Optimizing Trajectories with Dymos
A live demonstration of the Open-Source trajectory analysis tool Dymos is given where it is used to solve a submarine intercept problem.
Falck, Robert D.↗
Engineering topics
Falck, Robert D.
Publications and source records attributed to Falck, Robert D..
Propulsion System Optimization for a Turboelectric Tiltwing Urban Air Mobility Aircraft
An emerging potential market within the aviation industry is short, frequent air taxi flights within the urban airspace. These air taxis (also called urban air mobility or UAM vehicles) are envisioned to be vertical take-o and landing designs which are capable of carrying 1 to 15 passengers in an intra-urban environment with less than 50 nautical miles of range. Numerous vehicle conceptual designs have been proposed by various industry and government organizations to fulfill these potential missions. These concepts are enabled by recent advancements in a number of areas including propulsion and power systems. While new technologies are making these vehicles possible, this new UAM design space is large, unexplored, and multidisciplinary in nature. New challenges exist in identifying and creating optimized designs for these unique vehicles with new propulsion technologies. This work presents the development of a suite of propulsion system analysis tools, which when coupled together, can improve the multidisciplinary conceptual design and optimization of UAM vehicle propulsion systems. These analysis tools are then applied to the design optimization of a turboelectric propulsion system for a notional UAM tiltwing concept. The optimization demonstration for this vehicle shows how a tightly-coupled multidisciplinary design can be developed which considers both physical design characteristics and operating schedules. Furthermore, the results explore trade-o s in the thermal management system design and how those trade-o s impact the overall vehicle.
Hendricks, Eric S.↗
Multidisciplinary Optimization of a Turboelectric Tiltwing Urban Air Mobility Aircraft
Urban air taxis, also known as urban air mobility (UAM) vehicles, are anticipated to be an area of significant market growth in the near future. These vehicles are typically vertical take-off and landing (VTOL) designs which are capable of carrying 1 to 30 passengers in an intra-urban environment with flights of less than 50 nautical miles. Development of UAM vehicles and their integration into the airspace will be enabled by advancements in a number of areas including electrified propulsion systems, structures, acoustics, automation, and controls. However, the strong multidisciplinary interactions for these unique vehicles presents a significant new design challenge. This work describes the development of a multidisciplinary analysis and optimization environment which can be used to support the conceptual design of these UAM vehicles, using efficient gradient based optimization with analytic derivatives. The tools included in this multidisciplinary analysis model the aircraft trajectory, vehicle aerodynamics, structures, and electrified propulsion system. The multidisciplinary environment created in this research is unique in that all the physics tools are tightly integrated together, with the trajectory model directly calling the aerodynamics, structures, and propulsion models. This multidisciplinary analysis environment is then demonstrated in the design optimization of a turboelectric tiltwing UAM vehicle concept.
Hendricks, Eric S.↗
Optimal Control within the Context of Multidisciplinary Design, Analysis, and Optimization
Multidisciplinary design, analysis and optimization involves modeling the interactions of complex systems across a variety of disciplines. The optimization of such systems can be a computationally expensive exercise with multiple levels of nested nonlinear solvers running under an optimizer.The application of optimal control in project development often involves performing trajectory optimization for fixed vehicle designs or parametric sweeps across some key vehicle properties.This information is then relayed to the subsystem design teams who update their designs and relay some bulk characteristics back to the trajectory optimization procedure.This iteration is then repeated until the design closes.However, with increasing interest in more tightly coupled systems, such as electric and hybrid-electric aircraft propulsion and boundary layer ingestion, this process is prone to ignore subtle coupling between vehicle subsystem designs and vehicle operation on a given mission.Integrating trajectory optimization into a tightly coupled multidisciplinary design procedure can be computationally prohibitive, depending on the complexity of the subsystem analyses and the optimal control technique applied.To address these issues a new optimal control software tool, Dymos, has been developed.Dymos is built upon NASA's OpenMDAO software and can leverage its capabilities to efficiently compute gradients for the optimization and optimize complex models in parallel on distributed memory systems.This report provides some explanation into the numerical methods employed in Dymos and provides several use cases that demonstrate its performance on traditional optimal control problems and improvements ino techniques have been used extensively in recent decades to solve a variety of optimal control problems, typically in the form of aerospace vehicle trajectory optimization.
