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Traj_opt User's Guide
Trajectory optimization program Traj_opt was developed at Ames Research Center to help assess the potential benefits of ultrahigh temperature ceramic materials applied to reusable space vehicles with sharp noses and wing leading edges. Traj_opt loosely couples the Ames three-degrees-of-freedom trajectory package Traj (see NASA-TM-2004-212847) with the SNOPT optimization package (Stanford University Technical Report SOL 98-1). Traj_opt version January 22, 2003 is covered by this user guide. The program has been applied extensively to entry and ascent abort trajectory calculations for sharp and blunt crew transfer vehicles. The main optimization variables are control points for the angle of attack and bank angle time histories. No propulsion options are provided, but numerous objective functions may be specified and the nonlinear constraints implemented include a distributed surface heating constraint capability. Aero-capture calculations are also treated with an option to minimize orbital eccentricity at apoapsis. Traj_opt runs efficiently on a single processor, using forward or central differences for the gradient calculations. Results may be displayed conveniently with Gnuplot scripts. Control files recommended for five standard reentry and ascent abort trajectories are included along with detailed descriptions of the inputs and outputs.
Design and Execution of Dawn HAMO to LAMO Transfer at Ceres
On October 23, 2015, the Dawn spacecraft left the High Altitude Mapping Orbit (HAMO) around Ceres and began its final decent to the Low Altitude Mapping Orbit (LAMO), arriving on December 15. The transfer between the two science orbits, a tight spiraling trajectory with over 100 revolutions, required the operations team to perform weekly maneuver designs for a period of 50 days. While the first six weeks of the transfer executed as planned, unexpectedly the spacecraft incurred a multi-sigma delivery error to the final science orbit that was subsequently clean-up at the first orbit maintenance maneuver. In this paper we discuss the design architecture for the transfer in detail, including challenges the team faced in flying the transfer and lessons learned.
Design and Execution of Dawn HAMO to LAMO Transfer at Ceres
On October 23, 2015, the Dawn spacecraft left the High Altitude Mapping Orbit (HAMO) around Ceres and began its final decent to the Low Altitude Mapping Orbit (LAMO), arriving on December 15. The transfer between the two science orbits, a tight spiraling trajectory with over 100 revolutions, required the operations team to perform weekly maneuver designs for a period of 50 days. While the first six weeks of the transfer executed as planned, unexpectedly the spacecraft incurred a multi-sigma delivery error to the final science orbit that was subsequently clean-up at the first orbit maintenance maneuver. In this paper we discuss the design architecture for the transfer in detail, including challenges the team faced in flying the transfer and lessons learned.
Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion
A novel algorithm is presented that provides an improvement over a traditional parameter optimization method when solving time-optimal, finite-burn pseudo-rendezvous spacecraft trajectory problems. A hybrid optimization procedure is described that converts a set of multiple-impulses, representing high- or low-thrust maneuvers, to an exact time-optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. The Hybrid Method applies a control law derived from the Euler-Lagrange system of equations within the classical Indirect Method to a modern Direct Method. An iterative adjoint-control transformation and an evolving constraint vector are introduced to solve the optimal control two-point boundary value problem. This method requires no prior knowledge of the solution, which adds simplicity to the trajectory design process and aids automation. Examples are shown for low-thrust apogee raise maneuvers, non-coplanar Earth orbit transfers, and a modified Deep Space 1 low-thrust trajectory. A numerically significant improvement to objective cost is shown across all application problems compared to a traditional solution method, as well as a significant improvement to convergence speed for a select class of problems.
