Spacecraft Maneuvers Research Articles

Modeling and Control of a Flexible Spacecraft for Large-Angle Rapid Maneuvers

This paper deals with large-angle rapid slew maneuvers of a flexible spacecraft, which consists of a rigid central body and a flexible beam attached to it. Dynamic model for the spacecraft described by a coupled nonlinear hybrid system is derived. With the control torque applied to the rigid central body only, a PD control law is presented using the measurements of the attitude angle of the rigid body and its velocity. Based upon the Lyapunov method in infinite dimensional space, it is shown that implementation of the control algorithm results in the slew maneuvering with the simultaneous vibration suppression.

Determination of the optimal mode of operation of the small thrust motors of a maneuvering spacecraft

We consider the problem of constructing an optimal cyclogram for the small-thrust rocket motors that govern the descent of a spacecraft to earth or other orbital maneuvers. The problem is solved by the perturbation method, the perturbation in this case being the ratio of the thrust of the motor to the weight of the spacecraft.

The Algorithm of the Two-Impulse Time-Fixed Noncoplanar Rendezvous with Drag and Oblateness Effects

The algorithm that generates the exact solution of the two-impulse noncoplanar rendezvous in general elliptic orbit is presented. The motion of the maneuvering spacecraft is referred to a rotating reference frame attached to the passive spacecraft and dragging and precessing at the same rate as that spacecraft. An iterative scheme is devised to find the magnitude and orientation of the initiating impulse that brings the active spacecraft to a desired target point in the vicinity of the passive spacecraft in a given time. When the rendezvous point is the vicinity of the passive spacecraft and not at the passive vehicle location itself, the linear distance between the two vehicles will exhibit variations along their post-rendezvous common orbit which can be of the order of kilometers for highly eccentric orbits. These natural oscillations can be minimized by targeting the active vehicle to the immediate proximity of the passive spacecraft and be totally eliminated by targeting to the passive vehicle location itself.

ASTER preflight and inflight calibration and the validation of Level 2 products

Describes the preflight and inflight calibration approaches used for the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER). The system is a multispectral, high-spatial resolution sensor on the Earth Observing System's EOS-AM1 platform. Preflight calibration of ASTER uses well-characterized sources to provide calibration and preflight round-robin exercises to understand biases between the calibration sources of ASTER and other EOS sensors. These round-robins rely on well-characterized, ultra-stable radiometers. An experiment field in Yokohama, Japan, showed that the output from the source used for the visible and near-infrared (VNIR) subsystem of ASTER may be underestimated by 1.5%, but this is still within the 4% specification for the absolute, radiometric calibration of these bands. Inflight calibration will rely on vicarious techniques and onboard blackbodies and lamps. Vicarious techniques include ground-reference methods using desert and water sites. A recent joint field campaign gives confidence that these methods currently provide absolute calibration to better than 5%, and indications are that uncertainties less than the required 4% should be achievable at launch. The EOS-AM1 platform will also provide a spacecraft maneuver that will allow ASTER to see the Moon, allowing further characterization of the sensor. A method for combining the results of these independent calibration results is presented. The paper also describes the plans for validating the Level 2 data products from ASTER. These plans rely heavily upon field campaigns using methods similar to those used for the ground-reference, vicarious calibration methods.

Nonlinear Adaptive Control of Spacecraft Maneuvers

A novel method is presented to carry out near-minimum-time maneuvers of a spacecraft of unknown inertia. The formulation assumes the presence of three orthogonal reaction wheels located near the system mass center and oriented arbitrarily with respect to the spacecraft principal axes. Modie ed Rodrigues parameters along with their shadow set are used as the primary attitude coordinates. Open-loop maneuver laws are designed while solving the equations of motion by inversedynamics approach. This approach permits theapproximateimposition of the maximum saturation torque constraint. The torque proe les are near-bang-bang, with the instantaneous switches replaced by cubicsplinesof specie edduration.An adaptivetrackingcontrollawisdeveloped to determine perturbations to the nominal open-loop torque commands that will ensure the actual motion to follow the nominal motion in the presence of uncertainty in the inertia matrix and errors in the initial attitude. Global stability of the overall closed-loop controller is proved analytically and demonstrated by numerical simulations.

