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NASA NTRSDate not supplied

Minimum-Variance Control Allocation Considering Parametric Model Uncertainty

The control allocation problem was investigated for linear dynamical systems with known parametric uncertainty. Minimizing a cost function that penalizes the variance of the error in achieving commanded forces and moments on the vehicle resulted in a special case of the weighted pseudo-inverse allocator. Rather than an engineer designing the weighting matrix, it is computed from the covariances of the control effectiveness parameters. This minimum-variance allocator balances the effectiveness of the control inputs against the corresponding levels of uncertainty. The approach was demonstrated using simulations of aircraft with realistic uncertainty levels operating in open-loop and closed-loop configurations. Results showed that when model uncertainty is known, significant, and unevenly distributed amongst the controls, the minimum-variance allocator more often achieves the intended forces and moments on the vehicle in comparison to other allocators, which can lead to increased performance, reliability, and safety during flight tests. The cost for this robustness is a diminished achievable moment space for the vehicle.

Control allocation↗
NASA NTRS1993

Linearization of manipulator dynamics using spatial operators

Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.

Jain, A.↗
NASA NTRS2023

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗
NASA NTRS1991

Operator-assisted planning and execution of proximity operations subject to operational constraints

Future multi-vehicle operations will involve multiple scenarios that will require a planning tool for the rapid, interactive creation of fuel-efficient trajectories. The planning process must deal with higher-order, non-linear processes involving dynamics that are often counter-intuitive. The optimization of resulting trajectories can be difficult to envision. An interaction proximity operations planning system is being developed to provide the operator with easily interpreted visual feedback of trajectories and constraints. This system is hosted on an IRIS 4D graphics platform and utilizes the Clohessy-Wiltshire equations. An inverse dynamics algorithm is used to remove non-linearities while the trajectory maneuvers are decoupled and separated in a geometric spreadsheet. The operator has direct control of the position and time of trajectory waypoints to achieve the desired end conditions. Graphics provide the operator with visualization of satisfying operational constraints such as structural clearance, plume impingement, approach velocity limits, and arrival or departure corridors. Primer vector theory is combined with graphical presentation to improve operator understanding of suggested automated system solutions and to allow the operator to review, edit, or provide corrective action to the trajectory plan.

Grunwald, Arthur J.↗
NASA NTRS2006

Statistical Analyses of Satellite Cloud Object Data From CERES: Boundary-layer Cloud Objects During 1998 El Nino - Part 4

Three boundary-layer cloud object types, stratus, stratocumulus and cumulus, that occurred over the Pacific Ocean during January-August 1998, are identified from the CERES (Clouds and the Earth s Radiant Energy System) single scanner footprint (SSF) data from the TRMM (Tropical Rainfall Measuring Mission) satellite. This study emphasizes the differences and similarities in the characteristics of each cloud-object type between the tropical and subtropical regions and among different size categories and among small geographic areas. Both the frequencies of occurrence and statistical distributions of cloud physical properties are analyzed. In terms of frequencies of occurrence, stratocumulus clouds dominate the entire boundary layer cloud population in all regions and among all size categories. Stratus clouds are more prevalent in the subtropics and near the coastal regions, while cumulus clouds are relatively prevalent over open ocean and the equatorial regions, particularly, within the small size categories. The largest size category of stratus cloud objects occurs more frequently in the subtropics than in the tropics and has much larger average size than its cumulus and stratocumulus counterparts. Each of the three cloud object types exhibits small differences in statistical distributions of cloud optical depth, liquid water path, TOA albedo and perhaps cloud-top height, but large differences in those of cloud-top temperature and OLR between the tropics and subtropics. Differences in the sea surface temperature (SST) distributions between the tropics and subtropics influence some of the cloud macrophysical properties, but cloud microphysical properties and albedo for each cloud object type are likely determined by (local) boundary-layer dynamics and structures. Systematic variations of cloud optical depth, TOA albedo, cloud-top height, OLR and SST with cloud object sizes are pronounced for the stratocumulus and stratus types, which are related to systematic variations of the strength of inversion with cloud object sizes, produced by large-scale subsidence. The differences in cloud macrophysical properties over small regions are significantly larger than those of cloud microphysical properties and TOA albedo, suggesting a greater control of (local) large-scale dynamics and other factors on cloud object properties. When the three cloud object types are combined, the relative population among the three types is the most important factor for determining the cloud object properties in a Pacific transect where the transition of boundary-layer cloud types takes place.

Xu, Kuan-Man↗
NASA NTRS1984

Kinematic control of robot with degenerate wrist

Kinematic resolved rate equations allow an operator with visual feedback to dynamically control a robot hand. When the robot wrist is degenerate, the computed joint angle rates exceed operational limits, and unwanted hand movements can result. The generalized matrix inverse solution can also produce unwanted responses. A method is introduced to control the robot hand in the region of the degenerate robot wrist. The method uses a coordinated movement of the first and third joints of the robot wrist to locate the second wrist joint axis for movement of the robot hand in the commanded direction. The method does not entail infinite joint angle rates.

