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At least 577 records · Page 32

Performance analysis of the word synchronization properties of the outer code in a TDRSS decoder

A self-synchronizing coding scheme for NASA's TDRSS satellite system is a concatenation of a (2,1,7) inner convolutional code with a (255,223) Reed-Solomon outer code. Both symbol and word synchronization are achieved without requiring that any additional symbols be transmitted. An important parameter which determines the performance of the word sync procedure is the ratio of the decoding failure probability to the undetected error probability. Ideally, the former should be as small as possible compared to the latter when the error correcting capability of the code is exceeded. A computer simulation of a (255,223) Reed-Solomon code as carried out. Results for decoding failure probability and for undetected error probability are tabulated and compared.

Costello, D. J., Jr.↗

Probabilistic Study Conducted on Sensor-Based Engine Life Calculation

Turbine engine life management is a very complicated process to ensure the safe operation of an engine subjected to complex usage. The challenge of life management is to find a reasonable compromise between the safe operation and the maximum usage of critical parts to reduce maintenance costs. The commonly used "cycle count" approach does not take the engine operation conditions into account, and it oversimplifies the calculation of the life usage. Because of the shortcomings, many engine components are regularly pulled for maintenance before their usable life is over. And, if an engine has been running regularly under more severe conditions, components might not be taken out of service before they exceed their designed risk of failure. The NASA Glenn Research Center and its industrial and academic partners have been using measurable parameters to improve engine life estimation. This study was based on the Monte Carlo simulation of 5000 typical flights under various operating conditions. First a closed-loop engine model was developed to simulate the engine operation across the mission profile and a thermomechanical fatigue (TMF) damage model was used to calculate the actual damage during takeoff, where the maximum TMF accumulates. Next, a Weibull distribution was used to estimate the implied probability of failure for a given accumulated cycle count. Monte Carlo simulations were then employed to find the profiles of the TMF damage under different operating assumptions including parameter uncertainties. Finally, probabilities of failure for different operating conditions were analyzed to demonstrate the importance of a sensor-based damage calculation in order to better manage the risk of failure and on-wing life.

Guo, Ten-Huei↗

Simulation of Dynamic Crushing Behavior of Simulated Carbon/Epoxy Stanchions Using MAT58 and MAT213 in LS-DYNA

Carbon fiber-reinforced polymer (CFRP) composites have shown promise as a material for structures designed to absorb energy in crush-style impact loading. In complementing the lightweight and tailorable characteristics of CFRP structures, the benefits of impact energy absorption are particularly interesting in aerospace vehicles that require excellent crashworthiness performance. However, simulating the behavior of CFRP structures in dynamic, crushing-style impact loading is challenging because of the many damage and failure modes that are essential to capture in the model. For the present investigation, CFRP stanchions were tested using a crash sled experimental test rig. The stanchions were designed by the Composite Materials Handbook-17 (CMH-17) Crashworthiness Working Group for the purpose of comparing experimental crash sled tests to corresponding simulations of the tests. The stanchions are C-channel shaped and represent a geometry common in the interior of aerospace vehicle structures. Explicit simulations in LSDYNA were performed using a well-established composite material model (MAT58) and a next-generation material model (MAT213). Fully integrated shell elements were utilized instead of 3D solid elements to limit computation time. In all models, each of the sixteen plies were represented with individual layers of shell elements with tiebreak contact between each adjacent ply pair to simulate interlaminar fracture. Simulating the crushing of the stanchions occurred in two phases. First, the material models were calibrated using flat specimens that were manufactured with the same layup as the stanchions. While the original goal was calibration of material-related properties, meshdependent behavior was observed in simulations with either material model, and an unstructured mesh was selected to remediate undesirable mesh-dependent failure modes. Additionally, for both the MAT58 and MAT213 models, it was found that either the crush force or the failure mode could be modeled accurately, but no set of parameters could be identified to attain both results in the same model. Once satisfactory calibration was achieved, the same material parameters were applied to the stanchion crush simulations. The stanchion simulations showed that MAT213 more accurately predicted the experimentally determined crush force, and both material models predicted key aspects of the experimentally observed failure modes.

