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First International Orbital Debris Conference, held 9-12 December, 2019 in Sugar Land, Texas. The article of record as published may be found at https://doi.org/10.1016/j.jsse.2020.07.006 The Hubble Space Telescope (HST), launched in 1990, has without question given us a better understanding of the Universe [1]. The storied spacecraft has far exceeded its design life and, in spite of four repair missions, is nearing the end of its useful lifespan. Originally designed to be returned by the Space Shuttle, the HST has no on-board propulsion system. A 2012 study estimated that without intervention, the HST will re-enter the atmosphere in approximately 2027 with a 1:240 risk of fatality [2]. This study updates that analysis with more recent de-orbit technologies and updated trajectory information. We propose a design solution to safely perform a targeted de-orbit, assuming a worst-case scenario (a non-functional, tumbling spacecraft). Multiple de-orbit options are assessed to actively capture the satellite. Results frame an approach that could be accomplished with proven technologies at reasonable cost to improve the fatality risk as required by US Government regulation [3]. Moreover, delayed action would significantly increase mission cost and complexity so we recommend a project start in the near future.

The article of record as published may be found at https://doi.org/10.1016/j.automatica.2020.109151 New results are presented for the problem of minimum-time control of a general linear time-invariant normal system evolving from an arbitrary initial state to an arbitrary final state (no-rest to no-rest problem), subjected to bound controls. In particular, it is demonstrated that the above problem is equivalent to an associated minimum-time control problem of transferring the same system from a particular initial state to the state-space origin (no-rest to rest problem), where that particular initial state is related to the boundary states of the original problem through a transformation of the state-space onto itself. If the optimal control history that transfers the system from an arbitrary initial state to the origin is known, either analytically or numerically, then the new results provide a method to solve the problem of minimum-time control between two arbitrary states and moreover, to find all of the extremal controlled trajectories. A criterion of existence is also given for the solution of the minimum-time control between two arbitrary states. Finally, the analytic solution is presented for the minimum-time control of the double integrator between arbitrary states. That solution provides a significant example of applying the new results.

A set of laboratory experiments are conducted to demonstrate the autonomous capture of a simulated resident space object by a simulated spacecraft equipped with a robotic manipulator. A planar air-bearing test bed provides a quasi-weightless and drag-free dynamic environment on a plane. To control the chaser's base, floating, flying, and rotation-flying control approaches are implemented and compared. A resolved-motion-rate controller is used to control the manipulator's joints. Using these control methods a floating object at rest is successfully captured. Furthermore, the capture of a floating and rotating object is demonstrated using a flying base control approach. The originality of these experiments comes from the remarkably high dynamic coupling of the spacecraft–manipulator system used. Emphasis is given to the guidance and control problems, with the relative navigation problem being left outside the scope of this effort.

The article of record as published may be found at https://doi.org/10.2514/1.G001843 This paper proposes a guidance scheme for autonomous docking between a controlled spacecraft and an uncontrolled tumbling target in circular orbit. The onboard trajectory planning consists of a direct optimization method based on the inversion of the system dynamics. The trajectory components of the controlled spacecraft are imposed by using polynomial functions. Some of the polynomial coefficients are constrained to satisfy path constraints, whereas the remaining coefficients are varied parameters to be optimized. The optimal control problem is converted into a nonlinear programming problem by inverting the system dynamics. The proposed guidance scheme, based on the closed-loop implementation of this optimization problem, is applied to several scenarios. The resulting trajectories closely match the solutions of the correspondent optimal control problems. The guidance scheme is shown to perform precise maneuvers in most maneuvering situations, even in the presence of orbital perturbations. The sensitivity analysis to system uncertainties shows that the guidance is sensitive to noise on the target angular velocity, being the critical disturbance for this type of maneuvers.

The article of record as published may be found at http://doi.org/10.2514/1.G002460 This paper proposes a spacecraft attitude control technique based on the use of center-of-mass shifting. In particular, the position vector of the spacecraft’s center of pressure with respect to the center of mass is modified by shifting masses, which results in a change of the aerodynamic torque vector within the plane perpendicular to the aerodynamic drag. This results in an underactuated control system. To achieve full three-axis stabilization, additional actuators (either a reaction wheel or a set of magnetic torquers) are considered. An adaptive nonlinear attitude regulation control law was designed in order to obtain an ideal control torque based on the Lyapunov method and its stability was proven by LaSalle’s invariance principle. The control torque was then allocated to steer three shifting masses and either a reaction wheel or three magnetic torquers. Numerical simulations are reported, confirming the analytic results. The proposed method decreases the residual oscillation error typically associated with magnetic controlled attitude in the presence of residual aerodynamic torque. Therefore, it might contribute to achieve higher pointing accuracy of small spacecraft in low Earth orbit.