GPS for low-cost attitude determination: A review of concepts, in-flight experiences, and current developments

The Global Positioning System or GPS has been developed for the purpose of enabling accurate positioning and navigation anywhere on or near the surface of the Earth. In addition to the US system GPS-NAVSTAR, the Russian GLONASS system is also in place and operational. Other such systems are under study. The key measurement involved is the time of travel of signals from a particular GPS spacecraft to the navigating receiver. Navigation accuracies of the order of tenths of meters are achievable, and accuracies at the centimeter level can also be obtained with special enhancement techniques. In recent years spacecraft have already been exploring the use of GPS for in-orbit navigation. As the receiver is solid state, rugged, power-lean, and cheap, GPS for autonomous navigation will be an objective even for low-cost spacecraft of only modest sophistication. When the GPS receiver is equipped with multiple antennas with baselines even as low as about one meter, it can also give attitude information. In this case, the position of the spacecraft needs to be known with only very moderate accuracy. However, the phase differences between signals received by the different antennas now constitute the key measurements. In this case a centimeter level accuracy of range difference can be obtained. Receivers carrying out the processing of such measurements are already on the market, even in space-qualified versions. For spacecraft maneuvering at low rates, accuracies of the order of tenths of a degree are achievable. There are reasons for maintaining classical attitude sensor suites on a spacecraft even when a GPS receiver is added. In this case the classical sensors may be allowed to be of modest quality only, as subsequent fusion of their data with those from the GPS receiver may restore the accuracy of the final estimate again to an acceptable level. Hence, low-cost attitude sensors combined with a low-cost GPS receiver can still satisfy non-trivial attitude reconstitution accuracy requirements. As carrier phase difference measurements are ambiguous because of the unknown number of GPS signal cycles received, the estimated attitude is in principle ambiguous as well. Therefore, resolution of the GPS signal cycle ambiguity becomes a necessary task before determining the attitude for a stand-alone GPS attitude sensing system. This problem may be solved by introducing additional low-cost reference attitude sensors like three-axis magnetometers. This is also one of the advantages of integrated sensor systems. The paper is organized as follows. Global Positioning System and GPS observables are described in the first two sections. The main attitude determination concepts are presented in the next section. For small spacecraft, GPS integrated with other low-cost attitude sensors results in a data fusion concept, to be discussed next. The last section highlights experiences and on-going projects related to the spacecraft attitude determination using GPS.

Fuel/Time Optimal Control of Spacecraft Maneuvers

We address the problem of designing fuel/time-optimal controllers for spacecraft undergoing rest-to-rest maneuvers. A modification of the Switch Tune Optimization (STO) algorithm is used to determine the switch times and maneuver tone of the bang-off-bang control profile. The proposed algorithm is tested on an inertially symmetric spacecraft. As the weight on the fuel, alpha, is increased from zero, the number of switches in the control profiles vary from 5 to 10 to 9. After a specific value of alpha, it the eigenaxis control with two switches is the optimum. (Author)

Instrumentation analysis using parameter estimation of simulated data

References 1 Bayo, E., A Finite-Element Approach to Control the End-Point Motion of Single-Link Flexible Robot, Journal of Robotic Vol. 4, No. 1, 1987, pp. 63-75. Devasia, S., and Paden, B., Exact Tracking for Nonlinear TimeVarying Systems, Proceedings of the 33rd IEEE Conference on Decision and Control (Lake Buena Vista, FL), IEEE Control Systems Society, New York, 1994, pp. 2346-2355. Paden, B., Chen, D., Ledesma, R., and Bayo, E., Exponentially Stable Tracking Control for Multi-Joint Flexible Manipulators, Journal of Dynamic Measurement and Control, Vol. 115, March 1993, pp. 53-59. Martin, P., Devasia, S., and Paden, B., A Different Look at Tracking: Control of a VTOL Aircraft, Proceedings of the 33rd IEEE Conference on Decision and Control (Lake Buena Vista, FL), IEEE Control Systems Society, New York, 1994, pp. 2376-2381. Tomlin, C., Lygeros, J., and Shastri, S., Output Tracking for a Nonminimum Phase Dynamic CTOL Aircraft Model, Proceedings of the 34th IEEE Conference on Decision and Control (New Orleans, LA), IEEE Control Systems Society, New York, 1995, pp. 1867-1872. Singer, N. C., and Seering, W. P., Command Inputs to Reduce System Vibration, Journal of Dynamic Measurement and Control, Vol. 112, March 1990, pp. 76-82. Smith, O. J. M., Feedback Control McGraw-Hill, New York, 1958. Singer, N. C., and Seering, W. P., Using Acausal Shaping Techniques to Reduce Robot Vibration, Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 3, IEEE Control Systems Society, New York, 1988, pp. 1434-1439. Chun, H. M., Turner, J. D., and Juang, J., Disturbance-Accommodating Tracking Maneuvers of Flexible Spacecraft, Journal of the Astronautical Sciences, Vol. 33, No. 2, 1985, pp. 197-216. Cook, G., Discussion: Preshaping Command Inputs to Reduce System Vibration, Journal of Dynamic Measurement and Control, Vol. 115, June 1993, pp. 309, 310. Kwon, D., and Book, W. J., Inverse Dynamic Method Yielding Flexible Manipulator State Trajectories, Proceedings of the American Control Conference, American Automatic Control Council, New York, 1990, pp. 186-193. Isidori, A., Nonlinear Control Systems: An Introduction, SpringerVerlag, New York, 1989.

