Hank Pernicka

Magnetometer-only Attitude Determination Using Novel Two-step Kalman Filter Approach

Determining spacecraft attitude in real time using only magnetometer data presents a challenging filtering problem. A flexible and computationally efficient method for solving the spacecraft attitude using only an inexpensive and reliablemagnetometerwould be a useful option for satellitemissions, particularly thosewithmodest budgets. The primary challenge is that magnetometers only instantaneously resolve two axes of the spacecraft attitude. Typically, magnetometers are used in conjunction with other sensors to resolve all three axes. However, by using a filter over an adequately long orbit arc, the magnetometer data can yield full attitude, and in real time. The methodpresented solves the problemusing a two-step extendedKalmanfilter. In thefirst step, themagneticfield data are filtered to obtain the magnetic field derivative vector, which is combined with the magnetic field vector in the second step to fully resolve the attitude. A baseline scenario is developed, and a parametric study is conducted using the parameters of interest.

Vision-Based Relative State Estimation Using the Unscented Kalman Filter

A new approach for spacecraft absolute attitude estimation based on the unscented Kalman filter (UKF) is extended to relative attitude estimation and navigation. This approach for nonlinear systems has faster convergence than the approach based on the standard extended Kalman filter (EKF) even with inaccurate initial conditions in attitude estimation and navigation problems. The filter formulation employs measurements obtained from a vision sensor to provide multiple line(-) of(-) sight vectors from the spacecraft to another spacecraft. The line-of-sight measurements are coupled with gyro measurements and dynamic models in an UKF to determine relative attitude, position and gyro biases. A vector of generalized Rodrigues parameters is used to represent the local error-quaternion between two spacecraft. A multiplicative quaternion-error approach is derived from the local error-quaternion, which guarantees the maintenance of quaternion unit constraint in the filter. The scenario for bounded relative motion is selected to verify this extended application of the UKF. Simulation results show that the UKF is more robust than the EKF under realistic initial attitude and navigation error conditions.

Algorithm for Autonomous Longitude and Eccentricity Control for Geostationary Spacecraft

To lower satellite orbital maintenance cost, spacecraft designers are seeking flight software that provides more autonomy. Longitude and eccentricity are good candidates for autonomous control of geostationary spacecraft.The algorithm presented couples longitude control with eccentricity control. Longitude drift is modeled as onedegree-of-freedom motion and controlled with a quadratic equation predicting the subspacecraft Earth reference longitude after a predetermined amount of time. After formulation of the basic longitude control algorithm, addition of a differential corrections scheme resulted in an improved longitude error of ′0.015° longitude. Finally, implementation of longitude control and two-part maneuvers for eccentricity control successfully met the desired mission constraints. The algorithms developed form the basis for preparation of flight software for a geostationary spacecraft scheduled to launch in the next few years.

Low-Thrust Spacecraft Formation Keeping

Replacing large and costly satellites with formations of smaller satellites, flying in close proximity, is a current subject of interest. One of the keys to successful formation flying is the control system that maintains the formation geometry and provides proper positioning of each member of the formation. This study compares two active control system designs that can be used to maintain a formation composed of microsatellites with limited on-off thrusting capabilities in low Earth orbit. The two evaluated designs are based on a linear approach using optimal control theory and on a nonlinear approach based on Lyapunov stability concepts. In assessing the effectiveness of each controller, the performance criteria were the accuracy with which the formation is maintained and the propellant consumption. The final selection is a tradeoff between fuel consumption and controller robustness based on model uncertainties. Nomenclature amrs = semimajor axis of leader orbit Co = controllability matrix e3 = unit vector fixed in the Earth along the direction of the north pole axis Fx , Fy, Fz = components of the control force along the rotating x, y, and z axes, respectively f = control force vector (force applied by the onboard propulsion system) J = cost function associated with the optimal control J2 = Earth oblateness harmonic coefficient Kglobal, = positive gains associated with the nonlinear

Spacecraft Formation Flight About Libration Points Using Impulsive Maneuvering

As more advanced spacecraft operational capabilities are required to accomplish innovative scientific missions, a shift to the incorporation of distributed space systems is underway.One area of current focus is the relative dynamics of a formation of spacecraft orbiting a libration point. One interesting and current challenge in this research area is maintaining formation control during both passive and active modes of operation, with different modes requiring different levels of accuracy. The research described in this paper focuses on the development and analysis of discrete maneuvering techniques using differential correction methods for maintaining a two satellite formation within required error tolerances for a given operational mode. In particular, formation sizes and control tolerances are sought for which impulsive maneuvering becomes a practical option.