Deploying Traffic Smoothing Cruise Controllers Learned from Trajectory Data
Autonomous vehicle-based traffic smoothing con- trollers are often not transferred to real-world use due to challenges in calibrating many-agent traffic simulators. We show a pipeline to sidestep such calibration issues by collecting trajectory data and learning controllers directly from trajectory data that are then deployed zero-shot onto the highway. We construct a dataset of 772.3 kilometers of recorded drives on the I-24. We then construct a simple simulator using the recorded drives as the lead vehicle in front of a simulated platoon consisting of one autonomous vehicle and five human followers. Using policy-gradient methods with an asymmetric critic to learn the controller, we show that we are able to improve average MPG by 11% in simulation on congested trajectories. We deploy this controller to a mixed platoon of 4 autonomous Toyota RAV-4’s and 7 human drivers in a validation experiment and demonstrate that the expected time-gap of the controller is maintained in the real world test. Finally, we release the driving dataset [1], the simulator, and the trained controller at https://github.com/nathanlct/trajectory-training-icra.
New developments in astrodynamics algorithms for autonomous rendezvous
A the core of any autonomous rendezvous guidance system must be two algorithms for solving Lambert's and Kepler's problems, the two fundamental problems in classical astrodynamics. Lambert's problem is to determine the trajectory connecting specified initial and terminal position vectors in a specified transfer time. The solution is the initial and terminal velocity vectors. Kepler's problem is to determine the trajectory that stems from a given initial state (position and velocity). The solution is the state of an earlier or later specified time. To be suitable for flight software, astrodynamics algorithms must be totally reliable, compact, and fast. Although solving Lambert's and Kepler's problems has challenged some of the world's finest minds for over two centuries, only in the last year have algorithms appeared that satisfy all three requirements just stated. This paper presents an evaluation of the most highly regarded Lambert and Kepler algorithms.
An approximate method for the calculation of nonequilibrium radiative heat transfer
A simplified method for the calculation of radiative heat transfer in hypersonic reentry flows where local thermal nonequilibrium (LTNE) conditions exist is presented. This method has been incorporated into the computer code RADMC (RADiation/Modified Corrections), which utilizes an approximate 'two-state' model of the electronic levels of atoms and molecules in the determination of the populations of the excited states for both LTNE and local thermal equilibrium (LTE) conditions for each of the relevant chemical species. The population data are used to calculate a correction factor to the radiative cross sections in an eight-step nongray radiative heat-transfer model. Results have been obtained for various points along the proposed trajectory of the Aeroassist Flight Experiment and the Fire II trajectory, and compared with results obtained for the same flowfields from the NEQAIR radiative heat-transfer code.
Multi-revolution Extension of Solar-perturbed Moon-to-moon Transfer Families
Lunar flybys and solar perturbations present a golden opportunity to naturally modify trajectories of spacecraft launched in Moon-bound orbits. Leveraging the energy gained, or lost, from lunar flybys and multi-body effects allows for spacecraft to reach destinations not previously within their designed ?v budgets. Previous research studies have demonstrated the viability of collecting zero revolution Moon-to-Moon transfers into a referential database. This paper extends this capability to multi-revolution transfers and describes their main characteristics and increased versatility. Finally, a trajectory example is given for the escape phase of the NEA Scout mission.
Some Analytical Characteristics of the Optimum Two-Impulse Orbital Transfer Under Arbitrary Terminal Conditions
Optimum two-impulse orbital transfer for arbitrary terminal conditions, discussing analytic characteristics
BepiColombo Science Investigations During Cruise and Flybys at the Earth, Venus and Mercury
The dual spacecraft mission BepiColombo is the first joint mission between the European Space Agency (ESA) and the Japanese Aerospace Exploration Agency (JAXA) to explore the planet Mercury. BepiColombo was launched from Kourou (French Guiana) on October 20th, 2018, in its packed configuration including two spacecraft, a transfer module, and a sunshield. BepiColombo cruise trajectory is a long journey into the inner heliosphere, and it includes one flyby of the Earth (in April 2020), two of Venus (in October 2020 and August 2021), and six of Mercury (starting from 2021), before orbit insertion in December 2025. A big part of the mission instruments will be fully operational during the mission cruise phase, allowing unprecedented investigation of the different environments that will encounter during the 7-years long cruise. The present paper reviews all the planetary flybys and some interesting cruise configurations. Additional scientific research that will emerge in the coming years is also discussed, including the instruments that can contribute.
