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The purpose of this workshop was to address the following questions: What are the impediments to making more use of autonomy on robotic space missions? Which of those impediments apply to which kinds of space missions? What is/can/could be done to overcome those impediments? Highlights of the workshop’s treatment of these topics are given herein.

The purpose of this workshop was to address the following questions: What are the impediments to making more use of autonomy on robotic space missions? Which of those impediments apply to which kinds of space missions? What is/can/could be done to overcome those impediments? Highlights of the workshop’s treatment of these topics are given herein.

Unmanned Air Systems (UAS) are no longer coming, they are here, and operators from first responders to Google and Amazon are demanding access to the National Airspace System (NAS) for a wide variety of missions. This includes a proliferation of small UAS or sUAS that will operate beyond line of sight at altitudes of 500 ft and below. A myriad of issues continues to slow the development of verification, validation, and certification methods that will enable the safe introduction of UAS to the NAS. These issues include the lack of both a consensus in UAS categorization process and quantitative certification requirements, including the definition of handling qualities. Because of the wide variety of UAS types (fixed wing, rotary wing from traditional helicopters to multirotor configurations, ducted fans, airships, etc.) and vehicle size from micro vehicles to the Global Hawk with a wing span similar to that of a Boeing 737, there cannot be a one-size-fits-all set of requirements. To address these issues, Systems Technology Inc. (STI) has developed the UAS Handling Qualities Assessment (UAS-HQ) process and corresponding draft specification that will guide UAS stakeholders through a systematic evaluation process. The work described herein builds on the existing, highly successful, military rotorcraft handling qualities specifications that features a mission-oriented approach, a concept that originated at STI. The vehicle is first identified by a simple weight-based classification and then the associated vehicle mission task elements are considered. These missions have specific tasks inclusive to them that then dictate the criteria and demonstration maneuvers necessary to evaluate the UAS handling qualities. An assessment of both modeled responses and flight test data can then be conducted to examine the predicted versus actual handling qualities and, if required, design modifications can then be made. Mr. David Klyde, Vice President and Technical Director, Engineering Services, served as Principal Investigator, while Dr. Natalia Alexandrov served as the NASA LaRC technical representative. In the Phase II program, STI was joined by David Mitchell of Mitchell Aerospace Research and the University of Minnesota. Mr. Mitchell led the draft specification development effort, while the University of Minnesota UAV Lab conducted sUAS flight tests under the direction of Dr. Peter Seiler.

Under the NASA Aeronautics Research Mission Directorate (ARMD) Convergent Aeronautical Solutions (CAS) project, NASA Glenn Research Center has been leading Multifunctional Structures for High Energy Lightweight Load-bearing Storage (M-SHELLS) research efforts. The technology of integrating load-carrying structures with electrical energy storage capacity has the potential to reduce the overall weight of future electric aircraft. The proposed project goals were to develop M-SHELLS in the form of honeycomb coupons and subcomponents, integrate them into the structure, and conduct low-risk flight tests onboard a remotely piloted small aircraft. Experimental M-SHELLS energy-storing coupons were fabricated and tested in the laboratory for their electrical and mechanical properties. In this paper, finite element model development and structural analyses of two small test aircraft candidates are presented. The finite element analysis of the initial two-spar wing is described for strain, deflection, and weight estimation. After a test aircraft Tempest was acquired, a load- deflection test of the wing was conducted. A finite element model of the Tempest was then developed based on the test aircraft dimensions and construction detail. The component weight analysis from the finite element model and test measurements were correlated. Structural analysis results with multifunctional energy storage panels in the fuselage of the test vehicle are presented. Although the flight test was cancelled because of programmatic reasons and time constraints, the structural analysis results indicate that the mid-fuselage floor composite panel could provide structural integrity with minimal weight penalty while supplying electrical energy. To explore potential future applications of the multifunctional structure, analyses of the NASA X-57 Maxwell electric aircraft and a NASA N+3 Technology Conventional Configuration (N3CC) fuselage are presented. Secondary aluminum structure in the fuselage sub-floor and cargo area were partially replaced with reinforced five-layer composite panels with M-SHELLS honeycomb core. The N3CC fuselage weight reduction associated with each design without risking structural integrity are described. The structural analysis and weight estimation with the application of composite M-SHELLS panels to the N3CC fuselage indicate a 3.2% reduction in the fuselage structural weight, prior to accounting for the additional weight of core material required to complete the energy storage functionality.