Position and Attitude Control of Deep-Space Spacecraft Formation Flying Via Virtual Structure and Theta-D Technique

Control of deep-space spacecraft formation flying is investigated in this paper using the virtual structure approach and the − θ D suboptimal control technique. The circular restricted three-body problem with the Sun and the Earth as the two primaries is utilized as a framework for study and a two-satellite formation flying scheme is considered. The virtual structure is stationkept in a nominal orbit around the 2 L libration point. A maneuver mode of formation flying is then considered. Each spacecraft is required to maneuver to a new position and the formation line-of-sight is required to rotate to a desired orientation to acquire new science targets. During the rotation, the formation needs to be maintained and each spacecraft’s attitude must align with the rotating formation orientation. The basic strategy is used on a ‘Virtual structure’ approach. A nonlinear model is developed that describes the relative formation dynamics. This highly nonlinear position and attitude control problem is solved by employing a recently developed nonlinear control approach, called the -D technique. This method is based on solution to the Hamilton-JacobiBellman equation and yields a closed-form suboptimal feedback solution. The controller is designed such that the relative position error of the formation is maintained within one centimeter accuracy.

Tundra Constellation Design and Stationkeeping

Constellations of satellites in Tundra orbits provide an innovative alternative to the increasingly crowded geostationary orbit belt. The Tundra constellation uses three or more spacecraft in inclined geosynchronous orbits. The nominal orbit design for the constellation must minimize any undesirable perturbation effects to provide affordable stationkeeping costs. We describe a study of the Tundra orbit regime and design of constellations given a sample set of basic constraints. Frozen and partially frozen orbits are then sought from which to construct constellations allowing for reduced stationkeeping requirements. Perturbation effects from third-body and geopotential sources are quantified and used to select orbits that will provide the needed coverage while providing a reasonable propellant budget.

Bearings-Only Initial Relative Orbit Determination

A method for performing bearings-only initial relative orbit determination of a nearby space object in the absence of any information regarding the space object’s geometry and relative orbit is presented. To resolve the range ambiguity characteristic of a single optical sensor system, a second optical sensor is included at a known baseline distance on the observing spacecraft. To formulate an initial estimate of the space object’s relative orbit and its associated uncertainty, the angle measurements from both sensors are used to bound a region for all possible relative positions of the space object. A parameterized probability distribution in relative position that reflects uniform relative range uncertainty across the bounded region is constructed at two unique times. Linkage of the positional distributions is performed using a second-order relative Lambert solver to formulate a full-state probability density function in relative position and velocity, which can be further refined through processing subs...

Refrigerant-based propulsion system for small spacecraft

The MR SAT spacecraft under development at UMR requires a propulsion system that can be utilized to perform orbital maneuvers and three-axis attitude control to complete its mission objective of conducting spacecraft formation flight. This thesis documents the research, analysis design and development of the cold gas propulsion system that was integrated in the MR SAT spacecraft. The basis of design and safety requirements stemmed from the AFRL University Nanosat Program competition, in which the UMR SAT project placed third out of eleven schools from across the nation. The MR SAT propulsion system was a primary feature as it implements a refrigerant (R134a) propellant that has never been flown in space. As detailed in this thesis, through engineering modeling and laboratory testing R-134a is demonstrated to be a feasible propellant for small spacecraft. As the R-134a is stored as a saturated liquid in the tank, it was necessary to analyze the thermodynamic properties of the refrigerant and investigate phase changes for its use as a propellant. Also documented is the hardware selected and the integration into the MR SAT spacecraft, along with the laboratory testing that has been conducted. R-134a offers good performance characteristics and this thesis can be used as a design template by other small spacecraft developers who require a safe and inexpensive propulsion system.

Optimal Control for Proximity Operations and Docking

This paper proposes optimal control techniques for determining translational and rotational maneuvers that facilitate proximity operations and docking. Two candidate controllers that provide translational motion are compared. A state-dependent Riccati equation controller is formulated from nonlinear relative motion dynamics, and a linear quadratic tracking controller is formulated from linearized relative motion. A linear quadratic Gaussian controller using star trackers to provide quaternion measurements is designed for precision attitude maneuvering. The attitude maneuvers are evaluated for different final axis alignment geometries that depend on the approach distance. A six degrees-of-freedom simulation demonstrates that the controllers successfully perform proximity operations that meet the conditions for docking.