Frederick A. Leve

Hybrid Steering Logic for Single-Gimbal Control Moment Gyroscopes

The development of a hybrid steering logic that maintains attitude tracking precision while avoiding hyperbolic internal singularities or escaping elliptic singularities inherent to single-gimbal control moment gyroscopes is discussed. The hybrid steering logic enables null motion and limits torque error when approaching a hyperbolic internal singularity, or it adds torque error and limits null motion when approaching an elliptic internal or external singularity. The hybrid-steering-logic algorithm accomplishes these tasks through the definitions of novel singularity metrics that transition continuously from local-gradient to pseudoinverse methods when moving from hyperbolic to elliptic singularities. Analysis and simulations are presented to demonstrate the performance of the hybrid steering logic as compared with the two legacy methods. The development and results are applied to a four-single-gimbal-control-moment-gyroscope pyramid arrangement with a skew angle of θ = 54.74 deg.

Evaluation of Steering Algorithm Optimality for Single-Gimbal Control Moment Gyroscopes

Analytic optimization methods typically used to derive optimal steering algorithms for single-gimbal control moment gyros do not consider the structure of the Jacobian matrix mapping the gimbal rates onto the desired torque within their cost function. Many of the steering algorithms resulting from these optimization methods systematically take first and second derivatives, forming the Jacobian and Hessian matrices to obtain a solution. However, the optimality is usually a local result and cannot be mapped back to its resulting performance. It is shown that the majority of steering algorithms are optimal with respect to one specific cost function previously published and that the design of the weighting matrices within the cost is what distinguishes steering algorithms. The author analytically shows how the blended inverse, Moore-Penrose pseudoinverse, generalized inverse steering law, singularity robust inverse, generalized singularity robust inverse, singular direction avoidance, local-gradient methods, and the hybrid steering logic are derived from the same optimizations but their sense of optimality is lost because the structure of singularities is not considered in the optimization process. In addition, the author also points out that the design of the quadratic costs weighting matrix used for optimization and desired gimbal rate is of the highest importance in differentiation between steering law performance.

Spacecraft constrained attitude control using positively invariant constraint admissible sets on SO(3) × ℝ 3

This paper presents a constrained attitude control approach for performing spacecraft reorientation maneuvers that maintain specified body vectors within inclusion zones and out of exclusion zones, while respecting control authority limits. The controller uses a supervisory switching strategy with an inner-loop Lyapunov SO(3)-based controller and an outer-loop set-point guidance. A virtual net of orientation equilibria covering SO(3) is introduced, and positively invariant constraint admissible sets on SO(3) × ℝ3 of the inner loop controller are constructed to determine if equilibria are connected by a feasible trajectory. Optimization procedures to maximize the size of the positively-invariant sets are discussed. Graph search is used in the outer-loop to compute the set-point sequence leading from an initial orientation to a final orientation that rigorously enforces constraints. The proposed methodology reduces the search space of possible attitude maneuver solutions, and has computational and implementation simplicity. Numerical simulation results are reported to illustrate the performance of the proposed constrained attitude control methodology.

Optimization in Choosing Gimbal Axis Orientations of a CMG Attitude Control System

Control momentum gyros (CMGs) are often chosen for satellites where high attitude precision and torque are needed while using minimal input power. Control of these types of systems is complicated and is directly dependent on the number of actuators and their gimbal axis orientations with respect to the satellite body frame. This paper discusses the potential benets of optimizing these gimbal axis congurations

Dynamics and Control of Spacecraft With a Generalized Model of Variable Speed Control Moment Gyroscopes

The attitude dynamics model for a spacecraft with a variable speed control moment gyroscope (VSCMG) is derived using the principles of variational mechanics. The resulting dynamics model is obtained in the framework of geometric mechanics, relaxing some of the assumptions made in prior literature on control moment gyroscopes (CMGs). These assumptions include symmetry of the rotor and gimbal structure, and no offset between the centers of mass of the gimbal and the rotor. The dynamics equations show the complex nonlinear coupling between the internal degrees-of-freedom associated with the VSCMG and the spacecraft base bodys rotational degrees-of-freedom. This dynamics model is then further generalized to include the effects of multiple VSCMGs placed in the spacecraft base body, and sufficient conditions for nonsingular VSCMG configurations are obtained. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of VSCMGs are provided. A control scheme using a finite number of VSCMGs for attitude stabilization maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero is presented. The dynamics model of the spacecraft with a finite number of VSCMGs is then simplified under the assumptions that there is no offset between the centers of mass of the rotor and gimbal, and the rotor is axisymmetric. As an example, the case of three VSCMGs with axisymmetric rotors, placed in a tetrahedron configuration inside the spacecraft, is considered. The control scheme is then numerically implemented using a geometric variational integrator (GVI). Numerical simulation results with zero and nonzero rotor offset between centers of mass of gimbal and rotor are presented.

