David A. Barnharta*, Rahul Rughanib, Jeremy Allamc, Brian Weedend, Fred Slanee, Ian Christensonf
a
Department of Astronautical Engineering, University of Southern California Information Sciences Institute and Space Engineering Research Center, 4676 Admiralty Way, Suite 1001, Marina del Rey, CA 90292,
barnhart@isi.edu
b
Department of Astronautical Engineering, University of Southern California Information Sciences Institute and Space Engineering Research Center, 4676 Admiralty Way, Suite 1001, Marina del Rey, CA 90292,
rughani@usc.edu
c
Department of Astronautical Engineering, University of Southern California Information Sciences Institute and Space Engineering Research Center, 4676 Admiralty Way, Suite 1001, Marina del Rey, CA 90292,
jallam@usc.edu
* Corresponding Author
Keywords: Satellite, Rendezvous, Servicing, Proximity, Safety
ADACS…...Attitude Determination and Control System
CAD…………………………...Computer Aided Design
CLIENT……………Satellite or Platform to be Serviced
COLA………………..Collision On Launch Assessment
DART………….........Double Asteroid Redirection Test
ECD………………………...Effective Capture Distance
EMI………………………Electromagnetic Interference
ESA………………………...…European Space Agency
ESD…………………………….Electrostatic Discharge
GEO…………………………Geostationary Earth Orbit
GNC…………………Guidance Navigation and Control
ISS………………….………International Space Station
ITAR…………International Traffic in Arms Regulation
JAXA……………Japan Aerospace Exploration Agency
LEO……………………………………Low Earth Orbit
MCO…………………………Maximum Capture Offset
NASA...National Aeronautics and Space Administration
OOS…………………………………On Orbit Servicing
RCS………….……………….Reaction Control System
RPO…………….Rendezvous and Proximity Operations
SERVICER….Satellite or Platform that provides Service
STS………………………Space Transportation System
TTC…………………...Telemetry Tracking and Control
1. Introduction
Almost every major vehicle in a consumer’s daily life uses repurposing through value added reseller equipment and constant maintenance; the family car, boat or truck is built on this concept. Entire companies of 2nd and 3rd tier industries are built not just on repurposing components and hardware, but on the skill set to be able to effect the repurposing. All major systems in the world use this construct, with the single exception of satellites. Satellites costing anywhere from $1M to $1B are designed with a known lack of repurposing, for planned disposal at a projected end of life [1]. The exceptions to these have been human modules (Apollo), fly back Shuttles (STS) or early camera return capsules [2].
Only recently have demonstration missions been flown to explore “re-usability” of space systems…through the advent of “servicing” to extend or prolong a space platform’s life [OE Reference]. One project even looked at “repurposing” retired satellites to create completely new space elements. Today there are multiple missions planned and under way by combinations of public, private and public/private entities to create a true business in space that follows the successful models of “servicing”, “maintenance” and “re-use” of Earth bound platforms.
However, where Earth’s rules, regulations, policies and implementable guidelines exist that have evolved over the years to address safety of “services”, today space holds no such similar guidelines. The current treaties (OOSA, Liability Convention, etc) while addressing basic attributes of ownership and liability of one “state” to another operating space platforms, does not provide guidance regarding safety of two platforms/satellites rendezvous and connecting to each other. As an example, militaries around the world employ inflight refueling with aircraft that dictate speed and altitude and communication, marine merchant and military ships employ on and offloading from two ships at sea that have rules and regulations; but nowhere are there guidelines for how to space objects should approach or connect to each other. Why does it matter? The consequences of an action that causes debris on the Earth (car, ship or aircraft) is generally confined to the local area of the accident. That is, pieces of cars that crash (for example) fall to the ground and can be pushed to the side of the road. They do not stay hovering in the air in the lane where other drivers could hit them. In space, every piece of debris can affect an entire orbit; and every orbit is used by the global community of nations to fly their spacecraft.