Current rapidly-exploring random tree (RRT) algorithms rely on proximity query packages that often include collision checkers, tolerance verification, and distance computation algorithms for the generation of safe paths. In this paper, we broaden the information available to the path-planning algorithm by incorporating silhouette information of nearby obstacles in conflict. A silhouette-informed tree (SIT) is generated through the flight-safe region of a wire maze for a single unmanned aerial system (UAS). The silhouette is used to extract local geometric information of nearby obstacles and provide path alternatives around these obstacles. Thus, focusing the search for the generation of new tree branches near these obstacles, and decreasing the number of samples required to explore the narrow corridors within the wire maze. The SIT is then processed to extract a path that connects the initial location of the UAS with the goal, reduce the number of line segments in this path if possible, and smooth the resulting path using Pythagorean Hodograph Bezier curves. To ensure that the smoothed path remains in the flight-safe region of the configuration space, a tolerance verification algorithm for Bezier curves and convex polytopes in three dimensions is proposed. Lastly, temporal specifications are imposed on the smoothed path in the shape of an arbitrary speed profile.

Rising traffic density, along with autonomy and diversity of vehicles in the air, will fundamentally change the safety environment of the future air transportation system. The change in risk is two-fold: increasing chances of mid-air collisions with non-cooperative objects and increasing chances of crashes over highly populated areas. The changing nature of the vehicles populating the airspace means that civilian aircraft design must now explicitly include considerations of survivability in the event of collision with other vehicles, as well as prevention of damage to people, animals and property on the ground, to a much greater extent than today. This paper offers a preliminary perspective on how MDAO could contribute toward these goals. One of the conclusions is that, in contrast to traditional vehicle design, to accommodate the complexity of the future airspace safely and efficiently, vehicle design requirements, modeling, and design optimization must be closely connected to the properties of the airspace, including those of other vehicles in the air. Thus, the total measure of a vehicle's survivability should include the traditional survivability in malfunction scenarios, combined with new considerations of survivability in collisions and survivability of the public on the ground.

We report on an examination of potential benefits of infusing wireless technologies into various areas of aircraft and airspace operations. The analysis is done in support of a NASA seedling project Efficient Reconfigurable Cockpit Design and Fleet Operations Using Software Intensive, Network Enabled Wireless Architecture (ECON). The study has two objectives. First, we investigate one of the main benefit hypotheses of the ECON proposal: that the replacement of wired technologies with wireless would lead to significant weight reductions on an aircraft, among other benefits. Second, we advance a list of wireless technology applications and discuss their system benefits. With regard to the primary hypothesis, we conclude that the promise of weight reduction is premature. Specificity of the system domain and aircraft, criticality of components, reliability of wireless technologies, the weight of replacement or augmentation equipment, and the cost of infusion must all be taken into account among other considerations, to produce a reliable estimate of weight savings or increase.

