Modeling relationships using graph state variables
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A model for helicopter guidance on spiral trajectories
A point mass model is developed for helicopter guidance on spiral trajectories. A fully coupled set of state equations is developed and perturbation equations suitable for 3-D and 4-D guidance are derived and shown to be amenable to conventional state variable feedback methods. Control variables are chosen to be the magnitude and orientation of the net rotor thrust. Using these variables reference controls for nonlevel accelerating trajectories are easily determined. The effects of constant wind are shown to require significant feedforward correction to some of the reference controls and to the time. Although not easily measured themselves, the controls variables chosen are shown to be easily related to the physical variables available in the cockpit.
Mendenhall, S.↗
Evidence of Abrupt Transitions Between Sea Ice Dynamical Regimes in the East Greenland Marginal Ice Zone
Sea ice modulates the energy exchange between the atmosphere and the ocean through its kinematics. Marginal ice zone (MIZ) dynamics are complex and are not well resolved in routine observations. Here, we investigate sea ice dynamics in the Greenland Sea MIZ using two Lagrangian drift datasets. We find evidence of tidal currents strongly affecting sub-daily sea ice motion. Velocity anomalies show abrupt transitions aligned with gradients in seafloor topography, indicating changes in ocean currents. Remote-sensed ice floe trajectories derived from moderate resolution satellite imagery provide a view of small-scale variability across the Greenland continental shelf. Ice floe trajectories reveal an west-east increasing velocity gradient imposed by the East Greenland Current, with maximum velocities aligned along the continental shelf edge. These results highlight the importance of small scale ocean variability for ice dynamics in the MIZ.
Daniel M. Watkins↗
Orbital flux integrations: Parameter values for effective computer time reductions
To improve computer utilization and to reduce the cost of orbital flux integrations, the effects of integration parameters 'duration' (T) and 'stepsize' (delta t) on integration results were investigated. Over given ranges of T and delta t, and within specified acceptable accuracy restraints, optimal values of these parameters were established for circular subsynchronous trajectories, in terms of the variables altitude (H) and inclination (i). It is shown that (1) above a certain statistically important value, duration is independent of both h and i; (2) stepsize has a relative altitude dependence; and (3) stepsize is not a function of inclination. The substantial savings in computer time are discussed along with the possibility of greater savings by relaxing accuracy restrictions while not exceeding the minimum model-associated uncertainty factors of the environments.
Stassinopoulos, E. G.↗
Experimental evaluation of a perspective tunnel display for three-dimensional helicopter approaches
A computer-generated perspective tunnel display for a steep and strongly curved three-dimensional helicopter approach is studied. The necessary control variables for following a curved trajectory are analyzed, the effectiveness of superimposed predictor symbology is investigated, and a suitable predictor law is formulated. The theoretical considerations are validated by an extensive fixed-base simulator program. The tunnel display with a superimposed predictor symbol is shown to outperform conventional-type displays in its abilities to follow a curved trajectory in the presence of gust disturbances, to enter the trajectory from an unknown position outside this trajectory, as well as to monitor automatic approaches. The feasibility of the tunnel display for operation in actual flight has been demonstrated in an exploratory flight test.
Grunwald, A. J.↗
Redundancy of space manipulator on free-flying vehicle and its nonholonomic path planning
The nonholonomic mechanical structure of space robots and path planning is discussed. The angular momentum conservation works as a nonholonomic constraint while the linear momentum conservation is a holonomic one. Thus, a vehicle with a 6 d.o.f. manipulator is described as a 9 variable system with 6 inputs. This implies the possibility of controlling the vehicle orientation and the joint variables of the manipulator by actuating the joint variables, but only if the trajectory is carefully planned; however, both of them cannot be controlled independently. It means that by assuming feasible-path planning, a system that consists of a vehicle and a 6 d.o.f. manipulator can be utilized as 9 d.o.f. system. Initially, the nonholonomic mechanical structure of space vehicle/manipulator system is shown. Then a path planning scheme for nonholonomic systems is proposed using Lyapunov functions.