Adaptive structures for large precision antennas

Optimal controller design approach for high precision pointing maneuver of flexible spacecraft by using adaptive structures is investigated in this paper. A parameter optimization technique is used to find out controller parameters minimizing a desired objective function which represents pointing performance of a flexible space structure. Multi-input and multi-output configuration used in this study also provides insight on the effectiveness of actuator location for improved performance.

Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete‐time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

Robust closed-loop control design for spacecraft slew maneuver using thrusters

In this paper, a closed-loop switching function for on-off thruster firings is proposed to provide good attitude control performance in the presence of modeling errors for single-axis slew maneuver of a rigid spacecraft and to eliminate double-sided thruster firings. The size of a single-sided deadband in the switching function provides the capability of a tradeoff between maneuver time and fuel expenditure. The application of this switching function for the single-axis slew maneuvers of flexible spacecraft is also analyzed. The analytical simulations and experimental results demonstrate that the proposed switching function provides significant improvement in the slew maneuver performance.

Terminal spacecraft coplanar rendezvous control

The dynamics of relative motion between two nearby spacecraft for rendezvous is investigated in a local orbital coordinate system. An analysis by the phase plane method shows that a stable equilibrium state may exist in the motion. Based on this analysis, a control method called the range-rate control algorithm (RRCA) has been established. In addition, an omnidirectional version of the RRCA has also been introduced. The distance as well as the distance rate between the two spacecraft decrease exponentially to zero. The controlled trajectory is a stable and straight line in the orbital plane, whose orientation can be located freely. The numerical computation, corre- lated measurement, and propulsive implementation for the control algorithm are simple. A spacecraft rendezvous simulation is given as illustrative example. HE rendezvous operation of a maneuvering spacecraft to a target spacecraft usually consists of two successive phases: long-distance navigation and short-distance homing. In the naviga- tion phase, the orbit parameters as well as the distance between the two spacecraft may be seriously diverged. The main control task in this phase is impulsive orbit transfer, which requires both orbit determination and impulse generation techniques. This is a kind of open-loop control. The control accuracy achievable by these tech- niques is rather below that required for the subsequent docking of the two spacecraft. Therefore, what to do in the navigation phase is to bring the maneuvering spacecraft into the vicinity (say, . The orbital coordinate system Txyz of target space- craft is shown in Fig. 1. The axis Ty is directed upward away from Earth's center; the axis Tz aligns with the normal to the orbital plane and the axis Tx completes the right-hand system. The position of the maneuvering spacecraft in the system is given by a vector radius p. Then, the coplanar relative motion between the two spacecraft is determined by and its evolution in time, which is described by the following equations in linearized gravitation terms: p — p(a) -f- (p1)2 — pco2(3 sin2 (p — 1) = ap (1)

Near-optimal three-dimensional rotational maneuvers of spacecraft using manipulator arms

Near-optimal three-dimensional rotational maneuvers of spacecraft using manipulator arms

Active Mechanical Components as a Step towards Adaptive Structures in Space

Space missions require higher and higher performance such as high pointing accuracy and stability, and high shape precision. As a consequence the damping of in orbit vibraxtions induced, e.g., by the spacecraft manoeuvres on satellite appendages is mandatory. Passive damping becomes insufficient. More and more active technologies have to be considered. However project responsibles somewhat distrust these active technologies because of the technological risks which are still involved. This is the purpose of this paper to address the need for developing active mechanical components as a necessary step towards adaptive structures in space. The role of active interfaces is addressed in connection with typical applications will be particularly outlined. Two examples implementing an active interface are then more detailed: • damping augmentation of solar arrays • increasing the pointing stability of an inter satellite communication terminal The improvement of the static and dynamics behaviour of large reflectors is addressed in order to show the technological risk that requires intermediate development steps.

