Methodology for CubeSat Debris Collision Avoidance Based on Its Active ADCS System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article is comprehensive, logically organized, and contains valuable information on the methodology for CubeSat debris collision avoidance based on its active Attitude Determination and Control Systems (ADCS) system. The authors did excellent research on investigating the development of a methodology to avoid predicted high probability collisions with space debris, in the context of CubeSats in low-earth orbits, through the reaction wheel of their ADCS system. The authors demonstrated that the minimum deviation of 7% and a maximum deviation of 106% in the Vertical Distance Difference (VDD), along with a minimum of 68% and a maximum of 1045% in the Horizontal Distance Difference (HDD), all concerning the notification threshold. The authors should provide discussions on how to reduce both maximum and minimum deviations of both HDD and VDD to gain a better understanding of the subject. The submitted manuscript has significant scientific insights and the conclusions are soundly supported by the experimental data. Therefore, the manuscript requires minor revisions before being accepted in the well-circulated journal, Applied Sciences, in the current form.

Author Response

Dear reviewer:

 

Thank you very much for your kind review. We strongly agree with the comments and suggestions that you have given us. We have extensively worked on improving the paper accordingly, as we think the comments increase the quality of the research.

 

Please, find below our answers (in red), and how they refer to the lines where the document has been changed (in italics), to your kind suggestions (in bold).

 

Thank you very much, and kind regards.

 

This article is comprehensive, logically organized, and contains valuable information on the methodology for CubeSat debris collision avoidance based on its active Attitude Determination and Control Systems (ADCS) system. The authors did excellent research on investigating the development of a methodology to avoid predicted high probability collisions with space debris, in the context of CubeSats in low-earth orbits, through the reaction wheel of their ADCS system. The authors demonstrated that the minimum deviation of 7% and a maximum deviation of 106% in the Vertical Distance Difference (VDD), along with a minimum of 68% and a maximum of 1045% in the Horizontal Distance Difference (HDD), all concerning the notification threshold. The authors should provide discussions on how to reduce both maximum and minimum deviations of both HDD and VDD to gain a better understanding of the subject. The submitted manuscript has significant scientific insights and the conclusions are soundly supported by the experimental data. Therefore, the manuscript requires minor revisions before being accepted in the well-circulated journal, Applied Sciences, in the current form.

A more comprehensive discussion was added at the end of the discussion section, explaining the physical sense of the results, beyond the percentages obtained. Please, find the modifications below:

Interpreting Figure 11 and according to equation (1), drag acceleration is proportional to the atmosphere density and the velocity squared. So, as altitude decreases, atmosphere density increases, so drag acceleration is higher, making the vehicle to reduce its velocity faster. Also, the effect of velocity in drag acceleration is more relevant. It is well known, that the lower the circular orbit, the higher the orbital velocity, so increasing the velocity when moving to a lower orbit, has a higher effect on the drag acceleration, making the vehicle to reduce its velocity even faster. So, the tendency that we can appreciate in Figure 11 makes perfect sense, due to the addition of both effects, increase in atmospheric air density and orbital velocity. So, we can conclude that each maneuver analyzed increases HDD and VDD as the altitude decreases, and the increment is exponential due to the variation of the air density and the velocity squared.

Regarding the values obtained for the different combinations, we must come back to the consideration made in section 3.2, where the cases analysis was imposed for maneuvers between states where area-to-mass ratio are constant. Also, interchangeability between AB and BA maneuvers (i.e.) was considered because they would have the same effect but in opposite directions. The results obtained, and reflected in Figure 11, confirm that this hypothesis is right, because for all the cases of study the VDD is very small compared with the orbital radius (four orders of magnitude smaller), so the effect in relative change in air density and vehicle velocity can be neglected for the computation of drag acceleration for each combination, according to equation (1). So, we can consider that the drag acceleration would only depend on the area-to-mass ratio, in the time of analysis. 

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

In this study, the feasibility of a collision avoidance methodology for CubeSats lacking propulsion is discussed. The paper is interesting and meaningful for advancing our understanding and applicability of this innovative CubeSat collision avoidance approach. Referring to this manuscript, the content should be further improved considering the following issues:

 

1.     It is recommended that noun abbreviations be added to the Nomenclature.

2.     It is suggested to supplement the sizing, capacity and brand of instrument.

3.     Figure 1: the picture is not clear, it is recommended to optimize

4.     It is suggested the innovation of the paper in the introduction is more prominent.

5.     It is suggested that further qualitative and quantitative descriptions of figures and tables should be added.

6.     In the conclusion, it is suggested to simplify and highlight the innovation of this paper.

Author Response

Dear reviewer:

 

Thank you very much for your kind review. We strongly agree with the comments and suggestions that you have given us. We have extensively worked on improving the paper accordingly, as we think the comments increase the quality of the research.