The benefits and uses of drag devices for self-disposal of mid-sized spacecraft (~400 kg) in low Earth orbit are analyzed in this paper. Our analysis suggest that drag devices are well suited for small as well as for mid-sized spacecraft. The suitability and feasibility of drag devices for small spacecraft (

The article of record as published may be found at https://dx.doi.org/10.1016/j.paerosci.2019.100552 Hardware-in-the-loop simulation and test has been an essential part in the development of spacecraft formation flight, rendezvous, capture/docking, and spacecraft robotics systems since the Gemini project. The need to recreate the kinematics and/or dynamics of spacecraft motion on the ground has led to numerous simulators and testbeds at academic institutions, government facilities, and industry laboratories. The simulation facilities range from small air-bearing tables at universities to building-sized simulators for full-sized systems tests at NASA centers. For the first time to the best knowledge of the authors, the paper presents a systematic classification of spacecraft maneuver simulators into kinematic, dynamic, hybrid, and kino-dynamic systems and discusses the design alternatives, trade-offs and limitations to be considered for each type of simulator. The paper also lists current and past systems reported in literature, along with their primary characteristics. It is thus complementary to existing literature focused on air-bearing spacecraft attitude simulators and air-bearing maneuver simulators. The goal of the paper is to inform designers of new facilities of the current state of the art and the existing experience in the field, and to inform spacecraft developers of existing testbeds in order for them to be able to plan test and experiment campaigns.

Rendezvous and Proximity Operations (RPOs) of two autonomous spacecraft have been extensively studied in the past years, taking into account both the strict requirements in terms of spacecraft dynamics variations and the limitations due to the actuation system. In this paper, two different Model Predictive Control (MPC) schemes have been considered to control the spacecraft during the final phase of the rendezvous maneuver in order to ensure mission constraints satisfaction for any modeled disturbance affecting the system. Classical MPC suitably balances stability and computational effort required for online implementation whereas Tube-based Robust MPC represents an appealing strategy to handle disturbances while ensuring robustness. For the robust scheme, the computational effort reduction is ensured adopting a time-varying control law where the feedback gain matrix is evaluated offline, applying a Linear Matrix Inequality approach to the state feedback stabilization criterion. An extensive verification campaign for the performance evaluation and comparison in terms of constraint satisfaction, fuel consumption and computational cost, i.e. CPU time, has been carried out on both a three degrees-of-freedom (DoF) orbital simulator and an experimental testbed composed by two Floating Spacecraft Simulators reproducing a quasi-frictionless motion. Main conclusions are drawn with respect to the mission expectations.

Advanced missions of satellites are increasingly demanding more accurate and robust attitude maneuvering capabilities. However, it is difficult to achieve especially for small satellites due to limited hardware resources of sensors, actuators, and processors. In this paper, to achieve the desired performance, a multi-algorithmic hybrid attitude determination and control system (ADCS) that utilizes a family of control and estimation algorithms is developed and implemented in numerical simulations and experiments for a small satellite. The hybrid automaton framework of the ADCS is designed to accomplish the desired performance with the limited hardware capability by switching the control and estimation algorithms effectively for given situations in space. The performance of the hybrid ADCS is evaluated through numerical and hardware-in-the-loop simulations that are based on a three-dimensional air-bearing testbed, CubeSat Three-Axis Simulator (CubeTAS). Simulation and experimental results demonstrate the effectiveness of the multi-algorithmic hybrid ADCS. The significance of this paper is in demonstrating that the hybrid automaton framework can be an effective approach to handle operational situations in space. It also provides a design reference for a small satellite ADCS.

The article of record as published may be found at http://dx.doi.org/10.2514/1.G002585 This work addresses the problem of experimentally reproducing the orbital relative motion on a planar floating spacecraft simulator testbed. Floating spacecraft simulators are characterized by double-integrator dynamics on their three degrees of freedom. In this paper, the Clohessy–Wiltshire planar dynamics is scaled down, and it is emulated using an autonomous floating vehicle actuated using compressed-air thrusters. The dynamics scaling criteria are determined through the use of the Pi theorem; subsequently, the problem of accurate actuation of the equivalent transport acceleration and Coriolis acceleration is solved. Three different thrust modulation strategies (namely, pulse-width modulation, delta sigma modulation, and hybrid pulse-width delta sigma modulation) have been used to achieve an accurate conversion of the requested continuous-thrust time histories into sequences of actuated fixed-thrust pulses. The performances of the resulting system are evaluated through a set of simulations by comparing the nominal spacecraft trajectories with the correspondent equivalent floating simulator trajectories. Finally, a set of experimental results is presented.

The article of record as published may be found at http://dx.doi.org/10.2514/1.A33769 Ground-based testbeds are critical to develop and test different elements of spacecraft guidance, navigation, and control subsystems. This paper provides an in-detail description of a state-of-the-art air-bearing testbed used to develop guidance, navigation, and control methods for close-proximity operations. Test vehicles, representing spacecraft, float via air bearings over a horizontally leveled granite monolith and move with two translational degrees of freedom and one rotational degree of freedom under the effect of thrusters and reaction wheel actuators. This setup achieves a quasi-frictionless and low residual acceleration dynamic environment. The testbed experimental setup as well as the vehicle hardware and software architectures are discussed in detail. Characterization of different testbed elements is provided. Finally, a test campaign is used to showcase its capabilities and to illustrate the testbed operations.