Barker, L. K.↗
NASA NTRS1997

Dynamic Forms: Application to Aircraft Guidance - Part 2

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of waypoints through which the aircraft trajectory must pass. The waypoints typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory that satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multidimensional, multiaxis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions are required to be smooth. The proposed guidance algorithm is based on the inversion of the pure feedback approximation, followed by correction for the effects of zero dynamics. The paper describes the structure and major modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
NASA NTRS1996

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordination, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
NASA NTRS1997

Guidance of Nonlinear Systems

The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.

Meyer, George↗
NASA NTRS1993

Precision slew/settle technologies for flexible spacecraft

Many spacecraft missions in the next decade will require both a high degree of agility and precision pointing. Agility includes both rotational maneuvering for retargeting and translational motion for orbit adjustment and threat avoidance. The major challenge associated with such missions is the need for control over a wide range of amplitudes and frequencies, ranging from tens of degrees at less than 1 Hz to a few micron radians at hundreds of Hz. TRW's internally funded Precision Control of Agile Spacecraft (PCAS) project is concerned with developing and validating in hardware the tools necessary to successfully complete the combined agile maneuvering/precision pointing missions. Development has been undertaken on a number of fronts for quietly slewing flexible structures. Various methods for designing slew torque profiles have been investigated. Prime candidates for slew/settle scenarios include Inverse Dynamics and Parameterized Function Space. Joint work with Processor Bayo at the University of California, Santa Barbara and Professor Flashner at the University of Southern California has led to promising torque profile design methods. Active and passive vibration suppression techniques also play a key role for rapid slew/settle mission scenarios. Active members with local control loops and passive members with high loss factor viscoelastic material have been selected for hardware verification. Progress in each of these areas produces large gains in the quiet slewing of flexible spacecraft. The main thrust of the effort to date has been the development of a modular testbed for hardware validation of the precision control concepts. The testbed is a slewing eighteen foot long flexible truss. Active and passive members can be interchanged with the baseline aluminum members to augment the inherent damping in the system. For precision control the active members utilize control laws running on a high speed digital structural control processor. Tip and midspan motions of the truss are determined using optical sensors while accelerometers can be used to monitor the motions of other points of interest. Preliminary results indicate that a mix of technologies produces the greatest benefit. For example, shaping the torque profile produces large improvements in slew/settle performance, but without added damping settling times may still be excessive. With the introduction of moderate amounts of damping, slew/settle performance is vastly improved. On the other hand, introducing damping without shaping the torque profile may not yield the desired level of performance.

Manning, R. A.↗
NASA NTRS1994

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.↗
NASA NTRS1989

Computational dynamics for robotics systems using a non-strict computational approach

A Non-Strict computational approach for real-time robotics control computations is proposed. In contrast to the traditional approach to scheduling such computations, based strictly on task dependence relations, the proposed approach relaxes precedence constraints and scheduling is guided instead by the relative sensitivity of the outputs with respect to the various paths in the task graph. An example of the computation of the Inverse Dynamics of a simple inverted pendulum is used to demonstrate the reduction in effective computational latency through use of the Non-Strict approach. A speedup of 5 has been obtained when the processes of the task graph are scheduled to reduce the latency along the crucial path of the computation. While error is introduced by the relaxation of precedence constraints, the Non-Strict approach has a smaller error than the conventional Strict approach for a wide range of input conditions.

Orin, David E.↗
NASA NTRS1977

Study of synthesis techniques for insensitive aircraft control systems

Insensitive flight control system design criteria was defined in terms of maximizing performance (handling qualities, RMS gust response, transient response, stability margins) over a defined parameter range. Wing load alleviation for the C-5A was chosen as a design problem. The C-5A model was a 79-state, two-control structure with uncertainties assumed to exist in dynamic pressure, structural damping and frequency, and the stability derivative, M sub w. Five new techniques (mismatch estimation, uncertainty weighting, finite dimensional inverse, maximum difficulty, dual Lyapunov) were developed. Six existing techniques (additive noise, minimax, multiplant, sensitivity vector augmentation, state dependent noise, residualization) and the mismatch estimation and uncertainty weighting techniques were synthesized and evaluated on the design example. Evaluation and comparison of these six techniques indicated that the minimax and the uncertainty weighting techniques were superior to the other six, and of these two, uncertainty weighting has lower computational requirements. Techniques based on the three remaining new concepts appear promising and are recommended for further research.

Harvey, C. A.↗
NASA NTRS1981

Observations of the interaction of ozone and dynamics

Data on the global distribution of temperature and ozone obtained with the Limb Radiance Inversion Radiometer which flew on the Nimbus 6 spacecraft are analyzed within the conceptual framework of Hartmann and Garcia (1979). The analysis supports the conclusion that ozone perturbations are dynamically controlled when the photochemical time constant is much greater than the dynamical time constant; when the photochemical constant is much less than the dynamical constant, ozone perturbations are photochemically controlled. It is also shown that the transports of planetary waves, or eddy transports, appear to be strongly localized in the region between the regimes in which dynamical and photochemical controls operate.