 

Please, find below our answers (in red), and how they refer to the lines where the document has been changed (in italics), to your kind suggestions (in bold).

 

Thank you very much, and kind regards.

In this study, the feasibility of a collision avoidance methodology for CubeSats lacking propulsion is discussed. The paper is interesting and meaningful for advancing our understanding and applicability of this innovative CubeSat collision avoidance approach. Referring to this manuscript, the content should be further improved considering the following issues:

1. It is recommended that noun abbreviations be added to the Nomenclature.

It was reviewed and included the acronyms and abbreviations at the beginning of the document. It was also adapted the acronyms/abbreviations in the whole study to be consistent [remarked in red color]. It was included the subsection 2.2, that was wrongly numbered as 2.3 in the manuscript submitted. Please, find the acronyms and abbreviations tables below:

Nomenclature

a­drag	drag force acceleration
ρ	atmospheric density
V	satellite velocity
CD	drag coefficient
S	drag area
m	satellite mass
	Yaw angle
ω	Angular velocity
Q	Quaternioun
	Kalman gain

Acronyms/Abbreviations

LEO	Low Earth Orbit
ADCS	Attitude Determination and Control System
U	Unit
STK	System Tool Kit
CDM	Conjunction Data Message
ESA	European Space Agency
ESOC	European Space Operations Centre
IADC	Inter-Agency Space Debris Coordination Committee
COPUOS	Committee on the Peaceful Uses of Outer Space
ISO	International Organisation for Standardisation
NASA	National Aeronautics and Space Administration
JSpOC	Joint Space Operations Center
SSN	Space Surveillance Network
ISS	International Space Station
SST	Space Surveillance and Tracking
CDS	CubeSat Design Specification
UAV	Unmanned Aerial Vehicle
SGP4	Standard General Perturbations Satellite Orbit Model 4
HPOP	High-Precision Orbit Propagator
CA	Conjunction Assessment
TCA	Time of Closest Approach
LVLH	Local Vertical, Local Horizontal
TLE	Two-Line Element
VDD	Vertical Distance Difference
HDD	Horizontal Distance Difference
EQM	Engineering Qualification Model
GISTDA	Geo-Informatics and Space Technology Development Agency
CDS	CubeSat Design Specification
UAV	Unmanned Aerial Vehicle
SSO	Sun Synchronous Orbit
KF	Kalman filter
EKF	extended Kalman filter
UKF	unscented Kalman filter
IMU	Inertial Measurement Unit
RW	Reaction wheel

 

2. It is suggested to supplement the sizing, capacity and brand of instrument.

At the end of Section 3.1, next to LUME’s satellite description, we have added the size, capacity and brand of the reaction wheel.

The reaction Wheel used is a GOMSpace NanoTorque GSW-600, with a mass of 180 grams, a size of 44.0 x 44.0 x 27.0 (mm), and a flywheel inertia of 300 gm2

 

 

3. Figure 1: the picture is not clear, it is recommended to optimize

Figure 1 was optimized and added in a bigger and clearer size.

3. It is suggested the innovation of the paper in the introduction is more prominent.

The innovation of the paper is stated in lines 66-71 in the description, and the following has been added in lines 81-85 to elaborate on the idea:

This research introduces a novel application of the Extended Kalman Filter specifically tailored for the control of a reaction wheel in a CubeSat, designed addressing the specific constraints of CubeSats, such as limited computational resources, power constraints, and weight. The algorithm was tested in the lab to validate its effectiveness, confirming that this approach performed as expected under realistic conditions. It is a computationally efficient methodology and frugal in terms of power consumption, critical aspect of Cubesats, that usually operate under limited resources

4. It is suggested that further qualitative and quantitative descriptions of figures and tables should be added.

A qualitative and quantitative description of each figure and table is included, adding one or more sentences before or after the Figure. Hereinafter it is detailed for each Figure/Table across the manuscript:

Figure 1:

This figure shows the object count in the last sixty years, representing the actual objects on-orbit and the cumulative objects on-orbit in case they would not have been removed from orbit.

Table 1:

Table 1 indicates the top debris contributor events by National Aeronautics and Space Administration (NASA) [6] and this intentional breakup became the most severe orbital debris cloud in history [7]. The ranking showed in Table 1 is ordered by the number of catalogued debris, heading this ranking the intentional collision when China conducted its first anti-satellite missile test, destroying FY-1C with a kinetic kill vehicle.