pseudospectral↗
Multidisciplinary Optimization of Urban-Air-Mobility Class Aircraft Trajectories with Acoustic Constraints
The design and analysis of on-demand mobility class vehicles will require thorough acoustic analysis to ensure that more numerous aircraft can operate in densely populated areas without causing excessive levels of noise. This work is a step towards a comprehensive ODM vehicle analysis capability. The authors use 6DOF equations of motion to model the electric quad-rotor concept developed by NASA's Revolutionary Vertical Lift Technologies program. As a first step towards acoustic analysis, this trajectory is coupled to an acoustic model that tracks the sound pressure level perceived by an acoustic observer on the ground. The results show that the approach is successful in finding trajectories that minimize total propulsive impulse while obeying limits imposed on the sound pressure level. Future work will involve adding acoustic analysis of increasing fidelity and tying the resulting trajectories to the performance of the electric propulsion system.
electric aircraft↗
Development of a Multi-Phase Mission Planning Tool for NASA X-57 Maxwell
The physical design and operation of electric aircraft like NASA Maxwell X-57 are significantly different than conventionally fueled aircraft. Operational optimization will require close coupling of aerodynamics, propulsion, and power. To address the uncertainty of electric aircraft operation, a system level Mission Planning Tool is developed to simulate all aircraft trajectory phases: taxi, motor run-up, takeoff, climb, cruise, and descent. The Mission Planning Tool captures performance parameters at each point of the trajectory including battery state of charge, the temperatures of components in the electrical system, and propulsion system thrust. This work describes the modeling of each mission phase, and compares the results of simulating a user-specified trajectory, and using a collocated optimal control approach to determine an optimal trajectory. The results show that optimization of the mission show a significant increase in the final battery state of charge over the user- specified simulation strategy. These results will inform the operation of the NASA Maxwell X-57 test flights that will take place this year.
Schnulo, Sydney L.↗
Application of Modern Fortran to Spacecraft Trajectory Design and Optimization
In this paper, applications of the modern Fortran programming language to the field of spacecraft trajectory optimization and design are examined. Modern object-oriented Fortran has many advantages for scientific programming, although many legacy Fortran aerospace codes have not been upgraded to use the newer standards (or have been rewritten in other languages perceived to be more modern). NASA's Copernicus spacecraft trajectory optimization program, originally a combination of Fortran 77 and Fortran 95, has attempted to keep up with modern standards and makes significant use of the new language features. Various algorithms and methods are presented from trajectory tools such as Copernicus, as well as modern Fortran open source libraries and other projects.
Trajectory Optimizatio↗
Simulation Propulsion System and Trajectory Optimization
A number of new aircraft concepts have recently been proposed which tightly couple the propulsion system design and operation with the overall vehicle design and performance characteristics. These concepts include propulsion technology such as boundary layer ingestion, hybrid electric propulsion systems, distributed propulsion systems and variable cycle engines. Initial studies examining these concepts have typically used a traditional decoupled approach to aircraft design where the aerodynamics and propulsion designs are done a-priori and tabular data is used to provide inexpensive look ups to the trajectory ana-ysis. However the cost of generating the tabular data begins to grow exponentially when newer aircraft concepts require consideration of additional operational parameters such as multiple throttle settings, angle-of-attack effects on the propulsion system, or propulsion throttle setting effects on aerodynamics. This paper proposes a new modeling approach that eliminated the need to generate tabular data, instead allowing an expensive propulsion or aerodynamic analysis to be directly integrated into the trajectory analysis model and the entire design problem optimized in a fully coupled manner. The new method is demonstrated by implementing a canonical optimal control problem, the F-4 minimum time-to-climb trajectory optimization using three relatively new analysis tools: Open M-DAO, PyCycle and Pointer. Pycycle and Pointer both provide analytic derivatives and Open MDAO enables the two tools to be combined into a coupled model that can be run in an efficient parallel manner that helps to cost the increased cost of the more expensive propulsion analysis. Results generated with this model serve as a validation of the tightly coupled design method and guide future studies to examine aircraft concepts with more complex operational dependencies for the aerodynamic and propulsion models.