Incremental approaches to air transportation system development inherit current architectural constraints, which, in turn, place hard bounds on system capacity, efficiency of performance, and complexity. To enable airspace operations of the future, a clean-slate (ab initio) airspace design(s) must be considered. This ab initio National Airspace System (NAS) must be capable of accommodating increased traffic density, a broader diversity of aircraft, and on-demand mobility. System and subsystem designs should scale to accommodate the inevitable demand for airspace services that include large numbers of autonomous Unmanned Aerial Vehicles and a paradigm shift in general aviation (e.g., personal air vehicles) in addition to more traditional aerial vehicles such as commercial jetliners and weather balloons. The complex and adaptive nature of ab initio designs for the future NAS requires new approaches to validation, adding a significant physical experimentation component to analytical and simulation tools. In addition to software modeling and simulation, the ability to exercise system solutions in a flight environment will be an essential aspect of validation. The NASA Langley Research Center (LaRC) Autonomy Incubator seeks to develop a flight simulation infrastructure for ab initio modeling and simulation that assumes no specific NAS architecture and models vehicle-to-vehicle behavior to examine interactions and emergent behaviors among hundreds of intelligent aerial agents exhibiting collaborative, cooperative, coordinative, selfish, and malicious behaviors. The air transportation system of the future will be a complex adaptive system (CAS) characterized by complex and sometimes unpredictable (or unpredicted) behaviors that result from temporal and spatial interactions among large numbers of participants. A CAS not only evolves with a changing environment and adapts to it, it is closely coupled to all systems that constitute the environment. Thus, the ecosystem that contains the system and other systems evolves with the CAS as well. The effects of the emerging adaptation and co-evolution are difficult to capture with only combined mathematical and computational experimentation. Therefore, an ab initio flight simulation environment must accommodate individual vehicles, groups of self-organizing vehicles, and large-scale infrastructure behavior. Inspired by Massively Multiplayer Online Role Playing Games (MMORPG) and Serious Gaming, the proposed ab initio simulation environment is similar to online gaming environments in which player participants interact with each other, affect their environment, and expect the simulation to persist and change regardless of any individual player's active participation.

Rapidly expanding unmanned air traffic includes and will continue to include non-cooperative participants. Non-cooperative behavior may be due to technical failure, a lack of appropriate equipment, a careless or malicious operator. Regardless of the cause, the outcome remains: growing density of non-cooperative traffic will increase the risk of collision between unmanned vehicles and aircraft carrying humans. As a result, the degraded safety of airspace may limit access to airspace, with adverse consequences for the traveling public and the economy. Because encounters with small non-cooperative objects, such as birds or wayward drones, can happen too rapidly for an external control system to mitigate them, it is imperative that the aircraft that carry humans survive encounters with non-cooperative vehicles. To-date, design for survivability has been practiced explicitly in the military domain. Survivability against collisions in civil aviation has been limited to tolerances against bird strikes; and these tolerances have proved inadequate on occasion. The growing risk of collision with unmanned vehicles now requires the development of survivability discipline for civilian transport aircraft. The new discipline must be infused into multidisciplinary design methods, on par with traditional disciplines. In this paper, we report on a preliminary study of survivability considerations for the civil aviation domain.

Main Message: National and Global Needs - Develop scalable airspace operations management system to accommodate increased mobility needs, emerging airspace uses, mix, future demand. Be affordable and economically viable. Sense of Urgency. Saturation (delays), emerging airspace uses, proactive development. Autonomy is Needed for Airspace Operations to Meet Future Needs. Costs, time critical decisions, mobility, scalability, limits of cognitive workload. AutoMax to Accommodate National and Global Needs. Auto: Automation, autonomy, autonomicity for airspace operations. Max: Maximizing performance of the National Airspace System. Interesting Challenges and Path Forward.

The complexity of the present system for managing air traffic has led to "discreteness" in approaches to creating new concepts: new concepts are created as point designs, based on experience, expertise, and creativity of the proposer. Discrete point designs may be highly successful but they are difficult to substantiate in the face of equally strong substantiation of competing concepts, as well as the state of the art in concept evaluation via simulations. Hybrid concepts may present a compromise - the golden middle. Yet a hybrid of sometimes in principle incompatible concepts forms another point design that faces the challenge of substantiation and validation. We are faced with the need to re-design the air transportation system ab initio. This is a daunting task, especially considering the problem of transitioning from the present system to any fundamentally new system. However, design from scratch is also an opportunity to reconsider approaches to new concept development. In this position paper we propose an approach, Optimized Parametric Functional Design, for systematic development of concepts for management and control of airspace systems, based on optimization formulations in terms of required system functions and states. This reasoning framework, realizable in the context of ab initio system design, offers an approach to deriving substantiated airspace management and control concepts. With growing computational power, we hope that the approach will also yield a methodology for actual dynamic control of airspace

