חשפו את עתיד מאדים: הסוד לניווט מהדור הבא!

uh the song. Awesome. Um all right. Well, thank you so much for coming everybody. Um as Professor Mandel said, my name is Daniel. I'm a hopefully final year PhD student in the lab. Um and we're really excited to share this project with you today. Um this is something we've been working on in the engineering systems lab for the last three years or so. uh we've been really looking forward to sharing it at this conference. So jumping in, as we discussed a little

bit this morning, today our rovers and landers at Mars primarily rely on vision based techniques for position estimation. The way that that looks is that they take pictures of their surroundings. They map objects in those pictures to onboard maps and then they use that to estimate the relative position. That works really well, but it doesn't work well in things like, you know, degraded environments. So things like dust storms, it doesn't work well at night and it's not a terribly scalable system in the long run. What we would really like to have at Mars looking forward into the future in which we have many more assets at the planet is something like the global positioning system or Galileo which is the EU's version of GPS. Now there have been several other authors that have looked at this and realized this problem and they've proposed various different you know GPS analog navigation systems at Mars. So you have some that have proposed uh versions of global coverage const constellations similar to GPS. Others have also looked at more local constellations and these are very good. But the problem is that in general they haven't found a way to actually deploy these satellites to these orbits. And so that's unfortunate because deploying satellites to multiple different planes is really challenging. For one, putting any orbiter uh in orbit around another planet typically requires large amounts of propellant in order to enter orbit. Uh and so some clever engineers of the

past have found somewhat of a solution to that orbit insertion problem. They've proposed this concept of arow capture. The idea of arow capture is rather than using propulsion to decelerate when you revit the planet, you quite literally fly through the atmosphere of that planet that generates drag. Drag dissipates velocity and slows you into a captured orbit. The way that that looks is that you have some planet with an atmosphere. You're approaching hyperbolic. You enter the atmosphere here. You exit here. And then again between atmospheric entry and exit, you generate drag. Once you're outside of the atmosphere, you do some type of paraps rays which raises you into your final captured mission orbit. And that's great. The problem is that

two-dimensional arrow capture and two-dimensional propulsion don't really allow you to access multiple different red ascensions of the ascending node that you would need for something like a Walker delta type GPS constellation. And what I mean by that is that when you're arriving at the planet today, what we do in order to select the different orbits is we use a technique called Bplane targeting. The way that that works is that you have this plane perpendicular to the planet you're approaching and you can do very small burns to kind of vary your arrival point. That gives you kind of these families of different possible arrival trajectories. If I propagate those to completion, we see something like this. And what you'll notice is that all of those orbits intersect that dashed uh approach asmtote. What that's saying is that we can't get orbits from any given arrival that have variable kind of in equatorial plane uh angle uh angle orbits. Uh and so fortunately to this end we have a potential solution.

What we look at is in the engineering systems lab is this concept of threedimensional arrow capture. So rather than this 2D version, which is that what basically every aerocapture study over the last 50 years has looked at, what we look at is something that looks kind of like this. The idea here is that while you're performing arrow capture, you enter the atmosphere, you're decelerating. While you're decelerating, you have some amount of lift. You can take that lift vector and point it in a specific direction that creates a force which tends to allow you to rotate your orbit plane. And so in this case, we entered here and we performed as much as 50 degrees of plane rotation. Now, that's really nice. And so in a past journal article, we showed that the amount of plane rotation you get is proportional to the lift to drag ratio of your vehicle and the approach velocity. And if I just reveal those curves, that looks like this. So what this is showing is that if you're arriving faster, you have higher dynamic pressures. Higher dynamic pressures give you more lift. You can get more plane rotation. Similarly, on the y-axis, if you come with a vehicle that has more lift, well, once again, that gives you the ability to change your plane in much greater ways. And so, And so, once again, returning to this case