This represents a unique global problem; the “commons” of space is both available to all nations, yet not controlled or cleaned by any nation. Thus, events in orbit that create additional hazards affect far more than the local environment, indeed they are global in affect.
The current treaties that exist for Space are not adequate in adjudicating the new realities that technologies and capabilities are now enjoined in creating “on orbit servicing” and “rendezvous and proximity operations”. Thus, CONFERS aims to bridge that gap and provide guidance to mitigate catastrophes.
1.1 CONFERS
The Consortium for Execution of Rendezvous and Servicing Operations (CONFERS) is an industry-led initiative with initial seed funding provided by DARPA that aims to leverage best practices from government and industry to research, develop, and publish non-binding, consensus-derived technical and operations standards for OOS and RPO [3]. The goal for these standards is to provide the foundation for a new commercial repertoire of robust safe space-based capabilities to encourage and support the future in-space economy. CONFERS is open to participation by private sector stakeholders in the international satellite servicing community. All companies and academic institutions developing, operating, insuring, and purchasing OOS and RPO capabilities are encouraged to join and contribute their experience and expertise.
1.2 RPO
Similar to tow trucks, refueling tankers, cranes, and all manner of “service” platforms on Earth, the new capabilities for satellites to refuel each other, repair, upgrade and modify other satellites, on-orbit after launch are the in-space equivalent of these platforms. A key attribute to effect any “service” in space, is the ability to get up close and personal. The typical nomenclature used relative to this action is “rendezvous proximity operations” or RPO. RPO consists of timelines, actions, and maneuvers between two different space platforms, from distances >100km to within several meters.
2. Material and methods
USC SERC was given the task to assess the current state-of-the-art (SOA), uncover standards or best practices, and recommend possible actions to consider as potential safety standards in RPO and OOS for the CONFERS community to consider. The task was broken out into two single year efforts, with the first year focusing on RPO and second year OOS. This paper focuses on the results of the RPO work in the first year, where our methods are listed below.
Explain 2nd Evaluation (page 11-12)
Output points to metrics relative to “do no harm”.
The first step was to compile a literature review of all past and present missions that had elements of RPO events. After acquiring this data, relevant parameters about how the RPO was achieved was compiled into a table (e.g., delta-V, holds/gates, times, masses, orbits, etc.). Table XX shows a sample of the attributes looked at. Over 65 published references were used to compile the survey [4-60]. The goal of this was to discover any common elements between them with methods that could be used to develop best practice guidelines could be identified readily.
Put Table XX here, assume it crosses the entire page as its very long with all columns included. Just need one row with the column attributes identified.
The review showed that out of the 65 references found, only a handful contained enough details with attributes to be useful in comparison. From these, no discernable patterns were found, other than the identification of “safety nets” or “keep out zones” around the clients. Some maneuvers additionally used built-in safety ellipses, which required a final burn to physically match the clients position and velocity.
Over the range of 100km down to a few meters between a servicer and client, there are countless ways to rendezvous, and no specific trajectory that is inherently better than any other. There is also no consistency between authors and organizations on what nomenclature and diagrams they used to represent the entire RPO schema they used.
Initial conclusions showed that it is difficult to put a standard on RPO dynamics from afar (i.e. tens to hundreds of kilometers to few meters), and that a more appropriate focus moving forward would be to define metrics regarding “safe final approach RPO”. The result would then be a methodology to conform to, rather than a strict series of gates and approach vectors. Additionally, it would be useful to have a lexicon with included word ontologies for RPO and OOS, showing which terms, used by different companies and agencies, could be defined in a common language. The assertion is that multiple countries/languages and companies will engage in RPO related activities, and will require sharing of various pieces of information, thus having a common language with no mis-interpretation may help overall safety of operations.
3. Metrics consideration and calculation
Explain background on metrics (page 13-19).
Given that it was not feasible to define a standard for the full range of RPO (from distance to close in) at this time, the focus was to define a series of metrics to quantify the safety of what is considered the “final approach”, defined here as a “meters to contact”. The metrics proposed are independent of scale, allowing them to be applied to nanosats, space stations, and everything in-between.
