Showing papers in "Journal of Guidance Control and Dynamics in 2000"

Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying

Abstract: Thispaperconsiderstheproblemofrelativepositioncontrolformultiplespacecraftformatione ying.Specie cally, the full nonlinear dynamics describing the relative positioning of multiple spacecraft formation e ying are used to develop a Lyapunov-based, nonlinear, adaptive control law that guarantees global asymptotic convergence of the position tracking error in the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. Simulation results are included to illustrate the controller performance. that compensated for unknown, constant disturbances while pro- ducing globally asymptotically decaying position tracking errors. This controller, however, required exact knowledge of the space- craft parameters. In this paper we consider the full nonlinear dynamics describ- ing the relative positioning of MSFF for control design purposes. Using Lyapunov-based control design and stability analysis tech- niques, we develop a nonlinear adaptive control law that guarantees global asymptotic convergence of the spacecraft relative position to any sufe ciently smooth desired trajectory, despite the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. In the case when the parameters are ex- actlyknown,theproposedcontrolstrategyyieldsglobalexponential convergence of the tracking errors. In comparison to the work of Refs. 11 and 12, the proposed controller ensures stronger stability resultsandaccountsforawiderclassofparametricuncertainties.As inRefs.11-13, we will consider in this paper the idealized scenario where the spacecraft actuators are capable of providing continuous- time control efforts, as opposed to being of pulse type. 9 We note that the problem of pulse-type, nonlinear control design for MSFF constitutes an open research problem and is beyond the scope of this paper. The paper is organized as follows. Section II presents the non- linear dynamic model derivation. The control objective is stated in Sec. III. The control design and closed-loop stability analysis are presented in Sec. IV. Simulation results are provided in Sec. V, whereas some concluding remarks are given in Sec. VI.

Time-Explicit Representation of Relative Motion Between Elliptical Orbits

Abstract: Theclassictreatmentofrendezvousmechanicsandotherproblemsinvolvingtherelativemotionoftwospacecraft assumesa circularreferenceorbit, allowing a simpleclosed-form description ofthemotion. Asolution isdeveloped using an elliptical reference orbit, expanding the state transition matrix in powers of eccentricity, while retaining the explicit time dependence of the three-dimensional motion. The solution includes separate matrix elements for e rst-and second-order terms in eccentricity and for both Cartesian and cylindrical coordinates. Assessment of the maximum errors in position and velocity components over one complete revolution of the reference satellite shows that the solution is accurate for practical purposes with eccentricities in the range 0 ‐0.3. An example application is given for the proposed laser interferometer space antenna gravity wave experiment.

Singular Direction Avoidance Steering for Control-Moment Gyros

Abstract: A new form of the equations of motion for a spacecraft with Single Gimbal Control Moment Gyros is developed using a momentum approach. This set of four vector equations describing the rotational motion of the system is of order 2N + 7 where N is the number of CMGs. The control input is an N x I column vector of torques applied to the gimbal axes. A modification to the singularity robust Lyapunov control law presented by Oh and Vadali is examined and compared to their control law. Specifically, the attempt to avoid singular gimbal configurations is abandoned in favor of simply avoiding movement in the singular direction. The singular value decomposition is used to compute a pseudoinverse which prevents large gimbal rate commands near or at actual singularities.

Identification and Control of Limit Cycle Oscillations in Aeroelastic Systems

Abstract: Nonlinearities in the aeroelastic system induce pathologies such as the observed store-induced limit cycle oscillations found with certain high-performance aircraft configurations. Many prior studies, including efforts by these authors, focus on the nonlinear behavior of the uncontrolled, nonlinear aeroelastic system. These studies are briefly reviewed. More importantly, there is limited study for the active control of these nonlinear aeroelastic systems. Although a linear controller may stabilize the nonlinear system under some circumstances, empirical evidence suggests that these control methods -will prove unreliable in strongly nonlinear regimes and that stability is not guaranteed. Herein, the authors describe the development of control strategies appropriate for these nonlinear systems. A nonlinear controller, and the resulting closed-loop stability, based on a partial feedback linearization are discussed. The approach depends upon the exact cancellation of the nonlinearity and, as a co_nsequence, the authors introduce an adaptive method in which guarantees of stability are evident. The authors present experimental results obtained using the adaptive controller.

