Chattering-free Sliding Mode Control for Propellantless Rendez-vous using Differential Drag

peer reviewedThis paper develops a differential drag-based sliding mode controller for satellite rendez-vous. It is chattering-free and avoids bang-bang type control to adjust the relative motion more efficiently. In spite of uncertain nonlinear perturbations and disturbances, it is shown that the in-plane relative motion between two satellites can be effectively controlled by regulating the drag difference. An adaptive tuning rule is also presented such that the errors are suppressed to lie within a desired error box. The proposed controller is simple and easy to implement in a small satellite, and numerical simulations are carried out to demonstrate its effectiveness in a high fidelity environment

Feasibility of CubeSat Formation Flight Using Rotation to Achieve Differential Drag

This paper presents the results of a study conducted to understand the feasibility of CubeSat formation flight. The mechanism for separation and formation studied was differential drag, achieved by rotating the CubeSats to give them different cross-sectional areas. Intuitively, lower altitude orbits provide much higher separation effects. Although the most influential orbital effects occur with maximum and minimum cross-sectional areas, an attitude-controlled and a tumbling CubeSat may provide enough differential drag to meet separation requirements of a mission. Formation flight is possible, but due to the non-linearity of the system, gain scheduling may be the most effective method of long term formation control. Formation flight on missions with sun-tracking is also possible using the time in eclipse as the control time. Future studies will need to see how long formation can be maintained, as well as how significant altitude affects the total possible formation duration

Optimal Trajectories for Propellant-Free Rendezvous Missions

The paper provides a new approach to utilizing space environmental forces in time- and energy-optimal, propellant-less spacecraft rendezvous missions. Considering the nonlinear form of the relative dynamic equations, rendezvous missions are posed as optimal control problems subject to input saturation. We conduct a direct optimal control approach to obtain optimal trajectories and control inputs. Initially, we consider the differential drag only and conduct a comprehensive analysis of the effect of altitude on the required control input and achieved cost function. Lorentz forces are then utilized with the differential drag, reducing the time required for time-optimal missions. For energy-optimal missions with combined differential drag and Lorentz forces, a weighting matrix in the cost function is introduced to adjust the relative contributions of these forces

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

Differential drag is a technique for altering the semi-major axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecrafts cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASAs EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry

A Review and Gap Analysis of Exploiting Aerodynamic Forces as a Means to Control Satellite Formation Flight

Using several small, unconnected satellites flying in formation rather than a single monolithic satellite has many advantages. As an example, separate optical systems can be combined to function as a single larger (synthetic) aperture. When the aperture is synthesized, the independent optical systems are phased to form a common image field with its resolution determined by the maximum dimension of the array. Hence, a formation is capable of much finer resolution than it could be accomplished by any single element. In order for the formation to maintain its intended design despite present perturbations (formation keeping), to perform rendezvous maneuvers or to change the formation design (reconfiguration) control forces need to be generated. To this day, using chemical and/or electric thrusters are the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. In the mid-eighties, Caroline Lee Leonard published her pioneering work [1] proving the potential of using differential drag as a means of propellant-less source of control for satellite formation flight. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Since its control authority is limited to the in-plane motion, Horsley [2] proposed to use differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researches around the world have enhanced Leonard’s work over past decades which results in a multitude of available literature. Besides giving an introduction into the method the major contributions of this paper is twofold: first, an extensive literature review of the major contributions which led to the current state-of-the-art of different lift and drag based satellite formation control is presented. Second, based on these insights key knowledge gaps that need to be addressed in order to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain and advanced satellite surface materials as well as the necessity of robust control methods able to cope with the occurring uncertainties is assessed.Peer ReviewedPostprint (published version

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed.Peer ReviewedPostprint (author's final draft

Limited-duty-cycle Satellite Formation Control via Differential Drag

As CubeSat formation flying missions relying on differential drag control become increasingly common, additional missions based on this control must be studied. A mission planning tool is investigated to control the relative spacing of a CubeSat formation where differential drag is the sole control mechanism. System performance is investigated under varying perturbations and a range of system parameters, including limiting the control duty cycle. Optimal solutions based on using a pseudo spectral numerical solver, GPOPS-II, to minimize maneuver time. This study includes the development of a mission planning tool to work with the modeled CubeSat mission to calculate optimal maneuvers for its mission architecture. The effects of mission altitude, solar cycle, various maneuver sizes and formations, limited control, various computational methods, and error checkers were evaluated. The mission planning tool developed can properly execute all desired run parameters and options, though it suffers from computational complexity. Pseudo spectral methods executed in MatLab were determined to be poorly suited to the problem due to memory requirements involved. Limited duty cycle control can be applied with differential drag with varying effectiveness dependent on mission parameters

Autonomous Formation Flying and Proximity Operations Using Differential Drag on the Mars Atmosphere

Due to mass and volume constraints on planetary missions, the development of control techniques that do not require fuel are of big interest. For those planets that have a dense enough atmosphere, aerodynamic drag can play an important role. The use of atmospheric differential drag for formation keeping was first proposed by Carolina L. Leonard in 1986, and has been proven to work in Earth atmosphere by many missions. Moreover, atmospheric drag has been used in the Mars atmosphere as aerobraking technique to decelerate landing vehicles, and to circularize the orbit of the spacecraft. Still, no literature was available related to formation flying on Mars. To analyze the use of differential drag on the Mars atmosphere, the researcher accessed the two high resolution models available: NASA’s Mars-GRAM and ESA’s Mars Climate Database. These models allowed the simulation of conditions that a spacecraft would experience while in orbit around the planet. To explore the feasibility, the researcher first conducted a study where Mars atmosphere density was compared to Earth atmosphere, determining its applicability. Then, a simulation using MATLAB® was conducted, using a Keplerian two-body problem including the effects of Mars zonal harmonics (i.e. J2) and drag perturbations. Two 6U CubeSat were used in the simulation with deployable drag plates of different sizes, giving the possibility of having five differential drag scenarios as means of formation control. The conclusions showed that, although with some limitations, the use of differential drag as means of autonomous formation flying and proximity operations control is feasible using proven techniques previously validated in Low Earth Orbit. Lyapunov control was selected as the control strategy, where three different methods were evaluated and compared