Riccardo Bevilacqua

Rendezvous Maneuvers of Multiple Spacecraft Using Differential Drag Under J2 Perturbation

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.

Lyapunov-Based Thrusters' Selection for Spacecraft Control: Analysis and Experimentation

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-of-freedom 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.

Special Inclinations Allowing Minimal Drift Orbits for Formation Flying Satellites

The possibility of obtaining a natural periodic relative motion of formation flying Earth satellites is investigated both numerically and analytically. The numerical algorithm is based on a genetic strategy, refined by means of nonlinear programming, that rewards periodic relative trajectories. First, we test our algorithm using a point mass gravitational model. In this case the period matching between the considered orbits is a necessary and sufficient condition to obtain invariant relative trajectories. Then, the J2 perturbed case is considered. For this case, the conditions to obtain an invariant relative motion are known only in approximated closed forms which guarantee a minimalorbitdrift,notamotionperiodicity.Usingtheproposednumericalapproach,weimprovedthoseresultsand foundtwocouples ofinclinations (63.4and116.6deg,the criticalinclinations, and49and131deg,twonew“special” inclinations) that seemed to be favored by the dynamic system for obtaining periodic relative motion at small eccentricities.

Fuel-Optimal Spacecraft Rendezvous with Hybrid On-Off Continuous and Impulsive Thrust

J = cost function N = number of impulses NLT = number of low-thrust-independent thrusters p = primer-vector magnitude p = primer vector pm = primer-vector absolute maximum r = relative position vector rj = space collocation of the jth impulse tf = final time tint = intermediate time tj = time instant of the jth impulse application tm = midcourse time corresponding to the primer absolute maximum t0 = initial time u = thrust unit vector V = relative velocity vector x, y, z = coordinates in the local vertical, local horizontal coordinate system Vj = jth impulse vector t tj = Dirac’s delta at time tj # = anomaly on the circular orbit r = position adjoint vector V = velocity adjoint vector = control vector magnitude t = state transition matrix for the Clohessy–Wiltshire equations t = convolution integral matrix for the Clohessy– Wiltshire equations due to optimal unbounded control !LVLH = angular velocity of the local vertical, local horizontal coordinate system

Ad Hoc Wireless Networking and Shared Computation for Autonomous Multirobot Systems

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-Time Workshop™ 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 the Autonomous 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.

Spacecraft Rendezvous by Differential Drag Under Uncertainties

At low Earth orbits, differentials in the drag forces between spacecraft can be used for controlling their relative motion in the orbital plane. Current methods for determining the drag force may result in errors due to inaccuracies in the density models and drag coefficients. In this work, a methodology for relative maneuvering of spacecraft based on differential drag, accounting for uncertainties in the drag model, is proposed. A dynamical model composed of the mean semimajor axis and the argument of latitude is used for describing long-range maneuvers. For this model, a linear quadratic regulator is implemented, accounting for the uncertainties in the drag force. The actuation is the pitch angle of the satellites, considering saturation. The control scheme guarantees asymptotic stability of the system up to a certain magnitude of the state vector, which is determined by the uncertainties. Numerical simulations show that the method exhibits consistent robustness to accomplish the maneuvers, even in the ...

Lyapunov-Based Adaptive Feedback for Spacecraft Planar Relative Maneuvering via Differential Drag