Evaluation of the Dynamic Environment of an Asteroid: Applications to 433 Eros

Abstract: Methods of analysis to quickly and systematically evaluate the dynamical environment close to an asteroid are presented, concentrating on the effect of the asteroid’s gravity Ž eld and rotation state on a spacecraft orbit. Such an analysis is useful and needed for missions to small solar system bodies such as asteroids and comets, where the true mass, gravity Ž eld, and rotation state will not be known until after the spacecraft rendezvous with the body and these quantities are estimated. Generally, after these quantities have been estimated, the complete mission proŽ le must be redesigned in accordance with the actual values found at the asteroid. An integral part of this redesign is the characterization of dynamics close to the asteroid, speciŽ cally the computation of orbit stability close to the body and the practical limits on how close the spacecraft can  y to the body before large perturbations are experienced. Numerical computationsof such an evaluationapplied to the asteroid 433 Eros, the target of the Near Earth Asteroid Rendezvous (NEAR) mission, using preliminary models of the asteroid obtained during NEAR’s December 1998  yby of Eros are presented.

Direct Method for Rapid Prototyping of Near-Optimal Aircraft Trajectories

Abstract: Adirectmethod fora real-timegenerationofnear-optimal spatialtrajectoriesofshort-term maneuversonboard a e ying vehiclewith predetermined thrust history isintroduced. Thepaperstarts with a survey about the founders of the direct methods of calculus of variations and their followers in e ight mechanics, both in Russia and in the United States. It then describes a new direct method based on three cues: high-order polynomials from the virtual arc as a reference function for aircraft’ s coordinates, a preset history of one of the controls (thrust), and a few optimization parameters. The trajectory optimization problem is transformed into a nonlinear programming problem and then solved numerically using an appropriate algorithm in accelerated scale of time. A series of examples is presented. Calculated near-optimal trajectory is compared with real e ight data, and with the solution obtainedbyPontryagin’ smaximumprinciple.Fastconvergenceofthenumericalalgorithm,whichhasbeenalready implemented and tested onboard a real aircraft, is illustrated. Nomenclature aik = polynomial coefe cients g = acceleration due to gravity J = cost function j = quantity pertaining to the jth time node m = aircraft mass N = number of nodes n = polynomial order ¯ n = relative revolutions of engine’ s rotor nx, nz = tangential and normal projections of load factor, respectively Sh = penalty function T, ¯ T = total thrust and relative thrust (fraction of maximum thrust), respectively t = time t ¤

Singularity Avoidance Using Null Motion and Variable-Speed Control Moment Gyros

Abstract: A variable speed control moment gyroscope (VSCMG) null motion steering law is introduced that continuously attempts to minimize the condition number of the control in uence matrix By doing so, the gimbal angles are rearranged to less singular conŽ gurations without exerting a torque onto the spacecraft By allowing the reaction wheel speeds to be variable in this steering law, more general reconŽ gurations are possible than what are possible with conventionalCMG No a priori calculations of preferred sets of gimbal angles are necessary with this method Numerical studies show that superimposing this VSCMG null motion on the VSCMG steering law can result in a drastic reduction in the required reaction wheel power consumption when operating near CMG singular gimbal conŽ gurationsThe reaction wheel torque required by this VSCMG steering law is typically very small and achievable with existing CMG hardware

Linear Time-Varying Approach to Satellite Attitude Control Using Only Electromagnetic Actuation

Abstract: Recently, small satellite missions have gained considerable interest due to low-cost launch opportunities and technological improvement ofmicroelectronics. Required pointing accuracy of small, inexpensive satellites isoften relatively loose, within a couple of degrees. Application of cheap, lightweight, and power efe cient actuators is therefore crucial and viable. Linear attitude control strategies for a low-Earth-orbit satellite actuated by a set of mutually perpendicular electromagnetic coils are discussed. The principle is to use the interaction between the Earth’ s magnetic e eld and the magnetic e eld generated by the coils. A key challenge is that the mechanical torque can only be produced in a plane perpendicular to the local geomagnetic e eld vector; therefore, the satellite is not controllable when considered at e xed time. Availability of design methods for time-varying systems is limited; nevertheless, a solution of theperiodicRiccati equation gives an excellent framework fordevelopment and analysis of magnetic attitude control algorithms. An observation that thegeomagnetic e eld changesapproximately periodically when a satellite is on a near-polar orbit is used. Three types of attitude controllers are proposed: an ine nite horizon, a e nite horizon, and a constant gain controller. Their performance is evaluated and compared in the simulation study of the realistic environment.

