Ph.D Thesis

Ph.D StudentBen-Yaacov Ohad
SubjectLong Term Satellite Cluster Flight Using Differential
DepartmentDepartment of Aerospace Engineering
Supervisor PROF. Pinchas Gurfil
Full Thesis textFull thesis text - English Version


One of the emerging concepts in future space technologies is that of disaggregated satellites. The idea is to distribute a single satellite into multiple free-flying modules. One of the key issues in disaggregated spacecraft is relative position control, known as cluster keeping. Cluster keeping entails maximal and minimal inter-satellite distance constraints. As a result, two main controllers are necessary: a maximal distance controller to prevent an unacceptable drift, and a minimal distance controller to avoid collisions. The goal of this research is to develop differential drag-based cluster-keeping controllers suitable for implementation in long-term missions, for a cluster consisting of multiple modules.

Unlike previous work in differential drag-based formationkeeping, the present work develops a nonlinear method suitable for missions in excess of a year. It is first shown that the differential mean eccentricity is uncontrollable for near-circular orbits, and hence a nonlinear DD-based controller for matching the drag-related secular component of the semimajor axis is developed. An asymptotic stability proof for the controller is provided. Moreover, two new methods for DD-based cluster-keeping of multiple modules are developed, thus expanding existing literature, which usually deals with two satellites only. The results are validated using simulations based on the forthcoming Space Autonomous Mission for Swarming and Geolocation with Nanosatellites (SAMSON), showing that DD-based cluster-keeping can be effective for altitudes reaching about 600 km.

A DD-based maximum distance keeping method is developed that uses the Brouwer-Lyddane differential mean elements feedback for long-term control of the secular drift among satellites. The stability of the maximum distance keeping controller is proven using finite-time stability theory, and high-precision simulation results confirm that the new controller is able to arrest satellite relative drift for mission lifetimes exceeding a year.

The differential drag control law is examined under measurement noise, drag uncertainties, and initial condition-related uncertainties. The method used for uncertainty quantification is the Linear Covariance Analysis, which enables to propagate the uncertain state covariance without propagating the state itself. Validation using a Monte-Carlo simulation is provided. The results show that all uncertainties have relatively small effect on the inter-satellite distance, even in the long term, which validates the robustness of the used differential drag controller.

As a part of a complete DD-based solution for cluster keeping, a collision-avoidance method based on the same structure, albeit with differential osculating elements feedback, is developed and validated. Additionally, the possibility to regulate cross-track drift with DD is examined.

Calculating the projected cross-sectional area (PCSA) of a satellite along a given direction is essential for implementing differential drag-based control. This research also develops a new analytical method for calculating the PCSA, the concomitant torques and the satellite exposed surface area, based on the theory of convex polygons. The methodology also accounts for overlaps among projections, and is capable of providing the true PCSA in a computationally-efficient manner. Using the SAMSON mechanical model, it is shown that the new analytical method yields accurate results, which are similar to results obtained from alternative numerical tools.