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NASA NTRS1997

A Disturbance Rejection Approach to Actuator and Sensor Placement

For various reasons as discussed for instance in, the selection of actuator and sensor positions is still ad hoc. This is especially true for flexible structures where many candidate configurations can exist. This study is an attempt to make the selection process more methodical. One approach to actuator and sensor placement is to optimize a closed loop performance metric directly by selecting the actuators, sensors, and controller gains simultaneously. This direct approach makes sense if the desired closed loop performance is well defined. Since the individual actuator and sensor contributions to the closed loop performance metric is complex, the solution strategy usually employs non linear programming with many design and numerical iterations. A second approach is to select actuators and/or sensors based on open loop properties so that closed loop performance is indirectly optimized. Since the individual sensor and actuator contributions to the open loop metric is simple, nonlinear optimization is usually not needed. This approach will suggest efficient actuator and sensor configurations for any type of control law. The method suggested in this study falls into the latter class of approaches.

Lim, K. B.↗

NASA NTRS2003

Modeling and Evaluation of Miles-in-Trail Restrictions in the National Air Space

Miles-in-trail restrictions impact flights in the national air space on a daily basis and these restrictions routinely propagate between adjacent Air Route Traffic Control Centers. Since overly restrictive or ineffective miles-in-trail restrictions can reduce the overall efficiency of the national air space, decision support capabilities that model miles-in-trail restrictions should prove to be very beneficial. This paper presents both an analytical formulation and a linear programming approach for modeling the effects of miles-in-trail restrictions. A methodology for monitoring the conformance of an existing miles-in-trail restriction is also presented. These capabilities have been implemented in the Future ATM Concepts Evaluation Tool for testing purposes. To allow alternative restrictions to be evaluated in post-operations, a new mode of operation, which is referred to as the hybrid-playback mode, has been implemented in the simulation environment. To demonstrate the capabilities of these new algorithms, the miles-in-trail restrictions, which were in effect on June 27, 2002 in the New York Terminal Radar Approach Control, are examined. Results from the miles-in-trail conformance monitoring functionality are presented for the ELIOT, PARKE and WHITE departure fixes. In addition, the miles-in-trail algorithms are used to assess the impact of alternative restrictions at the PARKE departure fix.

Grabbe, Shon↗

NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

NASA NTRS2004

Subsonic Aircraft With Regression and Neural-Network Approximators Designed

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.

Patnaik, Surya N.↗

NASA NTRS2005

Decentralized Formation Flying Control in a Multiple-Team Hierarchy

This paper presents the prototype of a system that addresses these objectives-a decentralized guidance and control system that is distributed across spacecraft using a multiple-team framework. The objective is to divide large clusters into teams of manageable size, so that the communication and computational demands driven by N decentralized units are related to the number of satellites in a team rather than the entire cluster. The system is designed to provide a high-level of autonomy, to support clusters with large numbers of satellites, to enable the number of spacecraft in the cluster to change post-launch, and to provide for on-orbit software modification. The distributed guidance and control system will be implemented in an object-oriented style using MANTA (Messaging Architecture for Networking and Threaded Applications). In this architecture, tasks may be remotely added, removed or replaced post-launch to increase mission flexibility and robustness. This built-in adaptability will allow software modifications to be made on-orbit in a robust manner. The prototype system, which is implemented in MATLAB, emulates the object-oriented and message-passing features of the MANTA software. In this paper, the multiple-team organization of the cluster is described, and the modular software architecture is presented. The relative dynamics in eccentric reference orbits is reviewed, and families of periodic, relative trajectories are identified, expressed as sets of static geometric parameters. The guidance law design is presented, and an example reconfiguration scenario is used to illustrate the distributed process of assigning geometric goals to the cluster. Next, a decentralized maneuver planning approach is presented that utilizes linear-programming methods to enact reconfiguration and coarse formation keeping maneuvers. Finally, a method for performing online collision avoidance is discussed, and an example is provided to gauge its performance.

Mueller, Joseph .↗

NASA NTRS2006

Mission Operations Planning with Preferences: An Empirical Study

This paper presents an empirical study of some nonexhaustive approaches to optimizing preferences within the context of constraint-based, mixed-initiative planning for mission operations. This work is motivated by the experience of deploying and operating the MAPGEN (Mixed-initiative Activity Plan GENerator) system for the Mars Exploration Rover Mission. Responsiveness to the user is one of the important requirements for MAPGEN, hence, the additional computation time needed to optimize preferences must be kept within reasonabble bounds. This was the primary motivation for studying non-exhaustive optimization approaches. The specific goals of rhe empirical study are to assess the impact on solution quality of two greedy heuristics used in MAPGEN and to assess the improvement gained by applying a linear programming optimization technique to the final solution.

