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All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

optimal control↗
NASA NTRS2009

Decomposition Algorithm for Global Reachability Analysis on a Time-Varying Graph with an Application to Planetary Exploration

Hot air (Montgolfiere) balloons represent a promising vehicle system for possible future exploration of planets and moons with thick atmospheres such as Venus and Titan. To go to a desired location, this vehicle can primarily use the horizontal wind that varies with altitude, with a small help of its own actuation. A main challenge is how to plan such trajectory in a highly nonlinear and time-varying wind field. This paper poses this trajectory planning as a graph search on the space-time grid and addresses its computational aspects. When capturing various time scales involved in the wind field over the duration of long exploration mission, the size of the graph becomes excessively large. We show that the adjacency matrix of the graph is block-triangular, and by exploiting this structure, we decompose the large planning problem into several smaller subproblems, whose memory requirement stays almost constant as the problem size grows. The approach is demonstrated on a global reachability analysis of a possible Titan mission scenario.

Dijkstra's algorithm↗
NASA NTRS2008

An Efficient Reachability Analysis Algorithm

A document discusses a new algorithm for generating higher-order dependencies for diagnostic and sensor placement analysis when a system is described with a causal modeling framework. This innovation will be used in diagnostic and sensor optimization and analysis tools. Fault detection, diagnosis, and prognosis are essential tasks in the operation of autonomous spacecraft, instruments, and in-situ platforms. This algorithm will serve as a power tool for technologies that satisfy a key requirement of autonomous spacecraft, including science instruments and in-situ missions.

Vatan, Farrokh↗
NASA NTRS2005

Knowledge Representation Standards and Interchange Formats for Causal Graphs

In many domains, automated reasoning tools must represent graphs of causally linked events. These include fault-tree analysis, probabilistic risk assessment (PRA), planning, procedures, medical reasoning about disease progression, and functional architectures. Each of these fields has its own requirements for the representation of causation, events, actors and conditions. The representations include ontologies of function and cause, data dictionaries for causal dependency, failure and hazard, and interchange formats between some existing tools. In none of the domains has a generally accepted interchange format emerged. The paper makes progress towards interoperability across the wide range of causal analysis methodologies. We survey existing practice and emerging interchange formats in each of these fields. Setting forth a set of terms and concepts that are broadly shared across the domains, we examine the several ways in which current practice represents them. Some phenomena are difficult to represent or to analyze in several domains. These include mode transitions, reachability analysis, positive and negative feedback loops, conditions correlated but not causally linked and bimodal probability distributions. We work through examples and contrast the differing methods for addressing them. We detail recent work in knowledge interchange formats for causal trees in aerospace analysis applications in early design, safety and reliability. Several examples are discussed, with a particular focus on reachability analysis and mode transitions. We generalize the aerospace analysis work across the several other domains. We also recommend features and capabilities for the next generation of causal knowledge representation standards.

