David K. Geller

New approach to attitude/momentum control for the Space Station

A new approach to control moment gyro (CMG) momentum management and attitude control of the space station is presented. The control algorithm utilizes both the gravity-gradient and gyroscopic torques to seek torque equilibrium attitude in the presence of secular and cyclic disturbances. It is shown that, depending on mission requirements, either pitch attitude or pitch-axis CMG momentum can be held constant. It is also shown that a combination of yaw attitude and roll-axis CMG momentum can be held constant, whereas a combination of roll attitude and yaw-axis CMG momentum cannot. As a result, the overall attitude and CMG momentum oscillations caused by cyclic aerodynamic disturbances are minimized. A state feedback controller with minimal computer storage requirements for gain scheduling is also presented. An inherent physical property of the coupled roll/yaw dynamics is discussed in terms of a transmission zero of a multivariable system.

Navigating the Road to Autonomous Orbital Rendezvous

The fundamental techniques and approaches to orbital rendezvous have predominantly been defined by the United States and Russian space programs. Although both programs were initially pursuing the same goal, they chose two very distinct paths. Themanualmethod pursued by theUnited States has given it the capability to handle a variety of complex rendezvous and docking missions, whereas the Russians’ automated approach has come to symbolize efficiency and reliability. What is the reason that these two storied programs chose such different paths? How have these pioneering decisions affected the course of orbital rendezvous?Where is orbital rendezvous heading in the future? This paper provides a comprehensive overview of the programs,missions, and techniques that have set the standards for orbital rendezvous. In particular, it reveals the rationale and events behind the early engineering decisions regarding orbital rendezvous navigation systems, how they have come to influence ensuing programs, and why these traditional methods are beginning to be replaced by new autonomous approaches for current and future missions.

Relative angles-only navigation and pose estimation for autonomous orbital rendezvous

This paper explores the potential of using angles-only navigation to perform various autonomous orbital rendezvous and close proximity operations. A 32-state extended Kalman filter is developed that processes angular measurements from an optical navigation camera along with gyro and star tracker data to estimate the inertial position, velocity, attitude, and angular rates of both a target and chaser vehicle. The target satellite is assumed to be passive while the chaser may perform a variety of autonomous rendezvous and close proximity maneuvers. The navigation filter’s performance is evaluated and tested by running a coded prototype in a closed loop 6 degree-of-freedom simulation tool containing the various sensors, actuators, GN&C flight algorithms, and dynamics associated with a simple rendezvous scenario. The analysis performed for this study uses standard Monte-Carlo techniques. These results not only include the navigation errors associated with implementing an angles-only navigation scheme, but they also reveal the dispersions from the nominal trajectory associated with this particular technique in a closed-loop GN&C setting. The rendezvous scenario duplicates a similar close proximity scenario analyzed using linear covariance analysis. Both methods are compared to add validity to the results and highlight the advantages and potential of each approach for autonomous orbital rendezvous and close proximity operation analysis.

Linear Covariance Techniques for Orbital Rendezvous Analysis and Autonomous Onboard Mission Planning

A novel trajectory control and navigation analysis software approach is developed. The program quickly determines trajectory dispersions, navigation errors, and required maneuver Δv at selected key points along a nominal trajectory. It can be used for mission design and planning activities or in autonomous flight systems to help determine the best trajectories, the best maneuver locations, and the best navigation update times to ensure mission success. These features are illustrated with two simple examples. The software works by applying linear covariance analysis techniques to a closed-loop guidance, navigation, and control (GN&C) system. The nonlinear dynamics and flight software models of a closed-loop six-degree-of-freedom Monte Carlo simulation are linearized. Then, linear covariance techniques are used to produce a program that will accurately predict 3-σ trajectory dispersions, navigation errors, and Av variations. Although the application presented is orbital rendezvous, the tools, techniques, and mathematical formulations are applicable to a variety of other space missions and GN&C problems including atmospheric entry, low-thrust electric propulsion missions, translunar injection and lunar orbit insertion, lunar ascent/descent, and formation-flying missions.

