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Necessary conditions for optimal fixed-time powered transfers with multiple coasts and thrusts between circular orbits
During early conceptual design of complex systems, speed and accuracy are often at odds with one another. While many characteristics of the design are fluctuating rapidly during this phase there is nonetheless a need to acquire accurate data from which to down-select designs as these decisions will have a large impact upon program life-cycle cost. Therefore enabling the conceptual designer to produce accurate data in a timely manner is tantamount to program viability. For conceptual design of launch vehicles, trajectory analysis and optimization is a large hurdle. Tools such as the industry standard Program to Optimize Simulated Trajectories (POST) have traditionally required an expert in the loop for setting up inputs, running the program, and analyzing the output. The solution space for trajectory analysis is in general non-linear and multi-modal requiring an experienced analyst to weed out sub-optimal designs in pursuit of the global optimum. While an experienced analyst presented with a vehicle similar to one which they have already worked on can likely produce optimal performance figures in a timely manner, as soon as the "experienced" or "similar" adjectives are invalid the process can become lengthy. In addition, an experienced analyst working on a similar vehicle may go into the analysis with preconceived ideas about what the vehicle's trajectory should look like which can result in sub-optimal performance being recorded. Thus, in any case but the ideal either time or accuracy can be sacrificed. In the authors' previous work a tool called multiPOST was created which captures the heuristics of a human analyst over the process of executing trajectory analysis with POST. However without the instincts of a human in the loop, this method relied upon Monte Carlo simulation to find successful trajectories. Overall the method has mixed results, and in the context of optimizing multiple vehicles it is inefficient in comparison to the method presented POST's internal optimizer functions like any other gradient-based optimizer. It has a specified variable to optimize whose value is represented as optval, a set of dependent constraints to meet with associated forms and tolerances whose value is represented as p2, and a set of independent variables known as the u-vector to modify in pursuit of optimality. Each of these quantities are calculated or manipulated at a certain phase within the trajectory. The optimizer is further constrained by the requirement that the input u-vector must result in a trajectory which proceeds through each of the prescribed events in the input file. For example, if the input u-vector causes the vehicle to crash before it can achieve the orbital parameters required for a parking orbit, then the run will fail without engaging the optimizer, and a p2 value of exactly zero is returned. This poses a problem, as this "non-connecting" region of the u-vector space is far larger than the "connecting" region which returns a non-zero value of p2 and can be worked on by the internal optimizer. Finding this connecting region and more specifically the global optimum within this region has traditionally required the use of an expert analyst.
Several unmanned multiple-target mission opportunities to comets and asteroids were studied. The targets investigated include Grigg-Skjellerup, Giacobini-Zinner, Tuttle-Giacobini-Kresak, Borrelly, Halley, Schaumasse, Geographos, Eros, Icarus, and Toro, and the trajectories consist of purely ballistic flight, except that powered swingbys and deep space burns are employed when necessary. Optimum solar electric rendezvous trajectories to the comets Giacobini-Zinner/85, Borrelly/87, and Temple (2)/83 and /88 employing the 8.67 kw Sert III spacecraft modified for interplanetary flight were also investigated. The problem of optimizing electric propulsion heliocentric trajectories, including the effects of geocentric launch asymptote declination on launch vehicle performance capability, was formulated, and a solution developed using variational calculus techniques. Improvements were made to the HILTOP trajectory optimization computer program. An error analysis of high-thrust maneuvers involving spin-stabilized spacecraft was developed and applied to a synchronous meteorological satellite mission.
A concept for automatic terminal-area guidance, comprising two modes of operation, has been developed and evaluated in flight tests. In the first or predictive mode, fuel-efficient approach trajectories are synthesized in fast time. In the second or tracking mode, the synthesized trajectories are reconstructed and tracked automatically. An energy rate performance model derived from the lift, drag, and propulsion-system characteristics of the aircraft is used in the synthesis algorithm. The method optimizes the trajectory for the initial aircraft position and wind and temperature profiles encountered during each landing approach. The paper describes the design theory and discusses the results of simulations and flight tests using the Augmentor Wing Jet STOL Research Aircraft.
This report documents the generation of an outbound Earth to Moon transfer preliminary database consisting of four cases calculated twice a day for a 19 year period. The database was desired as the first step in order for NASA to rapidly generate Earth to Moon trajectories for the Constellation Program using the Mission Assessment Post Processor. The completed database was created running a flight trajectory and optimization program, called Copernicus, in batch mode with the use of newly created Matlab functions. The database is accurate and has high data resolution. The techniques and scripts developed to generate the trajectory information will also be directly used in generating a comprehensive database.