Composite Materials↗

Molecular dynamics simulations of ultrafast radiation induced melting at metal–semiconductor interfaces

Metal–semiconductor contacts in silicon carbide (SiC) diodes endure damages at the interface when exposed to harsh radiation environments. Due to the rapid rise in temperature and ultrafast cooling that follows the radiation impact, the structural properties of the materials can be altered through melting, recrystallization, and amorphization. A detailed understanding of the material failure modes at the interface is lacking, specifically at the nanoscale. We use molecular simulations to investigate the ultrafast melting at tungsten (W)–SiC interfaces following radiation damage and apply deep learning techniques to track the transient evolution of the local molecular structures. We show that W near the radiation track undergoes melting and, eventually, most of it recrystallizes with a noticeable degree of undercooling, while SiC is rendered permanently amorphous. The observation of local undercooling in W films is important as it can affect the device performance even before the bulk melting temperature of the material is reached. We also show that at high temperatures, the interface undergoes a fracture-like failure. The results presented here are significant in understating the different failure modes of SiC diode materials.

Ashwin Ravichandran↗

Piloted simulation tests of propulsion control as backup to loss of primary flight controls for a mid-size jet transport

Failures of aircraft primary flight-control systems to aircraft during flight have led to catastrophic accidents with subsequent loss of lives (e.g. , DC-1O crash, B-747 crash, C-5 crash, B-52 crash, and others). Dryden Flight Research Center (DFRC) investigated the use of engine thrust for emergency flight control of several airplanes, including the B-720, Lear 24, F-15, C-402, and B-747. A series of three piloted simulation tests have been conducted at Ames Research Center to investigate propulsion control for safely landing a medium size jet transport which has experienced a total primary flight-control failure. The first series of tests was completed in July 1992 and defined the best interface for the pilot commands to drive the engines. The second series of tests was completed in August 1994 and investigated propulsion controlled aircraft (PCA) display requirements and various command modes. The third series of tests was completed in May 1995 and investigated PCA full-flight envelope capabilities. This report describes the concept of a PCA, discusses pilot controls, displays, and procedures; and presents the results of piloted simulation evaluations of the concept by a cross-section of air transport pilots.

Bull, John↗

The effects of motion and g-seat cues on pilot simulator performance of three piloting tasks

Data are presented that show the effects of motion system cues, g-seat cues, and pilot experience on pilot performance during takeoffs with engine failures, during in-flight precision turns, and during landings with wind shear. Eight groups of USAF pilots flew a simulated KC-135 using four different cueing systems. The basic cueing system was a fixed-base type (no-motion cueing) with visual cueing. The other three systems were produced by the presence of either a motion system or a g-seat, or both. Extensive statistical analysis of the data was performed and representative performance means were examined. These data show that the addition of motion system cueing results in significant improvement in pilot performance for all three tasks; however, the use of g-seat cueing, either alone or in conjunction with the motion system, provides little if any performance improvement for these tasks and for this aircraft type.

Showalter, T. W.↗

Development of the Orion Crew-Service Module Umbilical Retention and Release Mechanism

