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A formation mission scenario is considered, consisting of small satellites (Chasers) that must keep a reference trajectory with respect to a larger and non-cooperating Target satellite. The Chaser must perform its formation guidance and control tasks within the framework of its thruster constraints: the case of a low thrust electrical engine is here considered. The constraints of such a thruster are relevant to number and orientation of thrusters, the admissible thrust levels and minimum and maximum ON time. The control algorithm developed to satisfy all these constraints is a model predictive control based on a mixed-integer genetic algorithm optimization, which provides a fast estimate of the necessary scheduled actions. The algorithm takes J 2 and drag perturbations into account; at the scope a differential orbital parameters linear relative dynamics model has been used, while the real-world dynamics is represented by a high precision orbital propagator. The developed orbital controller is particularly effective when trajectory keeping is required; different relative configurations, like Helix or Train formations, are taken as benchmark trajectories. The results show promising and robust performance in counteracting differential perturbations, even in the case in which the Target satellite performs scheduled orbital maneuvers which are not timely communicated to the Chaser satellite. • Micro satellites are characterized by hardware with limited capabilities. • Formation control can be much more demanding the classic standalone control. • An optimal control schedule with thruster and mission constraints is developed. • Mixed-integer GA optimization employed to compute control schedule. • Realistic performance has been tested with high precision orbital propagators. [ABSTRACT FROM AUTHOR] more...

On-orbit servicing often requires the use of robotic arms, and a key asset in this kind of operations is autonomy. In this framework, the use of optical devices is a solution, already analyzed in many researches both for autonomous rendezvous and docking and for the evaluation of the control of the manipulator. In the present paper, simulations for assessing the controller performance are realized in a high-fidelity purposely developed software architecture, in which not only the selected 6 DOF space manipulator is modeled, but also a virtual camera, acquiring in the loop images of the target CAD model imported, is included in the GNC loop. This approach allows to emphasis several problems that would not emerge in simulations with images characterized by easily-identifiable, purposely-created markers. At the scope, a specific GNC architecture is developed, based on finite-state machine logic. According to this approach, two different Image Based Visual Servoing strategies are alternatively performed, commanding only linear or angular velocity of the camera, switching between the two control techniques when the "stack" or "divergence" condition is triggered. In this way a stable and robust accomplishment of the tasks is achieved for many configurations and for different target models. • On-orbit servicing often requires the use of robotic arms. • The use of optical devices is a solution, but calls for performance verification. • A co-simulation between a CAD S/W and MATLAB is developed. • IBVS technique is verified in this high-fidelity environment. • To improve robustness, a modification of classic IBVS is implemented. [ABSTRACT FROM AUTHOR] more...

In the framework of on-orbit proximity operations, small satellites represent an appealing solution in terms of costs, effectiveness and realization, but show intrinsic power, mass and computation limitations that could be overcome if cooperation among many spacecraft is considered. In this research, a swarm of small satellites (called "Children S/C″), deployed from a larger platform (called "Mother S/C″), is employed in the inspection of a damaged spacecraft, which cannot be directly approached by the Mother S/C for safety reasons. The navigation process is delegated to the Mother S/C, that is equipped with a passive camera. A navigation algorithm runs on the Mother S/C, which identifies and tracks the Children S/C framed in the scene, even though false matches (i.e., incorrect tracking of a given child) could happen. The navigation algorithm is made robust through the generation at each time step of a propagated virtual image (based on the previous estimate of the swarm state) which is compared to the acquired image for the correct identification of each child. When the relative position estimates reach a satisfactory accuracy, the Mother S/C communicates to the Children S/C their current state and an optimal impulsive control strategy can be implemented to make the swarm fulfill the required inspection task. Simulations are carried out in a purposely developed software environment, in which images of rendered CAD models are acquired and processed to have a realistic validation of the estimation algorithm, showing satisfactory performance and robustness for the overall mission accomplishment. • Swarm of satellites can be an option for on-orbit missions. • Autonomous GNC loop is required for tight formations. • Visual navigation is a key asset for autonomous navigation. • Optimal impulsive control is computed using visual measurements. • Software set-up for realistic visual navigation is presented. [ABSTRACT FROM AUTHOR] more...

The advances in the computational capabilities and in the robustness of the dedicated algorithms are suggesting vision based techniques as a fundamental asset in performing space operations such as rendezvous, docking and on-orbit servicing. This paper discusses a vision based technique in a scenario where the chaser satellite must identify a non-cooperative target, and use visual information to estimate the relative kinematic state. A hardware-in-the-loop experiment is performed to test the possibility to perform a space rendezvous using the camera as a standalone sensor. This is accomplished using a dedicated test bed constituted by a dark room hosting a robotic manipulator. The camera is mounted on the end effector that moves replicating the satellite formation dynamics, including the control actions, which depend at each time step by the state estimation based on the visual algorithm, thus realizing a closed GNC loop. [ABSTRACT FROM AUTHOR] more...

Abstract: A uniqueness theorem for limit cycles of a class of plane differential systems is proved. The main result is applicable to second order O.D.E.’s with a dissipative term depending both on the position and on the velocity. [Copyright &y& Elsevier] more...

