Christopher D. Hall

Historical Review of Air-Bearing Spacecraft Simulators

An overview of air-bearing spacecraft simulators is provided. Air bearings have been used for satellite attitude determination and control hardware verie cation and software development for nearly 45 years. It is interesting to consider the history of this technology: how early systems were e rst devised and what diverse capabilities current systems provide. First a survey is given of planar systems that give a payload freedom to translate and spin. Then several classes of rotational air bearings are discussed: those which simulate three-axis satellite attitude dynamics. The subsequent section discusses perhaps the most interesting facilities: those that provide both translational and three-dimensional rotational freedom. Thediverse capabilities each styleofair-bearing testbed provides, themany settings they can be found in, and ways to improve facility performance are described.

Decentralized Coordinated Attitude Control Within a Formation of Spacecraft

The problem of controlling the attitude of spacecraft within a formation is investigated. A class of decentralized coordinated attitude control laws using behavior-based control is developed. The decentralized coordinated attitude control laws that comprise the class differ by the coordination architecture used by the spacecraft formation. The choice of behavior weights defines the coordination architecture. A corollary of Barbalat’s Lemma is used to prove that the class of control laws globally asymptotically stabilizes the spacecraft formation. Convergence of the system is shown to be a consequence of the closed-loop equations of motion. Numeric simulation is used to reinforce the analytic results, and to briefly investigate the effect of coordination architecture on performance.

Singular Direction Avoidance Steering for Control-Moment Gyros

A new form of the equations of motion for a spacecraft with Single Gimbal Control Moment Gyros is developed using a momentum approach. This set of four vector equations describing the rotational motion of the system is of order 2N + 7 where N is the number of CMGs. The control input is an N x I column vector of torques applied to the gimbal axes. A modification to the singularity robust Lyapunov control law presented by Oh and Vadali is examined and compared to their control law. Specifically, the attempt to avoid singular gimbal configurations is abandoned in favor of simply avoiding movement in the singular direction. The singular value decomposition is used to compute a pseudoinverse which prevents large gimbal rate commands near or at actual singularities.

Satellite Attitude Control and Power Tracking with Energy/Momentum Wheels

A control law for an integrated power/attitude control system (IPACS) for a satellite is presented. Four or more energy/momentum wheels in an arbitrary noncoplanar cone guration and a set of three thrusters are used to implement the torque inputs. The energy/momentum wheels are used as attitude-control actuators, as well as an energy storage mechanism, providing power to the spacecraft. In that respect, they can replace the currently used heavy chemical batteries. The thrusters are used to implement the torques for large and fast (slew) maneuvers during the attitude-initialization and target-acquisition phases and to implement the momentum management strategies. The energy/momentum wheels are used to provide the reference-tracking torques and the torques for spinningupor down thewheels for storing or releasing kineticenergy. The controller publishedina previous work by the authors is adopted here for the attitude-tracking function of the wheels. Power tracking for charging and discharging the wheels is added to complete the IPACS framework. The torques applied by the energy/momentum wheels are decomposed into two spaces that are orthogonal to each other, with the attitude-control torques and power-tracking torques in each space. This control law can be easily incorporated in an IPACS system onboard a satellite. The possibility of the occurrence of singularities, in which no arbitrary energy proe le can be tracked, is studied for a generic wheel cluster cone guration. A standard momentum management scheme is considered to nullthe total angular momentumof the wheels so as tominimizethe gyroscopic effects and prevent the singularity from occurring. A numerical example for asatellite inalow Earth near-polar orbit is provided totest the proposed IPACS algorithm. The satellite’s boresight axis is required to track a ground station, and the satellite is required to rotate about its boresight axis so that the solar panel axis is perpendicular to the satellite‐sun vector.

Spinup Dynamics of Axial Dual-Spin Spacecraft

We consider spinup dynamics of axial dual-spin spacecraft composed of two rigid bodies: an asymmetric platform and an axisymmetric rotor parallel to a principal axis of the platform. The system is free of external torques, and spinup of the rotor is effected by a small constant internal axial torque. The dynamics are described by four first-order differential equations. Conservation of angular momentum and the method of averaging are used to reduce the problem to a single first-order differential equation which is studied numerically. This reduction has a geometric counterpart that we use to simplify the investigation of spinup dynamics. In particular, a resonance condition due to platform asymmetry and associated with an instantaneous separatrix crossing is clearly identified using our approach.

