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NASA NTRS1984

Feedback laws for fuel minimization for transport aircraft

The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

Price, D. B.↗

NASA NTRS1989

Input preshaping with frequency domain information for flexible-link manipulator control

The application of an input preshaping scheme to flexible manipulators is considered. The resulting control corresponds to a feedforward term that convolves in real-time the desired reference input with a sequence of impulses and produces a vibration free output. The robustness of the algorithm with respect to injected disturbances and modal frequency variations is not satisfactory and can be improved by convolving the input with a longer sequence of impulses. The incorporation of the preshaping scheme to a closed-loop plant, using acceleration feedback, offers satisfactory disturbance rejection due to feedback and cancellation of the flexible mode effects due to the preshaping. A frequency domain identification scheme is used to estimate the modal frequencies on-line and subsequently update the spacing between the impulses. The combined adaptive input preshaping scheme provides the fastest possible slew that results in a vibration free output.

Tzes, Anthony↗

NASA NTRS1965

Computing and data transmission for the prediction steering of the Goonhilly satellite-communication aerial

The Goonhilly satellite-communication aerial uses an 85-ft. diameter paraboloidal reflector with waveguide feed at the focus. The aerial is movable in azimuth and elevation, and is provided with independent feedback control systems for these two motions. During a satellite pass, the aerial must be steered so that its axis points continuously, and with high accuracy, in the direction of the satellite. Of the various possible methods of achieving this result, that based on prediction of satellite position has been adopted for the first transatlantic communication experiments using the Telstar and Relay satellites. The process by which orbital predictions originating in the USA are converted to substantially continuous real-time azimuth and elevation pointing instructions at Goonhilly is described herein.

GROUND STATION↗

NASA NTRS1986

Design of multivariable controllers for robot manipulators

The paper presents a simple method for the design of linear multivariable controllers for multi-link robot manipulators. The control scheme consists of multivariable feedforward and feedback controllers. The feedforward controller is the minimal inverse of the linearized model of robot dynamics and contains only proportional-double-derivative (PD2) terms. This controller ensures that the manipulator joint angles track any reference trajectories. The feedback controller is of proportional-integral-derivative (PID) type and achieves pole placement. This controller reduces any initial tracking error to zero as desired and also ensures that robust steady-state tracking of step-plus-exponential trajectories is achieved by the joint angles. The two controllers are independent of each other and are designed separately based on the linearized robot model and then integrated in the overall control scheme. The proposed scheme is simple and can be implemented for real-time control of robot manipulators.

Seraji, H.↗

NASA NTRS1989

Performance evaluation of a six-axis generalized force-reflecting teleoperator

Work in real-time distributed computation and control has culminated in a prototype force-reflecting telemanipulation system having a dissimilar master (cable-driven, force-reflecting hand controller) and a slave (PUMA 560 robot with custom controller), an extremely high sampling rate (1000 Hz), and a low loop computation delay (5 msec). In a series of experiments with this system and five trained test operators covering over 100 hours of teleoperation, performance was measured in a series of generic and application-driven tasks with and without force feedback, and with control shared between teleoperation and local sensor referenced control. Measurements defining task performance included 100-Hz recording of six-axis force/torque information from the slave manipulator wrist, task completion time, and visual observation of predefined task errors. The task consisted of high precision peg-in-hole insertion, electrical connectors, velcro attach-de-attach, and a twist-lock multi-pin connector. Each task was repeated three times under several operating conditions: normal bilateral telemanipulation, forward position control without force feedback, and shared control. In shared control, orientation was locally servo controlled to comply with applied torques, while translation was under operator control. All performance measures improved as capability was added along a spectrum of capabilities ranging from pure position control through force-reflecting teleoperation and shared control. Performance was optimal for the bare-handed operator.

Hannaford, B.↗

NASA NTRS1989

A real-time guidance algorithm for aerospace plane optimal ascent to low earth orbit

Problems of onboard trajectory optimization and synthesis of suitable guidance laws for ascent to low Earth orbit of an air-breathing, single-stage-to-orbit vehicle are addressed. A multimode propulsion system is assumed which incorporates turbojet, ramjet, Scramjet, and rocket engines. An algorithm for generating fuel-optimal climb profiles is presented. This algorithm results from the application of the minimum principle to a low-order dynamic model that includes angle-of-attack effects and the normal component of thrust. Maximum dynamic pressure and maximum aerodynamic heating rate constraints are considered. Switching conditions are derived which, under appropriate assumptions, govern optimal transition from one propulsion mode to another. A nonlinear transformation technique is employed to derived a feedback controller for tracking the computed trajectory. Numerical results illustrate the nature of the resulting fuel-optimal climb paths.

Calise, A. J.↗

NASA NTRS1982

Experimental evaluation of the concept of supevisory manipulation

A computer-controlled teleoperator system which is based on task-referenced sensor-aided control has been developed to study supervisory manipulation. This system, called SUPERMAN, is capable of performing complicated tasks in real-time by utilizing the operator for high-level functions related to the unpredictable portions of a task, while the subordinate machine performs the more well-defined subtasks under human supervison. To determine whether supervisory control schemes such as these offer any advantage over manual control under real-time conditions, a number of experiments involving both simple and complicated tasks were performed. Six representative tasks were chosen for the study: (1) obtaining a tool from a rack, (2) returning the tool to the rack, (3) removing a nut, (4) placing samples in a storage bin, (5) opening and closing a valve, and (6) digging with a shovel. The experiments were performed under simulated conditions using four forms of manual control (i.e., switch rate, joystick rate, master-slave position control, and master-slave with force feedback), as well as supervisory control. Through these experiments the effectiveness and quality of control were evaluated on the basis of the time required to complete each portion of the task and the type and number of errors which occurred.