General attitude maneuvers of spacecraft with flexible structures

An efficient composite control strategy is proposed in this paper permitting simultaneous multi-axis reorientation of a spacecraft with flexible structures. The proposed control, separating large and small motions of the dynamic system, includes three parts that can be independently designed and tuned. For each maneuver, an open-loop referencing attitude control trajectory is derived by considering the spacecraft as rigid and executed by part 1. Flexural deformations of the structures are stabilized by part 2. Part 3, encompassing part 1 and part 2 control results and external disturbances, is an optimal guidance that tracks part 1 reference trajectory and achieves the specified final attitude in finite time. Three simulation cases are included in which a flexible model spacecraft is used. Collocated actuators and sensors are placed on the hub and on the flexible structures of the spacecraft.

Optimal power-limited rendezvous for linearized equations of motion

The form of solution of the optimal power-limited rendezvous problem for linear equations of motion is made to conform to previous developments by the author. The solution is then applied to the problem of rendezvous of a spacecraft with an object in the vicinity of a nominal Keplerian orbit. For the case in which the nominal orbit is circular, the controllability matrix can be inverted symbolically, resulting in a closed-form solution for the thrusting function. This result can be expressed as a closed-loop feedback law. For noncircular nominal orbits, a feedback law can be approximated by repeated numerical matrix inversions and reinitialization of the problem. PTIMAL power-limited terminal rendezvous of a spacecraft based on linearized equations of motion offers the mathematical advantage of closed-form or nearly closed-form solutions of the linearized trajectory optimization problem. In many cases this leads to thrust control in the form of optimal feedback laws, or at least, control functions that can be easily reinitialized on a regular basis. This gain in adaptivity may, to some extent, compensate for the loss in accuracy due to the linearization. There are many potential applications of a linearized analysis of optimal power-limited rendezvous. These typically involve the maneuvering of a low-thrust spacecraft near a real or fictitious object in a nominal orbit. Examples include maneuvers in the vicinity of artificial satellites, space stations, small comets, or asteroids. Examples where the object is fictitious include low-thrust satellite station keeping or interplanetar y missions in which the usual high-thrust midcourse maneuver is replaced by a continuous long-term lowthrust correction toward the nominal orbital position and velocity. Early work on the computation of power-limited , variable exhaust-velocity spacecraft trajectories was performed by Irving,1 Ross and Leitman,2 Edelbaum,3 Saltzer and Fetheroff,4 Melbourne,5 and Melbourne and Sauer.6'7 Immediately after these initial studies, investigators began to look at various linear models.812 Billik8 and Gobetz9 used linearization about nominal circular orbits, Edelbaum10 used linearization with respect to the orbital parameters of an ellipse, Gobetz11 linearized about an ellipse of low eccentricity, and Euler12 used the Tschauner-Hempel13'14 linearization for general elliptical orbits. More general discussions that include linear and nonlinear models for both power-limited and constant-exhaust-velocity problems can be found in the works of Edelbaum15 and Marec.16 Recently, optimal power-limited low-thrust trajectories to return to an original station in orbit after an impulsive maneuver away from this orbit were examined by Lembeck and Trussing17 using equations linearized about a circular orbit. The same linearized equations were used by Coverstone-Carroll and Trussing18 to investigate the cooperative power-limited rendezvous of two spacecraft near a nominal circular orbit. Power-limited trajectories in an inverse-square gravity field have also been considered by Prussing.19 In the present paper, we consider the fixed-time linear, powerlimited rendezvous problem. We utilize a somewhat more general cost function than usual, an integral of the product of a weighting

On-orbit propellant motion resulting from an impulsive acceleration

In-space docking and separation maneuvers of spacecraft that have large fluid mass fractions may cause undesirable spacecraft motion in response to the impulsive-acceleration-induced fluid motion. An example of this potential low-gravity fluid management problem arose during the development of the shuttle/Centaur vehicle. Experimentally verified numerical modeling techniques were developed to establish the propellant dynamics, and subsequent vehicle motion, associated with the separation of the Centaur vehicle from the shuttle cargo bay. Although the shuttle/Centaur development activity has been suspended, the numerical modeling techniques are available to predict on-orbit liquid motion resulting from impulsive accelerations for other missions and spacecraft.

