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Abstract: In this paper the dynamics of a spacecraft with a system of stabilization out-of-operation is studied. The deployment of the ring flexible antenna is performed after placing the spacecraft into orbit and damping the initially undesired rotations by a special jet-propelled system. Basically the antenna is a pre-stressed tape reeled on a special drum. Deploying from the drum, the tape takes the shape of an elastic ring of 30m in diameter. The objective of the study is the mechanical and computational modelling of the spacecraft dynamics. The equations of motion are derived in Lagrangian form. Numerical simulations of operational mode of the system are performed. As it is shown in main result, which restrictions must be imposed on parameters of the process of deployment for maintenance of the shape of the deployed design. [Copyright &y& Elsevier]

Abstract: Control of space robots in the 3D space is known as one of the difficult problems in nonlinear control theory, and if there exist initial angular momenta for space robots, the control problem becomes an increasing challenge. However, it is quite important to take into account the existence of initial angular momenta from the aspect of realistic situations. This paper deals with a control problem for a 3D space robot of two rigid bodies with an initial angular momentum. First, we give a model of a space robot with an initial angular momentum, called the ball-in-socket joint model. We next propose a near-optimal control method for general nonlinear affine control systems based on the finite dimensional orthonormal basis and give some theoretical analysis for the method. Moreover, a near-optimal control algorithm is also shown. Then, we apply the near-optimal control algorithm to a 3D attitude control problem of the ball-in-socket joint model with an initial angular momentum, and illustrate numerical simulations in order to show the effectiveness of our method. [Copyright &y& Elsevier]

Abstract: This paper presents a general framework for synchronized multiple spacecraft rotations via consensus-based virtual structure. In this framework, attitude control systems for formation spacecrafts and virtual structure are designed separately. Both parametric uncertainty and external disturbance are taken into account. A time-varying sliding mode control (TVSMC) algorithm is designed to improve the robustness of the actual attitude control system. As for the virtual attitude control system, a behavioral consensus algorithm is presented to accomplish the attitude maneuver of the entire formation and guarantee a consistent attitude among the local virtual structure counterparts during the attitude maneuver. A multiple virtual sub-structures (MVSSs) system is introduced to enhance current virtual structure scheme when large amounts of spacecrafts are involved in the formation. The attitude of spacecraft is represented by modified Rodrigues parameter (MRP) for its non-redundancy. Finally, a numerical simulation with three synchronization situations is employed to illustrate the effectiveness of the proposed strategy. [Copyright &y& Elsevier]

Abstract: For an imaging spacecraft to provide higher resolution imaging capability, the satellite will require larger mirrors. Because of the weight and launch constraints for space-based optics systems, the mirrors will have to be segmented and light-weight, resulting in increased flexibility and lower structural frequencies. Consequently, achieving surface accuracy requirements for high resolution imaging with these large aperture light-weight mirrors become a challenging task. This paper investigates the use of adaptive optics for wavefront sensing and surface control of large segmented mirrors. An robust control technique is considered for the control of the adaptive optics system with the reduced number of inputs and outputs using singular value decomposition and Zernike polynomials. The robust controller design with the reduced model is validated with a computer simulation for a full plant in the presence of disturbances. [ABSTRACT FROM AUTHOR]