Optimization↗
Trajectory Optimization of Electric Aircraft Subject to Subsystem Thermal Constraints
Electric aircraft pose a unique design challenge in that they lack a simple way to reject waste heat from the power train. While conventional aircraft reject most of their excess heat in the exhaust stream, for electric aircraft this is not an option. To examine the implications of this challenge on electric aircraft design and performance, we developed a model of the electric subsystems for the NASA X-57 electric testbed aircraft. We then coupled this model with a model of simple 2D aircraft dynamics and used a Legendre-Gauss-Lobatto collocation optimal control approach to find optimal trajectories for the aircraft with and without thermal constraints. The results show that the X-57 heat rejection systems are well designed for maximum-range and maximum-efficiency flight, without the need to deviate from an optimal trajectory. Stressing the thermal constraints by reducing the cooling capacity or requiring faster flight has a minimal impact on performance, as the trajectory optimization technique is able to find flight paths which honor the thermal constraints with relatively minor deviations from the nominal optimal trajectory.
electric propulsion↗
Parallel Aircraft Trajectory Optimization with Analytic Derivatives
Trajectory optimization is an integral component for the design of aerospace vehicles, but emerging aircraft technologies have introduced new demands on trajectory analysis that current tools are not well suited to address. Designing aircraft with technologies such as hybrid electric propulsion and morphing wings requires consideration of the operational behavior as well as the physical design characteristics of the aircraft. The addition of operational variables can dramatically increase the number of design variables which motivates the use of gradient based optimization with analytic derivatives to solve the larger optimization problems. In this work we develop an aircraft trajectory analysis tool using a Legendre-Gauss-Lobatto based collocation scheme, providing analytic derivatives via the OpenMDAO multidisciplinary optimization framework. This collocation method uses an implicit time integration scheme that provides a high degree of sparsity and thus several potential options for parallelization. The performance of the new implementation was investigated via a series of single and multi-trajectory optimizations using a combination of parallel computing and constraint aggregation. The computational performance results show that in order to take full advantage of the sparsity in the problem it is vital to parallelize both the non-linear analysis evaluations and the derivative computations themselves. The constraint aggregation results showed a significant numerical challenge due to difficulty in achieving tight convergence tolerances. Overall, the results demonstrate the value of applying analytic derivatives to trajectory optimization problems and lay the foundation for future application of this collocation based method to the design of aircraft with where operational scheduling of technologies is key to achieving good performance.
aircraft↗
Breakthrough Capability for UVOIR Space Astronomy: Reaching the Darkest Sky
We describe how availability of new solar electric propulsion (SEP) technology can substantially increase the science capability of space astronomy missions working within the near-UV to far-infrared (UVOIR) spectrum by making dark sky orbits accessible for the first time. We present two case studies in which SEP is used to enable a 700 kg Explorer-class and 7000 kg flagship-class observatory payload to reach an orbit beyond where the zodiacal dust limits observatory sensitivity. The resulting scientific performance advantage relative to a Sun-Earth L2 point (SEL2) orbit is presented and discussed. We find that making SEP available to astrophysics Explorers can enable this small payload program to rival the science performance of much larger long development-time systems. Similarly, we find that astrophysics utilization of high power SEP being developed for the Asteroid Redirect Robotics Mission (ARRM) can have a substantial impact on the sensitivity performance of heavier flagship-class astrophysics payloads such as the UVOIR successor to the James Webb Space Telescope.