Observability Criteria for Angles-Only Navigation

The possibility of implementing angles-only navigation for orbital rendezvous, satellite formation flight, and other relative motion applications possesses great potential that is often discarded because of its inherent and misunderstood limitation in determining range. To formally characterize the conditions required for observability, an analytical expression for the observability criteria for angles-only navigation is derived. As anticipated, the criteria clearly shows that with angle measurements alone, the relative position and velocity cannot be determined for systems with linear dynamics. However, with a calibrated thrust maneuver, observability can be guaranteed for all possible relative trajectories. The solution, intended for relative orbital motion scenarios, is also valid for any system with linear dynamics and line-of-sight (LOS) measurements. An intuitive graphical interpretation is also provided along with several examples related to orbital rendezvous. The derived analytical observability criteria can be extended to include nonlinear systems. It can also be used to derive optimal maneuvers to maximize observability and determine the degree of detectability for a selected relative trajectory when sensor noise is considered.

Robust H infinity control design for the space station with structured parameter uncertainty

A robust H-infinity control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H-infinity controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Optimal Orbital Rendezvous Maneuvering for Angles-Only Navigation

A NGLES-ONLY navigation has great potential for orbital rendezvous, satellite formation flight, and other relative motion applications, but is often discarded because of its inherent and misunderstood limitation in determining range. A common consensus in the published literature, regardless of the application, is that maneuvers are generally required to obtain target observability when using only anglemeasurements [1–6]. For the bearings-only tracking problem, Nardone and Aidala [7] and Hepner and Geering [8] also showed that certain types of maneuvers, particularly those maneuvers that cause position changes that lie along the instantaneous bearing lines associated with a constant velocity trajectory, do not necessarily guarantee observability. If certain maneuvers produce observability and others do not, then the next natural step that has received considerable attention is to determinewhichmaneuvers and trajectories are optimal in maximizing observability [9–16]. Despite these significant advances in deriving optimal maneuvers for the bearings-only tracking problem, these results are typically established on the premise of a constant moving target, an assumption valid for many naval applications that motivated the earlier research efforts but not applicable to orbital rendezvous. Although the influence of maneuvering for angles-only navigation has been considered for orbital rendezvous [17–19], there does not exist in the published literature derivations of performing optimal maneuvers to maximize observability. This Note develops the mathematical framework to analytically derive optimal maneuvers for angles-only navigation using a previously derived observability criteria [20–22]. The concept of having levels or degrees of observability is formally defined as a function of the measurement error and then used to form the theoretical foundation to derive optimal maneuvers that maximize the observability of the relative state. A simple yet common orbital rendezvous example is provided to illustrate the possibility of designing optimal orbital rendezvous maneuvers for angles-only navigation. Although the topic is introduced in the context of orbital rendezvous, the fundamental concepts can be applied to any linear dynamic system (and extended to nonlinear systems) for which the relative position and velocity are estimated using only angular measurements.

Periodic-disturbance accommodating control of the Space Station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Orbital Rendezvous: When is Autonomy Required?

The ability to control the relative motion of two orbiting spacecraft from the ground is approximately a function of four key parameters: relative state knowledge errors, maneuver execution errors, environment modeling errors, and the time delay between the execution of successive maneuvers. Based on these four parameters an assessment of the grounds capability to control relative position can be made and a minimum safe-approach distance can be determined. Approximate analytic expressions for minimum ground-controlled separations are presented and then validated with a detailed linear covariance analysis. The analytic expressions are shown to be accurate to within ±25%.

Angles-Only Navigation State Observability During Orbital Proximity Operations

Angles-only navigation during proximity operations suffers from a well-documented range-observability problem when a single camera is assumed to be at the center of mass of the host vehicle. Inspired by this range-observability problem, this paper explores relative-position/-velocity observability when a single camera is offset from vehicle center of mass. Within the context of the Clohessy–Wiltshire dynamics, it is shown that relative position and velocity are generally observable when the camera offset is included in the problem formulation, enabling a range observability without Δv requirements. Although special cases are identified when the state is unobservable, the conclusion is that the relative state is generally observable even in the case of v-bar station keeping during attitude hold when the angle measurements are constant. The thesis that state observability results when the motion of the camera does not obey the Clohessy–Wiltshire dynamics is presented.