Table 2:

Table 2 shows five categories of space debris based on their diameter: 1 mm, 3 mm, 1 cm, 5 cm, and 10 cm. It is shown the effect that a collision in each category produce in terms of kinetic energy and its equivalent in kg of TNT, comparing the energy with impacts of objects of daily life (i.e. a sphere of diameter 1 mm and a mass of 0.0014 g would have the same effect than an impact of a baseball ball). From bigger to smaller, the first category includes objects that are 10 cm or larger, which can cause explosive damage if they collide with a spacecraft.

Figure 2:

Figure 2 presents a timeline of collision avoidance operational activities at Geo-Informatics and Space Technology Development Agency (GISTDA) (started in 2008), describing the operations to be performed during the previous 3 days before the TCA, including: the notification, the discussion and decision, the maneuver planning, the telecommand ready, and the execution maneuver.

Figure 3:

Any satellite with a weight below 10 kg is classified as a nanosatellite. CubeSats adhere to standardized dimensions known as "Units" or "U," which measure 10 cm x 10 cm x 10 cm. These small satellites are available in six sizes: 1U, 1.5U, 2U, 3U, 6U and 12U, and their weight is usually less than 2 kg per U [15]. Figure 3 shows the current CubeSat family as it is defined in the CDS. 1U, 1.5U, 2U and 3U CubeSats have a base of 10 cm x 10 cm, changing the height to complete the number of units. 6U CubeSats have a base of 10 cm x 20 cm and 12U CubeSats have a base of 20 cm x 20 cm, and both have the height of a 3U.

Figure 4:

The objective is to utilize the exo-brake parachute in the exosphere to decelerate and slow down reentry speed for potential small payload return from LEO, as displayed on Figure 4, where a 3U CubeSat incorporates a deployed parachute, previously stored in the upper unit.

Figure 5:

Figure 5 shows the Lume-1 before its lauch. It is an active, 2.1 kg, 2U- CubeSat, with a Sun Synchronous Orbit (SSO) with an inclination of 97.3° and a semi-mayor axis of 6878 km in the orbit insertion [22].

Table 3:

It is worth noting that CubeSats adhere to a constrained mass budget, allowing for an estimated mass of 1 kilogram per unit. Consequently, a 2U CubeSat will have a mass of 2 kg, a 3U CubeSat will weigh 3 kg, and a 6U CubeSat will carry a mass of 6 kg (Table 3). Three different states, equivalent in drag force: A, B and C, can be defined considering the drag area-mass ratio. As an illustrative example, when calculating drag effects, a 6U satellite oriented with its 2-unit face aligned in the direction of velocity produces an equivalent impact to that of a 2U satellite oriented with its 1-unit face directed toward the velocity vector. This equivalence arises because the drag area-to-mass ratio remains constant in both cases.

Table 4:

In summary, the possible maneuvers are consolidated in Table 4, where we have three distinct maneuvers to analyze: AB, AC, and BC. In this table, the initial and final position states are shown, corresponding to a maneuver named after the combinations of both states (i.e. initial A position and final B position results in AB maneuver that can be applied to 2U and 6U CubeSats). Also, interchangeability between AB and BA maneuvers (i.e.) was considered because they would have the same effect but in opposite directions. These maneuvers exhibit intricate interactions between drag area, orbital parameters, and satellite trajectories, contributing to a comprehensive understanding of satellite behavior in collision avoidance scenarios.

Figure 6:

The three CubeSats show similar evolutions during the two days regarding HDD and VDD, but with different effects. SAT-L, the one with the lowest orbit, shows the highest distance in each instant, and SAT-H, the one with the highest orbit, shows the lowest distance in each instant. SAT-M shows intermediate distances, between SAT-L and SAT-H. In all cases, the VDD varies proportionally with time and HDD shows an exponential behavior. The maximum VDD achieved by the maneuver corresponds to SAT-L, with 159.67 m, an intermediate value of VDD is reached by SAT-M with 85.36 m, and the minimum VDD is 42.33 m for SAT-H. On the other hand, the maximum HDD achieved by the maneuver corresponds to SAT-L, with 7.84 km, an intermediate value of HDD is reached by SAT-M with 4.16 km, and the minimum HDD is 2.06 km for SAT-H.  

Figure 7:

The three CubeSats show similar evolutions during the two days regarding HDD and VDD, but with different effects. SAT-L, the one with the lowest orbit, shows the highest distance in each instant, and SAT-H, the one with the highest orbit, shows the lowest distance in each instant. SAT-M shows intermediate distances, between SAT-L and SAT-H. In all cases, the VDD varies proportionally with time and HDD shows an exponential behavior. The maximum VDD achieved by the maneuver corresponds to SAT-L, with 212.80 m, an intermediate value of VDD is reached by SAT-M with 113.79 m, and the minimum VDD is 56.43 m for SAT-H. On the other hand, the maximum HDD achieved by the maneuver corresponds to SAT-L, with 10.45 km, an intermediate value of HDD is reached by SAT-M with 5.54 km, and the minimum HDD is 2.72 km for SAT-H.