Bresina, John L.↗

NASA NTRS1992

Spacecraft attitude and velocity control system

A spacecraft attitude and/or velocity control system includes a controller which responds to at least attitude errors to produce command signals representing a force vector F and a torque vector T, each having three orthogonal components, which represent the forces and torques which are to be generated by the thrusters. The thrusters may include magnetic torquer or reaction wheels. Six difference equations are generated, three having the form ##EQU1## where a.sub.j is the maximum torque which the j.sup.th thruster can produce, b.sub.j is the maximum force which the j.sup.th thruster can produce, and .alpha..sub.j is a variable representing the throttling factor of the j.sup.th thruster, which may range from zero to unity. The six equations are summed to produce a single scalar equation relating variables .alpha..sub.j to a performance index Z: ##EQU2## Those values of .alpha. which maximize the value of Z are determined by a method for solving linear equations, such as a linear programming method. The Simplex method may be used. The values of .alpha..sub.j are applied to control the corresponding thrusters.

Paluszek, Michael A.↗

NASA NTRS2008

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Panossian, H.↗

NASA NTRS2009

Direct Multiple Shooting Optimization with Variable Problem Parameters

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.↗

NASA NTRS2000

Cylindrical Optic Figuring and Dwell Time Optimization

Grazing incidence x-ray telescopes consist of surfaces which are nearly cylindrical in shape. The abrasive figuring of these surfaces is accomplished by moving a grinding tool along a helical path on this almost cylindrical surface. The measurement of the surface is, however, performed along "axial" scan lines which intercept this helical path. This approach to figuring and measuring permits a relatively simple scheme to be implemented for the determination of the optimal dwell times of the figuring tool. These optimal dwell times are determined by a deconvolution which approaches the problem in a linear programming context and uses the Simplex Method. The approach maximizes the amount of material removed at any point subject to inequality constraints. The effect of using these ''optimum" dwell times is to significantly improve the tools effectiveness at removing the higher spatial frequencies while staying (strictly) within the bounds and constraints imposed by the hardware. In addition, the ringing at the edges of the optic, frequently present in deconvolution problems, is completely eliminated.

Waluschka, Eugene↗

NASA NTRS2009

Control Allocation with Load Balancing

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the actuator deflections. The paper discusses the alternative choice of the l(infinity) norm, or sup norm. Minimization of the control effort translates into the minimization of the maximum actuator deflection (min-max optimization). The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are also investigated through examples. In particular, the min-max criterion results in a type of load balancing, where the load is th desired command and the algorithm balances this load among various actuators. The solution using the l(infinity) norm also results in better robustness to failures and to lower sensitivity to nonlinearities in illustrative examples.

Bodson, Marc↗

NASA NTRS2009

Air Traffic Sector Configuration Change Frequency

Several techniques for partitioning airspace have been developed in the literature. The question of whether a region of airspace created by such methods can be used with other days of traffic, and the number of times a different partition is needed during the day is examined in this paper. Both these aspects are examined for the Fort Worth Center airspace sectors. A Mixed Integer Linear Programming method is used with actual air traffic data of ten high-volume low-weather-delay days for creating sectors. Nine solutions were obtained for each two-hour period of the day by partitioning the center airspace into two through 18 sectors in steps of two sectors. Actual track-data were played back with the generated partitions for creating histograms of the traffic-counts. The best partition for each two-hour period was then identified based on the nine traffic-count distributions. Numbers of sectors in such partitions were analyzed to determine the number of times a different configuration is needed during the day. One to three partitions were selected for the 24-hour period, and traffic data from ten days were played back to test if the traffic-counts stayed below the threshold values associated with these partitions. Results show that these partitions are robust and can be used for longer durations than they were designed for

Chatterji, Gano Broto↗

NASA NTRS2010

Applied Joint-Space Torque and Stiffness Control of Tendon-Driven Fingers

Existing tendon-driven fingers have applied force control through independent tension controllers on each tendon, i.e. in the tendon-space. The coupled kinematics of the tendons, however, cause such controllers to exhibit a transient coupling in their response. This problem can be resolved by alternatively framing the controllers in the joint-space of the manipulator. This work presents a joint-space torque control law that demonstrates both a decoupled and significantly faster response than an equivalent tendon-space formulation. The law also demonstrates greater speed and robustness than comparable PI controllers. In addition, a tension distribution algorithm is presented here to allocate forces from the joints to the tendons. It allocates the tensions so that they satisfy both an upper and lower bound, and it does so without requiring linear programming or open-ended iterations. The control law and tension distribution algorithm are implemented on the robotic hand of Robonaut-2.