Spacecraft three-axis simulators provide frictionless and, ideally, torque-free hardware simulation platforms that are crucial for validating spacecraft attitude determination and control strategies. To reduce the gravitational torque, the distance between the simulator center of mass and the center of rotation needs to be minimized. This work proposes an automatic mass balancing system for spacecraft simulators, which uses only the three sliding masses during the balancing process, without need of further actuators. The proposed method is based on an adaptive nonlinear feedback control that aims to move, in real time, the center of mass toward the spacecraft simulator's centerof rotation. The stability of the feedback system and the convergence of the estimated unknown parameter (thedistance between the center of mass and the center of rotation) are analyzed through Lyapunov stability theory. The proposed method is experimentally validated using the CubeSat Three-Axis Simulator at the Spacecraft Robotics Laboratory of the Naval Postgraduate School. © 2013 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

The article of record as published may be found at http://dx.doi.org/10.1007/s12567-017-0155-7 An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear–quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser’s maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a groundbased air-bearing test bed, using spacecraft simulators that float over a granite table.

The performance of an inverse dynamics guidance and control strategy is experimentally evaluated for the planar maneuver of a “chaser” spacecraft docking with a rotating “target.” The experiments were conducted on an air-bearing proximity maneuver testbed. The chaser spacecraft simulator consists of a three-degree-of-freedom autonomous vehicle floating via air pads on a granite table and actuated by thrusters. The target consists of a docking interface mounted on a rotational stage with the rotation axis perpendicular to the plane of motion. Given a preassigned trajectory, the guidance and control strategy computes the required maneuver control forces and torque via an inverse dynamics operation. The recorded data of 150 experimental test runs were analyzed using two-way analysis of variance and post hoc Tukey tests. The metrics were maneuver success, vehicle mass change, maneuver duration, thruster duty cycle, and maneuver work. The results showed that the guidance and control algorithm provided robust p...

This paper proposes a rapid attitude trajectory generation method for satellite reorientation, which is suitable for both rest-to-rest and track-to-track maneuvers. The problem is first formulated and solved using academic software readily used for generating optimal guidance trajectories offline. Then, the problem is reformulated using a Bezier polynomial parametrization of the quaternion trajectory, which naturally satisfies the unit quaternion norm constraint. The parameters of the quaternion trajectory polynomial and of the speed profile are varied to arrive at a quasi-optimal solution that is both feasible and exactly matches the endpoint conditions specified in the problem. The reduction in the number of varied parameters due to the predetermined structure of the trajectory leads to a fast computational speed as well as a solution that satisfies the end constraints at each iteration. The paper includes numerical simulation results obtained for several cases.

The article of record as published may be located at http://dx.doi.org/10.1016/j.actaastro.2009.09.015 A new method is introduced to control and analyze the rotational motion of anaxially symmetric rigid-body spacecraft. In particular, this motion is seen as the combination of the rotation of a virtual sphere with respect to the inertial frame, and the rotation of the body, about its symmetry axis, with respect to this sphere. Two new exact solutions are introduced for the motion of axially symmetric rigid bodies subjected to a constant external torque in the following cases: (1) torque parallel to the angular momentum and (2) torque parallel to the vectorial component of the angular momentum on the plane perpendicular to the symmetry axis. By building upon these results, two rotational maneuvers are proposed for axially symmetric spacecraft: a detumbling maneuver and a nutation canceling maneuver. The two maneuvers are the minimum time maneuvers for spherically constrained maximum torque. These maneuvers are simple and elegant, as they reduce the control of the three degrees-of-freedom nonlinear rotational motion to a single degree-of-freedom linear problem. Furthermore, the complete (both for the dynamics and for the kinematics) and exact analytic solutions are found for the two maneuvers. An extended survey is reported in the introduction of the paper of the few cases where the rotation of a rigid body is fully reduced to an exact analytic solution in closed form.

http://dx.doi.org/10.1016/j.actastro.2008.08.001 A direct method for rapid generation of combined time-propellant near-opotimal trajectories of proximity maneuvers of a chaser spacecraft required to dock a target one, with predetermined thrust history along a master direction, is presented. The predetermined thrust history is generated by applying the Pontryagin maximum principle. The new direct method, already implemented and tested on board real aircraft, is based on three concepts: high-order polynomials as reference functions, preset on-off sequence of a master control, and reduction of the optimization problem to the determination of a small set of parameters. Presetting the master control, the remaining controls act as slaves, guarantying the chaser to move along the desired path. Seeking of the optimum strategy is transformed into a nonlinear programming problem, and then numerically solved hrough an ad hoc algorithm in accelerated time scale. Examples are reported to prove the rapidness of the approach to generate a sub-optimal docking trajectory.

The article of record may be found at http://dx.doi.org/10.1016/j.actaastro.2014.11.041 This paper investigates the application of the inverse dynamics in the virtual domain method to Euler angles, quaternions, and modified Rodrigues parameters for rapid optimal attitude trajectory generation for spacecraft reorientation maneuvers. The impact of the virtual domain and attitude representation is numerically investigated for both minimum time and minimum energy problems. Owing to the nature of the inverse dynamics method, it yields sub-optimal solutions for minimum time problems. Further- more, the virtual domain improves the optimality of the solution, but at the cost of more computational time. The attitude representation also affects solution quality and compu- tational speed. For minimum energy problems, the optimal solution can be obtained without the virtual domain with any considered attitude representation.