Nakamura, Yoshihiko↗
Case studies in configuration control for redundant robots
A simple approach to configuration control of redundant robots is presented. The redundancy is utilized to control the robot configuration directly in task space, where the task will be performed. A number of task-related kinematic functions are defined and combined with the end-effector coordinates to form a set of configuration variables. An adaptive control scheme is then utilized to ensure that the configuration variables track the desired reference trajectories as closely as possible. Simulation results are presented to illustrate the control scheme. The scheme has also been implemented for direct online control of a PUMA industrial robot, and experimental results are presented. The simulation and experimental results validate the configuration control scheme for performing various realistic tasks.
Seraji, H.↗
Measuring Density Of Air By Ultraviolet Rayleigh Scattering
Report presents theoretical and experimental studies directed toward development of optoelectronic instrument to measure density of air at altitudes from 50 to 90 km and possibly beyond. Instrument mounted in Space Shuttle orbiter and operated during reentry into atmosphere. Data gathered by instrument needed because density of upper atmosphere highly variable in space and time and this variability affects aerodynamic behavior and trajectory of reentering Shuttle. Variations in density also meteorologically significant.
Mckenzie, Robert L.↗
Selection of Slow and Fast Variables in the Three-Dimensional Flight Dynamics
A transformation from the altitude and velocity state variables of three-dimensional flight mechanics to a new set of more desirable variables is found. The new variables provide a greater time-scale separation, decrease system coupling, and give better estimates of the fast-variable values along the reduced solution. One of the new variables is the often-used specific energy, whereas the other variable changes along a given trajectory, depending on the nature of the local reduced solution. Numerical examples are included.
Ardema, M.↗
Environmental Characteristics of Convective Systems During TRMM-LBA
In this paper, data collected from 51 days of continual upper atmospheric soundings and TOGA radar at ABRACOS Hill during the TRMM-LBA experiment are used to describe the mean thermodynamic and kinematic airmass properties of wet season convection over Rondonia, Brazil. Distinct multi-day easterly and westerly lower tropospheric wind regimes occurred during the campaign with contrasting airmass characteristics. Westerly wind periods featured modest CAPE (1000 J/kg), moist conditions (>90% RH) extending through 700 mb and shallow (900 mb) speed shear on the order of 10(exp -4)/s. This combination of characteristics promoted convective systems that featured a relatively large fraction of stratiform rainfall and weak convection nearly devoid of lightning. The environment is very similar to the general airmass conditions experienced during the Darwin, Australia monsoon convective regime. In contrast, easterly regime convective systems were more strongly electrified and featured larger convective rain rates and reduced stratiform rainfall fraction. These systems formed in an environment with significantly larger CAPE (1500 J/kg), drier lower and middle level humidities (< 80% RH) and a wind shear layer that was both stronger (10(exp -3)/s) and deeper (700 mb). The larger CAPE resulted from strong insolation under relatively cloud-free skies (owing to reduced column humidity) and was also weakly capped in the lowest 1-2 km, thus contributing to a more explosive growth of convection. The time series of low- and mid-level averaged humidity exhibited marked variability between westerly and easterly regimes and was characterized by low frequency (i.e., multi-day to weekly) oscillations. The synoptic scale origins of these moisture fluctuations are examined, which include the effects of variable low-level airmass trajectories and upper-level, westward migrating cyclonic vortices. The results reported herein provide an environmental context for ongoing dual Doppler analyses and numerical modeling case studies of individual TRMM-LBA convective systems.
Halverson, Jeffrey B.↗
Theory of prediction of solar eclipse as observed from a sounding rocket using rocket trajectory and eclipse ephemeris
The present paper deals with the problem of determining various solar eclipse variables as observed from a sounding rocket for various rocket trajectories. By applying the methods described to a set of trajectories, a set of boundary conditions, launch azimuth, quadrant elevation, and launch time may be selected to optimize any aspect of eclipse observation within the constraints imposed by rocket performance.
Mcgarvey, J. F.↗
Thermal protection optimization for the space shuttle.