Figure 8:

The three CubeSats show similar evolutions during the two days regarding HDD and VDD, but with different effects. SAT-L, the one with the lowest orbit, shows the highest distance in each instant, and SAT-H, the one with the highest orbit, shows the lowest distance in each instant. SAT-M shows intermediate distances, between SAT-L and SAT-H. In all cases, the VDD varies proportionally with time and HDD shows an exponential behavior. The maximum VDD achieved by the maneuver corresponds to SAT-L, with 53.13 m, an intermediate value of VDD is reached by SAT-M with 28.42 m, and the minimum VDD is 14.10 m for SAT-H. On the other hand, the maximum HDD achieved by the maneuver corresponds to SAT-L, with 2.61 km, an intermediate value of HDD is reached by SAT-M with 1.38 km, and the minimum HDD is 0.68 km for SAT-H.

Figure 9

Figure 9 The CubeSat used in the laboratory tests. It is a nanosatellite based on the Cubesat standard, with an easy to assemble lightweight structure that allows the integration of custom subsystems and payloads. The attitude determination and control subsystem allows the implementation of different control laws, including a magnetometer, two magnetotorquers, a reaction wheel and four sun sensors.

 

Figure 10

Evolution of the attitude of the spacecraft with time, under the control law. The delay time (time to achieve the 50% of the final value is near a second; the rising time of the signal is achieved almost in two seconds, while settling time rounds 2.5 seconds with a maximum signal value with respect to the final value under 5%.

Table 5:

Table 5 shows a summary of the values of HDD and VDD obtained for a two-day period after maneuver, obtained for the different maneuvers and orbits under study, indicating the semimajor axis of the orbit corresponding to SAT-H, SAT-M, and SAT-L.

Figure 11:

Interpreting Figure 11 and according to equation (1), drag acceleration is proportional to the atmosphere density and the velocity squared. So, as altitude decreases, atmosphere density increases, so drag acceleration is higher, making the vehicle to reduce its velocity faster. Also, the effect of velocity in drag acceleration is more relevant. It is well known, that the lower the circular orbit, the higher the orbital velocity, so increasing the velocity when moving to a lower orbit, has a higher effect on the drag acceleration, making the vehicle to reduce its velocity even faster. So, the tendency that we can appreciate in Figure 11 makes perfect sense, due to the addition of both effects, increase in atmospheric air density and orbital velocity. So, we can conclude that each maneuver analyzed increases HDD and VDD as the altitude decreases, and the increment is exponential due to the variation of the air density and the velocity squared.

Regarding the values obtained for the different combinations, we must come back to the consideration made in section 3.2, where the cases analysis was imposed for maneuvers between states where area-to-mass ratio are con-stant. Also, interchangeability between AB and BA maneuvers (i.e.) was considered because they would have the same effect but in opposite directions. The results obtained, and reflected in Figure 11, confirm that this hypothesis is right, because for all the cases of study the VDD is very small compared with the orbital radius (four orders of mag-nitude smaller), so the effect in relative change in air density and vehicle velocity can be neglected for the computa-tion of drag acceleration for each combination, according to equation (1). So, we can consider that the drag accelera-tion would only depend on the area-to-mass ratio, in the time of analysis. 

5. In the conclusion, it is suggested to simplify and highlight the innovation of this paper.

The following lines have been added in the conclusion section:

 

An application of the application of the Extended Kalman Filter (EKF) is introduced, specifically customized for the precise control of reaction wheels in CubeSats. Unlike conventional applications, this algorithm has been meticulously designed to address the inherent constraints associated with CubeSats, including restricted computational resources, stringent power limitations, and the imperative consideration of weight. Recognizing that CubeSats typically operate within these challenging parameters, the algorithm's adaptability to such constraints makes it a noteworthy advancement in the field. Rigorous testing in a laboratory setting has substantiated the algorithm's efficacy, revealing its capability to perform seamlessly under realistic conditions. The validation process not only underscores the algorithm's reliability but also positions it as a promising solution for the intricate task of managing attitude control in CubeSats.

Of particular significance is the algorithm's emphasis on computational efficiency and power frugality, two critical attributes in the context of CubeSat technology. Given the miniature scale of CubeSats and their reliance on limited resources, the algorithm's efficiency becomes paramount. The research team's dedication to developing a methodology that not only meets performance expectations but also operates within the stringent power constraints sets a new standard for attitude control in small satellite systems. By demonstrating its computational efficiency and power thriftiness, this research not only contributes a valuable tool for CubeSat missions but also marks a substantial stride toward overcoming the persistent challenges associated with resource-constrained environments in the realm of space exploration.

 

 

Author Response File: Author Response.docx