orbits, if I again fly those exact same orbits that we approached on, but now I do some amount of plane rotation during arrow capture, well, now we see captured orbits that look something like this. And what you'll notice is that we've shifted those orbits off of that dashed incoming approach asmtote. Uh meaning that we've allowed for some RAN rotation. So the possibility to deploy to many different orbits with different RAN is suddenly uh kind of in play here. So pretty early on we realized that um the combination of this Bplane angle and this error capture plane rotation are fundamentally coupled. Um via a derivation that's too long to go into in this presentation. We showed that the inclinations I and the rans omega that you can get are equations that look like that. And what I'll do is just plot these two things. So again, my two inputs are that plane rotation and that Bplane angle. First, I'll plot the inclination contours. They look like that. They make circles around the origin. And second, I'll plot my rand contours. They like look like that and kind of make fans going up and down. And I can just put some dots on here to help explain what's going on. So if I put a dot on the y- ais that's zero arrow capture plane rotation it's just bplane targeting well you get an orbit that looks like that similarly I can bplane target in the opposite direction it still is just a two dimensional orbit if now I put a dot on the x-axis so that's approaching on a bplane of zero so equatorial and then performing some amount of plane rotation this is about 45 degrees I can do the exact same thing in the opposite direction and then I can combine the two so something with positive x positive and I can get to quickly kind of very interesting bespoke orbits. And the takeaway here is that with a capture plane rotation and Bplane targeting, you have a pretty wide range of orbits that you can get to from really any approach vector. And so conveniently, that takes

me to the objective of this talk, which once again is that we'd like to find ways to deploy these multiplane, multi-rand PNT constellations at Mars from one single approach. Uh, and as part of doing that, I'm going to answer a few questions. The first is that there's likely some trade-off between cost or mass and performance. We'd like to investigate that. Uh and secondly, we'd like to look at what plane rotations do we need to do to access these constellations? What vehicles do we need? Can we fit them inside of launch vehicles? Uh things like that. Uh so I have to go into methods just a little bit. Um Walker delta type constellations like GPS are defined by four variables. That's the number of planes, the number of satellites per plane, the inclination of the constellation, and its altitude. And what we'll do is we'll sweep across all of those different variables uh and try to do uh two minimizations of two competing objectives. The first is that we'd like to minimize POP. Uh P do for our purposes is essentially uh proportional to user position error. And so what we want is the lowest possible P dot because that gives us the lowest possible air on the surface of the planet. Uh and then the second thing of course is that well we want to minimize mass. Mass is the sum of essentially

three things. The first is the payload. That's all of our satellites and all of our uh on all of our planes. We have a couple different reference concepts for how big these satellites are. Uh GPS is about three three uh 3,800 kg per satellite. Uh Galileo, Europe's version is about 700 kg. Uh Galileo is much lighter because it doesn't have the military payloads that GPS has. Uh, and so we actually expect Galileo to weigh much more than you would uh need for a PNT sat at Mars. The reason being that you don't necessarily need all the redundancy that Galileo has. You don't need, you know, the anti-jamming and things like that that these sets have. Uh, and they're also designed for operation in MOO, which involves pretty significant rad hardening, which you won't really need in the Martian environment. Uh, and so in our trade study, we sweep across three different values of these satellites, and we'll present the results on that later. Uh secondly, you need arrowshells to fit these things in in order to do the plane rotations. We look at three different options for these arrow shells. The one on the left is a low LD sphere cone. It has really nice packing statistics, but because its lift to drag ratio is so low, it doesn't really get much plane rotation. Similarly, stuff on the right has really high lift to drag ratio, but it's very difficult to fit things in. And so, typically, you would prefer stuff on the left, but you sometimes have to go to stuff on the right. Uh and in each of these we just scale with uh with the payload mass that we're flying. Uh and then the final component of the mass that we have on here is that you also need a crew stage. The crew stage is a thing that attaches onto the aeros shell. It provides radiation, some comm some propulsion uh ability in the interplanetary cruise. Uh for Mars, typically crew stages are around 15% of the total mass. So we just add that on.