The dynamics equations of a spacecraft consisting of two bodies mutually rotating around a common gimbal axis are derived by the use of the Newton‐Euler approach. One of the bodies contains a cluster of single-gimbal variable-speed control moment gyros. The equations include all of the inertia terms and are written in a general form, valid for any cluster configurations and any number of actuators in the cluster. A guidance algorithm has been developed under the assumtion that the two bodies of the spacecraft are optically coupled telescopes that relay laser signals. The reference maneuver is found by the imposition of the connectivity between the source and the target on the ground. A new nonlinear control law is designed for the spacecraft attitude and joint rotation by the use of Lyapunov’s direct method. An acceleration-based steering law is used for the variable-speed control moment gyros. The analytical results are tested by numerical simulations conducted for both regulation and tracking cases. I. Introduction T HE dynamics and control of multibody spacecraft are a challenging problem because of the complexity of the dynamics equations and the time-varying inertia of the system. The problem becomes even more interesting when gimbaled momentum exchange devices are considered to control attitude. Control moment gyros (CMGs) are unique among attitude control actuators because they can provide high output torque without using expendable fuels and can provide a level of precision and continuity unachievable with jet thrusters. Indeed, CMGs have been used for decades on space stations and on military spacecraft when fast slewing capability and high pointing accuracy were required. The use of CMGs is also currently under consideration for several future civil spacecraft requiring high agility (as in Refs. 1 and 2). A main drawback to the use of CMGs is the presence of singular gimbal-angle configurations at which the CMG cluster is unable to produce the required torque, or, in some cases, any torque at all. 3−5 Many previous studies have considered the problem of the dynamics and control of spacecraft by the use of single-gimbal CMGs.

This paper presents the results of both numerical and experimental studies on the guidance, dynamics and control of the Bifocal Relay Mirror spacecraft. This proposed spacecraft consists of two large gimbaled telescopes, that are optically coupled and used to redirect a laser beam from a ground-based source to a distant point. The attitude control system consists of reaction wheels, star trackers and gyros. The optical control system consists of fast steering mirrors and optical tracker sensors. The very tight pointing and jitter requirements, together with the multi-body nature of the spacecraft, make the control of the system very challenging. Numerical simulations have been performed on a complete analytical model of the system dynamics, in order to compare two different control approaches proposed for the attitude and tracking/pointing. Moreover experiments were carried out on a spacecraft simulator test-bed, modelling the transmitter portion of the Bifocal Relay Mirror spacecraft. The main tasks of the presented experiments were: first, to validate the attitude stabilization control together with the target acquisition-tracking-pointing and laser jitter rejection; second, to prove the effectiveness of the test-bed itself as an important tool to be used in the following researches.

Minimizingvibrationsofamaneuverede exiblemanipulatorisachallengingtask.Resultsarepresentedofaseries of experimental tests carried out on the Space Robot Simulator assembly, which has been set up at the Spacecraft Research and Design Center of the Naval Postgraduate School. The manipulator is planar with two rotational degrees of freedom and two links, of which either one or both can be e exible in bending. The manipulator e oats on air cushions on a granite table. The task of the experiments was to test the effectiveness of the command input shaping technique on the near-minimum-time tracking control of a e exible manipulator. A recently introduced sliding mode control method with smooth joint friction compensation was applied to track either an open- or a closed-reference end-effector path, mapped into joint space. This controller guarantees a very precise tracking of thejoint referencemotion, despite thehigh and poorlymodeled jointfriction torques. Satisfying results,intermsof vibration reduction, have been obtained on point-to-point trajectories and on closed-path trajectories. The results are compared with those obtained with a different command shaping technique.

The article of record as published may be located at http://dx.doi.org/10.1016/j.actaastro.2014.01.002 In this work we study the problem of minimum energy docking maneuvers between two Floating Spacecraft Simulators. The maneuvers are planar and conducted autonomously in a cooperative mode. The proposed guidance strategy is based on the direct method known as Inverse Dynamics in the Virtual Domain, and the nonlinear programming solver known as Sequential Gradient-Restoration Algorithm. The combination of these methods allows for the quick prototyping of near-optimal trajectories, and results in an implementable tool for real-time closed-loop maneuvering. The experimental results included in this paper were obtained by exploiting the recently upgraded Floating Spacecraft-Simulator Testbed of the Spacecraft Robotics Laboratory at the Naval Postgraduate School. A direct performances comparison, in terms of maneuver energy and propellant mass, between the proposed guidance strategy and a LQR controller, demonstrates the effectiveness of the method.