Brooks, T. L.↗

NASA NTRS1988

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. This approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for one-dimensional, single-input/single-output, parabolic (heat/diffusion) and hereditary systems using spline-based, Ritz-Galerkin, finite element approximation. Numerical studies indicate convergence of the feedback gains with less than 2 percent performance degradation over full-order LQG controllers for the parabolic system and 10 percent degradation for the hereditary system.

Bernstein, Dennis S.↗

NASA NTRS1990

A laboratory breadboard system for dual-arm teleoperation

The computing architecture of a novel dual-arm teleoperation system is described. The novelty of this system is that: (1) the master arm is not a replica of the slave arm; it is unspecific to any manipulator and can be used for the control of various robot arms with software modifications; and (2) the force feedback to the general purpose master arm is derived from force-torque sensor data originating from the slave hand. The computing architecture of this breadboard system is a fully synchronized pipeline with unique methods for data handling, communication and mathematical transformations. The computing system is modular, thus inherently extendable. The local control loops at both sites operate at 100 Hz rate, and the end-to-end bilateral (force-reflecting) control loop operates at 200 Hz rate, each loop without interpolation. This provides high-fidelity control. This end-to-end system elevates teleoperation to a new level of capabilities via the use of sensors, microprocessors, novel electronics, and real-time graphics displays. A description is given of a graphic simulation system connected to the dual-arm teleoperation breadboard system. High-fidelity graphic simulation of a telerobot (called Phantom Robot) is used for preview and predictive displays for planning and for real-time control under several seconds communication time delay conditions. High fidelity graphic simulation is obtained by using appropriate calibration techniques.

Bejczy, A. K.↗

NASA NTRS1975

An optical/digital processor - Hardware and applications

A real-time two-dimensional hybrid processor consisting of a coherent optical system, an optical/digital interface, and a PDP-11/15 control minicomputer is described. The input electrical-to-optical transducer is an electron-beam addressed potassium dideuterium phosphate (KD2PO4) light valve. The requirements and hardware for the output optical-to-digital interface, which is constructed from modular computer building blocks, are presented. Initial experimental results demonstrating the operation of this hybrid processor in phased-array radar data processing, synthetic-aperture image correlation, and text correlation are included. The applications chosen emphasize the role of the interface in the analysis of data from an optical processor and possible extensions to the digital feedback control of an optical processor.

Casasent, D.↗

NASA NTRS1986

Controlling Flexible Manipulators, an Experimental Investigation

Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.

Hastings, Gordon Greene↗

NASA NTRS1987

Open control/display system for a telerobotics work station

A working Advanced Space Cockpit was developed that integrated advanced control and display devices into a state-of-the-art multimicroprocessor hardware configuration, using window graphics and running under an object-oriented, multitasking real-time operating system environment. This Open Control/Display System supports the idea that the operator should be able to interactively monitor, select, control, and display information about many payloads aboard the Space Station using sets of I/O devices with a single, software-reconfigurable workstation. This is done while maintaining system consistency, yet the system is completely open to accept new additions and advances in hardware and software. The Advanced Space Cockpit, linked to Grumman's Hybrid Computing Facility and Large Amplitude Space Simulator (LASS), was used to test the Open Control/Display System via full-scale simulation of the following tasks: telerobotic truss assembly, RCS and thermal bus servicing, CMG changeout, RMS constrained motion and space constructible radiator assembly, HPA coordinated control, and OMV docking and tumbling satellite retrieval. The proposed man-machine interface standard discussed has evolved through many iterations of the tasks, and is based on feedback from NASA and Air Force personnel who performed those tasks in the LASS.

Keslowitz, Saul↗

NASA NTRS1984

Closed-form recursive formula for an optimal tracker with terminal constraints

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. Two examples are given to illustrate the validity and usefulness of the formulations.

Juang, J.-N.↗

NASA NTRS1985

Energy management of three-dimensional minimum-time intercept

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot (bank angle and load factor) consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. Some numerical results comparing open-loop optimal and approximate feedback solutions are presented.

Kelley, H. J.↗

NASA NTRS1986

Real-time open-loop frequency response analysis of flight test data

A technique has been developed to compare the open-loop frequency response of a flight test aircraft real time with linear analysis predictions. The result is direct feedback to the flight control systems engineer on the validity of predictions and adds confidence for proceeding with envelope expansion. Further, gain and phase margins can be tracked for trends in a manner similar to the techniques used by structural dynamics engineers in tracking structural modal damping.

Bosworth, J. T.↗

NASA NTRS1986

Closed-form recursive formula for an optimal tracker with terminal constraints

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

Juang, J. N.↗

NASA NTRS1989

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗

NASA NTRS1990

A discrete-time adaptive control scheme for robot manipulators

A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. The scheme utilizes feedback, feedforward, and auxiliary signals, obtained from joint angle measurement through simple expressions. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation. Simulations and experimental results are given to demonstrate the performance of the scheme.

Tarokh, M.↗