Okay. So getting into the results, as I said again, our goal is to minimize POP and to minimize total mass. That means our utopia point is down there in the bottom left. And I'll just show the trade space for one set of the inputs. So this is the number of planes. And what you can see here is that yeah, there is definitely some type of trade-off going on, right? You can get to really really small values of P do but at the expense of really high mass. Uh and so I think this chart is a bit tough to interpret in a presentation. So I'll just pick a couple designs on here to look at. This is design A. It's kind of a low performance, low mass option. Uh it has five planes, four sats per plane, 60° inclination. Uh this is design B. It's similar to the Galileo constellation. Three planes, eight sats per plane. And then design C, which is our highest performance option. Uh this is a six plane, eight sat per plane constellation. Uh and we'd like to look at um how to deploy this at Mars. So I'll take one of these and just move it up here. This is the P dot for this map for this constellation. And so what this shows is that under certain assumptions, the position uncertainty that we get at the surface of the planet near the equator is around 3.1 m. Uh which is very nice. And then this one doesn't have so much variance across the entire map. So near the poles, we actually also only have around 4 meters of uncertainty. So this is well within the GPS standard. Uh and we're excited about that. Uh and so as I said at the beginning, our goal here is to figure out how to deploy these things. So what I'll do is I'll bring back back that plane rotation and Bplane angle chart and I'll just put the dots on here for this constellation. So we have six planes, six dots. They're all spaced and ran by about 60°. You'll notice two of them are on that y-axis. So no plane rotation required. The others are kind of in groups of two on either side needing about plus orus 45 degrees of rotation. And there are kind of four different dplane angles that I need to fly. And so if we want to go and fly that, that looks something like this. So what you're seeing here is the four

groups are approaching on four different B planes. They enter the planet's atmosphere. They perform arrow capture. Uh once they're done performing arrow capture, they're rising out of the atmosphere. Now they're just rising up to their target epoapse. I'm only highlighting one in blue just to help show what's going on. Uh once they're at epo, they perform that parapsis raise maneuver. And I can take this and spin it around. So what you can see is that we've spaced in inclination and ran very nicely, right? Our kind of take at the beginning was that it's really hard to get to these different rands propulsively. And so just looking at this from another view, so looking from the north pole down, you can see that again those rands are spaced out very evenly. We're at all those different inclinations. Uh and so this has you know this technique has shown that well yeah we are from this one approach vector and in theory one launch able to get into all those different orbits for that constellation. Uh and so one of the questions that comes up with this of course is well you have a bunch of satellites in this orbit plane now but you need to somehow separate them right you need to get them to different uh slots inside of that plane. The way that this works is that as you're approaching parapsis rather or as you're approaching epoapsis rather than doing that full parapsis rays burn you basically just do smaller burns to enter slightly smaller orbits. They'll sit on these slightly lower orbits for some period of time which allows them to kind of phase apart over time. And so what I can do is I can combine that technique with our approach trajectories and that looks like this. So once again, the exact same trajectories. They reach epoapsis, they split, they enter all these different phasing orbits. Now they'll sit on these phasing orbits for a period of about 6 to 7 days. Uh you'll see that this looks pretty similar to how Starlink deployment looks. And that's because conceptually it's really the same idea. Um you kind of have a train of satellites that are all approaching together. They're separating and then they sit on these phasing orbits for a while. Uh and so we're we're excited about that. Um, you know, with this technique, you uh, again, because you're arriving in directly inserting into those different target orbit planes, you only need an amount of time equal to the amount of time to phase. Um, and so in this case, we picked about six days. Uh, so six days to deploy into these target orbits is really, uh, not very bad.