The Orion CSM umbilical retention and release mechanism supports and protects all of the cross-module commodities between the spacecrafts crew and service modules. These commodities include explosive transfer lines, wiring for power and data, and flexible hoses for ground purge and life support systems. The mechanism employs a single separation interface which is retained with pyrotechnically actuated separation bolts and supports roughly two dozen electrical and fluid connectors. When module separation is commanded, either for nominal on-orbit CONOPS or in the event of an abort, the mechanism must release the separation interface and sever all commodity connections within milliseconds of command receipt. There are a number of unique and novel aspects of the design solution developed by the Orion mechanisms team. The design is highly modular and can easily be adapted to other vehiclesmodules and alternate commodity sets. It will be flight tested during Orions Exploration Flight Test 1 (EFT-1) in 2014, and the Orion team anticipates reuse of the design for all future missions. The design packages fluid, electrical, and ordnance disconnects in a single separation interface. It supports abort separations even in cases where aerodynamic loading prevents the deployment of the umbilical arm. Unlike the Apollo CSM umbilical which was a destructive separation device, the Orion design is resettable and flight units can be tested for separation performance prior to flight.Initial development testing of the mechanisms separation interface resulted in binding failures due to connector misalignments. The separation interface was redesigned with a robust linear guide system, and the connector separation and boom deployment were separated into two discretely sequenced events. These changes addressed the root cause of the binding failure by providing better control of connector alignment. The new design was tuned and validated analytically via Monte Carlo simulation. The analytical validation was followed by a repeat of the initial test suite plus test cases at thermal extremes and test cases with imposed mechanical failures demonstrating fault tolerance. The mechanism was then exposed to the qualification vibration environment. Finally, separation testing was performed at full speed with live ordnance.All tests of the redesigned mechanism resulted in successful separation of the umbilical interface with adequate force margins and timing. The test data showed good agreement with the predictions of the Monte Carlo simulation. The simulation proved invaluable due to the number of variables affecting the separation and the uncertainty associated with each. The simulation allowed for rapid assessment of numerous trades and contingency scenarios, and can be easily reconfigured for varying commodity sets and connector layouts.

Separation↗

A Selection of Composites Simulation Practices at NASA Langley Research Center

One of the major areas of study at NASA Langley Research Center is the development of technologies that support the use of advanced composite materials in aerospace applications. Amongst the supporting technologies are analysis tools used to simulate the behavior of these materials. This presentation will discuss a number of examples of analysis tools and simulation practices conducted at NASA Langley. The presentation will include examples of damage tolerance analyses for both interlaminar and intralaminar failure modes. Tools for modeling interlaminar failure modes include fracture mechanics and cohesive methods, whilst tools for modeling intralaminar failure involve the development of various progressive failure analyses. Other examples of analyses developed at NASA Langley include a thermo-mechanical model of an orthotropic material and the simulation of delamination growth in z-pin reinforced laminates.

Ratcliffe, James G.↗

Thermal High- and Low-Cycle Fatigue Behavior of Thick Thermal Barrier Coating Systems

Ceramic thermal barrier coatings have received increasing attention for advanced gas turbine and diesel engine applications because of their ability to provide thermal insulation to engine components. However, the durability of these coatings under the severe thermal cycling conditions encountered in a diesel engine (ref. 1) still remains a major issue. In this research at the NASA Lewis Research Center, a high-power laser was used to investigate the thermal fatigue behavior of a yttria-stabilized zirconia coating system under simulated diesel engine conditions. The mechanisms of fatigue crack initiation and propagation, and of coating failure under complex thermal low-cycle fatigue (LCF, representing stop/start cycles) and thermal high-cycle fatigue (HCF, representing operation at 1300 rpm) are described. Continuous wave and pulse laser modes were used to simulate pure LCF and combined LCF/HCF, respectively (ref. 2). The LCF mechanism was found to be closely related to the coating sintering and creep at high temperatures. These creep strains in the ceramic coating led to a tensile stress state during cooling, thus providing the major driving force for crack growth under LCF conditions. The combined LCF/HCF tests induced more severe coating surface cracking, microspallation, and accelerated crack growth than did the pure LCF test. HCF thermal loads also facilitated lateral crack branching and ceramic/bond coat interface delaminations. HCF is associated with the cyclic stresses originating from the high-frequency temperature fluctuation at the ceramic coating surface. The HCF thermal loads act on the crack by a wedging mechanism (ref. 1), resulting in continuous crack growth at temperature. The HCF stress intensity factor amplitude increases with the interaction depth and temperature swing, and decreases with the crack depth. HCF damage also increases with the thermal expansion coefficient and the Young's modulus of the ceramic coating (refs. 1 and 3).