Space↗
Comparison of Low-Thrust Control Laws for Application in Planetocentric Space
Recent interest at NASA for the application of solar electric propulsion for the transfer of significant payloads in cislunar space has led to the development of high-fidelity simulations of such missions. With such transfers involving transfer times on the order of months, simulation time can be significant. In the past, the examination of such missions typically began with the use of lower-fidelity trajectory optimization tools such as SEPSPOT to develop and tune guidance laws which delivered optimal or near- optimal trajectories, where optimal is generally defined as minimizing propellant expenditure or time of flight. The transfer of these solutions to a high-fidelity simulation is typically an iterative process whereby the initial solution may nearly, but not precisely, meet mission objectives. Further tuning of the guidance algorithm is typically necessary when accounting for high-fidelity perturbations such as those due to more detailed gravity models, secondary-body effects, solar radiation pressure, etc. While trajectory optimization is a useful method for determining optimal performance metrics, algorithms which deliver nearly optimal performance with minimal tuning are an attractive alternative.
SOLAR ELECTRIC PROPULSION↗
Products from NASA's In-Space Propulsion Program Applicable to Low-Cost Planetary Missions
NASAs In-Space Propulsion Technology (ISPT) program has been developing technologies for lowering the cost of planetary science missions. The technology areas include electric propulsion technologies, spacecraft bus technologies, entry vehicle technologies, and design tools for systems analysis and mission trajectories. The electric propulsion technologies include critical components of both gridded and non-gridded ion propulsion systems. The spacecraft bus technologies under development include an ultra-lightweight tank (ULTT) and advanced xenon feed system (AXFS). The entry vehicle technologies include the development of a multi-mission entry vehicle, mission design tools and aerocapture. The design tools under development include system analysis tools and mission trajectory design tools.
Anderson, David↗
The Status of Spacecraft Bus and Platform Technology Development under the NASA In-Space Propulsion Technology Program
NASA's In-Space Propulsion Technology (ISPT) program has been developing technologies for lowering the cost of planetary science missions. The technology areas include electric propulsion technologies, spacecraft bus technologies, entry vehicle technologies, and design tools for systems analysis and mission trajectories. The electric propulsion technologies include critical components of both gridded and non-gridded ion propulsion systems. The spacecraft bus technologies under development include an ultra-lightweight tank (ULTT) and advanced xenon feed system (AXFS). The entry vehicle technologies include the development of a multi-mission entry vehicle, mission design tools and aerocapture. The design tools under development include system analysis tools and mission trajectory design tools.
Anderson, David↗
Optimization of Low-Thrust Spiral Trajectories by Collocation
As NASA examines potential missions in the post space shuttle era, there has been a renewed interest in low-thrust electric propulsion for both crewed and uncrewed missions. While much progress has been made in the field of software for the optimization of low-thrust trajectories, many of the tools utilize higher-fidelity methods which, while excellent, result in extremely high run-times and poor convergence when dealing with planetocentric spiraling trajectories deep within a gravity well. Conversely, faster tools like SEPSPOT provide a reasonable solution but typically fail to account for other forces such as third-body gravitation, aerodynamic drag, solar radiation pressure. SEPSPOT is further constrained by its solution method, which may require a very good guess to yield a converged optimal solution. Here the authors have developed an approach using collocation intended to provide solution times comparable to those given by SEPSPOT while allowing for greater robustness and extensible force models.