Controllability Issues in Nonlinear State-Dependent Riccati Equation Control

Inthelastfewyears,algorithmsusingstate-dependentRiccatiequations (SDREs)havebeenproposedforsolving nonlinear control problems. Under state feedback, pointwise solutions of an SDRE must be obtained along the system trajectory. To ensure the control is well dee ned, global controllability and observability of state-dependent system factorizations are commonly assumed. Here connections between controllability of the state-dependent factorizations and truesystem controllability are rigorously established. Itisshown thata localequivalencealways holdsfortheclassofsystemsconsidered,andspecialcasesthatimplyglobalequivalencearealsogiven.Additionally, a notion of nonlinear stabilizability is introduced, which is a necessary condition for global closed-loop stability. The theory is illustrated by application to a e ve-state nonlinear model of a dual-spin spacecraft.

Spinup dynamics of gyrostats

Attention is given to the spinup dynamics of gyrostats containing a single axisymmetric rotor. Spinup of the rotor is due to a small constant torque applied by a motor on the platform. The dynamics are described by four firstorder differential equations, which are put into noncanonical Hamiltonian form. Using conservation of angular momentum and the method of averaging, the equations of motion are reduced to a single scalar first-order equation for the slow evolution of the Hamiltonian. This reduction is formally valid for small spinup torques and in regions of phase space where the unperturbed motion is periodic. The unperturbed separatrices are therefore regions where averaging fails to describe the motion adequately and are also indicative of dramatic changes in the attitude dynamics. Exact solutions to the averaged equation are used to justify further the projection of solutions of the four-dimensional system onto the plane of the slow states. The reduced two-dimensional slow state space is used to construct a single planar diagram that is useful for portraying spinup dynamics.

Necessary conditions for circularly-restricted static coulomb formations

A noncanonical Hamiltonian formulation of the Coulomb formation dynamics is used to develop necessary conditions for static Coulomb formations with constant charges. With a static or frozen formation the satellites perform non-Keplerian orbits and maintain constant relative position vectors. As seen by an observer following the center of mass motion, the spacecraft formation would appear to behave equivalently to a rigid body in orbit. Previous research has demonstrated the existence of such static Coulomb formations analytically by employing symmetry simplifying assumptions with linearized relative motion dynamics, or by using numerical genetic search algorithms. These static solutions are used as reference geometries and charges for feedback law developments. This paper presents nonlinear static formation conditions for the circularly restricted problem. Hamiltonian formulations have been used to study equilibrium conditions of rigid bodies in orbit. Analogous techniques are employed to study necessary conditions to achieve a static Coulomb formation. Analytical results using the full and truncated formation gravity potential function are presented. Numerical results illustrate convergence performance improvements of an evolutionary search algorithm where the presented necessary conditions are enforced.

Survey of Technology Developments in Flywheel Attitude Control and Energy Storage Systems

Advances in microprocessors and composite materials in the past decade, along with limitations of chemical batteries for U.S. Air Force mission concepts, have caused a renewed interest in flywheel energy storage systems for space applications. This interest has also been driven in the past by the promise of using flywheel systems for energy storage and as attitude control actuators. The primary issues are power efficiency, mass and size, and long-term stability. Flywheels as one-to-one replacements for spacecraft batteries are competitive for only a few special missions. When flywheels replace components in two major bus subsystems, the potential mass and volume benefits are attractive. This especially benefits future small satellite missions that seek agile slewing with high peak power. The objective of this paper is to describe the progression of the flywheel technology state of the art for combined energy storage and attitude control systems in space applications and the current energy storage and attitude control systems efforts.

Control of a Rotating Variable-Length Tethered System

Techniques are developed and illustrated to control the motion of a tethered satellite system (TSS) comprising n point masses and interconnected arbitrarily by m idealized tethers. In particular, the control problem of a triangular and symmetrical TSS with n =3 point masses and m =3 tethers is discussed. The equations of motion are derived by the use of Lagrange’s equations. Several mission scenarios for a proposed NASA mission that consider the operation of an infrared telescope are introduced and asymptotic tracking laws based on input-state feedback linearization are developed. The effects of smoothness and nonsmoothness of desired mission trajectories on control performance are discussed. It is shown that required thrust levels can be significantly decreased by the use of additional tether length control to keep the TSS in a state corresponding to an instantaneous relative equilibrium at any point in time during the mission. In the final section, a mathematical model is proposed for the total required control impulse to facilitate a trade study that discusses the effects of the individual system parameters on the control input.