I N 1989, Leonard et al. [1] introduced the concept of using differential drag at low Earth orbits (LEOs) for propellantless inplane spacecraft relative motion control. This method consists of varying the aerodynamic drag experienced by different spacecraft, by opening or closing a set of drag surfaces, or varying the attitude of asymmetrical spacecraft, thus generating differential accelerations between them. Since there is no propellant exhaust and no plume impingement, highly sensitive onboard sensors may operate in a cleaner environment. Moreover, since the relative accelerations generated by the drag forces are small, equipment sensitive to shocks or vibrations may benefit from the use of differential drag, assuming that drag control devices operate without exciting vibration modes of the spacecraft. The main limitation of using differential drag for relative motion control is that one must operate at a relatively low LEO. In this regime, differential drag forces can be made large enough to achieve effective control. However, this increased drag force results in faster orbit decay, and thus a more limited mission life. However, these formation-flying orbits are of interest since they can be used for communications, astronomical, atmospheric, and Earth observation applications [2,3]. In this work, a chaser and a target spacecraft are considered. The reference frame commonly used for spacecraft relative motion is the local-vertical/local-horizontal (LVLH) reference frame, centered at the target spacecraft, where x points from Earth to the target spacecraft, y points along the track of the target spacecraft, and z completes the right-handed frame. The state of the system consists of the position and velocity, in the LVLH frame, of the chaser spacecraft relative to the target spacecraft. Atmospheric differential drag is projected on the alongtrack direction and can provide effective control only in the orbital plane (x and y). The control law is based on the assumption that the control is either positive maximum ( 1), which implies chaser maximizing (opening) its drag surface and target minimizing (closing) it; negative maximum (−1), which implies chaser maximizing (opening) its drag surface and target minimizing (closing) it; or zero (0), which implies same surface on chaser and target: that is, no differential acceleration, as previously done in [4–6]. In previous work [7], a Lyapunov controller was developed for maneuvering using differential drag. An analytical expression for the magnitude of the differential drag acceleration that ensures stability was also found. Partial derivatives of this critical value in terms ofQ (Lyapunov equation matrix) and Ad (reference linear dynamics matrix) were presented in [8,9] for the case in which the controller acts as a regulator. Furthermore, an adaptation that chooses an appropriate positive definite matrix P in a quadratic Lyapunov function, by modifying the Q and Ad matrices based on the partial derivatives, was developed. Nonetheless, the adaptation was limited to regulation maneuvers, since the partial derivatives were developed for that case only. The foremost contribution of this work consists of the complete analytical expressions for the mentioned partial derivatives for the general case in which the spacecraft are tracking a linear reference model, which can also be used for tracking a guidance trajectory or a desired final state (regulation). Simulations validate the adaptive Lyapunov controller for a fly-around maneuver followed by a longterm formation-keeping period and a rendezvous maneuver via the Systems Tool Kit (STK®). An assessment of the performances of the designed adaptive Lyapunov controller and a comparison versus a nonadaptive Lyapunov controller [7] are shown.

Guidance Navigation and Control for Autonomous Multiple Spacecraft Assembly: Analysis and Experimentation

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 targets state vector by introducing, as extra state components, the targets 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.

Operational Capabilities of a Six Degrees of Freedom Spacecraft Simulator

This paper presents a novel six degrees of freedom ground-based experimental testbed, designed for testing new guidance, navigation, and control algorithms for nano-satellites. The development of innovative guidance, navigation and control methodologies is a necessary step in the advance of autonomous spacecraft. The testbed allows for testing these algorithms in a one-g laboratory environment, increasing system reliability while reducing development costs. The system stands out among the existing experimental platforms because all degrees of freedom of motion are dynamically reproduced. The hardware and software components of the testbed are detailed in the paper, as well as the motion tracking system used to perform its navigation. A Lyapunov-based strategy for closed loop control is used in hardware-in-the loop experiments to successfully demonstrate the system’s capabilities.

Differential Drag-Based Reference Trajectories for Spacecraft Relative Maneuvering Using Density Forecast

Abc = element of matrix Ad to which aDcrit is the most sensitive Ad = stable linear reference state-space matrix As = Schweighart and Sedwick model state-space matrix aDcrit = magnitude of the differential drag acceleration ensuring stability aDrel = magnitude of the differential aerodynamic drag acceleration aPrelx, aPrely = differential accelerations caused by orbital perturbations excluding drag, along x and y directions of the local vertical/local horizontal frame CDC, CDT = chaser and target spacecraft’s drag coefficients e = tracking error vector it = target’s initial orbit inclination J2 = second-order harmonic of Earth gravitational potential field (Earth flattening) lb, ub = lower and upper bounds for the optimization mC, mT = chaser and target spacecraft’s mass Re = Earth mean radius Rt = position vector of the target in relation to the Earth SC, ST = chaser and target spacecraft’s crosswind surface area u = on/off control signal V = Lyapunov function vs = spacecraft velocity vector magnitude with respect to the Earth’s atmosphere xn = state-space vector of the nonlinear system including relative position and velocity between the spacecraft in the local vertical/local horizontal orbital frame xt = reference state-space vector in the local vertical/ local horizontal orbital frame δAop = modifications made to matrix Ad for the optimized adaptation μ = Earth’s gravitational parameter ρ = atmospheric density ω = magnitude of the orbital angular velocity of the target