The article of record may be found at http://dx.doi.org/10.1016/j.actaastro.2014.07.038 The problem of spinning-up an axially symmetric spacecraft subjected to an external torque constant in magnitude and parallel to the symmetry axis is considered. The existing exact analytic solution for an axially symmetric body is applied for the first time to this problem. The proposed solution is valid for any initial conditions of attitude and angular velocity and for any length of time and rotation amplitude. Furthermore, the proposed solution can be numerically evaluated up to any desired level of accuracy. Numerical experiments and comparison with an existing approximated solution and with the integration of the equations of motion are reported in the paper. Finally, a new approximated solution obtained from the exact one is introduced in this paper.

The article of record may be found at http://dx.doi.org/10.2514/1.35328 A software interface between the MATLAB/Simulink environment and the Satellite Tool Kit Environment is introduced. This research is based on the need for validating model performance and visualizing simultaneous multiple-spacecraft proximity maneuvers for emerging missions. It is common for spacecraft systems to be modeled with MATLAB and Simulink. Furthermore, the software package Satellite Tool Kit is often used for animating and evaluating spacecraft maneuvers. In this research, a MATLAB/Satellite Tool Kit interface was developed to propagate six-degree-of-freedom spacecraft models, compared against Satellite-Tool-Kit-generated ephemeris, and animated for analysis. MATLAB script with necessary formatting is used for Satellite Tool Kit initialization and animation. The MATLAB/Satellite Tool Kit simulation interface allows variations in number, shape, and dimensions of spacecraft. Additionally, numerous model and simulation parameters can be selected and synchronized between MATLAB and Satellite Tool Kit. Furthermore, either predetermined, or randomly distributed, initial spacecraft positions and orientations are permitted by the interface. The paper gives enough details to allow the interested readers to adapt to their needs and further develop the proposed software interface.

The article of record as published may be located at http://dx.doi.org/10.2514/1.47645 This paper formulates and solves the problem of minimum-time and minimum-energy optimal trajectories of rendezvous of a powered chaser and a passive tumbling target, in a circular orbit. Both translational and rotational dynamics are considered. In particular, ending conditions are imposed of matching the positions and velocities of two points of interest onboard the vehicles. A collision-avoidance condition is imposed as well. The optimal control problems are analytically formulated through the use of the Pontryagin minimum principle. The problems are then solved numerically, by using a direct collocation method based on the Gauss pseudospectral approach. Finally, the obtained solutions are verified through the minimum principle, solved by a shooting method. The simulation results show that the pseudospectral solver provides solutions very close to the optimal ones, except in the case of presence of singular arcs when it may not provide a feasible solution. The computational time needed by the pseudospectral solver is a small fraction of the one needed by the indirect approach, but it is still considerably too large to allow for its use in real-time onboard guidance. The authors thank James Riker, Chief Scientist of the U.S. Air Force Research Laboratory (AFRL) Space Vehicles Directorate, for his support of this project. The authors would also like to thank AFRL Space Vehicles Program managers William K. Schum and Lawrence Robbie Robertson.

http://dx.doi.org/10.1016/j.actaastro.2010.08.012 This work introduces a novel control algorithm for close proximity multiple spacecraft autonomous maneuvers, based on hybrid linear quadratic regulator/artificial potential function (LQR/APF), for applications including autonomous docking, on-orbit assembly and spacecraft servicing. Both theoretical developments and experimental validation of the proposed approach are presented. Fuel consumption is sub-optimized in real-time through re-computation of the LQR at each sample time, while performing collision avoidance through the APF and a high level decisional logic. The underlying LQR/APF controller is integrated with a customized wall-following technique and a decision logic, overcoming problems such as local minima. The algorithm is experimentally tested on a four spacecraft simulators test bed at the Spacecraft Robotics Laboratory of the NAval Postgraduate School. The metrics to evaluate the control algorithm are: autonomy of the system in making decisions, successful completion of the maneuver, required time, and propellant consumption.

This work introduces theoretical developments and experimental verification for Guidance, Navigation, and Control of autonomous multiple spacecraft assembly. We here address the in-plane orbital assembly case, where two translational and one rotational degrees of freedom are considered. Each spacecraft involved in the assembly is both chaser and target at the same time. The guidance and control strategies are LQR-based, designed to take into account the evolving shape and mass properties of the assembling spacecraft. Each spacecraft runs symmetric algorithms. The relative navigation is based on augmenting the target's state vector by introducing, as extra state components, the target's control inputs. By using the proposed navigation method, a chaser spacecraft can estimate the relative position, the attitude and the control inputs of a target spacecraft, flying in its proximity. The proposed approaches are successfully validated via hardware-in-the-loop experimentation, using four autonomous three-degree-of-freedom robotic spacecraft simulators, floating on a flat floor.