Uh, okay. So, of course, too, we need to look at, well, yeah, you can send all these satellites to the planet, but can you even fit them in a launch vehicle? Do you have enough mass? Uh, and so I just want to pull up one of the constellation rotation spaces again. So, this is the five plane 55° constellation that I mentioned earlier. And what you can use this chart to do is, well, as I said, things that need zero plane rotation, you don't really need much lift. So, you can get away with vehicles that look like a sphere cone like this. Really nice packing statistics. For the stuff that needs the largest possible plane rotations, you have to use more lifty stuff. That would be things like this biconic geometry. And then for stuff in the middle, we have to use something with an LD kind of between the sphere cone and the biconic. That would be something like an ellipse, which looks like this. Now, what we've done is we've taken the satellites and used them to size how big we think these entry vehicles need to be. And of course, we've then gone and said, well, can we fit them inside of uh inside of our launch vehicle? And so this is just kind of showing a uh representative idea of how these things would fit inside of a Falcon Heavy. Uh this is for the 200 kilogram sat version. Um so Falcon Heavy has a payload to Mars of about 16 to 17 tons. So if your satellites are really light, then yeah, it looks like you can probably fit them all in there and you can go fly this. Of course, if your satellites become heavier, something like 450, 750 kilograms, well, then you're probably looking at something like a Starship or an SLS launch, maybe a ride share, uh, with some other mission. Um, and so quickly it gets it gets heavy. Uh, so just to to finish this up here,

so um, it's worth comparing our method to, you know, some other possible methods of deploying these constellations. So the the strategy that I've proposed to you involves essentially one heavy launch, multiple different aeros shells. We do have a pretty big periapsis raise maneuver, but we can manage that. Uh and then it takes, you know, between 5 and 10 days in order to do orbit phasing once you're in the system. You might be thinking, well, you know, could I just do this with propulsion? Uh and yeah, so if you need something like 50 degrees 55 degrees of plane change, which is what I'm showing here, well, even for very low arrival velocities, you're looking at between 3 and 4 km/s of delta V. For higher arrivals, you're looking at between six and seven. Uh pretty quickly, this is infeasible for any type of um interplanetary chemical engine. You might consider doing it with electric, but then you're looking at this time of flight trade-off as well, and you still have to somehow inject into those target orbits, uh, which gets tough. Uh, you might think, well, what about rand procession using J2? So J2 is a gravitational perturbation induced by the oblateness of the planet. Uh, J2 is actually what Starlink uses to kind of phase apart and enter different rands over time. Uh, and so at Earth in LEO, uh, J2 gives us about five degrees of rand procession per day. Out at Mio, it's much lower, only around 0.06. J2 at Mars is a little bit higher than it is at Earth. So, in low Mars orbit, we get about six degrees per day. In medium Mars orbit, which is where we are, we get about 0.07 degrees per day. And this kind of shows why, for instance, you don't really use J2 to deploy things in Earth MO. It's because it's really slow. The same thing holds at Mars. So at Mars, if we wanted 120 degrees of rotation, which is what we would need for a six plane, it's going to take us 220 days. And that's only for the raw value, right? What we care about is kind of the delta between planes, which typic, you know, very quickly you're starting to take many years in order to get into these uh into these planes. Uh and finally, you might also think, well, what about, you know, I've told you this issue with I have fixed RAN, right? I need to get to multiple different right ascensions of the ascending node. You might think, well, what if I take different transfer trajectories or different Lambert arcs to get out there? Uh, and that could work, but the issue is that in any given launch window, you're still only looking at around 30 degrees of RAN control. And of course, you're also going to need multiple upper stages. So, typically, very quickly, our mass is growing very rapidly. And so to this end, we don't think that, you know, arrow capture with plane rotation is the only way of deploying constellations to other planets, but we do think it shows some kind of nice uh advantages compared to other techniques. Uh so just to finish up here, I'll summarize what we've done. So uh today in this talk, we looked at this set of paro optimal pnt constellations and we showed that we can achieve GPS- like performance at Mars with these types of uh systems. Um, we demonstrated that you can likely deploy them from a single approach vector and you would use arrow capture with plane rotation to do it. Um, we looked at how these might fit inside of different launch vehicles. And finally, we showed once again that there are some really unique advantages to this type of uh this type of maneuver uh that show certain advantage over certainly propulsive deployment and kind of other techniques for deployment constellations. Uh, so with that, I'll finish up. Thank you so much for listening. I really appreciate it and I'm happy to take questions.