Falck, Robert D.↗
Breakthrough Capability for the NASA Astrophysics Explorer Program: Reaching the Darkest Sky
We describe a mission architecture designed to substantially increase the science capability of the NASA Science Mission Directorate (SMD) Astrophysics Explorer Program for all AO proposers working within the near-UV to far-infrared spectrum. We have demonstrated that augmentation of Falcon 9 Explorer launch services with a 13 kW Solar Electric Propulsion (SEP) stage can deliver a 700 kg science observatory payload to extra-Zodiacal orbit. This new capability enables up to ~13X increased photometric sensitivity and ~160X increased observing speed relative to a Sun- Earth L2, Earth-trailing, or Earth orbit with no increase in telescope aperture. All enabling SEP stage technologies for this launch service augmentation have reached sufficient readiness (TRL-6) for Explorer Program application in conjunction with the Falcon 9. We demonstrate that enabling Astrophysics Explorers to reach extra-zodiacal orbit will allow this small payload program to rival the science performance of much larger long development time systems; thus, providing a means to realize major science objectives while increasing the SMD Astrophysics portfolio diversity and resiliency to external budget pressure. The SEP technology employed in this study has strong applicability to SMD Planetary Science community-proposed missions. SEP is a stated flight demonstration priority for NASA's Office of the Chief Technologist (OCT). This new mission architecture for astrophysics Explorers enables an attractive realization of joint goals for OCT and SMD with wide applicability across SMD science disciplines.
capabiity↗
Concept Design of High Power Solar Electric Propulsion Vehicles for Human Exploration
Human exploration beyond low Earth orbit will require enabling capabilities that are efficient, affordable and reliable. Solar electric propulsion (SEP) has been proposed by NASA s Human Exploration Framework Team as one option to achieve human exploration missions beyond Earth orbit because of its favorable mass efficiency compared to traditional chemical propulsion systems. This paper describes the unique challenges associated with developing a large-scale high-power (300-kWe class) SEP vehicle and design concepts that have potential to meet those challenges. An assessment of factors at the subsystem level that must be considered in developing an SEP vehicle for future exploration missions is presented. Overall concepts, design tradeoffs and pathways to achieve development readiness are discussed.
Hoffman, David J.↗
Extra-Zodiacal-Cloud Astronomy via Solar Electric Propulsion
Solar electric propulsion (SEP) is often considered as primary propulsion for robotic planetary missions, providing the opportunity to deliver more payload mass to difficult, high-delta-velocity destinations. However, SEP application to astrophysics has not been well studied. This research identifies and assesses a new application of SEP as primary propulsion for low-cost high-performance robotic astrophysics missions. The performance of an optical/infrared space observatory in Earth orbit or at the Sun-Earth L2 point (SEL2) is limited by background emission from the Zodiacal dust cloud that has a disk morphology along the ecliptic plane. By delivering an observatory to a inclined heliocentric orbit, most of this background emission can be avoided, resulting in a very substantial increase in science performance. This advantage enabled by SEP allows a small-aperture telescope to rival the performance of much larger telescopes located at SEL2. In this paper, we describe a novel mission architecture in which SEP technology is used to enable unprecedented telescope sensitivity performance per unit collecting area. This extra-zodiacal mission architecture will enable a new class of high-performance, short-development time, Explorer missions whose sensitivity and survey speed can rival flagship-class SEL2 facilities, thus providing new programmatic flexibility for NASA's astronomy mission portfolio. A mission concept study was conducted to evaluate this application of SEP. Trajectory analyses determined that a 700 kg-class science payload could be delivered in just over 2 years to a 2 AU mission orbit inclined 15 to the ecliptic using a 13 kW-class NASA's Evolutionary Xenon Thruster (NEXT) SEP system. A mission architecture trade resulted in a SEP stage architecture, in which the science spacecraft separates from the stage after delivery to the mission orbit. The SEP stage and science spacecraft concepts were defined in collaborative engineering environment studies. The SEP stage architecture approach offers benefits beyond a single astrophysics mission. A variety of low-cost astrophysics missions could employ a standard SEP stage to achieve substantial science benefit. This paper describes the results of this study in detail, including trajectory analysis, spacecraft concept definition, description of telescope/instrument benefits, and application of the resulting SEP stage to other missions. In addition, the benefits of cooperative development and use of the SEP stage, in conjunction with a SEP flight demonstration mission currently in definition at NASA, are considered.
Benson, Scott W.↗