Miller, Robert A.↗

Using Degradation Modeling to Identify Fragile Operational Conditions in Human- and Component-driven Resilience Assessment

Studying failure events shows that many high-impact events result from the complex interactions between precipitating failure events and degraded operational conditions. Often, when a system is put in operations, unforeseen practical realities (e.g., maintenance and/or workforce availability) lead the system to be operated in configurations outside its envisioned nominal range. However, design-time failure models often assume that the failure events are initiated in an idealized, nominal state of system operation, resulting in an incomplete assessment of future risk. To solve this, this paper develops a framework to consider degraded operational performance in scenario-based resilience models which uses a corresponding model of performance degradation to determine the values of deteriorated model parameters in the resilience model. This framework is demonstrated on a remotely-piloted rover to determine the (individual and combined) effect of drive-train wear and operator fatigue on the resilience of the rover to drive-train faults. This demonstration showed the substantial impact that degradation has on resilience, highlighting the need to account for degradation in resilience models–specifically, unconsidered degradation can lead to overestimates of resilience (and thus underestimates of safety margin) and because resilience can degrade prior to visible unreliability, which can lead to an operational environment with a high propensity for high-impact unforeseen failure events.

resilience↗

Behavior of ceramics at 1200 C in a simulated gas turbine environment

This report summarizes programs at the NASA Lewis Research Center evaluating several classes of commercial ceramics, in a high gas velocity burner rig simulating a gas turbine engine environment. Testing of 23 ceramics in rod geometry identified SiC and Si3N4 as outstanding in resistance to oxidation and thermal stress and identified the failure modes of other ceramics. Further testing of a group of 15 types of SiC and Si3N4 in simulated vane shape geometry has identified a hot pressed SiC, a reaction sintered SiC, and hot pressed Si3N4 as the best of that group. SiC and Si3N4 test specimens were compared on the basis of weight change, dimensional reductions, metallography, fluorescent penetrant inspection, X-ray diffraction analyses, and failure mode.

Sanders, W. A.↗

Verification and Validation Process for Progressive Damage and Failure Analysis Methods in the NASA Advanced Composites Consortium

The Advanced Composites Consortium is a US Government/Industry partnership supporting technologies to enable timeline and cost reduction in the development of certified composite aerospace structures. A key component of the consortium's approach is the development and validation of improved progressive damage and failure analysis methods for composite structures. These methods will enable increased use of simulations in design trade studies and detailed design development, and thereby enable more targeted physical test programs to validate designs. To accomplish this goal with confidence, a rigorous verification and validation process was developed. The process was used to evaluate analysis methods and associated implementation requirements to ensure calculation accuracy and to gage predictability for composite failure modes of interest. This paper introduces the verification and validation process developed by the consortium during the Phase I effort of the Advanced Composites Project. Specific structural failure modes of interest are first identified, and a subset of standard composite test articles are proposed to interrogate a progressive damage analysis method's ability to predict each failure mode of interest. Test articles are designed to capture the underlying composite material constitutive response as well as the interaction of failure modes representing typical failure patterns observed in aerospace structures.

Wanthal, Steven↗

Full-Scale Crash Test and Finite Element Simulation of a Composite Prototype Helicopter

A full-scale crash test of a prototype composite helicopter was performed at the Impact Dynamics Research Facility at NASA Langley Research Center in 1999 to obtain data for validation of a finite element crash simulation. The helicopter was the flight test article built by Sikorsky Aircraft during the Advanced Composite Airframe Program (ACAP). The composite helicopter was designed to meet the stringent Military Standard (MIL-STD-1290A) crashworthiness criteria and was outfitted with two crew and two troop seats and four anthropomorphic dummies. The test was performed at 38-ft/s vertical and 32.5-ft/s horizontal velocity onto a rigid surface. An existing modal-vibration model of the Sikorsky ACAP helicopter was converted into a model suitable for crash simulation. A two-stage modeling approach was implemented and an external user-defined subroutine was developed to represent the complex landing gear response. The crash simulation was executed with a nonlinear, explicit transient dynamic finite element code. Predictions of structural deformation and failure, the sequence of events, and the dynamic response of the airframe structure were generated and the numerical results were correlated with the experimental data to validate the simulation. The test results, the model development, and the test-analysis correlation are described.