Bridge-Mediated Metal-to-Metal Electron and Hole Transfer in a Supermolecular Dinuclear Complex: A Computational Study Using Quantum Electron–Nuclear Dynamics
Bimetallic electron donor–acceptor complexes can facilitate electron and energy transfer with excellent structural control through synthetic design. In this work, we investigate the photochemical dynamics in a Ru–Cu bimetallic complex after photoexcitation of the Ru-centered charge transfer state. The physical underpinnings of the metal-to-metal directional charge transfer process are unraveled via analyses of the quantum electronic dynamics and electron–nuclear trajectories. Here, the effects of molecular vibrations in the photoexcited state on the charge transfer processes are also analyzed.
An analysis and comparison of several trajectory optimization methods
Methods of solving problem associated with optimum transfer of spacecraft
Planetary mission handbook. Appendix A: Graphical trajectory data
Graphical data is presented for Type 1 ballistic transfers to Jupiter (1974 to 1986), Saturn (1976 to 1986) and Uranus (1985). There are four graphs for each launch opportunity, namely the hyperbolic excess speed at earth departure, the hyperbolic excess speed at planet arrival, the declination of the hyperbolic departure asymptote, and the declination of the hyperbolic approach asymptote.
Visions of tomorrow: A focus on national space transportation issues; Proceedings of the Twenty-fifth Goddard Memorial Symposium, Greenbelt, MD, Mar. 18-20, 1987
The present conference on U.S. space transportation systems development discusses opportunities for aerospace students in prospective military, civil, industrial, and scientific programs, current strategic conceptualization and program planning for future U.S. space transportation, the DOD space transportation plan, NASA space transportation plans, medium launch vehicle and commercial space launch services, the capabilities and availability of foreign launch vehicles, and the role of commercial space launch systems. Also discussed are available upper stage systems, future space transportation needs for space science and applications, the trajectory analysis of a low lift/drag-aeroassisted orbit transfer vehicle, possible replacements for the Space Shuttle, LEO to GEO with combined electric/beamed-microwave power from earth, the National Aerospace Plane, laser propulsion to earth orbit, and a performance analysis for a laser-powered SSTO vehicle.
Unmanned, space-based, reusable orbital transfer vehicle, DARVES. Volume 2: Data and calculations
Results for trajectory analysis, fuel analysis, and analysis of aerobraking maneuvers are presented. Calculations are included for thickness and mass of the propellant tanks; determination of weight (avionics module); numerical integration program; hydrostatic pressure due to acceleration; and propellant tank pressurization.
Magellan orbits Venus
Various events surrounding Magellan's orbit of Venus are recounted. Significant events include the successful firing of a solid rocket motor while the spacecraft was behind Venus to transfer it from a solar-centered trajectory to an orbit around the planet. The spacecraft orbits Venus every 3.26 hours at a maximum altitude of 8500 km and minimum altitude of 291 km in an elliptical orbit. The successful August 16 test of the synthetic-aperture radar system is discussed, noting that it produced two strips, each about 20 km x 16,000 km, revealing details as small as 120 m. Two anomalies causing a delay in the start of mapping operations and subsequent breaks in the communication link with earth for 14.5 hours and 17.7 hours are discussed. Protective measures directed from the spacecraft's ROM during breach of contact are listed, and possible causes of the anomalies are suggested, such as solar activity or hardware or software elements, although the actual cause is not yet known.
Heating Analysis of the Lockheed Lifting Body
Computational fluid dynamic (CFD) analysis is performed on the Lockheed Lifting Body Single-Stage-to-Orbit vehicle to determine the heat transfer to the vehicle during its descent trajectory. Seven species, chemical nonequilibriurn computations using the GASP code will be completed at several trajectory points to assess the thermal protection requirements of the vehicle. Sophisticated surface boundary conditions including in-depth conduction, catalycity, and a variable temperature wall have been incorporated into the flow solver.