The Air Traffic Monotonic Lagrangian Grid (ATMLG) is used to simulate a 24 hour period of air traffic flow in the National Airspace System (NAS). During this time period, there are 41,594 flights over the United States, and the flight plan information (departure and arrival airports and times, and waypoints along the way) are obtained from an Federal Aviation Administration (FAA) Enhanced Traffic Management System (ETMS) dataset. Two simulation procedures are tested and compared: one based on the Monotonic Lagrangian Grid (MLG), and the other based on the stationary Latitude-Longitude (Lat- Long) grid. Simulating one full day of air traffic over the United States required the following amounts of CPU time on a single processor of an SGI Altix: 88 s for the MLG method, and 163 s for the Lat-Long grid method. We present a discussion of the amount of CPU time required for each of the simulation processes (updating aircraft trajectories, sorting, conflict detection and resolution, etc.), and show that the main advantage of the MLG method is that it is a general sorting algorithm that can sort on multiple properties. We discuss how many MLG neighbors must be considered in the separation assurance procedure in order to ensure a five-mile separation buffer between aircraft, and we investigate the effect of removing waypoints from aircraft trajectories. When aircraft choose their own trajectory, there are more flights with shorter duration times and fewer CD&R maneuvers, resulting in significant fuel savings.

The Air Traffic Monotonic Lagrangian Grid (ATMLG) is presented as a tool to evaluate new air traffic system concepts. The model, based on an algorithm called the Monotonic Lagrangian Grid (MLG), can quickly sort, track, and update positions of many aircraft, both on the ground (at airports) and in the air. The underlying data structure is based on the MLG, which is used for sorting and ordering positions and other data needed to describe N moving bodies and their interactions. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. Recent upgrades to ATMLG include adding blank place-holders within the MLG data structure, which makes it possible to dynamically change the MLG size and also improves the quality of the MLG grid. Additional upgrades include adding FAA flight plan data, such as way-points and arrival and departure times from the Enhanced Traffic Management System (ETMS), and combining the MLG with the state-of-the-art strategic and tactical conflict detection and resolution algorithms from the NASA-developed Stratway software. In this paper, we present results from our early efforts to couple ATMLG with the Stratway software, and we demonstrate that it can be used to quickly simulate air traffic flow for a very large ETMS dataset.

This paper proposes a model for evaluating long-term measures to reduce congestion at airports in the National Airspace System (NAS). This model is constructed with the goal of assessing the global impacts of congestion management strategies, specifically slot restrictions. We develop the Minimax Node Throughput Problem (MINNTHRU), a multicommodity network flow model that provides insight into air traffic patterns when one minimizes the worst-case operation across all airports in a given network. MINNTHRU is thus formulated as a model where congestion arises from network topology. It reflects not market-driven airline objectives, but those of a regulatory authority seeking a distribution of air traffic beneficial to all airports, in response to congestion management measures. After discussing an algorithm for solving MINNTHRU for moderate-sized (30 nodes) and larger networks, we use this model to study the impacts of slot restrictions on the operation of an entire hub-spoke airport network. For both a small example network and a medium-sized network based on 30 airports in the NAS, we use MINNTHRU to demonstrate that increasing the severity of slot restrictions increases the traffic around unconstrained hub airports as well as the worst-case level of operation over all airports.