Jackson, Karen E.↗

Simulation of Malfunctions for the ISS Double-Gimbal Control Moment Gyroscope

This paper presents a simplified approach to simulation of malfunctions of the Control Moment Gyroscope (CMG) on board the International Space Station (ISS). These malfunctions will be used as part of flight training of CMG failure scenarios in the guidance navigation control (GNC) subsystem of the Training Systems for 21st Century (TS21) simulator. The CMG malfunctions are grouped under mechanical, thermal and electrical categories. A malfunction can be as simple as one which only affects the telemetry or a complex one that changes the state and behavior of the CMG model. In both cases, the ISS GNC flight software will read the telemetry and respond accordingly. The user executes these malfunctions by supplying conditional data which modify internal model states and then elicit a response as seen on the user displays. Ground operators and crew on board the ISS use CMG malfunction procedures to better understand and respond to anomalies observed within the CMG subsystem.

Inampudi, Ravi↗

CO2 Removal for the International Space Station – 4-Bed Molecular Sieve Material Selection and System Design

Efforts over the past three years have focused on the study of candidate sorbent materials for use in a 4BMS molecular sieve system. The accumulation of knowledge has been invaluable for further decisions and for reflecting on the conclusions of past decisions. The goal of the next generation CO2 removal system is continuous, failure-free operation for nearly 20,000 hours, but no complex life support system has yet reached this lofty goal. In addition to reliability, CO2 removal performance improvements have been intensively studied. The achievements toward this end include highly detailed isotherm measurements which drive system simulations as well as testing physical design improvements. Looking back on the successes and failures of past systems, correlating data from long-duration tests, and carefully projecting future results are all needed for the success of the next system. This work intends to reveal the path we have taken and illuminate the steps to come for CO2 removal life support with the 4BCO2 flight demonstration.

Cmarik, Gregory E.↗

Characterization of Triaxial Braided Composite Material Properties for Impact Simulation

The reliability of impact simulations for aircraft components made with triaxial braided carbon fiber composites is currently limited by inadequate material property data and lack of validated material models for analysis. Improvements to standard quasi-static test methods are needed to account for the large unit cell size and localized damage within the unit cell. The deformation and damage of a triaxial braided composite material was examined using standard quasi-static in-plane tension, compression, and shear tests. Some modifications to standard test specimen geometries are suggested, and methods for measuring the local strain at the onset of failure within the braid unit cell are presented. Deformation and damage at higher strain rates is examined using ballistic impact tests on 61- by 61- by 3.2-mm (24- by 24- by 0.125-in.) composite panels. Digital image correlation techniques were used to examine full-field deformation and damage during both quasi-static and impact tests. An impact analysis method is presented that utilizes both local and global deformation and failure information from the quasi-static tests as input for impact simulations. Improvements that are needed in test and analysis methods for better predictive capability are examined.

Roberts, Gary D.↗

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal↗

Trajectory optimization for a National Launch System vehicle

A trajectory design process is presented for a proposed National Launch System (NLS) vehicle configuration. A software trajectory planner was developed to generate near optimal pitch plane trajectories for variable mission plans, variable launch site selections, and last minute wind conditions at the time of launch. In addition, the trajectory planner performs in-flight near optimal trajectory redesign in the event of an engine-out or unexpected wind dispersions. The trajectory planner iteratively simulates trial trajectories defined by variables corresponding to a parameterized trajectory shape. The trajectory planner optimizes these trajectory parameters according to the fuel used to realize the trajectories. For prelaunch scenarios, the trajectory planner generated near optimal trajectories of consistent fuel performance irrespective of the winds encountered at the launch site. In-flight trajectory redesigns were also shown to be effective in fulfilling the mission plan and preserving the structural integrity of the vehicle. The in-flight redesign results indicate that closed-loop guidance in the early stages of ascent is highly effective in accommodating engine failures or wind dispersions. All trajectory designs were verified using a 6DOF simulation with flight controllers.

Chen, Eugene S.↗