Throop, David R.↗
NASA NTRS2010

Decomposition Algorithm for Global Reachability on a Time-Varying Graph

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

Kuwata, Yoshiaki↗
NASA NTRS2008

Verification and Planning Based on Coinductive Logic Programming

Coinduction is a powerful technique for reasoning about unfounded sets, unbounded structures, infinite automata, and interactive computations [6]. Where induction corresponds to least fixed point's semantics, coinduction corresponds to greatest fixed point semantics. Recently coinduction has been incorporated into logic programming and an elegant operational semantics developed for it [11, 12]. This operational semantics is the greatest fix point counterpart of SLD resolution (SLD resolution imparts operational semantics to least fix point based computations) and is termed co- SLD resolution. In co-SLD resolution, a predicate goal p( t) succeeds if it unifies with one of its ancestor calls. In addition, rational infinite terms are allowed as arguments of predicates. Infinite terms are represented as solutions to unification equations and the occurs check is omitted during the unification process. Coinductive Logic Programming (Co-LP) and Co-SLD resolution can be used to elegantly perform model checking and planning. A combined SLD and Co-SLD resolution based LP system forms the common basis for planning, scheduling, verification, model checking, and constraint solving [9, 4]. This is achieved by amalgamating SLD resolution, co-SLD resolution, and constraint logic programming [13] in a single logic programming system. Given that parallelism in logic programs can be implicitly exploited [8], complex, compute-intensive applications (planning, scheduling, model checking, etc.) can be executed in parallel on multi-core machines. Parallel execution can result in speed-ups as well as in larger instances of the problems being solved. In the remainder we elaborate on (i) how planning can be elegantly and efficiently performed under real-time constraints, (ii) how real-time systems can be elegantly and efficiently model- checked, as well as (iii) how hybrid systems can be verified in a combined system with both co-SLD and SLD resolution. Implementations of co-SLD resolution as well as preliminary implementations of the planning and verification applications have been developed [4]. Co-LP and Model Checking: The vast majority of properties that are to be verified can be classified into safety properties and liveness properties. It is well known within model checking that safety properties can be verified by reachability analysis, i.e, if a counter-example to the property exists, it can be finitely determined by enumerating all the reachable states of the Kripke structure.

Bansal, Ajay↗
NASA NTRS2013

Rewriting Modulo SMT

Combining symbolic techniques such as: (i) SMT solving, (ii) rewriting modulo theories, and (iii) model checking can enable the analysis of infinite-state systems outside the scope of each such technique. This paper proposes rewriting modulo SMT as a new technique combining the powers of (i)-(iii) and ideally suited to model and analyze infinite-state open systems; that is, systems that interact with a non-deterministic environment. Such systems exhibit both internal non-determinism due to the system, and external non-determinism due to the environment. They are not amenable to finite-state model checking analysis because they typically are infinite-state. By being reducible to standard rewriting using reflective techniques, rewriting modulo SMT can both naturally model and analyze open systems without requiring any changes to rewriting-based reachability analysis techniques for closed systems. This is illustrated by the analysis of a real-time system beyond the scope of timed automata methods.

Rocha, Camilo↗
NASA NTRS2014

Rewriting Modulo SMT and Open System Analysis

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze infinite-state open systems, i.e., systems that interact with a non-deterministic environment. Such systems exhibit both internal non-determinism, which is proper to the system, and external non-determinism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.

Rocha, Camilo↗
NASA NTRS2001

The Logic of Reachability

In recent years, Graphplan style reachability analysis and mutual exclusion reasoning have been used in many high performance planning systems. While numerous refinements and extensions have been developed, the basic plan graph structure and reasoning mechanisms used in these systems are tied to the very simple STRIPS model of action. In 1999, Smith and Weld generalized the Graphplan methods for reachability and mutex reasoning to allow actions to have differing durations. However, the representation of actions still has some severe limitations that prevent the use of these techniques for many real-world planning systems. In this paper, we 1) separate the logic of reachability from the particular representation and inference methods used in Graphplan, and 2) extend the notions of reachability and mutual exclusion to more general notions of time and action. As it turns out, the general rules for mutual exclusion reasoning take on a remarkably clean and simple form. However, practical instantiations of them turn out to be messy, and require that we make representation and reasoning choices.