Abstract: Optical navigation for a lunar lander consists of estimating a lander''s 3-dimensional (3-D) relative dynamic motion with respect to a preselected landing site using a passive 2-dimensional (2-D) video image sequence. Lunar landing missions require a lander to perform an autonomous accurate landing with simple mechanical structure, easy operation and low cost. These requirements have motivated the need to develop an advanced navigation system. Existing navigation systems trade-off simplicity, accuracy and cost. High accuracy navigation systems typically imply complexity and high cost. In this paper, we consider a scenario where the descending phase starts from an initial altitude of 10km with a time-of-descent of 100s. The navigation camera is an off-the-shelf optical instrument used to take the video image sequence of the landing site during the landing phase. It is fed into the motion estimation algorithm to be processed. The continuous wavelet transform (CWT) is used to analyse each image frame of the input digital video image sequence. The output is a 2-D video image motion trajectory map, which represents the projection motion of the landing site. The 2-D video image motion is projected back to the 3-D lander''s relative motion based on a geometric analysis. The outputs of this estimation algorithm are the 3-D attitude motion parameters of the lander at a time corresponding to an image being taken. The attitude determination and control system (ADCS) of the lander uses these data to perform the lander''s attitude control task. In this article, we provide the motion modelling for a lunar lander during the descending phase. The projection of a 3-D planar to 2-D image plane is analysed which build the correspondence between the 3-D lander''s motion and the 2-D image motion. This link provides the evidence for the geometry analysis. CWT is reviewed and CWT for video image sequence analysis is also introduced. Numerical simulation of the estimated 2-D video image sequence under the lander performing a 3-D translation and yaw rotation during the terminal descent are shown to verify the proposed concepts. The analysis of the results show that the proposed method achieves highly accurate 2-D video image motion estimation of less then 1% error with significant savings of cost, mass and volume. It leads to the accurate estimation of the lander''s 3-D relative motion with respect to the landing site. [Copyright &y& Elsevier]

Abstract: This paper deals with maneuver control and vibration suppression of a two-link flexible arm with embedded smart materials. First, by using extended Hamilton’s principle and assumed mode method, equations of motion of the two-link flexible arm with PZT patches as sensor and actuator are obtained. Inspecting the resulting equations reveals that the dynamics of the flexible structure that encompasses the vibrations of the links and their rigid in-plane maneuver takes place in two different time scales. Consistent with this characteristic, a slow subsystem associated with rigid motion dynamics and a fast subsystem associated with link flexible dynamics are identified by using the singular perturbation theory. Then, a hybrid controller is proposed as a combination of two distinct controllers for these subsystems and their stability is studied using the Lyapunov approach. The controller consists of a variable structure control (VSC) for maneuvering control of the slow subsystem and a Lyapunov based controller for vibration suppression of the flexible structure. According to the numerical simulation results it can be concluded that the proposed hybrid controller has a suitable and efficient performance for maneuver control and suppressing the transverse vibrations of the structure. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses a synchronization strategy for a network of chaotic systems with particular spatial distribution by using unidirectional and bidirectional time-delayed state feedback. The results show that even in a very demanding scenario, it is possible to achieve synchronization among the systems, so that chaos-based communication can be implemented properly on a satellite formation flying environment. The performance picture of the overall synchronization strategy is shown in numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a dual-stage control system design method for the rotational maneuver control and vibration stabilization of a flexible spacecraft. In this design approach, the sub-systems of attitude control and vibration suppression are designed separately using the low order model. Based on the sliding mode control (SMC) theory, a discontinuous attitude control law in the form of the input voltage of the reaction wheel is derived to control the orientation of the spacecraft, incorporating the L2-gain performance criterion constraint. The resulting closed-loop system is proven to be uniformly ultimately bounded stability and the effect of the external disturbance on both attitude quaternion and angular velocity can be attenuated to the prescribed level as well. In addition, an adaptive version of the control law is designed for adapting the unknown upper bounds of the lumped disturbance such that the limitation of knowing the bound of the disturbance in advance is released. For actively suppressing the induced vibration, strain rate feedback control method is also investigated by using piezoelectric materials as additional sensors and actuators bonded on the surface of the flexible appendages. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance and uncertainty. [Copyright &y& Elsevier]