Numerical method solution of nonlinear two- point boundary value problem associated with optimum transfer of spacecraft
Game theory for optimal parameter control of payload delivery by limited thrust engine space flight
Optimal coplanar orbit transfer treated by Contensou-Busemann approach with metric tensor completed by smallest possible convex hull
Ares I-X was the designation given to the flight test version of the Ares I rocket which was developed by NASA (also known as the Crew Launch Vehicle (CLV) component of the Constellation Program). The Ares I-X flight test vehicle achieved a successful flight test on October 28, 2009, from Pad LC-39B at Kennedy Space Center, Florida (KSC). As part of the flight plan approval for the test vehicle, a range safety malfunction turn analysis was performed to support the risk assessment and vehicle destruct criteria development processes. Several vehicle failure scenarios were identified which could have caused the vehicle trajectory to deviate from its normal flight path. The effects of these failures were evaluated with an Ares I-X 6 degrees-of-freedom (6-DOF) digital simulation, using the Program to Optimize Simulated Trajectories Version II (POST2) simulation tool. The Ares I-X simulation analysis provided output files containing vehicle trajectory state information. These were used by other risk assessment and vehicle debris trajectory simulation tools to determine the risk to personnel and facilities in the vicinity of the launch area at KSC, and to develop the vehicle destruct criteria used by the flight test range safety officer in the event of a flight test anomaly of the vehicle. The simulation analysis approach used for this study is described, including descriptions of the failure modes which were considered and the underlying assumptions and ground rules of the study.
Various transition methods are used here to study the viscous effects encountered in low density, hypersonic flight, through the transition from free molecular to continuum flow. Methods utilizing Viking data, Shuttle Orbiter data, a Potter number parameter, and a Shock Reynolds number were implemented in the Program to Optimize Simulated Trajectories (POST). Simulations of the Aeroassist Flight Experiment (AFE) using open loop guidance were used to assess the aerodynamic performance of the vehicle. A bank angle was found for each transition method that would result in a 200 nautical-mile apogee. Once this was done, the open loop guidance was replaced by the proposed guidance algorithm for the AFE. Simulations were again conducted using that guidance and the different transitions for comparison. For the gains used, the guidance system showed some sensitivity in apogee altitude to the transition method assumed, but the guidance was able to successfully complete the mission.
This work develops and implements an NMPC control system to facilitate fuel-optimal platooning of Class 8 vehicles over challenging terrain. Prior research has shown that Cooperative Adaptive Cruise Control (CACC), which allows multiple Class 8 vehicles to follow in close succession, can save between 3 and 8% in overall fuel consumption on flat terrain. However, on more challenging terrain, e.g. rolling hills, platooning vehicles can experience diminished fuel savings, and, in some cases, an increase in fuel consumption relative to individual vehicle operation. This research explores the use of Nonlinear Model Predictive Control (NMPC) with predefined route grade profiles to allow platooning vehicles to generate an optimal velocity trajectory with respect to fuel consumption. In order to successfully implement the NMPC system, a model relating vehicle velocity to fuel consumption was generated and validated using experimental data. Additionally, the predefined route grade profiles were created by using the vehicle's GPS velocity over the desired terrain. The real-time NMPC system was then implemented on a two-truck platoon operating over challenging terrain, with a reference vehicle running individually. The results from NMPC platooning are compared against fuel results from a classical proportional-integral-derivative (PID) headway control method. Furthermore, this comparison yields the comparative fuel savings and energy efficiency benefit of NMPC system. In the final analysis, significant fuel savings of greater than 14 and 20% were seen for the lead and following vehicles relative to their respective traditional cruise control and platooning architectures.
This paper presents global path planning algorithms for the Titan aerobot based on user defined waypoints in 2D and 3D space. The algorithms were implemented using information obtained through a planner user interface. The trajectory planning algorithms were designed to accurately represent the aerobot's characteristics, such as minimum turning radius. Additionally, trajectory planning techniques were implemented to allow for surveying of a planar area based solely on camera fields of view, airship altitude, and the location of the planar area's perimeter. The developed paths allow for planar navigation and three-dimensional path planning. These calculated trajectories are optimized to produce the shortest possible path while still remaining within realistic bounds of airship dynamics.
