Kwangwon Lee

Laser-based Relative Navigation Using GPS Measurements for Spacecraft Formation Flying

This study presents a precise relative navigation algorithm using both laser and Global Positioning System (GPS) measurements in real time. The measurement model of the navigation algorithm between two spacecraft is comprised of relative distances measured by laser instruments and single differences of GPS pseudo-range measurements in spherical coordinates. Based on the measurement model, the Extended Kalman Filter (EKF) is applied to smooth the pseudo-range measurements and to obtain the relative navigation solution. While the navigation algorithm using only laser measurements might become inaccurate because of the limited accuracy of spacecraft attitude estimation when the distance between spacecraft is rather large, the proposed approach is able to provide an accurate solution even in such cases by employing the smoothed GPS pseudo-range measurements. Numerical simulations demonstrate that the errors of the proposed algorithm are reduced by more than about 12% compared to those of an algorithm using only laser measurements, as the accuracy of angular measurements is greater than 0.001° at relative distances greater than 30 km.

Spacecraft Formation Keeping via Discrete-Time Hamilton-Jacobi Theory

This study presents a higher-order optimal tracking controller for spacecraft formation keeping based on the discrete-time Hamilton-Jacobi theory. In the frame of a typical optimal tracking problem in discrete-time domain, an infinite-horizon optimal feedback controller in generic form is first derived by employing generating functions which represent two-point boundary value problem of Hamiltonian phase flow. This systematic approach does not require any initial guess or iteration. It is also not adversely affected by the complexity of performance index, dynamics, and desired tracking trajectories. The proposed higher-order controller is applied to a spacecraft formation keeping problem, which demonstrates superior tracking performance to optimal tracking controller in continuous-time domain in terms of both tracking error and fuel consumption.

Near-Optimal Guidance and Control for Spacecraft Collision Avoidance Maneuvers

This study presents a semi-analytic and sub-optimal guidance/control for a controlled/active spacecraft to avoid collision with other free/inactive space objects. The collision avoidance problem is formulated as a typical optimal feedback control problem with a penalty term incorporated into the performance index. The penalty function is designed such that its value increases sharply as a spacecraft approaches other space objects. The Pontryagin’s principle is used to form a two point boundary value problem for a standard Hamiltonian system, whose solution is obtained in terms of the generating functions which appear in the theory of canonical transformation. The resultant algorithm allows one to develop near-optimal guidance/control laws as truncated power series in feedback form and generate near-optimal trajectories without any initial guess or iterative process. This procedural advantage over typical direct optimization approaches comes at the expense of reasonable efforts of developing higher-order generating functions and empirically updating the design parameters of penalty function. Numerical examples demonstrate that the proposed algorithm successfully accomplishes collision avoidance by appropriately detouring other space objects or forbidden regions.

CANYVAL-X Mission Development Using CubeSats

Current space telescopes have a single structure, and consequently, their focal length cannot be increased sufficiently. Sometimes, this problem may prevent the improvement of the resolution of the telescope. To solve this problem, the concept of virtual telescope has been proposed. A virtual telescope consists of two spacecraft: one has a lens system and the other has a detector system. By using formation flying, the two spacecraft can be simplified as a virtual telescope system. Then, their relative orbit distance can serve as a baseline for the virtual telescope system [1, 2]. The most important issue in a virtual telescope is to perform inertial alignment with respect to a celestial object and to maintain it in space. Inertial alignment means that the relative position and relative attitude of the two spacecraft are simultaneously aligned with a target.

Improved GPS-based Satellite Relative Navigation Using Femtosecond Laser Relative Distance Measurements

This study developed an approach for improving Carrier-phase Differential Global Positioning System (CDGPS) based realtime satellite relative navigation by applying laser baseline measurement data. The robustness against the space operational environment was considered, and a Synthetic Wavelength Interferometer (SWI) algorithm based on a femtosecond laser measurement model was developed. The phase differences between two laser wavelengths were combined to measure precise distance. Generated laser data were used to improve estimation accuracy for the float ambiguity of CDGPS data. Relative navigation simulations in real-time were performed using the extended Kalman filter algorithm. The GPS and laser-combined relative navigation accuracy was compared with GPS-only relative navigation solutions to determine the impact of laser data on relative navigation. In numerical simulations, the success rate of integer ambiguity resolution increased when laser data was added to GPS data. The relative navigational errors also improved five-fold and two-fold, relative to the GPS-only error, for 250 m and 5 km initial relative distances, respectively. The methodology developed in this study is suitable for application to future satellite formation-flying missions.

Performance Analysis of Generating Function Approach for Optimal Reconfiguration of Formation Flying

The use of generating functions for solving optimal rendezvous problems has an advantage in the sense that it does not require one to guess and iterate the initial costate. This paper presents how to apply generating functions to analyze spacecraft optimal reconfiguration between projected circular orbits. The series-based solution obtained by using generating functions demonstrates excellent convergence and approximation to the nonlinear reference solution obtained from a numerical shooting method. These favorable properties are expected to hold for analyzing optimal formation reconfiguration under perturbations and non-circular reference orbits.