Probability of Collision Between Space Objects

Abstract: The International Space Station is being designed to perform debris avoidance maneuvers based on certain criteria developed from the probability of collision Pc. Existing methods to determine the Pc are based on the dee nitionofacollision/conjunctionplanethatcontainsallofthepositionuncertaintyassociatedwiththeproblem.In thispaperwedevelopa directand more naturalway of obtaining probability ofcollision and presentanalternative but equivalent dee nition for Pc that leads to the same results obtained earlier. Because debris avoidance is crucial for every orbiting asset in low Earth orbit, a study of this nature helps to establish the equivalence of different methods for risk assessment and evaluation. HE International Space Station (ISS) shall continuously face the threat of collision with orbiting debris. Hence, there needs to be a comprehensive methodology that can assess the risks posed byindividualdebrisencountersand suggestmaneuverswhenneces- sary. Such a study shall not only benee t the ISS, but also any future orbital asset placed in low Earth orbits. Thus, although we refer to the ISS in the rest of our paper, the analysis presented here holds true for any other orbiting asset of size and orbit comparable with that of the upcoming ISS. Space shuttle (SS) maneuvers are commanded to avoid poten- tial collisions with cataloged space objects (maintained by the U.S. Space Command ) whenever the estimated conjunction with an ob- jectfalls within a box centered on the estimated SSposition. The di- mensionsofthisconjunctionboxare §5 kmin thein-track direction and §2kmintheradialandout-of-planedirections.Thedimensions of such a conjunction box are probably based on prior estimates of position error covariances. The determination was made that this simple criterion, or any other known deterministic criterion 1,2 when applied to the ISS, would result in too many maneuvers. 3 In addi- tion, unnecessary maneuvers waste fuel and hamper the micrograv- ity experiments onboard the ISS. Although the size of the conjunc- tion box could be decreased to decrease the manuever rate, such a step clearly increases the risk to unacceptable levels. Therefore, the ISS needs a more rigorous probability-based approach for collision avoidance. 4

Aircraft Pitch Control via Second-Order Sliding Technique

Abstract: Control of high-performa nce low-cost unmanned air vehicles involves the problems of incomplete measurements, external disturbances and modeling uncertainties Sliding mode control combines high precision with robustness to the aforementioned factors The idea behind this approach is the choice of a particular constraint which, when maintained, will provide the process with the required features and remove, therefore, the plant's uncertainty However, standard sliding modes are characterized by a high-frequency switching of control, which causes problems in practical applications (so-called chattering effect) A second order sliding controller implemented in the present paper features bounded continuously time-dependent control and provides higher accuracy than the standard sliding mode, while preserving precise constraint fulfillment within a finite time It possesses, also, significant adaptive properties The general approach is demonstrated by solving a real-life pitch control problem Results of a computer simulation and flight tests are presented I Introduction Aircraft and missile systems are equipped with control systems whose tasks are to provide stability, disturbance attenuation and reference signal tracking, while their aerodynamic coefficients vary over a wide dynamic range due to large Mach-altitude fluctuations and due to aerodynamic coefficient uncertainties resulting from inaccurate wind tunnel measurements It is common practice, when designing a control system for an unmanned air vehicle (UAV), to represent the flight envelope by a grid of Mach-altitude operating

Reusable Launch Vehicle Control in Multiple Time Scale Sliding Modes

Abstract: A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Attitude-Determination Filtering via Extended Quaternion Estimation

Abstract: The quaternion estimation (QUEST) batch attitude-determination algorithm has been extended to work in a general Kalman-e lter framework. This has been done to allow the inclusion of a complicated dynamics model and to allow the estimation of additional quantities beyond the attitude quaternion. The QUEST algorithm, which workswith vectorattitude observations, servesasa starting pointbecause itisable to work with a poor (orno)e rst guess of the attitude. This paper’ s extended version of QUEST uses square-root information e ltering techniques and linearization of the dynamics to propagate the state and its covariance. The measurement update problem is solved by a technique that is an extension of the original QUEST algorithm’ s eigenvalue/eigenvector solution. The paperdemonstrates the new algorithm’ sperformance on an attitude determination problem that usesstar-tracker and rate-gyro measurements. The new algorithm is able to converge from initial attitude errors of 180 deg and initial rate-gyro bias errors as large as 2400 deg/h.

Second Estimator of the Optimal Quaternion

Abstract: ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 Žgures; a page of text may be substituted for a Žgure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contributions (see inside back cover).

Transonic Flutter Suppression Control Law Design and Wind-Tunnel Test Results

Abstract: Fluttersuppressioncontrollawdesignandwind-tunneltestresultsintransonice owforaNACA0012wingmodel, under the benchmark active control technology program at NASA Langley Research Center, will be presented. Two control law design processes using classical and minimax techniques are described. Design considerations for improving the multivariable system robustness are outlined. The classical control law was digitally implemented and tested in the NASA Langley Transonic Dynamics Tunnel. In wind-tunnel tests in air and heavy gas medium, the closed-loop e utter dynamic pressure was increased by over 50% up to the wind-tunnel upper limit. The active e utter suppression system also provided signie cant robustness, relative to gain and phase perturbations, even in the presence of transonic shocks and e ow separation.