Abstract: This paper presents a double line-of-sight (LOS) measuring relative navigation technique for far or medium range (tens of kilometers ∼ several kilometers) autonomous rendezvous. In this new relative navigation technique, two chase spacecraft with inter-spacecraft crosslink form a measuring baseline relative to the target spacecraft in space and, respectively, measure LOS angles of the target and their own inertial states. The processing noise model of the relative navigation system is developed based on the spacecraft relative dynamics equations described in inertial frame. The measurement model including LOS angles of the target and the bearing and length of the measuring baseline is established. A discrete-time extended Kalman filter (EKF) is developed to estimate the relative motion of the target. The degree of observability of the navigation system is analyzed by the condition number. Numerical simulation results indicate that: (1) the relative position and velocity of the target can be estimated with sufficient accuracy using the double LOS measuring relative navigation technique, (2) compared with that of single LOS angles-only navigation, the observability of double LOS measuring relative navigation is improved, (3) the separation angle between two LOS vectors influences the estimation errors and the observability of the navigation system. [Copyright &y& Elsevier]

Abstract: In this paper, effectiveness of aerodisk/aerospike assemblies as retractable drag-reduction devices for large-angle blunt cones flying at hypersonic Mach numbers is simulated numerically at various angles of attack. Different lengths of spike have been chosen to investigate the effect of the aerospike on the surrounding flowfield of nose cone. The compressible, 3-D full Navier–Stokes equations are solved with k−ω (SST) turbulence model for free stream Mach number of 5.75 and different angles of attack namely 3, 7, 10, and 12. The visualized shock structure and the computed drag on the blunt cone with aerospike agree well with the experimental result. The effect of reattachment of point on the surface convective heat-load reduction is investigated for different kind of spikes with varying length to diameter ratio. Additional modifications to the tip of the spike are examined in order to obtain different bow shocks, including a cut spike, and a flat and hemispherical aerodisk mounted on the tip of the spike. The numerical results presented the pressure distributions and the surface heat reduction for different type of spike. Some discrepancies existed, especially on the length of the recirculation region. [Copyright &y& Elsevier]

Abstract: In this paper, the minimum-time orbital trajectories for Earth–Moon and Moon–Earth flights of a continuous-thrust spacecraft are obtained by the time-domain finite element method. The problem is formulated using a simplified version of the restricted three-body model at the Cartesian coordinate system. Moreover, the performance index is considered as the minimum-time problem with free final time. Through the calculus of variation, the problem is discretized in the time-domain and the resulting equations are constructed in finite element form. Finally, by setting out the discrete equations, a set of nonlinear algebraic equations is generated. The optimum answer is then attained using the Newton–Raphson method. The capability of the time-domain finite element method is examined to verify its accuracy. The trajectory results are also compared with the published results and good agreement is observed. Numerical simulations highlighting the effects of the effective exhaust velocity parameter on the shape of flight trajectory and time-of-flight are presented. [Copyright &y& Elsevier]

Abstract: This paper deals with the cislunar transfer problem. A new type of distant retrograde orbit (DRO) is proposed and its stability is investigated. The Lyapunov orbits tangential to the retrograde orbit are applied to design the entry of transfer trajectories, i.e., the invariant manifolds of Lyapunov orbit around are applied to achieve the quick transfer to DRO, meanwhile the Lyapunov orbit around is used as the entrance to weak stability boundary (WSB) transfer, so that the low energy transfer to DRO is achieved. The numerical simulations is given to validated the feasibility of the two transfer modes. [Copyright &y& Elsevier]

Abstract: A new concept using flexible tether–net system to perform on-orbit capture is presented in this paper. As a promising on-orbit capture strategy, the tether–net system has many exciting advantages by contrast with the existing orbital capture system. However, under the disturbance of orbital dynamics an attitude libration, which leads to a capture error, will be presented when the capture net is ejected towards the target aiming at investigating the relationship between the capture error and initial capture conditions, the governing equations of the tether–net system in orbital frame is developed by applying Lagrange equations. In order to optimize capture operation, the in-plane capture constraints are studied by numerical simulations with an effort to damp the in-plane libration and compensate the capture error, the control scheme based on tether tension is investigated firstly, after that an integrated control scheme is proposed by introduced the thrusters into the system, the nonlinear closed-loop dynamics is linearized by feedforward strategy, the simulation results show that feedforward controller is effective for in-plane libration damping and enable the capture net to track an expected trajectory. [Copyright &y& Elsevier]