The traditional spacecraft system is a monolithic structure with a single mission focused design and lengthy production and qualification schedules coupled with enormous cost. Additionally, there rarely, if ever, is any designed preventive maintenance plan or re-fueling capability. There has been much research in recent years into alternative options. One alternative option involves autonomous on-orbit servicing of current or future monolithic spacecraft systems. The U.S. Department of Defense (DoD) embarked on a highly successful venture to prove out such a concept with the Defense Advanced Research Projects Agency’s (DARPA’s) Orbital Express program. Orbital Express demonstrated all of the enabling technologies required for autonomous on-orbit servicing to include refueling, component transfer, autonomous satellite grappling and berthing, rendezvous, inspection, proximity operations, docking and undocking, and autonomous fault recognition and anomaly handling (Kennedy, 2008). Another potential option involves a paradigm shift from the monolithic spacecraft system to one involving multiple interacting spacecraft that can autonomously assemble and reconfigure. Numerous benefits are associated with autonomous spacecraft assemblies, ranging from a removal of significant intra-modular reliance that provides for parallel design, fabrication, assembly and validation processes to the inherent smaller nature of fractionated systems which allows for each module to be placed into orbit separately on more affordable launch platforms (Mathieu, 2005). With respect specifically to the validation process, the significantly reduced dimensions and mass of aggregated spacecraft when compared to the traditional monolithic spacecraft allow for not only component but even full-scale on-the-ground Hardware-In-the-Loop (HIL) experimentation. Likewise, much of the HIL experimentation required for on-orbit servicing of traditional spacecraft systems can also be accomplished in ground-based laboratories (Creamer, 2007). This type of HIL experimentation complements analytical methods and numerical simulations by providing a low-risk, relatively low-cost and potentially highreturn method for validating the technology, navigation techniques and control approaches associated with spacecraft systems. Several approaches exist for the actual HIL testing in a laboratory environment with respect to spacecraft guidance, navigation and control. One 11

The article of record as published may be located at http://dx.doi.org/10.2514/1.47296 This paper introduces a method for spacecraft rotation and translation control by on–off thrusters with guaranteed Lyapunov-stable tracking of linear dynamic models. In particular, the proposed control method switches on, at each time step, only those thrusters needed to maintain stability. Furthermore, the strategy allocates the configuration so that the minimum number of actuators is used. One of the benefits of the proposed method is that it substitutes both the thruster mapping and the pulse modulation algorithms typically used for real-time allocation of the firing thrusters and for determining the duration of the firing. The proposed approach reduces the computational burden of the onboard computer versus the use of classical thruster mapping algorithms, which typically involve iterative matrix operations. The paper presents analytical demonstrations, numerical simulations on a six-degree-offreedom spacecraft, and experimental tests on a hardware-in-the-loop three-degree-of-freedom spacecraft simulator floating over air pads on a flat floor. The method proves to be effective and easy to implement in real time. This research was performed while R. Bevilacqua was holding a National Research Council Research Associateship Award at the Spacecraft Robotics Laboratory of the Naval Postgraduate School.

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = acceleration due to the control effort Do = obstacle region of influence da = goal acceleration decay constant dg = goal exponential decay constant do = stopping distance constant JLQR = linear quadratic regulator cost function KLQR = linear quadratic regulator state feedback gain ka = acceleration shaping parameter kd = docking safety parameter kg = velocity shaping function ko = obstacle function ks = safety function kv = velocity shaping parameter Lo = obstacle exterior surface N = linear quadratic regulator gain matrix Q = linear quadratic regulator state gain matrix R = linear quadratic regulator control effort gain matrix r = Euclidean norm distance or relative range r = relative distance vector rc = position vector of the chaser spacecraft rg = position vector of the chaser spacecraft from the goal rinit = initial distance of the chaser spacecraft from the goal rm = maximum allowable distance of the chaser spacecraft from the goal ro = position vector of the chaser spacecraft from the obstacle rt = position vector of the target spacecraft with respect to the Earth S = solution of the Riccati equation u = control effort vector V = potential function Vg = goal potential function Vo = obstacle potential function vm = maximum relative velocity vo = desired velocity of chaser spacecraft toward an obstacle vobs = velocity of chaser spacecraft toward an obstacle x = state vector x, y, z = positions, or states, along the Cartesian axis Q = linear quadratic regulator state performance gain R = linear quadratic regulator control effort gain t = time increment = standard deviation for the obstacle’s region of influence ! = orbital angular velocity

AIAA Guidance, Navigation, and Control Conference, 10 - 13 August 2009, Chicago, Illinois, AIAA 2009-6290 This work introduces a novel approach and its experimental verification for propellant sub-optimal multiple spacecraft assembly via a Linear Quadratic Regulator (LQR). The attitude dynamics of the spacecraft are linearized at each time step, about the current state vector, and the relative dynamics between two spacecraft are assumed as a double integrator. This allows for implementation in real-time of a LQR that computes the optimal gain matrix depending on the current phase of the spacecraft’s mission. As a result, both the attitude and position are sub-optimally controlled. The presented logic compensates for the structural evolution related to an incremental assembly by updating the system’s dynamics matrices. The actuators’ reallocation and command of the assembled structure is dealt with through inter-robot wireless ad-hoc communication. Each spacecraft runs symmetric algorithms, differing only in the number of docking ports that each possesses for the mission, which are related to the number of assembling spacecraft and the final structure’s desired shape. Once the spacecraft are assembled, one acts as master by performing the required navigation and control of the new structure through real-time wireless commanding of the other spacecraft’s actuators. The improved third generation (3G-i) of spacecraft simulators developed at the Spacecraft Robotics Laboratory SRL of the Naval Postgraduate School (NPS) is presented to demonstrate experimental verification of the proposed methodology. Features of the (3G-i) robots include an unique customized construction of rapid prototyped thermoplastic (polycarbonate) that incorporates a lightweight modular design with a small footprint, thus maximizing the entire surface of the SRL robotic testbed. This research was partially supported by DARPA. This research was performed while Dr. Bevilacqua was holding a National Research Council Research Associateship Award at the Spacecraft Robotics Laboratory of the US Naval Postgraduate School.