Linear Theory of a Dual-Spin Projectile in Atmospheric Flight

Abstract: : The equations of motion for a dual-spin projectile in atmospheric flight are developed and subsequently utilized to solve for angle of attack and swerving dynamics. A combination hydrodynamic and roller bearing couples forward and aft body roll motions. Using a modified projectile linear theory developed for this configuration, it is shown that the dynamic stability factor, S(g), and the gyroscopic stability factor, S(g) are altered compared to a similar rigid projectile, due to new epicyclic fast and slow arm equations. Swerving dynamics including aerodynamic jump are studied using the linear theory.

Sliding Mode Control with Optimal Sliding Surfaces for Missile Autopilot Design

Abstract: A new method is introduced to design sliding mode control with optimally selected sliding surfaces for a class of nonlinear systems The nonlinear systems are recursively approximated as linear time-varying systems, and corresponding time-varyingsliding surfaces are designedfor each approximatedsystem so thatagivenoptimization criterion isminimizedThe control input,which is designedbyusing an approximatedsystem, is then applied to the nonlinear system The method is used to design an autopilot for a missile where the design requirement is to follow a given acceleration command The sliding surface is selected such that a performance index formed as a function of angle of attack, pitch rate, and velocity error is minimized It is shown that the response of the approximating sequence of linear time-varying systems converges to the response of the missile

Comparing Linear Parameter-Varying Gain-Scheduled Control Techniques for Active Flutter Suppression

Abstract: Two linear parameter-varying gain-scheduled controllers for active e utter suppression of the NASA Langley Research Center’ s Benchmark Active Control Technology (BACT) wing section are presented and compared to a previously presented gain-scheduled controller. The BACT wing section changes signie cantly as a function of Mach and dynamic pressure. The two linear parameter-varying (LPV) gain-scheduled controllers incorporate these changes as well as bounds on the rate of change of Mach and dynamic pressure. The inclusion of rate bounds in the design process allows for improved performance over a larger range of operating conditions than previously achieved by a linear fractional transformation gain-scheduled controller. The LPV controllers differ in that one primarily reduces coupling between the trailing-edge e ap and the pitch and plunge modes, whereas the second optimizes wind gust attenuation. Closed-loop stability and improved performance are demonstrated via time simulations in which both Mach and dynamic pressure are allowed to vary in the presence of a Dryden wind-gust disturbance.

Tensegrity Flight Simulator

Abstract: Inthispaperweproposeanewmotionsimulatorbasedonatendon-controlledtensegritystructure.Thesimulator isequipped with anonlinearcontrollerthatachievesrobusttrackingofdesired motions.Thecontrollerparameters can be tuned to guarantee tracking to within a prespecie ed tolerance and with a prescribed rate of exponential convergence. The design is verie ed through numerical simulations forspecie clongitudinal motions of a symmetric aircraft.

Drag-Based Predictive Tracking Guidance for Mars Precision Landing

Abstract: Future Mars missions require precision landing capability. An entry guidance law is developed for a lander with flying capabilities consistent with those expected for the lander in the 2001 mission. The lander flight path is controlled by bank angle adjustments. The guidance law belongs to the class of drag-based predictive tracking guidance laws which includes the entry guidance law for the Space Shuttle Orbiter. Modifications relative to the Shuttle entry guidance law are introduced to accommodate the very low lift capability and the combination of a low bandwidth attitude control system and a fixed trim angle of attack. Monte Carlo results show that even with a maximum lift-to-drag ratio of only 0.12 a specified parachute deployment latitude/longitude point can be achieved with 99% certainty to within 13.2 km under the assumed worst case dispersions. The dynamic pressure and Mach number constraints for parachute deployment are also satisfied with 99% certainty.

Active control of wind-tunnel model aeroelastic response using neural networks

Abstract: Under a joint research and development effort conducted by NASA and The Boeing Company (formerly McDonnell Douglas), three neural-network-based control systems were developed and tested. The control systems were experimentally evaluated using a transonic wind-tunnel model in the NASA Langley Research Center Transonic Dynamics Tunnel. One system used a neural network to schedule flutter suppression control laws, another employed a neural network in a predictive control scheme, and the third employed a neural network in an inverse model control scheme. All three of these control schemes successfully suppressed flutter to or near the limits of the testing apparatus and represent the first experimental applications of neural networks to flutter suppression. The findings of this project are summarized.