Optimal cooperative power-limited rendezvous between coplanar circular orbits

Minimum-fuel rendezvous of two power-limited spacecraft is investigated. Both vehicles are active and provide thrust to complete the rendezvous. Total propellant consumption is minimized. A direct-minimization method, direct collocation with nonlinear programming, is used to obtain cooperative rendezvous solutions in an inverse- square gravitational field. Unconstrained and constrained circular terminal orbits are considered. The optimal solutions depend upon the power-to-mass ratios of the spacecraft, the initial orbits, and the specified transfer time. Optimal cooperative rendezvous solutions are compared with optimal active-passive solutions and with previously reported linearized solutions. ISTORICALLY, spacecraft rendezvous has involved one thrusting (active) vehicle and one coasting (passive) vehicle. A cooperative power-limited (PL) rendezvous is an orbital maneuver in which two PL spacecraft are active. With both vehicles thrust- ing, a reduction in total propellant consumption is obtained when compared to the traditional active-passive rendezvous. The practical application of cooperative rendezvous occurs if both vehicles have comparable size and propulsive capability. It would make no sense to consider cooperative rendezvous between a small spacecraft and a space station. Early studies of cooperative control considered general linear or nonlinear systems with various performance indices.14 Recently, cooperative rendezvous methodology has been applied to spacecraft maneuvering. Prussing and Conway5 determined the optimal termi- nal maneuver for a cooperative impulsive rendezvous. Mirfakhraie6 and Mirfakhraie and Conway7 developed a method for determin- ing fuel-optimal trajectories for the fixed-time impulsive cooper- ative rendezvous. Coverstone-Carroll and Prussing8 obtained an- alytical solutions for fixed-time PL cooperative rendezvous using the Hill-Clohessy-Wiltshire linearized gravity field to approximate the inverse-square gravity field. In this article, fixed-time cooper- ative and active-passive (noncooperative) rendezvous solutions are obtained for two PL spacecraft in an inverse-square gravity field. Transfer times, maximum exhaust powers, and the initial orbits of the spacecraft are varied to determine their influence on the optimal cooperative solution. Optimal solutions subject to circular terminal- orbit constraints are also examined. Necessary Conditions for Optimal Solution

Multicriterion structure/control design for optimal maneuverability and fault tolerance of flexible spacecraft

A multicriterion design problem for optimal maneuverability and fault tolerance of flexible spacecraft is considered. The maneuverability index reflects the time required to perform rest-to-rest attitude maneuvers for a given set of angles, with the postmaneuver spillover within a specified bound. The performance degradation is defined to reflect the maximum possible attitude error after maneuver due to the effect of faults. The fault-tolerant design is to minimize the worst performance degradation from all admissible faults by adjusting the design of the spacecraft. It is assumed that admissible faults can be specified by a vector of real parameters. The multicriterion design for optimal maneuverability and fault tolerance is shown to be well defined, leading to a minimax problem. Analysis for this nonsmooth problem leads to closed-form expressions of the generalized gradient of the performance degradation function with respect to the fault parameters and structural design variables. Necessary and sufficient conditions for the optimum are derived, and the closed-form expressions of the generalized gradients are applied for their interpretation. The bundle method is applicable to this minimax problem. Approximate methods which efficiently solve this minimax problem with relatively little computational difficulties are presented. Numerical examples suggest that it is possible to improve the fault tolerance substantially with relatively little loss in maneuverability.

Attitude stabilization of a rigid spacecraft using two control torques: A nonlinear control approach based on the spacecraft attitude dynamics

The attitude stabilization problem of a rigid spacecraft using control torques supplied by gas jet actuators about only two of its principal axes is considered. If the uncontrolled principal axis of the spacecraft is not an axis of symmetry, then the complete spacecraft dynamics are small time locally controllable. However, the spacecraft cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback. A discontinuous stabilizing feedback control strategy is constructed which stabilizes the spacecraft to any equilibrium attitude. If the uncontrolled principal axis of the spacecraft is an axis of symmetry, the complete spacecraft dynamics are not even assessible. However, the spacecraft dynamics are strongly accessible and small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized to any equilibrium attitude using time-invariant continuous feedback, but again a discontinuous stabilizing feedback control strategy is constructed. In both cases, the discontinuous feedback controllers are constructed by switching between several feedback functions which are selected to accomplish a sequence of spacecraft maneuvers. The results of the paper show that although standard nonlinear control techniques are not applicable, it is possible to construct a nonlinear discontinuous control law based on the dynamics of the particular physical system.