Smith, David E.↗
NASA NTRS2008

NASA Tech Briefs, November 2008

Topics covered include: Digital Phase Meter for a Laser Heterodyne Interferometer; Vision System Measures Motions of Robot and External Objects; Advanced Precipitation Radar Antenna to Measure Rainfall From Space; Wide-Band Radar for Measuring Thickness of Sea Ice; Vertical Isolation for Photodiodes in CMOS Imagers; Wide-Band Microwave Receivers Using Photonic Processing; L-Band Transmit/Receive Module for Phase-Stable Array Antennas; Microwave Power Combiner/Switch Utilizing a Faraday Rotator; Compact Low-Loss Planar Magic-T; Using Pipelined XNOR Logic to Reduce SEU Risks in State Machines; Quasi-Optical Transmission Line for 94-GHz Radar; Next Generation Flight Controller Trainer System; Converting from DDOR SASF to APF; Converting from CVF to AAF; Documenting AUTOGEN and APGEN Model Files; Sequence History Update Tool; Extraction and Analysis of Display Data; MRO DKF Post-Processing Tool; Rig Diagnostic Tools; MRO Sequence Checking Tool; Science Activity Planner for the MER Mission; UAVSAR Flight-Planning System; Templates for Deposition of Microscopic Pointed Structures; Adjustable Membrane Mirrors Incorporating G-Elastomers; Hall-Effect Thruster Utilizing Bismuth as Propellant; High-Temperature Crystal-Growth Cartridge Tubes Made by VPS; Quench Crucibles Reinforced with Metal; Deep-Sea Hydrothermal-Vent Sampler; Mars Rocket Propulsion System; Two-Stage Passive Vibration Isolator; Improved Thermal Design of a Compression Mold; Enhanced Pseudo-Waypoint Guidance for Spacecraft Maneuvers; Altimetry Using GPS-Reflection/Occultation Interferometry; Thermally Driven Josephson Effect; Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer; Gold Nanoparticle Labels Amplify Ellipsometric Signals; Phase Matching of Diverse Modes in a WGM Resonator; WGM Resonators for Terahertz-to-Optical Frequency Conversion; Determining Concentration of Nanoparticles from Ellipsometry; Microwave-to-Optical Conversion in WGM Resonators; Four-Pass Coupler for Laser-Diode-Pumped Solid-State Laser; Low-Resolution Raman-Spectroscopy Combustion Thermometry; Temperature Sensors Based on WGM Optical Resonators; Varying the Divergence of Multiple Parallel Laser Beams; Efficient Algorithm for Rectangular Spiral Search; Algorithm-Based Fault Tolerance Integrated with Replication; Targeting and Localization for Mars Rover Operations; Terrain-Adaptive Navigation Architecture; Self-Adjusting Hash Tables for Embedded Flight Applications; Schema for Spacecraft-Command Dictionary; Combined GMSK Communications and PN Ranging; System-Level Integration of Mass Memory; Network-Attached Solid-State Recorder Architecture; Method of Cross-Linking Aerogels Using a One-Pot Reaction Scheme; An Efficient Reachability Analysis Algorithm.

Source record↗
NASA NTRS2010

Model-Checking with Edge-Valued Decision Diagrams

We describe an algebra of Edge-Valued Decision Diagrams (EVMDDs) to encode arithmetic functions and its implementation in a model checking library along with state-of-the-art algorithms for building the transition relation and the state space of discrete state systems. We provide efficient algorithms for manipulating EVMDDs and give upper bounds of the theoretical time complexity of these algorithms for all basic arithmetic and relational operators. We also demonstrate that the time complexity of the generic recursive algorithm for applying a binary operator on EVMDDs is no worse than that of Multi-Terminal Decision Diagrams. We have implemented a new symbolic model checker with the intention to represent in one formalism the best techniques available at the moment across a spectrum of existing tools: EVMDDs for encoding arithmetic expressions, identity-reduced MDDs for representing the transition relation, and the saturation algorithm for reachability analysis. We compare our new symbolic model checking EVMDD library with the widely used CUDD package and show that, in many cases, our tool is several orders of magnitude faster than CUDD.

Roux, Pierre↗
NASA NTRS2011

Simulation and Verification of Synchronous Set Relations in Rewriting Logic

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.

Rocha, Camilo↗
NASA NTRS2013

Safe Maneuvering Envelope Estimation Based on a Physical Approach

This paper discusses a computationally efficient algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. This approach differs from others since it is physically inspired. This more transparent approach allows interpreting data in each step, and it is assumed that these physical models based upon flight dynamics theory will therefore facilitate certification for future real life applications.