Abstract: The use of orbital solid rocket motors (SRM) is responsible for the release of a high number of slag and Al2O3 dust particles which contribute to the space debris environment. This contribution has been modeled for the ESA space debris model MASTER (Meteoroid and Space Debris Terrestrial Environment Reference). The current model version, MASTER-2005, is based on the simulation of 1076 orbital SRM firings which mainly contributed to the long-term debris environment. SRM firings on very low earth orbits which produce only short living particles are not considered. A comparison of the modeled flux with impact data from returned surfaces shows that the shape and quantity of the modeled SRM dust distribution matches that of recent Hubble Space Telescope (HST) solar array measurements very well. However, the absolute flux level for dust is under-predicted for some of the analyzed Long Duration Exposure Facility (LDEF) surfaces. This indicates that some past SRM firings are not included in the current event database. Thus it is necessary to investigate, if additional historical SRM burns, like the retro-burn of low orbiting re-entry capsules, may be responsible for these dust impacts. The most suitable candidates for these firings are the large number of SRM retro-burns of return capsules. This paper focuses on the SRM retro-burns of Russian photoreconnaissance satellites, which were used in high numbers during the time of the LDEF mission. It is discussed which types of satellites and motors may have been responsible for this historical contribution. Altogether, 870 additional SRM retro-burns have been identified. An important task is the identification of such missions to complete the current event data base. Different types of motors have been used to de-orbit both large satellites and small film return capsules. The results of simulation runs are presented. [Copyright &y& Elsevier]

Abstract: A simplified design and optimization method of aerospike nozzle contour and the results of tests and numerical simulation of aerospike nozzles are presented. The primary nozzle contour is approximated by two circular arcs and a parabola; the plug contour is approximated by a parabola and a third-order polynomial. The maximum total impulse from sea level to design altitude is adopted as objective to optimize the aerospike nozzle contour. Experimental studies were performed on a 6-cell tile-shaped aerospike nozzle, a 1-cell linear aerospike nozzle and a 3-cell aerospike nozzle with round-to-rectangle (RTR) primary nozzles designed by method proposed in present paper. Three aerospike nozzles achieved good altitude compensation capacities in the tests and still had better performance at off-design altitudes compared with that of the bell-shaped nozzle. In cold-flow tests, 6-cell tile-shaped aerospike nozzle and 1-cell linear aerospike nozzle obtained high thrust efficiency at design altitude. Employing gas H2/gas O2 (GH2/GO2) as propellants, hot-firing tests were carried out on a 3-cell aerospike nozzle engine with RTR primary nozzles. The performance was obtained under two nozzle pressure ratios (NPR) lower than design altitude. Efficiency reached 92.0–93.5% and 95.0–96.0%, respectively. Pressure distribution along plug ramp was measured and the effects of variation in the amount of base bleed on performance were also examined in the tests. [Copyright &y& Elsevier]