This paper describes the continued development of a dynamic air-traffic model, ATMLG, intended for rapid evaluation of rules and methods to control and optimize transport systems. The underlying data structure is based on the Monotonic Lagrangian Grid (MLG), which is used for sorting and ordering positions and other data needed to describe N moving bodies, and their interactions. In ATMLG, the MLG is combined with algorithms for collision avoidance and updating aircraft trajectories. Aircraft that are close to each other in physical space are always near neighbors in the MLG data arrays, resulting in a fast nearest-neighbor interaction algorithm that scales as N. In this paper, we use ATMLG to examine how the ability to maintain a required separation between aircraft decreases as the number of aircraft in the volume increases. This requires keeping track of the primary and subsequent collision avoidance maneuvers necessary to maintain a five mile separation distance between all aircraft. Simulation results show that the number of collision avoidance moves increases exponentially with the number of aircraft in the volume.

The promise of the Next Generation Air Transportation System (NextGen) is strongly tied to the concept of trajectory-based operations in the national airspace system. Existing efforts to develop trajectory management concepts are largely focused on individual trajectories, optimized independently, then de-conflicted among each other, and individually re-optimized, as possible. The benefits in capacity, fuel, and time are valuable, though perhaps could be greater through alternative strategies. The concept of agent-based trajectories offers a strategy for automation of simultaneous multiple trajectory management. The anticipated result of the strategy would be dynamic management of multiple trajectories with interacting and interdependent outcomes that satisfy multiple, conflicting constraints. These constraints would include the business case for operators, the capacity case for the Air Navigation Service Provider (ANSP), and the environmental case for noise and emissions. The benefits in capacity, fuel, and time might be improved over those possible under individual trajectory management approaches. The proposed approach relies on computational agent-based modeling (ABM), combinatorial mathematics, as well as application of "traffic physics" concepts to the challenge, and modeling and simulation capabilities. The proposed strategy could support transforming air traffic control from managing individual aircraft behaviors to managing systemic behavior of air traffic in the NAS. A system built on the approach could provide the ability to know when regions of airspace approach being "full," that is, having non-viable local solution space for optimizing trajectories in advance.

Strictly evolutionary approaches to improving the air transport system a highly complex network of interacting systems no longer suffice in the face of demand that is projected to double or triple in the near future. Thus evolutionary approaches should be augmented with active design methods. The ability to actively design, optimize and control a system presupposes the existence of predictive modeling and reasonably well-defined functional dependences between the controllable variables of the system and objective and constraint functions for optimization. Following recent advances in the studies of the effects of network topology structure on dynamics, we investigate the performance of dynamic processes on transport networks as a function of the first nontrivial eigenvalue of the network's Laplacian, which, in turn, is a function of the network s connectivity and modularity. The last two characteristics can be controlled and tuned via optimization. We consider design optimization problem formulations. We have developed a flexible simulation of network topology coupled with flows on the network for use as a platform for computational experiments.

The cumulative degree distributions of transport networks, such as air transportation networks and respiratory neuronal networks, follow power laws. The significance of power laws with respect to other network performance measures, such as throughput and synchronization, remains an open question. Evolving methods for the analysis and design of air transportation networks must address network performance in the face of increasing demands and the need to contain and control local network disturbances, such as congestion. Toward this end, we investigate functional relationships that govern the performance of transport networks; for example, the links between the first nontrivial eigenvalue of a network's Laplacian matrix - a quantitative measure of network synchronizability - and other global network parameters. In particular, among networks with a fixed degree distribution and fixed network assortativity (a measure of a network's preference to attach nodes based on a similarity or difference), those with the small eigenvalue are shown to be poor synchronizers, to have much longer shortest paths and to have greater clustering in comparison to those with large. A simulation of a respiratory network adds data to our investigation. This study is a beginning step in developing metrics and design variables for the analysis and active design of air transport networks.