Gille, J. C.↗
NASA NTRS1988

Adaptive guidance for an aero-assisted boost vehicle

An adaptive guidance system incorporating dynamic pressure constraint is studied for a single stage to low earth orbit (LEO) aero-assist booster with thrust gimbal angle as the control variable. To derive an adaptive guidance law, cubic spline functions are used to represent the ascent profile. The booster flight to LEO is divided into initial and terminal phases. In the initial phase, the ascent profile is continuously updated to maximize the performance of the boost vehicle enroute. A linear feedback control is used in the terminal phase to guide the aero-assisted booster onto the desired LEO. The computer simulation of the vehicle dynamics considers a rotating spherical earth, inverse square (Newtonian) gravity field and an exponential model for the earth's atmospheric density. This adaptive guidance algorithm is capable of handling large deviations in both atmospheric conditions and modeling uncertainties, while ensuring maximum booster performance.

Pamadi, Bandu N.↗
NASA NTRS1990

Adaptive impedance control of redundant manipulators

A scheme for controlling the mechanical impedance of the end-effector of a kinematically redundant manipulator is presented. The proposed control system consists of two subsystems: an adaptive impedance controller which generates the Cartesian-space control input F (is a member of Rm) required to provide the desired end-effector impedance characteristics, and an algorithm that maps this control input to the joint torque T (is a member of Rn). The F to T map is constructed so that the robot redundancy is utilized to improve either the kinematic or dynamic performance of the robot. The impedance controller does not require knowledge of the complex robot dynamic model or parameter values for the robot, the payload, or the environment, and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme is very general and is computationally efficient for on-line implementation.

Colbaugh, R.↗
NASA NTRS2020

Investigation Of Prandtl-Ishlinskii Hysteresis Compensation for Deep Space Optical Communications Pointing Control

This paper studies the simulated performance of the Deep Space Optical Communication (DSOC) laser downlink pointing control system that has a pointing requirement at the sub-microradian scale. To achieve the required pointing precision, the DSOC Flight Laser Transceiver (FLT) point-ahead mirror (PAM) employs piezoelectric actuators, which are widely used in precision applications due to their high motion resolution, rapid response, and high output forces. However, a piezoelectric actuator's performance is often limited by nonlinearities in their response, most significantly hysteresis. To study the effect of hysteresis on our simulated pointing performance, an invertible hysteresis model is developed using the Classical Prantdl-Ishlinskii (CPI) method. The simulation includes models of DSOC hardware and electronic system components based on key parameters (bias, frequency response, noise), with the hysteresis modeled in the PAM piezo actuator dynamics. A Proportional-Integral controller provides feedback with measurements from two potential sources: strain gauge sensors or a photon-counting camera. To compensate for hysteresis behavior, a feedforward inverse CPI hysteresis model is implemented in the control system. Two CPI models are built using different sampling methods (uniform sampling and cosine spacing) and controller performance is compared. For the maximum command range of ±400 μrad at 1 mHz, results show that the feedforward combined with feedback control reduces output tracking error by 50% or 58% (to 0.20 or 0.38 μrad) compared to feedback control alone (from 0.40 or 0.90 μrad), corresponding to the uniform-sampled and cosine-sampled CPI models, respectively.

Marinello, Lindsey A.↗
NASA NTRS2000

X-38 Vehicle 131R Free Flights 1 and 2

The X-38 program is using a modern flight control system (FCS) architecture originally developed by Honeywell called MACH. During last year's SAE G&C subcommittee meeting, we outlined the design, implementation and testing of MACH in X-38 Vehicles 132, 131R & 201. During this year's SAE meeting, I'll focus upon the first two free flights of V131R, describing what caused the roll-over in FF1 and how we fixed it for FF2. I only have 30 minutes, so it will be a quick summary including VHS video. X-38 is a NASA JSC/DFRC experimental flight test program developing a series of prototypes for an International Space Station (ISS) Crew Return Vehicle (CRV), often described as an ISS "lifeboat." X-38 Vehicle 132 Free Flight 3 was the first flight test of a modern FCS architecture called Multi-Application ControlH (MACH), developed by the Honeywell Technology Center in Minneapolis and Honeywell's Houston Engineering Center. MACH wraps classical Proportional+integral (P+I) outer attitude loops around modern dynamic inversion attitude rate loops. The presentation at last year's SAE Aerospace Meeting No. 85 focused upon the design and testing of the FCS algorithm and Vehicle 132 Free Flight 3. This presentation will summarize flight control and aerodynamics lessons learned during Free Flights 1 and 2 of Vehicle 131R, a subsonic test vehicle laying the groundwork for the orbital/entry test of Vehicle 201 in 2003.

Munday, Steve↗