Recovering Linear Controllability of an Underactuated Spacecraft by Exploiting Solar Radiation Pressure

This paper describes a method for recovering linear controllability for the attitude of an underactuated spacecraft by accounting for the effects of solar radiation pressure in the spacecraft attitude model. The developments are based on a spacecraft model that has at least two functional reaction wheels. A solar radiation pressure torque model that is a function of spacecraft attitude is incorporated and, under suitable assumptions, can be simplified for spacecraft with body symmetry. Conditions are given under which a symmetric-body spacecraft will experience zero solar radiation pressure torque. The stability of the underactuated spacecraft model is discussed, and necessary and sufficient conditions are given for linear controllability to be regained when solar radiation pressure torques are included in the spacecraft attitude model. With linear controllability restored, conventional controllers can be designed for underactuated spacecraft. Controllability of a cuboid spacecraft under the influence of ...

Spacecraft actuator alignment determination through null-motion excitation

Current methods of system identification inject random or sinusoidal signals into the system and obtain feedback to learn or infer system parameters. In general, these methods do not consider the learning convergence property of the signal or its effects upon the overall system. In addition, the richness of a random signal is reduced when passed through the actuator that acts as a low-pass filter. Furthermore, the choice of both random and sinusoidal signals typically do not consider the effect of the motion on the controlling body (e.g., movement of the tool point for a robot manipulator with respect to its joint motion, movement of the entire satellite with respect to its attitude actuators, or movement of the Mars rover with respect to its wheels). A design of experiments is developed here to support reaction wheel assembly parameter identification to satisfy persistence of excitation, thereby learning system parameters without inducing large perturbations to the controllable body (e.g., spacecraft bus). This approach exploits the null-motion solutions of overactuated systems and provides a gradient-based method to identify the direction along the null space to be excited for fast local convergence of the learned parameters. The discussed method hypothesizes that a family of null-motion solutions from the excitation law will cause small but measurable perturbations upon the controllable body. Also, the motion of the actuators has the ability of being of larger amplitude and frequency than would be available structurally for the controllable body states, which makes it valid for some current satellite programs. The outcome of this research is a design of experiments structured for direct nonlinear adaptive control for an overactuated system to determine actuator alignment. This is accomplished using excitation through the null space, combined with a proposed gradient-based method (all assuming known mass and environment properties).

Geometric approach to attitude dynamics and control of spacecraft with variable speed control moment gyroscopes

The attitude dynamics of a spacecraft with a variable speed control moment gyroscope (VSCMG), in the presence of conservative external inputs, are derived in the framework of geometric mechanics. A complete dynamics model, that relaxes some of the assumptions made in prior literature on control moment gyroscopes, is obtained. These dynamics equations show the complex nonlinear coupling between the internal degrees of freedom associated with the CMG and the spacecraft base bodys attitude degrees of freedom. General ideas on how this coupling can be used to control the angular momentum of the base body of the spacecraft using changes in the momentum variables of a finite number of VSCMGs, are provided. Placement of VSCMGs in the spacecraft base body is carried out in a manner that avoids singularities in the transformation between VSCMG angular rates and required instantaneous base body angular momentum. A control scheme using n VSCMGs for slew to rest attitude maneuvers in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented. Numerical simulation results obtained for a spacecraft with three VSCMGs confirm the stability properties of the feedback system.

Geometric Mechanics Based Modeling of the Attitude Dynamics and Control of Spacecraft With Variable Speed Control Moment Gyroscopes

The attitude dynamics of a spacecraft with a variable speed control moment gyroscope (VSCMG), in the presence of external torques and internal inputs, is derived using variational principles. A complete dynamics model, that relaxes some of the assumptions made in prior literature on control moment gyroscopes, is obtained. A non-standard VSCMG model, that has an offset between the center of the gimbal axis and the center of the rotor (flywheel) is considered. The dynamics equations show the complex nonlinear coupling between the internal degrees of freedom associated with the VSCMG and the spacecraft base body’s attitude degrees of freedom. Some of this coupling is induced by the non-zero offset between the gimbal axis and the rotor center. This dynamics model is then generalized to include the effects of multiple control moment gyroscopes placed in the base body with non-parallel gimbal axes. It is shown that the dynamical coupling can improve the control authority on the angular momentum of the base body of the spacecraft using changes in the momentum variables of the VSCMG. Numerical simulations confirm the use of these VSCMGs for attitude control for a given de-tumbling maneuver.Copyright

New Startup Method Using Internal Momentum Management of Variable-Speed Control Moment Gyroscopes

gyroscopes is developed. The method provides closed-loop internal momentum tracking control to enable the flywheels to start from rest and reach desired wheel speeds. The proposed controller functioning as a variable-speed control moment gyroscope steering law is developed in terms of the gimbal rates and the flywheel accelerations, which are weighted by a singularity measure. Specifically, using null motion, a strategy is developed to simultaneously perform gimbal reconfiguration for singularity avoidance andinternal momentum management for flywheel startup. A Lyapunov-based stability analysis is used to prove asymptotic attitude tracking and exponential internal momentum tracking despite the effects of uncertain, time-varying satellite inertia properties and uncertain actuatorinertiaproperties.Numericalsimulationsillustratetheperformanceoftheadaptivecontrollerasavariablespeed control moment gyroscope steering law.