Ares-I-X is the designation given to the flight test version of the Ares-I rocket (also known as the Crew Launch Vehicle - CLV) being developed by NASA. As part of the preliminary flight plan approval process for the test vehicle, a range safety malfunction turn analysis was performed to support the launch area risk assessment and vehicle destruct criteria development processes. Several vehicle failure scenarios were identified which could cause the vehicle trajectory to deviate from its normal flight path, and the effects of these failures were evaluated with an Ares-I-X 6 degrees-of-freedom (6-DOF) digital simulation, using the Program to Optimize Simulated Trajectories Version 2 (POST2) simulation framework. The Ares-I-X simulation analysis provides output files containing vehicle state information, which are used by other risk assessment and vehicle debris trajectory simulation tools to determine the risk to personnel and facilities in the vicinity of the launch area at Kennedy Space Center (KSC), and to develop the vehicle destruct criteria used by the flight test range safety officer. The simulation analysis approach used for this study is described, including descriptions of the failure modes which were considered and the underlying assumptions and ground rules of the study, and preliminary results are presented, determined by analysis of the trajectory deviation of the failure cases, compared with the expected vehicle trajectory.
This paper discusses optimal entry trajectories for the space shuttle that minimize the weight of an entry thermal protection system. The analysis was made using mathematical models of two types of thermal protection systems that were under consideration for the space shuttle: a metallic thermal protection system, and a reusable surface insulation thermal protection system. Optimal entries were generated using maximum orbiter nose temperature as a parameter. Thermal protection system weights were computed for both fixed and variable angles of attack using three-dimensional entry trajectories. Results indicated that variable angle-of-attack entries require less thermal protection system weight than entries at a constant angle of attack (35 deg) for both systems considered. Results also showed that 95 to 99 per cent of the thermal protection system weight requirement resulted from flight regimes in which the flow was still laminar.
Aerocruise maneuver for optimizing orbital plane change with respect to cruise speed
Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.
The development of methodologies, techniques, and tools for analysis and simulation of stage separation dynamics is critically needed for successful design and operation of multistage reusable launch vehicles. As a part of this activity, the Constraint Force Equation (CFE) methodology was developed and implemented in the Program to Optimize Simulated Trajectories II (POST2). The objective of this paper is to demonstrate the capability of POST2/CFE to simulate a complete end-to-end mission. The vehicle configuration selected was the Two-Stage-To-Orbit (TSTO) Langley Glide Back Booster (LGBB) bimese configuration, an in-house concept consisting of a reusable booster and an orbiter having identical outer mold lines. The proximity and isolated aerodynamic databases used for the simulation were assembled using wind-tunnel test data for this vehicle. POST2/CFE simulation results are presented for the entire mission, from lift-off, through stage separation, orbiter ascent to orbit, and booster glide back to the launch site. Additionally, POST2/CFE stage separation simulation results are compared with results from industry standard commercial software used for solving dynamics problems involving multiple bodies connected by joints.
On December 11, 2013, the International Space Station (ISS) experienced a failure of the External Thermal Control System (ETCS) Loop A Pump Module (PM). To minimize the number of extravehicular activities (EVA) required to replace the PM, jettisoning the faulty pump was evaluated. The objective of this study was to independently evaluate the jettison options considered by the ISS Trajectory Operations Officer (TOPO) and to provide recommendations for safe jettison of the ETCS Loop A PM. The simulation selected to evaluate the TOPO options was the NASA Engineering and Safety Center's (NESC) version of Program to Optimize Simulated Trajectories II (POST2) developed to support another NESC assessment. The objective of the jettison analysis was twofold: (1) to independently verify TOPO posigrade and retrograde jettison results, and (2) to determine jettison guidelines based on additional sensitivity, trade study, and Monte Carlo (MC) analysis that would prevent PM recontact. Recontact in this study designates a propagated PM trajectory that comes within 500 m of the ISS propagated trajectory. An additional simulation using Systems Tool Kit (STK) was run for independent verification of the POST2 simulation results. Ultimately, the ISS Program removed the PM jettison option from consideration. However, prior to the Program decision, the retrograde jettison option remained part of the EVA contingency plan. The jettison analysis presented showed that, in addition to separation velocity/direction and the atmosphere conditions, the key variables in determining the time to recontact the ISS is highly dependent on the ballistic number (BN) difference between the object being jettisoned and the ISS.