The next step was a survey of potential metrics today from academic to operational that might apply to this, however most existing metrics were found to be inadequate for the purpose of directly minimizing values for the final approach safety. From this survey, some metrics use non-linear algebraic equations and Pareto or Monte Carlo analysis for optimization prior to execution of trajectory, others are theoretical, and have not been applied to actual trajectories. Table XX shows a subset of the types of “metrics” encountered (with main references identified). None of the metrics encountered were not directly translatable to immediate on orbit operations, and most importantly, very few took into account the possible result of non-planned contact, where mass and volume of the servicer and client are considered.
Table XX, Survey of Identifiable possible RPO metrics
After review of both the historical RPO events and evaluating existing possible metrics, a system of three initial metrics was developed to encompass the areas of interest for safety in the final approach to contact portion of RPO maneuvers. These were focused on elements that can be calculated by potential servicers of any size, shape and type, and are concerned with “harm” to the client with off-nominal conditions. The assertion here is that RPO final approach events will become ubiquitous throughout the industry, and thus the search was for metrics that could be scalable and common amongst any potential “service” that a servicer may want to engage in. The three metrics proposed are Contact Velocity, Plume Impingement, and Pointing Error. The metric equations have all been designed to yield as their output a unit ratio, such that if the value is less than one, the operation is considered to have minimal risk (from a first-order analysis). If the value is greater than one, the potential risk is very high and may result in some form of failure or anomaly.
3.1 First Metric: Contact Velocity
The Contact Velocity metric was derived from an alternative perspective that the servicer will contact the client, with the goal to minimize any damage by limiting the speed at which an “inadvertent collision” occurs. The scenario in this case is that the final burn fails to halt the servicer’s approach to the client, and the servicer contacts the client with its pre-stop velocity. It is important to note the assumptions made for this scenario:
1. Contact is assumed to occur on a local structure intended for docking or grapple/contact (i.e., bus structure, docking ring, but not a solar panel e.g.)
2. Trajectory and approach are nominal, only velocity is off.
3. Impulse time of the contact is assumed to be 5ms (taken from high speed automotive collision data as a starting point relative to potential assessable deformation on the client.)
The metric takes as inputs the following:
· Mass of client
· Mass of servicer
· Material properties of client
· Impact area on servicer
· Estimated impulse time
· Safety factor
· Coefficient of restitution
· Projected velocity of approach (final burn planned delta-V)
The output of the metric is the ratio of the projected velocity over the max permissible velocity
[INSERT EQUATION OF METRIC DEFINITION HERE]
We assume the projected velocity of contact is already known; it is equivalent to the delta-V of the final burn to approach, where the final burn is unsuccessful and this velocity is not cancelled out.
The maximum permissible velocity is then computed using the inputted parameters. From the input clients material properties, the maximum allowable pressure of impact can be determined by using material yield as the failure criteria. A safety factor can also applied. The maximum pressure can in turn be used to determine the maximum force (using the impact area), which in turn yields the maximum impulse (using the proposed impulse time). Finally, from the maximum impulse, the maximum contact velocity can be calculated using inelastic collision theory (using coefficient of restitution, CR).
[INSERT FLOWCHART DIAGRAM OF PROCESS HERE]
An interesting corollary to note is that as the CR goes up, the maximum impact velocity goes down, counter to common intuition. This is because the coefficient of restitution is a measure of the elasticity of a collision. If CR equals one, then the collision is perfectly elastic, meaning all the momentum is transferred from the servicer to the client (think of the cue ball impacting another ball on a pool table). If CR equals zero, the collision is perfectly inelastic, resulting in the two objects fusing and moving at a common velocity. In this case, all of the chaser’s momentum is not transferred to the client, since it must retain some momentum in order to match velocity with the target. Thus, the servicer can impact at a higher velocity without causing more damage, in comparison to an elastic collision. This can be visualized in the following plot, illustrating the factor of two difference in the allowable velocities for elastic and inelastic collisions.