The article of record as published may be located at http://dx.doi.org/10.2514/1.40734 A wireless ad hoc network is introduced that enables inter-robot communication and shared computation among multiple robots with PC/104-based single board computers running the real-time application interface patched Linux operating system. Through the use of IEEE 802.11 ad hoc technology and User Datagram Protocol, each robot is able to exchange data without the need of a centralized router or wireless access point. The paper presents three key aspects of this novel architecture to include: 1) procedures to install the real-time application interface patched operating system and wireless ad hoc communication protocol on a multiple robot system; 2) development of a Simulink® library to enable intercommunication among robots and provide the requisite software-hardware interfaces for the onboard sensor suite and actuator packages; 3) methods to rapidly generate and deploy real-time executables using Mathwork’s Real-TimeWorkshop™ to enable an autonomous robotic system. Experimental test results from the Spacecraft Robotics Laboratory at the Naval Postgraduate School are presented which demonstrate negligible network latencies and real-time distributed computing capability on theAutonomous Spacecraft Assembly Test Bed.A complete manual is also included to replicate the network and software infrastructures described in this work. Also, the developed Simulink® library can be requested from the authors. This research was partially supported by Defense Advanced Research Projects Agency (DARPA), and was performed while R. Bevilacquawas holding a National Research Council Research Associateship Award at the Spacecraft Robotics Laboratory of the US Naval Postgraduate School.

The article of record may be found at http://dx.doi.org/10.1016/j.actaastro.2008.11.001 This paper deals with the design, development and experimentation of a new test stand for the accurate and precise charac- terization of small cold-gas nozzles having thrust of the order of 0.1N and specific impulse of the order of 10s. As part of the presented research, a new cold-gas supersonic nozzle was designed and developed based on the quasi one-dimensional theory. The test stand is based on the ballistic-pendulum principle: in particular, it consists of a suspended gondola hosting the propul- sion system and the sample nozzle. The propulsion system consists of an air tank, pressure regulator, solenoid valve, battery and digital timer to command the valve. The gondola is equipped with a fin, immersed in water, to provide torsional and lat- eral oscillation damping. A laser sensor measures the displacement of the gondola. The developed test stand was calibrated by using a mathematical model based on the inelastic collision theory. The obtained accuracy was of ∼1%. Sample experimental results are reported regarding the comparison of the new supersonic nozzle with a commercially available subsonic nozzle. The obtained measurements of thrust, mass flow rate and specific impulse are precise to a level of ∼3%. The broad goal of the presented research was to contribute to an upgraded design of a spacecraft simulator used for laboratory validation of guidance, navigation and control algorithms for autonomous docking manoeuvres.

A multiple spacecraft close-proximity control algorithm was implemented and tested with the Synchronized Position Hold Engage and Reorient Experimental Satellites (SPHERES) facility onboard the International Space Station (ISS). During flight testing, a chaser satellite successfully approached a virtual target satellite, while avoiding collision with a virtual obstacle satellite. This research contributes to the control of multiple spacecraft for emerging missions, which may require simultaneous gathering, rendezvous, and docking. The unique control algorithm was developed at NPS and integrated onto the MIT SPHERES facility. The control algorithm implemented combines the efficiency of the Linear Quadratic Regulator (LQR), and the robust collision avoidance capability of the Artificial Potential Function method (APF). The LQR control effort serves as the attractive force toward goal positions, while the APF-based repulsive functions provide collision avoidance for both fixed and moving obstacles. The amalgamation of these two control methods into a multiple spacecraft close-proximity control algorithm yielded promising results as demonstrated by simulations performed at NPS. Comprehensive simulation evaluation enabled implementation and testing of the spacecraft control algorithm on the SPHERES facility at MIT. Finally, successful ground testing enabled execution of flight testing onboard the ISS. The NPS’s Spacecraft Robotics Laboratory (SRL) and MIT’s Space Systems Laboratory (SSL) simulations, the MIT’s SSL SPHERES ground testing, and the SPHERES flight testing results are all presented in this paper.