Passivity-Based Robust Control with Application to Benchmark Active Controls Technology Wing

Abstract: A passivity-based robust control design methodology is presented. A brief review of the stability results is given for passive linear and nonlinear systems followed by four different passie cation methods for rendering nonpassive systems passive. The robust control methodology via robust passie cation is demonstrated by application to the Benchmark Active Controls Technology subsonic wing. The controller design is shown to provide robust stability and satisfactory performance.

Optimal Variable-Structure Control Tracking of Spacecraft Maneuvers

Abstract: An optimal control approach using variable-structure (sliding-mode) tracking for large angle spacecraft maneuvers is presented. The approach expands upon a previously derived regulation result using a quaternion parameterization for the kinematic equations of motion. This parameterization is used since it is free of singularities. The main contribution of this paper is the utilization of a simple term in the control law that produces a maneuver to the reference attitude trajectory in the shortest distance. Also, a multiplicative error quaternion between the desired and actual attitude is used to derive the control law. Sliding-mode switching surfaces are derived using an optimal-control analysis. Control laws are given using either external torque commands or reaction wheel commands. Global asymptotic stability is shown for both cases using a Lyapunov analysis. Simulation results are shown which use the new control strategy to stabilize the motion of the Microwave Anisotropy Probe spacecraft.

Precision Spacecraft Pointing Using Single-Gimbal Control Moment Gyroscopes with Disturbance

Abstract: Whereas previous work has shown that gain stabilization methods in the attitude control of spacecraft can mitigate external disturbances of a e xed frequency, recent work in cases where the frequency of the disturbance is time variant is summarized here.Specie cally, theapplication ofgain stabilization in the form of a variableperiodic disturbancerejection e lter is shown to bea viablemethod ofmitigating these disturbances. To usethis e lter forthe time-variant case, the character of the source of the disturbance needs to be known a priori with some accuracy. An implementation for a spacecraft steered by single-gimbal control moment gyroscopes where the disturbance is related to the gimbal rate is demonstrated. In addition, performance of the subject e lter is demonstrated in the presence of estimation error and phase shift.

Design of Reliable Control Systems Possessing Actuator Redundancies

Abstract: Theexplicitdee nitionsof actuatorredundancies areintroduced. Adesign schemeis then presented to synthesize reliable control against actuator failures for dynamic systems possessing actuator redundancies. The properly designed controller is able to guarantee the stability and to maintain the steady-state tracking performance in the event of actuator failures. The design method is based on a robust regional eigenvalue assignment technique with the help of a precompensator. The effectiveness of the proposed method has been verie ed using an example of the aircraft bank angle control problem.

Safety Constrained Free-Flyer Path Planning at the International Space Station

Abstract: A path-planning tool is presented to generate safe trajectories from an initial docking release, to a specified observation point, and back to docking for a small free-flying robot camera around the International Space Station. The tool makes use of ellipse of safety trajectories to enforce long-term passive safe requirements in the presence of differential air drag during the fly around phases of the maneuver during transfer between the docking port and observation point. Short-term passive safety (2-3 orbits) is also maintained during all station-keeping and approach maneuvers by checking the safety of the observation point at the initial planning stage, and through the use of precalculated velocities profiles along the r-bar forced motion approaches to the observation point and docking. The observation phase of the mission is enhanced through the use of artificial Laplace potential functions within a constrained volume, to allow for limited maneuvering close to the observation point enabling the available view to be translated and rotated.

Computationally efficient control allocation

Abstract: A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

Space-Based Space Surveillance with the Space-Based Visible

Abstract: Space surveillance is the activity of keeping a current catalog of information on manufactured, Earth-bound resident space objects. Some necessary functions to perform this task are search and detection, acquisition and tracking, tasking and scheduling, and data reduction and processing. The Midcourse Space Experiment satellite, launched 24April 1996, carries the Space-Based Visible sensor packagedesigned for conducting space surveillance froma spaceplatform.Other contributionsto this issue discuss Space-BasedVisible operations,data reduction, and accuracy. The Space-Based Visible provides high-accuracy angle measurements (right ascension and declination). Based on these data, space-based space surveillance catalog maintenance can be demonstrated. To this end, orbits are calculated based on ground-based data, space-based data, and various combinations of these data. From these results a number of surveillance functions can be demonstrated, for example, compatibility and fusion of space-based and ground-based metric (position) data. When an independent, high-accuracy orbit is available, an assessment of the orbit accuracy is made. In other cases, differences between the orbits are computed. In addition, access to the complete geosynchronous belt and catalog maintenance for geosynchronous satellites will be demonstrated. Effectiveness of space-based space surveillance data is assessed.