Abdallah, Muhammad E.↗

NASA NTRS2010

Resource Balancing Control Allocation

Next generation aircraft with a large number of actuators will require advanced control allocation methods to compute the actuator commands needed to follow desired trajectories while respecting system constraints. Previously, algorithms were proposed to minimize the l1 or l2 norms of the tracking error and of the control effort. The paper discusses the alternative choice of using the l1 norm for minimization of the tracking error and a normalized l(infinity) norm, or sup norm, for minimization of the control effort. The algorithm computes the norm of the actuator deflections scaled by the actuator limits. Minimization of the control effort then translates into the minimization of the maximum actuator deflection as a percentage of its range of motion. The paper shows how the problem can be solved effectively by converting it into a linear program and solving it using a simplex algorithm. Properties of the algorithm are investigated through examples. In particular, the min-max criterion results in a type of resource balancing, where the resources are the control surfaces and the algorithm balances these resources to achieve the desired command. A study of the sensitivity of the algorithms to the data is presented, which shows that the normalized l(infinity) algorithm has the lowest sensitivity, although high sensitivities are observed whenever the limits of performance are reached.

Frost, Susan A.↗

NASA NTRS2009

A Method for Scheduling Air Traffic with Uncertain En Route Capacity Constraints

A method for scheduling ground delay and airborne holding for flights scheduled to fly through airspace with uncertain capacity constraints is presented. The method iteratively solves linear programs for departure rates and airborne holding as new probabilistic information about future airspace constraints becomes available. The objective function is the expected value of the weighted sum of ground and airborne delay. In order to limit operationally costly changes to departure rates, they are updated only when such an update would lead to a significant cost reduction. Simulation results show a 13% cost reduction over a rough approximation of current practices. Comparison between the proposed as needed replanning method and a similar method that uses fixed frequency replanning shows a typical cost reduction of 1% to 2%, and even up to a 20% cost reduction in some cases.

Arneson, Heather↗

NASA NTRS2010

Incorporating Active Runway Crossings in Airport Departure Scheduling

A mixed integer linear program is presented for deterministically scheduling departure and ar rival aircraft at airport runways. This method addresses different schemes of managing the departure queuing area by treating it as first-in-first-out queues or as a simple par king area where any available aircraft can take-off ir respective of its relative sequence with others. In addition, this method explicitly considers separation criteria between successive aircraft and also incorporates an optional prioritization scheme using time windows. Multiple objectives pertaining to throughput and system delay are used independently. Results indicate improvement over a basic first-come-first-serve rule in both system delay and throughput. Minimizing system delay results in small deviations from optimal throughput, whereas minimizing throughput results in large deviations in system delay. Enhancements for computational efficiency are also presented in the form of reformulating certain constraints and defining additional inequalities for better bounds.

Gupta, Gautam↗

NASA NTRS2010

Air Traffic Sector Configuration Change Frequency

A Mixed Integer Linear Programming method is used for creating sectors in Fort Worth, Cleveland, and Los Angeles centers based on several days of good-weather traffic data. The performance of these sectors is studied when they are subjected to traffic data from different days. Additionally, the advantage of using different sector designs at different times of day with varying traffic loads is examined. Specifically, traffic data from 10 days are used for design, and 47 other days are played back to test if the traffic-counts stay below the design values used in creating the partitions. The primary findings of this study are as follows. Sectors created with traffic from good-weather days can be used on other good-weather days. Sector configurations created with two hours of traffic can be used for 6 to 12 hours without exceeding the peak-count requirement. Compared to using a single configuration for the entire day, most of the sector-hour reduction is achieved by using two sector configurations -one during daytime hours and one during nighttime hours.

Chatterji, Gano B.↗

NASA NTRS2017

Optimization Routine for Generating Medical Kits for Spaceflight Using the Integrated Medical Model

The Integrated Medical Model (IMM) is a MATLAB model that provides probabilistic assessment of the medical risk associated with human spaceflight missions.Different simulations or profiles can be run in which input conditions regarding both mission characteristics and crew characteristics may vary. For each simulation, the IMM records the total medical events that occur and “treats” each event with resources drawn from import scripts. IMM outputs include Total Medical Events (TME), Crew Health Index (CHI), probability of Evacuation (pEVAC), and probability of Loss of Crew Life (pLOCL).The Crew Health Index is determined by the amount of quality time lost (QTL). Previously, an optimization code was implemented in order to efficiently generate medical kits. The kits were optimized to have the greatest benefit possible, given amass and/or volume constraint. A 6-crew, 14-day lunar mission was chosen for the simulation and run through the IMM for 100,000 trials. A built-in MATLAB solver, mixed-integer linear programming, was used for the optimization routine. Kits were generated in 10% increments ranging from 10%-100% of the benefit constraints. Conditions wheremass alone was minimized, volume alone was minimized, and where mass and volume were minimizedjointly were tested.

Medical Kit↗