This paper discusses optimal entry trajectories for the space shuttle that minimize the weight of an entry thermal protection system. The analysis was made using mathematical models of two types of thermal protection systems that were under consideration for the space shuttle: a metallic thermal protection system, and a reusable surface insulation thermal protection system. Optimal entries were generated using maximum orbiter nose temperature as a parameter. Thermal protection system weights were computed for both fixed and variable angles of attack using three-dimensional entry trajectories. Results indicated that variable angle-of-attack entries require less thermal protection system weight than entries at a constant angle of attack (35 deg) for both systems considered. Results also showed that 95 to 99 per cent of the thermal protection system weight requirement resulted from flight regimes in which the flow was still laminar.
Garcia, F., Jr.↗
Error analysis of multi-conic techniques
A general error analysis of three recently developed multi-conic methods of three-body trajectory integration has been carried out. Single-step error functions for position and velocity have been derived as Taylor series in powers of the time step and also in integral form. These error functions are used to investigate the relative accuracy of the three methods in various regions of the earth-moon space and to provide a method of variable step size control for the trajectory integration procedure. Numerical results are used to compare the multi-step performance of the methods for both large and small step sizes.
D'Amario, L. A.↗
Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning
Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often may thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The method is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.
Low Thrust↗
Multi-Objective Hybrid Optimal Control for Interplanetary Mission Planning
Preliminary design of low-thrust interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. Because low-thrust trajectory design is tightly coupled with systems design, power and propulsion characteristics must be chosen as well. In addition, a time-history of control variables must be chosen which defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. The customer who commissions a trajectory design is not usually interested in a point solution, but rather the exploration of the trade space of trajectories between several different objective functions. This can be very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a multi-objective hybrid optimal control problem. The methods is demonstrated on hypothetical mission to the main asteroid belt and to Deimos.
Trajectory Design↗
Heuristic search in robot configuration space using variable metric
A method to generate obstacle free trajectories for both mobile robots and linked robots is proposed. The approach generates the shortest paths in a configuration space. The metric in the configuration space can be adjusted to obtain a tradeoff between safety and velocity by imposing extra costs on paths near obstacles.
Verwer, Ben J. H.↗
An Algorithm for Trajectory Generation in Redundant Manipulators with Joint Transmission Accommodation
Trajectory generation for manipulators involves generating incremental updates of joint variables to achieve a desired end–effector motion. The Jacobian matrix maps incremental joint motion to incremental end–effector motion in a linear fashion and is typically used in manipulator trajectory generation algorithms. In the case of a redundant manipulator, the Jacobian matrix is not square or invertible and therefore algorithms based on pseudoinverses and their variations are commonly used for trajectory generation. These methods either are computationally not efficient or do not utilize all the joints in motion generation and therefore do not completely exploit the redundancy of the manipulator. The method presented in this paper is a simple method that maximizes transmission of all joint variables onto a desired end–effector motion trajectory. The method is based on aligning the null–space of an augmented Jacobian matrix with the path of the desired end–effector motion, from which a linear combination of joints that projects fully onto the desired end–effector trajectory is obtained. In this manner, all joints of the redundant manipulator are used to generate the end–effector trajectory accommodating the ability of each joint in terms of its motion transmission.
Ravani, Bahram↗
Rapid Preliminary Design of Interplanetary Trajectories Using the Evolutionary Mission Trajectory Generator
Preliminary design of interplanetary missions is a highly complex process. The mission designer must choose discrete parameters such as the number of flybys, the bodies at which those flybys are performed, and in some cases the final destination. In addition, a time-history of control variables must be chosen that defines the trajectory. There are often many thousands, if not millions, of possible trajectories to be evaluated. This can be a very expensive process in terms of the number of human analyst hours required. An automated approach is therefore very desirable. This work presents such an approach by posing the mission design problem as a hybrid optimal control problem. The method is demonstrated on notional high-thrust chemical and low-thrust electric propulsion missions. In the low-thrust case, the hybrid optimal control problem is augmented to include systems design optimization.
Design↗