[INSERT FIGURE FROM SLIDE #22 HERE]
Recommended CR values lie between 0.4 – 0.6. As a rule of thumb, if the satellite is made from malleable or [RR3] flexible materials, a lower CR value of 0.4 should be used, and if the satellite is rigid or has a substantial amount of composite material, a higher CR value of 0.6 should be used. A CR of 0.5 can be used for in-between cases. If the final metric value is less than one, the maneuver is considered to be the lowest risk. If not, it will result in a collision that can potentially critically damage the client spacecraft if the stopping burn fails on the servicer.
3.2 Second Metric: Plume Impingement
The Plume Impingement metric was derived from the servicer plume potentially impinging on the client satellite as it approaches. The metric was assumed to occur at the worst location on the client that would impart the highest induced torque (i.e. the solar array that has a very high lever arm to the client). The following assumptions were made:
1. The torque acts on only one axis.
2. The satellite and solar arrays acts as a rigid body (i.e. there is no flexing when the plume impinges).
3. Plume impacts normal to the surface and acts as an instantaneous force
4. Client ADACS is turned off
Note, we did not look at plume effects on optics or external sensitive objects like solar cells or electronics. Only on the resultant physical torque imposed to the client, that would potentially result in the client beginning to rotate away from the servicer.
Calculation Approach
The metric is calculated as the ratio of omega projected to omega max.
Omega max= theta/retreat time.
Theta is the angle from the servicer to the next object/component on the client that could impact it under rotation. Retreat Time (RT) is a value that varies based on the design of each chaser satellite. A long Retreat Time necessitates a small omega projected.
[insert theta and maximum angular velocity image here]
[DB4]
Omega projected is calculated by first taking the projected plume normal to the surface. Then using the distance from the center of mass and the client’s body moment of inertia, the torque is calculated. The torque is used to calculate omega projects - the final rotation rate of the target.
[insert calculation approach slide here]
**add equations from latex and explanations for metric here. Metric value x = …. And omega_max is based on retreat time of the satellite decided by the user. A metric value < 1 is considered safe. Also need to explain theta angle after latex equations are added.**
3.3 Third Metric: Pointing Error
The Pointing Error metric was derived from the desire for the client to be within range of a servicer’s robotic appendage to capture, grab, or hold the client via grapple or docking fixture. The final approach needs to place the servicer within range of the capture mechanism, which requires a certain amount of ADACS knowledge and ADACS pointing accuracy. If the maximum capture offset (MCO) is less than the effective capture distance (ECD) the metric value is less than 1 and the maneuver is considered with minimal risk.
The two assumptions for this metric are:
1. Ranging accuracy is perfect, only angular accuracy has some induced error
2. The error assumes compound offsets from sensors and actuators.
3. Braking burn has the correct magnitude, however the direction is offset by the angular accuracy.
4. Both client and servicer will either be in the correct orientation for capture at the end of the burn, or have attitude control to reach the correct orientation.
The MCO is calculated using simple geometry (see figure…). This metric is a tradeoff between GNC control refinement and capture hardware compliance. For coarser GNC accuracy, larger compliance is needed for the capture hardware, and vice versa.
[DB5] For example, if the servicer has a large error in the ADACS system, allowing for only 5 deg accuracy on pointing, then to compensate the servicer will need a longer robotic arm to bridge the MCO gap. Conversely, if the servicer has very high pointing accuracy (e.g., 0.01 deg), then a very long robotic arm is not necessary, and a shorter, less expensive arm can be used without jeopardizing the mission.
[INSERT calculation approach image]
4. Results
Chart #33. Expand to include more cases, make estimates on the variables and data we don’t have.
Applying the derived metrics to the data from the initial survey of all published rendezvous operations, it can be seen from the following table that the values are all less than one, with the exception of the Apollo 11 Lunar Orbit Rendezvous (LOR) , meaning the previous methodologies were considered “low risk” practices, as expected. The LOR value is high because the rendezvous was performed under manual control, with [relatively] low-accuracy guidance equipment [4].