Abstract: Multibody dynamics for space applications is dictated by space environment such as space-varying gravity forces, orbital and attitude perturbations, control forces if any. Several methods and formulations devoted to the modeling of flexible bodies undergoing large overall motions were developed in recent years. Most of these different formulations were aimed to face one of the main problems concerning the analysis of spacecraft dynamics namely the reduction of computer simulation time. By virtue of this, the use of symbolic manipulation, recursive formulation and parallel processing algorithms were proposed. All these approaches fall into two categories, the one based on Newton/Euler methods and the one based on Lagrangian methods; both of them have their advantages and disadvantages although in general, Newtonian approaches lend to a better understanding of the physics of problems and in particular of the magnitude of the reactions and of the corresponding structural stresses. Another important issue which must be addressed carefully in multibody space dynamics is relevant to a correct choice of kinematics variables. In fact, when dealing with flexible multibody system the resulting equations include two different types of state variables, the ones associated with large (rigid) displacements and the ones associated with elastic deformations. These two sets of variables have generally two different time scales if we think of the attitude motion of a satellite whose period of oscillation, due to the gravity gradient effects, is of the same order of magnitude as the orbital period, which is much bigger than the one associated with the structural vibration of the satellite itself. Therefore, the numerical integration of the equations of the system represents a challenging problem. This was the abstract and some of the arguments that Professor Paolo Santini intended to present for the Breakwell Lecture; unfortunately a deadly disease attacked him and shortly took him to death, leaving his work unfinished. In agreement with Astrodynamics Committee it was decided to prepare a paper based on some research activities that Paolo Santini performed during almost 50 years in the aerospace field. His researches spanned many arguments, encompassing flexible space structures, to optimization, stability analysis, thermal analysis, smart structure, etc. just to mention the ones more related to the space field (Paolo Santini was also one the pioneers of the studies of composite wing structures, aeroelasticity and unsteady aerodynamics for aeronautical applications). Following notes have been prepared by Paolo Gasbarri who was one of Paolo Santini collaborators for almost 15 years, they will attempt to offer a sketch of Professor Santini''s activity by focusing on three main topics: the stability of flexible spacecrafts, the dynamics of multibody systems and the use of the smart structure technology for the space applications. [Copyright &y& Elsevier]

Abstract: We consider the problem of a spacecraft subjected to constant body-fixed forces and moments about all three axes during a spinning-up, thrusting maneuver. In applications, undesired forces and moments can arise due to thruster imbalances and misalignments and to center-of-mass offset. In previous works, approximate analytical solutions have been found for the attitude motion, and for the change in inertial velocity and inertial position. In this paper we find asymptotic and limiting-case expressions which we derive from the analytic solutions, in order to obtain simplified, practical formulas that lend insight into the motion. Specifically, we investigate how the motion evolves (1) as time grows without bound and (2) for geometric cases of the sphere, the thin rod, and the thin plate. Closed-forms or upper-bound limits are provided for angular velocities, Eulerian angles, angular momentum pointing error, transverse and axial velocities, and transverse and axial displacements. Summaries for the asymptotic limits (for zero initial conditions) are provided in tabular form. Results are verified by numerical simulations. [Copyright &y& Elsevier]

Abstract: The present paper deals with the study the dynamics of the spacecraft with gyro-gravitational system of stabilization. The deployment of the boom of the gravitational stabilizer commences after placing the spacecraft into the orbit and completion of the preliminary damping, when the gyroscopes are uncaged. Primarily the boom is the pre-stressed tape wound on the special drum. When the drum starts deploying the tape, it turns into the elastic cylindrical rod with the mass at its tip. The objective of the study is the creation of the generalized mathematical model and the conducting of the computer modelling of the spacecraft dynamics. The equations of motion are worked out with the use of the Lagrangian formalism. The numerical simulation of typical modes of system functioning is conducted. It is shown that the folding and the following deployment of the boom result in the turn of the spacecraft by 180° about the axis of the pitch. The results illustrate the behaviour of the main system variables. [Copyright &y& Elsevier]

This paper describe schemes for onboard relative position and attitude estimation and control for the final translational phase of an autonomous space rendezvous and docking system. Different estimators for attitude and position parameters based on a vision system outputs are given. Relative position control based on phase–plane control technique and relative attitude control based on relative quaternion feedback scheme are described. Based on the study, it turns out that fixed gain observers are sufficient for the estimation of position and attitude. Sensitivity of different parameters on these estimators and controllers are also described. A detailed computer simulation provides the expected range of parameters for which a successful maneuver towards the target can be achieved. [Copyright &y& Elsevier]