Six degrees of freedom equations of motion and trajectory equations of a rigid fin stabilized missile with variable mass
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Donegan, J. J.↗
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Optimal trajectories for the aeroassisted flight experiment
The optimal trajectories of the aeroassisted flight experiment (AFE) spacecraft are analyzed in a three-dimensional space using the full system of six ODEs describing the atmospheric pass. The optimal trajectories are computed for two possible transfers: indirect ascent to a 178 NM perigee via a 197 NM apogee and direct ascent to a 178 NM apogee. For each transfer, two cases are investigated: (1) the bank angle is continuously variable, and (2) the trajectory is divided into segments along which the bank angle is constant. It is shown that the optimal trajectories for both cases coalesce into a two subarc trajectory, with the bank angle constant in each subarc. It is also shown that, during the atmospheric pass, the peak values of the changes of the orbital inclination and the longitude of the ascending node are nearly zero.
Miele, A.↗
A discrete decentralized variable structure robotic controller
A decentralized trajectory controller for robotic manipulators is designed and tested using a multiprocessor architecture and a PUMA 560 robot arm. The controller is made up of a nominal model-based component and a correction component based on a variable structure suction control approach. The second control component is designed using bounds on the difference between the used and actual values of the model parameters. Since the continuous manipulator system is digitally controlled along a trajectory, a discretized equivalent model of the manipulator is used to derive the controller. The motivation for decentralized control is that the derived algorithms can be executed in parallel using a distributed, relatively inexpensive, architecture where each joint is assigned a microprocessor. Nonlinear interaction and coupling between joints is treated as a disturbance torque that is estimated and compensated for.
Tumeh, Zuheir S.↗
Optimal trajectories for the aeroassisted flight experiment. Part 4: Data, tables, and graphs
The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. Data, tables, and graphs relative to the following transfers are presented: (IA) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (DA) direct ascent to a 178 NM apogee. For both transfers, two cases are investigated: (1) the bank angle is continuously variable; and (2) the trajectory is divided into segments along which the bank angle is constant. For case (2), the following subcases are studied: two segments, three segments, four segments, and five segments; because the time duration of each segment is optimized, the above subcases involve four, six, eight, and ten parameters, respectively. Presented here are systematic data on a total of ten optimal trajectories (OT), five for Transfer IA and five for Transfer DA. For comparison purposes and only for Transfer IA, a five-segment reference trajectory RT is also considered.
Miele, A.↗
Going With the Flow: Using a Particle Dispersion Model to Reveal Links Between Ocean Ecosystems and Marine Aerosols
Marine biogenic particle contributions to atmospheric aerosol concentrations are not well understood though they are important for determining cloud optical and cloud nucleating properties. Here we examine the relationship between marine aerosol measurements with satellite and model fields of ocean biology and meteorological variables during the North Atlantic Aerosols and Marine Ecosystems Study (NAAMES). NAAMES consisted of four field campaigns between November 2015 and April 2018 that aligned with the four major phases of the annual phytoplankton bloom cycle. The FLEXPART Lagrangian particle dispersion model is used to connect these variables spatiotemporally to ship-based aerosol. We find that correlations between some aerosol measurements with satellite measured and modelled variables increase with increasing trajectory length. This indicates biological and meteorological processes over the air mass history are influential to measured particle properties. For example, results show organic aerosol mass is driven by biogenic volatile organic compound (VOC) emissions from photosynthesis by phytoplankton stocks during advection into the region. In contrast, primary marine aerosol (PMA) concentrations showed better correlations to variables weighted with shorter air mass residence times, which reflects their localized origin as primary emissions. Evidence also suggest variability in PMA concentrations likely play an important role in VOC emission removal. The removal of VOCs lessen their impact on particle number and mass concentrations. The sensitivity of marine aerosols to the main ecosystem-atmosphere drivers and its dependence on air mass history are to be further discussed.
Kevin J Sanchez↗
Noise Reduction Trajectory Analysis of a Supersonic Business Jet using Novel Optimization Tools
Proposals to reduce airport noise during takeoff and landing for supersonic aircraft using methods such as variable noise reduction systems add complexity to conceptual flight models. To better optimize these takeoff and landing profiles for noise certification, new modeling methods are explored in this paper with the end goal of more effectively determining the sensitivities of airframe, propulsion, and mission design variables on overall airport noise. Takeoff and landing trajectories are modeled for a notional supersonic business jet concept developed by NASA for use in environmental impact studies conducted by the International Civil Aviation Organization. Optimization tools capable of gradient-based optimal control and collocation solving methods are examined with the aim of achieving faster solutions in a more comprehensive design space. The benefits and limitations of these new methods are compared with existing methods used in previous studies of the airplane concept. It is found that the new modeling methods match closely when compared with existing tools for a standard takeoff and landing case, with a cumulative effective perceived noise difference of 0.1 EPNdB. Comparisons between takeoff trajectories with a variable noise reduction system match within 0.8 EPNdB and 1.3 EPNdB, due to highlighted differences in the modeling approaches.
