Could a swarm of probes autonomously establish orbit around an asteroid?

Question

To position a spacecraft around an asteroid, one must know the orbital parameters and orientation of the asteroid and the spacecraft. Formation flying will be more complex in terms of positioning relative to an asteroid. In case of formation flying in LEO, one uses GPS to accurately determine the position of the spacecraft. Since GPS is not useful in deep space, formation flying with local navigation system / positioning system is more important.

Considering two or more bodies flying in a swarm configuration relatively to one another, what are the possibilities of using wireless ad hoc networks, or other known similar technologies that can be useful to position the spacecraft autonomously?

Answer 1

Let's break your question into separate tasks:

• Autonomous orbit determination (autonomous because the DSN won't be there to help you when you need it)
• Autonomous attitude determination
• Situational awareness for formation flying (relative positions, velocities, attitudes and attitude rates), most efficiently done in a cooperative manner
• Cooperative collision avoidance
• Non-cooperative collision avoidance

Let's state it from the start: you can't rely on other craft in the swarm to fulfil your mission since losing one craft implies at best, degraded capabilities for all others, and at worst, mission failure.

Hence, you can't rely on cooperative ways of finding out where the heck your own craft is, and this means extracting range, range rate, attitude, attitude rate information from comms links is a bonus, but never a primary method of running the show. There are some mitigating factors, but they are marginal at best.

Autonomous orbit determination has to contend with uncertainties in:

• asteroid's terrain
• asteroid's gravity
• asteroid's rotation parameters
• all extra perturbations
• systematic biases in the craft's instruments

To overcome all this and more, you've got to use several physical principles (I don't really know the mission you have in mind, so I am not concerned by the exact mass budget) and fuse data from all of them in a smart way (possibly, to uncover systematic errors and compensate for equipment malfunctions):

• passive optical triangulation and ranging (a lot of thought goes into pattern recognition here, luckily you have installed a camera on your craft, haven't you?);
• active optical (ranges, range rates, angles) with a lidar;
• active radar (nice if you can get synthetic aperture pictures from the asteroid, otherwise you are forced to use a terrain model obtained by other means which introduces the possibility of undetected misalignment - your camera and your radar, for instance, are looking at slightly different spots).

For autonomous attitude determination, there's nothing new here: star and Sun trackers, laser gyros, and MEMS accelerometers.

For formation flying and collision avoidance, you have to think about corner cases when one of the sats in the swarm has lost attitude control and is outgassing, threatening to collide with others. You can use optical reflectors and targets to make combined lidar/camera measurements.

If the satellites in your formation have comm links on, you can obtain extra information to feed into your fusion algorithm from the low-level params read from the comms card:

• Doppler frequency shift
• time difference of arrival, including TDOA sent back to your sat by others

Needless to say, run-of-the-mill industrial and retail wireless protocols and cards don't usually cater to this niche segment. You have to design your own protocol and find ways to implement it in hard- (FPGA) and software (SDR).

References:

• Grelier et al. Formation flying radio frequency instrument: First flight results from the PRISMA mission. 5th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC). 2010. DOI (paywalled).

• Another look at the PRISMA mission: http://issfd.org/ISSFD_2009/FormationFlyingI/Delpech.pdf

TL;DR

• Commercial off-the-shelf wireless won't be able to provide navigation data to swarms operating near an asteroid

• Specially designed wireless comms networks will be able to supplement but not replace autonomous navigation and attitude determination equipment

• Optical, radar, and wireless comms technologies can and should be used in synergy to improve navigation and formation flying accuracy.

Answer 2

With the right sensors and software, one probe could autonomously establish an "orbit" around an asteroid. I put that in quotes, since the gravity field will make the trajectory more complicated than the orbit you may be thinking of, depending on the distance from the asteroid.

A wide range of sensors might be employed, including things like LIDARs and RADARs. Though it could be done with just cameras and an IMU. Cameras can provide attitude information using stars, orbit determination using the target asteroid and other asteroids, and distance and location relative to the shape and surface features on the target asteroid.

The software would at first have the probe do distant flybys and then closer over time in order to map the gravity field, spin rate, and take images of the asteroid. As those maps are built up, the probe can reduce the distance of the flybys safely and enter orbit-like trajectories.

If you have lots of probes at lots of asteroids, then it would make sense to have all the software and smarts on board. Initially though, you would use and develop software mostly on the ground for these tasks as you learn how to do it reliably and efficiently. Later you would migrate the software to the probes.

Several probes at the same asteroid would be able to map it much faster, exchanging accumulated map and gravity field information between the probes. Though now you have the added complication of collision avoidance with other probes.

I don't know that there would be much value in collecting inter-probe data types, e.g. inter-probe doppler or range. They can each do their own navigation independently using maps of the asteroid, and report their trajectories to each other just for the purposes of collision avoidance. (TCAS around the asteroid.)

If one of the probes dies, you need to predict where that one could be from its last reported position and velocity. Hopefully it will soon leave the system or crash into the asteroid. Otherwise the uncertainty on its position will grow over time. Then you will just have to rely on Big Sky Theory for collision avoidance with that one.