aerodynamics↗
NASA NTRS2015

On-Line Safe Flight Envelope Determination for Impaired Aircraft

The design and simulation of an on-line algorithm which estimates the safe maneuvering envelope of aircraft is discussed in this paper. The trim envelope is estimated using probabilistic methods and efficient high-fidelity model based computations of attainable equilibrium sets. From this trim envelope, a robust reachability analysis provides the maneuverability limitations of the aircraft through an optimal control formulation. Both envelope limits are presented to the flight crew on the primary flight display. In the results section, scenarios are considered where this adaptive algorithm is capable of computing online changes to the maneuvering envelope due to impairment. Furthermore, corresponding updates to display features on the primary flight display are provided to potentially inform the flight crew of safety critical envelope alterations caused by the impairment.

algorithms↗
NASA NTRS2015

Piloted Simulator Evaluation of Maneuvering Envelope Information for Flight Crew Awareness

The implementation and evaluation of an efficient method for estimating safe aircraft maneuvering envelopes are discussed. A Bayesian approach is used to produce a deterministic algorithm for estimating aerodynamic system parameters from existing noisy sensor measurements, which are then used to estimate the trim envelope through efficient high- fidelity model-based computations of attainable equilibrium sets. The safe maneuverability limitations are extended beyond the trim envelope through a robust reachability analysis derived from an optimal control formulation. The trim and maneuvering envelope limits are then conveyed to pilots through three axes on the primary flight display. To evaluate the new display features, commercial airline crews flew multiple challenging approach and landing scenarios in the full motion Advanced Concepts Flight Simulator at NASA Ames Research Center, as part of a larger research initiative to investigate the impact on the energy state awareness of the crew. Results show that the additional display features have the potential to significantly improve situational awareness of the flight crew.

maneuvers↗
NASA NTRS2019

Mission Design for the Lunar Pallet Lander

Due to lighting conditions, the program decided to only fly to the north pole in June 2022 and south pole in December 2022. Starting with the June 2022 landing sites at the north pole, a trajectory scan was run for one landing per day for the latitudes from 85 up to 88 degrees at 0.5 degree increments. Each landing site was at lunar dawn, which determined the landing site’s longitude as described in the previous section. The results of the June 2022 scan showed that LPL had the capability to reach a landing site at least once per day for the region examined as see in in Figure 12. There appears to be a correlation between the landing site’s altitude and the propellant remaining above the lander’s FPR, Figure 13. This is most likely due to the >10 km altitude constraint at SRM burnout. This constraint was applied to keep the lander high above the lunar terrain to avoid mountains, but can be relaxed when the full terrain data is added. Figure 12. June 2022 Nominal Usable Propellant Remaining vs Landing Date/time Similarly, the December 2022 landing sites were run showing that LPL was also capable of reaching a landing site at the Moon at least once per day. Figure 14 shows the results of the December scan, however, there were 3 landing sites that LPL could not reach. Two were very low in altitude (-5 and -4 km in altitude), which looking at the altitude trends in Figure 15, indicates that these sites may not be feasible with the current mission design. It may be possible to achieve the low altitude landing sites by lowering the SRM burnout altitude constraint, but that requires detailed terrain modeling, planned for a future phase of the analysis. The third non-reachable landing site is most likely due to an optimization error, as its altitude was high enough, at -2 km, that it should not have been a problem for the lander to arrive there. More analysis is required to verify this observation.

Craig, Scott↗
NASA NTRS2017

Traverse Planning with Temporal-Spatial Constraints

We present an approach to planning rover traverses in a domain that includes temporal-spatial constraints. We are using the NASA Resource Prospector mission as a reference mission in our research. The objective of this mission is to explore permanently shadowed regions at a Lunar pole. Most of the time the rover is required to avoid being in shadow. This requirement depends on where the rover is located and when it is at that location. Such a temporal-spatial constraint makes traverse planning more challenging for both humans and machines. We present a mixed-initiative traverse planner which addresses this challenge. This traverse planner is part of the Exploration Ground Data Systems (xGDS), which we have enhanced with new visualization features, new analysis tools, and new automation for path planning, in order to be applicable to the Re-source Prospector mission. The key concept that is the basis of the analysis tools and that supports the automated path planning is reachability in this dynamic environment due to the temporal-spatial constraints.

temporal-spatial constraints↗