supersonic↗
Spatial Coding of Eye Movements Relative to Perceived Orientations During Roll Tilt with Different Gravitoinertial Loads
This purpose of this study was to examine the spatial coding of eye movements during roll tilt relative to perceived orientations while free-floating during the microgravity phase of parabolic flight or during head tilt in normal gravity. Binocular videographic recordings obtained in darkness from six subjects allowed us to quantify the mean deviations in gaze trajectories along both horizontal and vertical coordinates relative to the aircraft and head orientations. Both variability and curvature of gaze trajectories increased during roll tilt compared to the upright position. The saccades were less accurate during parabolic flight compared to measurements obtained in normal gravity. The trajectories of saccades along perceived horizontal orientations tended to deviate in the same direction as the head tilt, while the deviations in gaze trajectories along the perceived vertical orientations deviated in the opposite direction relative to the head tilt. Although subjects were instructed to look off in the distance while performing the eye movements, fixation distance varied with vertical gaze direction independent of whether the saccades were made along perceived aircraft or head orientations. This coupling of horizontal vergence with vertical gaze is in a consistent direction with the vertical slant of the horopter. The increased errors in gaze trajectories along both perceived orientations during microgravity can be attributed to the otolith's role in spatial coding of eye movements.
Wood, Scott↗
Fuzzy logic based robotic controller
Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.
Attia, F.↗
Pursuit Latency for Chromatic Targets
The temporal dynamics of eye movement response to a change in direction of stimulus motion has been used to compare the processing speeds of different types of stimuli (Mulligan, ARVO '97). In this study, the pursuit response to colored targets was measured to test the hypothesis that the slow response of the chromatic system (as measured using traditional temporal sensitivity measures such as contrast sensitivity) results in increased eye movement latencies. Subjects viewed a small (0.4 deg) Gaussian spot which moved downward at a speed of 6.6 deg/sec. At a variable time during the trajectory, the dot's direction of motion changed by 30 degrees, either to the right or left. Subjects were instructed to pursue the spot. Eye movements were measured using a video ophthalmoscope with an angular resolution of approximately 1 arc min and a temporal sampling rate of 60 Hz. Stimuli were modulated in chrominance for a variety of hue directions, combined with a range of small luminance increments and decrements, to insure that some of the stimuli fell in the subjects' equiluminance planes. The smooth portions of the resulting eye movement traces were fit by convolving the stimulus velocity with an exponential having variable onset latency, time constant and amplitude. Smooth eye movements with few saccades were observed for all stimuli. Pursuit responses to stimuli having a significant luminance component are well-fit by exponentials having latencies and time constants on the order of 100 msec. Increases in pursuit response latency on the order of 100-200 msec are observed in response to certain stimuli, which occur in pairs of complementary hues, corresponding to the intersection of the stimulus section with the subjects' equiluminant plane. Smooth eye movements can be made in response to purely chromatic stimuli, but are slower than responses to stimuli with a luminance component.
Mulligan, Jeffrey B.↗
The Plasma Wave Environment of Europa
The Galileo spacecraft has executed nine close flybys of Jupiter's moon Europa for which plasma wave observations were obtained. This paper presents an analysis of the observations from these flybys taking into consideration the variable geometry of the trajectories in an attempt to characterize the general plasma-wave environment associated with the interaction of the Jovian magnetosphere with the moon. A wide variety of plasma-wave phenomena are found to be associated with this interaction. While there are apparently temporal variations which complicate the analysis, a crude model of the distribution of these phenomena around Europa is derived. Primarily on the upstream side of Europa, and working inward to the moon, electron-cyclotron harmonics are first observed, followed by a region within about two Europa radii of the moon with whistler-mode hiss or chorus, and culminating in a region closest to the moon where a band at the upper hybrid resonance frequency is sometimes enhanced over its ambient intensity. The wake region is approximately two Europa radii across and comprises a broadband, highly variable, and bursty electrostatic phenomenon. Upon closer inspection, these bursty emissions appear as solitary structures similar to those in Earth's auroral zone and plasma sheet boundary layer. In addition to the survey of wave phenomena in the vicinity of Europa, we provide density profiles derived primarily from the upper hybrid resonance frequency which is readily apparent throughout most of each of the flybys. Finally, we suggest that the whistler mode, electron cyclotron harmonic, and upper hybrid resonance emissions are driven by some combination of factors including variations in the magnetic field near Europa and the loss and production of plasma at Europa as a result of the interaction of the Jovian magnetosphere with the moon. By analogy with studies of the ion and electron holes and broadband electrostatic noise at Earth and Jupiter, we argue that the electrostatic solitary structures in the wake are associated with currents and beams coupling Europa to Jupiter's ionosphere.
Kurth, W. S.↗
A review of some existing literature concerning discontinuous state variables in the calculus of variations.