This paper is one of a set of papers, developed simultaneously and presented within a single conference session, that are intended to highlight systems analysis and design capabilities within the Systems Analysis and Concepts Directorate (SACD) of the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC). This paper focuses on the specific capabilities of uncertainty/risk analysis, quantification, propagation, decomposition, and management, robust/reliability design methods, and extensions of these capabilities into decision analysis methods within SACD. These disciplines are discussed together herein under the name of Decision Support Methods and Tools. Several examples are discussed which highlight the application of these methods within current or recent aerospace research at the NASA LaRC. Where applicable, commercially available, or government developed software tools are also discussed

This report reviews six classes of models that are used for studying transportation network topologies. The report is motivated by two main questions. First, what can the "new science" of complex networks (scale-free, small-world networks) contribute to our understanding of transport network structure, compared to more traditional methods? Second, how can geographic information systems (GIS) contribute to studying transport networks? The report defines terms that can be used to classify different kinds of models by their function, composition, mechanism, spatial and temporal dimensions, certainty, linearity, and resolution. Six broad classes of models for analyzing transport network topologies are then explored: GIS; static graph theory; complex networks; mathematical programming; simulation; and agent-based modeling. Each class of models is defined and classified according to the attributes introduced earlier. The paper identifies some typical types of research questions about network structure that have been addressed by each class of model in the literature.

The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.

Integrating autonomous disciplines into a problem amenable to solution presents a major challenge in realistic multidisciplinary design optimization (MDO). We propose a linguistic approach to MDO problem description, formulation, and solution we call reconfigurable multidisciplinary synthesis (REMS). With assistance from computer science techniques, REMS comprises an abstract language and a collection of processes that provide a means for dynamic reasoning about MDO problems in a range of contexts. The approach may be summarized as follows. Description of disciplinary data according to the rules of a grammar, followed by lexical analysis and compilation, yields basic computational components that can be assembled into various MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. The range of contexts for reasoning about MDO spans tasks from error checking and derivative computation to formulation and reformulation of optimization problem statements. In highly structured contexts, reconfigurability can mean a straightforward transformation among problem formulations with a single operation. We hope that REMS will enable experimentation with a variety of problem formulations in research environments, assist in the assembly of MDO test problems, and serve as a pre-processor in computational frameworks in production environments. Part 1 of two companion papers, discusses the fundamentals of REMS. This paper, Part 2 illustrates the methodology in more detail.

Opportunities for breakthroughs in the large-scale computational simulation and design of aerospace vehicles are presented. Computational fluid dynamics tools to be used within multidisciplinary analysis and design methods are emphasized. The opportunities stem from speedups and robustness improvements in the underlying unit operations associated with simulation (geometry modeling, grid generation, physical modeling, analysis, etc.). Further, an improved programming environment can synergistically integrate these unit operations to leverage the gains. The speedups result from reducing the problem setup time through geometry modeling and grid generation operations, and reducing the solution time through the operation counts associated with solving the discretized equations to a sufficient accuracy. The opportunities are addressed only at a general level here, but an extensive list of references containing further details is included. The opportunities discussed are being addressed through the Fast Adaptive Aerospace Tools (FAAST) element of the Advanced Systems Concept to Test (ASCoT) and the third Generation Reusable Launch Vehicles (RLV) projects at NASA Langley Research Center. The overall goal is to enable greater inroads into the design process with large-scale simulations.

Bilevel problem formulations have received considerable attention as an approach to multidisciplinary optimization in engineering. We examine the analytical and computational properties of one such approach, collaborative optimization. The resulting system-level optimization problems suffer from inherent computational difficulties due to the bilevel nature of the method. Most notably, it is impossible to characterize and hence identify solutions of the system-level problems because the standard first-order conditions for solutions of constrained optimization problems do not hold. The analytical features of the system-level problem make it difficult to apply conventional nonlinear programming algorithms. Simple examples illustrate the analysis and the algorithmic consequences for optimization methods. We conclude with additional observations on the practical implications of the analytical and computational properties of collaborative optimization.

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis

We, discuss criteria by which one can classify, analyze, and evaluate approaches to solving multidisciplinary design optimization (MDO) problems. Central to our discussion is the often overlooked distinction between questions of formulating MDO problems and solving the resulting computational problem. We illustrate our general remarks by comparing several approaches to MDO that have been proposed.