In this work, the residual atmospheric drag is exploited to perform rendezvous maneuvers among multiple spacecraft in low Earth orbits. These maneuvers are required, for instance, for autonomous on-orbit assembly. By varying the level of aerodynamic drag of each spacecraft, relative differential accelerations are generated among the spacecraft of the group and therefore their relative orbits are controlled. Each of the spacecraft is assumed to include a drag plate, which can be actively opened or closed, to vary the atmospheric drag. The recently developed Schweighart–Sedwick model is used to describe the relative dynamics of different spacecraft with respect to a circular orbit with the inclusion of J2 effects. Furthermore, the natural relative dynamics of each chaser with respect to the target is decoupled into a secular motion and a periodic oscillation. In particular, the following two-phase control method is proposed. First, the secular motion of each chaser is controlled via differential drag in order for the spacecraft to sequentially move from an arbitrary initial condition to a closed stable relative orbit around the target spacecraft. After the relative orbit stabilization, a relative eccentricity control is applied to each spacecraft to zero-out the semi-axis of the relative orbit around the target and to achieve the rendezvous condition. The control algorithm considers mutual constraints among the values of differential drag that the different spacecraft can experience. Potential collisions are avoided by changing the maneuvering initial time. The main advantage of the proposed technique is that it enables a fleet of spacecraft to rendezvous without propellant expenditure. Furthermore, no numerical optimization is needed, because the control policy is based on closed-form analytical solutions. The proposed technique was validated via numerical simulations. This research was partially supported by the Defense Advanced Research Projects Agency. This research was performed while R. Bevilacqua was holding a National Research Council Research Associateship Award at the Spacecraft Robotics Laboratory of the Naval Postgraduate School.

A novel hardware-in-the-loop spacecraft simulator is introduced for the laboratory validation of guidance, navigation and control algorithms. This three-degrees-of-freedom robotic vehicle uses the principle of air-floating along a flat floor in order to reproduce in two dimensions the frictionless and weightlessness conditions of the orbital flight. For the first time in its class, to the authors' knowledge, the new spacecraft simulator uses miniature control moment gyroscopes for the attitude control and rotating thrusters for both attitude and translational control. A pseudo-GPS, a LIDAR and a fiber optic gyroscope are used as navigation sensors. The paper presents in details the design of the robotic vehicle and the results of preliminary experiments.

This paper presents the current status of the research effort on autonomous proximity-navigation and spacecraft docking, which is on-going at the Spacecraft Servicing and Robotics Laboratory of the Naval Postgraduate School. An experimental test-bed has been designed and is in the advance integration phase, which can be used for validating analytical and numerical results regarding dynamic models and control laws. The test-bed consists of two spacecraft models floating via air-pads on a flat surface to simulate in two dimensions the weightlessness of the orbital flight. A custom-developed vision navigation sensor is used to determine the relative position and orientation of the two spacecraft. This paper presents an overall description of the test-bed and reports the preliminary experimental results of autonomous navigation of the chaser-spacecraft model in the proximity of the target spacecraft

This paper introduces the preliminary development of a test -bed related to the research project named Autonomous Multi -agent Physically Interacting Spacecraft System (AMPHIS ) which is ongoing at the Spacecraft Robotics Laboratory. A new laboratory test bed i s under development which will enable hardware -in -the -loop simulation of autonomous proximity operations of a cluster of small spacecraft . The test -bed, which is an evolution of a previously developed Autonomous Docking test -bed, consists of three degrees -of -freedom spacecraft simulator s floating via air pads on a flat floo r. In particular, this paper introduces a new spacecraft simulator which is being currently integrated, using on -off thrusters for the t ranslation and a small control -moment -gyro for the rotation. I. Introduction UTONOMOUS on -orbit assembly capability pr esents great potential return for both civilian and military space ap plications of the future. Additionally, this capability poses a follow -up challenge for currently evolving autonomous docking capabilities. Furthermore, the potential demands for on -orbi t assembly expand the arena for research to such topics as sensor systems, data fusion and real -time optimal control. Al though much research conducted during the last decade has focused on t he navigation and control of multi -robotic system assembly for ter restr ial applications, comparably little has concentrated on the problem of on -orbit spacecraft assembly. The current paper presents the status of an on -going research effort on autonomous proximity navigation, guidance and control of a group of unmanned spacecraft. The spacecraft are considered to initially be in close -formation orbital flight and then autonomously maneuver to dock one with respect to the other to create a single system. On -the -ground experimentation is a low -risk , relatively low -cost an d potentially high -return method for validating space craft systems technology, navigation techniques and control approaches, complementing analytical developments and numerical simulations. 1

The article of record may be found at http://dx.doi.org/10.2514/1.22092 A new laboratory test bed is introduced that enables the hardware-in-the-loop simulation of the autonomous approach and docking of a chaser spacecraft to a target spacecraft of similar mass. The test bed consists of a chaser spacecraft and a target spacecraft simulator floating via air pads on a flat floor. The prototype docking interface mechanism of the Defense Advanced Research Projects Agency’s Orbital Express mission is integrated on the spacecraft simulators. Relative navigation of the chaser spacecraft is obtained by fusing the measurements from a single-camera vision sensor and an inertial measurement unit, through Kalman filters. The target is collaborative in the sense that a pattern of three infrared light emitting diodes is mounted on it as reference for the relative navigation. Eight cold-gas on–off thrusters are used for the translation of the chaser vehicle. They are commanded using a nonlinear control algorithm based on Schmitt triggers. Furthermore, a reaction wheel is used for the vehicle rotation with a proportional derivative linear control. Experimental results are presented of both an autonomous proximity maneuver and an autonomous docking of the chaser simulator to the nonfloating target. The presented results validate the proposed estimation and control methods and demonstrate the capability of the test bed.