Discontinuous integrands in calculus of variations formulations of trajectory optimization and maximum payload problems with discontinuous state variables
TRAJECTORY OPTIMIZATION↗
Capture Conditions for Merging Trajectory Segments to Model Realistic Aircraft Descents
A typical commercial aircraft trajectory consists of a series of flight segments. An aircraft switches from one segment to another when certain specified variables reach their desired values. Trajectory synthesis for air traffic control automation must be consistent with practical pilot procedures. We examine capture conditions for merging trajectory segments to model commercial aircraft descent in trajectory synthesis. These conditions translate into bounds on measurements of atmospheric wind, pressure, and temperature. They also define ranges of thrust and drag feasible for a descent trajectory. Capture conditions are derived for the Center-TRACON Automation System developed at NASA Ames Research Center for automated air traffic control. Various uses of capture conditions are discussed. A Boeing 727-200 aircraft is used to provide numerical examples of capture conditions.
Zhao, Yiyuan↗
Spatial coding of eye movements relative to perceived earth and head orientations during static roll tilt
This purpose of this study was to examine the spatial coding of eye movements during static roll tilt (up to +/-45 degrees) relative to perceived earth and head orientations. Binocular videographic recordings obtained in darkness from eight subjects allowed us to quantify the mean deviations in gaze trajectories along both horizontal and vertical coordinates relative to the true earth and head orientations. We found that both variability and curvature of gaze trajectories increased with roll tilt. The trajectories of eye movements made along the perceived earth-horizontal (PEH) were more accurate than movements along the perceived head-horizontal (PHH). The trajectories of both PEH and PHH saccades tended to deviate in the same direction as the head tilt. The deviations in gaze trajectories along the perceived earth-vertical (PEV) and perceived head-vertical (PHV) were both similar to the PHH orientation, except that saccades along the PEV deviated in the opposite direction relative to the head tilt. The magnitude of deviations along the PEV, PHH, and PHV corresponded to perceptual overestimations of roll tilt obtained from verbal reports. Both PEV gaze trajectories and perceptual estimates of tilt orientation were different following clockwise rather than counterclockwise tilt rotation; however, the PEH gaze trajectories were less affected by the direction of tilt rotation. Our results suggest that errors in gaze trajectories along PEV and perceived head orientations increase during roll tilt in a similar way to perceptual errors of tilt orientation. Although PEH and PEV gaze trajectories became nonorthogonal during roll tilt, we conclude that the spatial coding of eye movements during roll tilt is overall more accurate for the perceived earth reference frame than for the perceived head reference frame.
NASA Discipline Neuroscience↗
Engineering approximations for Jovian entry
A code has been written to describe the behavior of an ablating heat shield throughout the entire maneuver into a planetary atmosphere. The code includes a trajectory computation for a variable mass, a computation of the heating history and distribution over the probe, ablation effects, indepth material response, and shape change. The code draws the initial and final shapes of the heat shield and computes its initial and final mass. Results are compared with those of other investigators, and solutions are obtained for a silica heat shield entering three model atmospheres of Jupiter. The effects of varying half cone angle and entry angle are examined as well as shape change effects. The so-called 'cusping effect' in the stagnation region is examined.
Lasher, L. E.↗
Conflict resolution maneuvers during near miss encounters with cockpit traffic displays
The benefits and liabilities associated with pilots' use of a cockpit traffic display to assess the threat posed by air traffic and to make small maneuvers to avoid situations which would result in collision avoidance advisories are experimentally studied. The crew's task was to fly a simulated wide-body aircraft along a straight course at constant altitude while intruder aircraft appeared on a variety of converging trajectories. The main experimental variables were the amount and quality of the information displayed on the intruder aircraft's estimated future position. Pilots were to maintain a horizontal separation of at least 1.5 nautical miles or a vertical separation of 500 ft, so that collision avoidance advisories would not be triggered. The results show that pilots could usually maneuver to provide the specified separation but often made course deviations greater than 1.5 nm or 500 ft.
Palmer, E.↗
An inverse dynamic method yielding flexible manipulator state trajectories
An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, torque is calculated in the time domain for a certain end point trajectory, as well as trajectories of all state variables. The open loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and its good experimental result is presented.
Kwon, Dong-Soo↗
An inverse dynamic method yielding flexible manipulator state trajectories
An inverse dynamic equation for a flexible manipulator is derived in a state form. By dividing the inverse system into the causal part and the anticausal part, one can calculate torque in the time domain for a certain end-point trajectory, as well as trajectories of all state variables. The open-loop control of the inverse dynamic method shows an excellent result in simulation. For practical applications, a control strategy adapting feedback tracking control to the inverse dynamic feedforward control is illustrated, and experimental results are presented.
Kwon, Dong-Soo↗
The ASAC Flight Segment and Network Cost Models
To assist NASA in identifying research art, with the greatest potential for improving the air transportation system, two models were developed as part of its Aviation System Analysis Capability (ASAC). The ASAC Flight Segment Cost Model (FSCM) is used to predict aircraft trajectories, resource consumption, and variable operating costs for one or more flight segments. The Network Cost Model can either summarize the costs for a network of flight segments processed by the FSCM or can be used to independently estimate the variable operating costs of flying a fleet of equipment given the number of departures and average flight stage lengths.
Kaplan, Bruce J.↗