formulated as penalties in the cost function. Various aircraft on multiple trajectores (landing and takeoff) can be considered. The modular design employed allows for the substitution of alternate models of the population distribution, aircraft noise, flight paths, and annoyance, or for the addition of other features (e.g., fuel consumption) in the cost function. A reduction in the required amount of searching over local minima was achieved through use of the presence of statistical lateral dispersion in the flight paths.
Jacobson, I. D.↗
Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass- Or Time-Optimal Solutions
This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood-allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.
Hughes, Kyle M.↗
Integration of Uncertain Ramp Area Aircraft Trajectories and Generation of Optimal Taxiway Schedules at Charlotte Douglas (CLT) Airport
The integration of aircraft maneuver characteristics into an optimal taxiway scheduling solution is challenging due to the uncertainties that are intrinsic to ramp area aircraft trajectories. To address the challenge, we build a stochastic model of ramp area aircraft trajectories that is used to generate a probabilistic measure of conflict within the Charlotte Douglas International Airport (CLT) ramp area. Parameters of the conflict distributions are estimated and passed to a Mixed Integer Linear Program that solves for an optimal taxiway schedule constrained to be conflict free in the presence of trajectory uncertainties. Here we extend our previous research by accounting for departing and arriving aircraft whereas our prior formulation only accounted for departing aircraft.
taxiway schedule↗
Optimal hybrid propulsion systems thrust trajectories in a patched-conic N-body force field
Euler-Lagrange equations for approximating optimal thrust trajectories for limited hybrid propulsion system in N-body dynamic environment
Pines, S.↗
Optimization of multiple flyby trajectories
A procedure has been developed which minimizes total delta-V (instantaneous velocity change) for a multiple flyby trajectory with constraints on flyby altitude and orientation. The solution is found by varying the locations of maneuver points between each flyby to minimize the delta-Vs at the maneuver points. Each trajectory segment connecting consecutive maneuver points is found by solving an N-body analog to Lambert's problem. Multiconic techniques are used for trajectory propagation and for computation of the state transition matrix. The constrained parameter optimization problem is converted to an unconstrained problem by means of penalty functions and then solved with a quasi-Newton algorithm utilizing analytic first derivatives. This procedure has been successfully applied to Galileo satellite tour trajectories.
Damario, L. A.↗