We are concerned with plane differential systems of the formx˙ = P(x,y), y˙ = Q(x,y), withP, Q analytic. We propose a formal-numeric method to localize the attractors and the repellers of the system. Such a method consists of looking for a power series solution to a PDE of the typePSHAPE="BUILT" ALIGN="C" STYLE="S">∂V∂x + QSHAPE="BUILT" ALIGN="C" STYLE="S">∂V∂y = μ(V), with μ is an arbitrary analytic function. Whenμ(V) = ρ(V − V2),ρ > 0, the attractors are contained in the setV = 1, the repellers in the setV = 0. [Copyright &y& Elsevier] more...

In the near future robotic systems will be playing an increasingly important role in space applications such as repairing, refueling, re-orbiting spacecraft and cleaning up the increasing amount of space debris. Space Manipulator Systems (SMSs) are robotic systems made of a bus (which has its own actuators such as thrusters and reaction wheels) equipped with one or more deployable arms. The present paper focuses on the issue of maintaining a stable first contact between the arms terminal parts (i.e. the end-effectors) and a non-cooperative target satellite, before the actual grasp is performed. The selected approach is a modified version of the Impedance Control algorithm in which the end-effector is controlled in order to make it behave like a mass-spring-damper system regardless of the reaction motion of the base, so to absorb the impact energy. The effects of non-modeled dynamics in control determination such as the structural flexibility of the manipulator and the target satellite are considered as well, and their impact on control effectiveness is analyzed. The performance of the proposed control architecture and a parametric analysis are studied by means of a co-simulation involving the MSC Adams multibody code (for describing the dynamics of the space robot and target) together with Simulink (for the determination of the control actions). The results show that the first contact phase of the grasping operation of a large satellite requires careful tuning of the control gains and a proper selection of the end-effector dimensions; otherwise, the large geometric and inertia characteristics of the target could lead to a failure with serious consequences. Both successful and underperforming cases are presented and commented in the paper. [ABSTRACT FROM AUTHOR] more...

In the near future robotic systems will be playing an increasingly important role in space applications such as repairing, refueling, re-orbiting spacecraft and cleaning up the increasing amount of space debris. Space Manipulator Systems (SMSs) are robotic systems made of a platform (which has its own actuators such as thrusters and reaction wheels) equipped with one or more deployable arms. The present paper focuses on the issue of maintaining a stable first contact between the arms terminal parts (i.e. the end-effectors) and a target satellite, before the actual grasp is performed. The selected approach is a modified version of the Impedance Control algorithm, in which the end-effector is controlled in order to make it behave like a mass-spring-damper system regardless of the reaction motion of the base, so to absorb the impact energy. The usual approach consists in considering a point mass target and one-dimensional contact dynamics; however, the contact between the chaser and the target could generate a perturbation on the attitude of the target. On account of this, in the present work a more realistic scenario, consisting in a 2D rigid target and a relevant 2D contact dynamics, is considered. A two-arm configuration of the SMS is modelled and its effectiveness analyzed. The performance of the proposed control architecture is evaluated by means of a co-simulation involving the MSC Adams multibody code (for describing the dynamics of the space robot and target) together with Simulink (for the determination of the control actions). The co-simulation is a particularly useful tool to implement robust control applied to detailed dynamic systems. Several numerical results complete the work. [ABSTRACT FROM AUTHOR] more...

The dynamics and the control of space manipulators floating in 3D space is analyzed in this paper. A minimum state variable approach for describing the dynamics of a free-floating space manipulator under gravity and gravity gradient forces is presented. A new control strategy involving a combination of Reaction Null and Jacobian Transpose controllers, including also the gravity gradient compensation, is suggested and compared with the Jacobian Transpose control and the conventional Proportional Derivative control. Several numerical examples will be presented and discussed, considering platforms with single and double manipulators, showing the advantages and drawbacks related to these control strategies. [ABSTRACT FROM AUTHOR] more...

Abstract: One of the most important problems for performing a good design of the spacecraft attitude control law is connected to its robustness when some uncertainty parameters are present on the inertial and/or on the elastic characteristics of a satellite. These uncertainties are generally intrinsic on the modeling of complex structures and in the case of large flexible structures they can be also attributed to secondary effects associated to the elasticity. One of the most interesting issues in modeling large flexible space structures is associated to the evaluation of the inertia tensor which in general depends not only on the geometric ‘fixed’ characteristic of the satellite but also on its elastic displacements which of course in turn modify the ‘shape’ of the satellite. Usually these terms can be considered of a second order of magnitude if compared with the ones associated to the rigid part of a structure. However the increasing demand on the dimension of satellites due to the presence for instance of very large solar arrays (necessary to generate power) and/or large antennas has the necessity to investigate their effects on their global dynamic behavior in more details as a consequence. In the present paper a methodology based on classical Lagrangian approach coupled with a standard Finite Element tool has been used to derive the full dynamic equations of an orbiting flexible satellite under the actions of gravity, gravity gradient forces and attitude control. A particular attention has been paid to the study of the effects of flexibility on the inertial terms of the spacecraft which, as well known, influence its attitude dynamic behavior. Furthermore the effects of the attitude control authority and its robustness to the uncertainties on inertial and elastic parameters has been investigated and discussed. [Copyright &y& Elsevier] more...