 It is a noon hour on Thursday folks that are also here in our Think Tech studios downtown Honolulu momentarily transposed to looks like Kahana Bay or somewhere anyway our show where the drone leads will you bring to our public the inquiring public all the new and infer new information you need to think about drones from operations regulations and sometimes technology and today we're going to talk about the math of drones math of drones what's that all about joining us from far away Syracuse New York in the snow belt and humidity belt we have Dr. Sasi Prabhakahan of CEO president and chief of AK Robotics Sasi welcome on board from a far away location here hello thanks thanks for the introduction yeah thank you okay and then acrobatics yeah I can call that we'll call it acrobatics okay yeah we'll re-pronounce your company name and we'll keep pronouncing your own name as Sasi to make it the easy part but you've got an intriguing outline of things behind you there that we can see we can see somebody moving around so before we talk about math let's talk about what you got behind you there this is my R&D office are based in like a city of Syracuse and it's an upstate so here we have our R&D lab and we can see a net cage so then we come up with a new estimation team or some kind of related to the drone yeah to be safe yeah we just do everything the other side and consider to be safe yeah like that is the validation testing part because that's what AFA is also looking at like they need a space and reliable drone yeah and we are on that one so first we wanted to make ourselves safe and comfortable operating the drone and once you come up and do everything good yeah then we will launch it in our field to get all these certification AFA approval not affecting and having people so here you have all over like a wind stop testing computers and the drone components actually we build both the hardware and software for the flight stack so we are specialized in autonomous navigation guidance and control so we'll talk more about that one why autonomy is more important and what is the safe autonomy yeah and that is what we all care about and these are some of the platforms that we build to validate our uh finding so we do the guidance navigation control so we put all these things as source code embedded in this platform do an indoor testing we have optical motion tracking system validated against step one then once everything is good take it out and do a real-time uh turnout and kind of case study so this is what it's all about that's pretty cool so right in your own office right where you work and do your daily work you've got the test range as well they get an indoor test range leading to outdoor testing and we'll talk about that in a minute but before we're talking about acrobotics let's talk about how that company came into being and where you think it's all headed because this whole world of drones is just exploding as you very well know yeah so this is a good question so uh i'm personally like uh i was like a researcher still i'm a researcher but before that uh before starting this company i was like a postdoc scientist at drug use university where we are again doing the code research about unmanned systems and before that i was a phd student and still i was doing all these guidance control and navigation problems for the general unmanned systems like including spacecraft self-driving cars and eavs as well so as things getting really tightened now it's becoming a big boom for this unmanned system autonomous vehicle the state of new york uh wanted to stand uh uh stop in this particular domain so they wanted to keep the upstate new york as their drone capital or the drone central like so all the global companies all the global like r&d labs can come here through the testing and they wanted to build an ecosystem here so the government spent a lot of money on the fund there is so many active projects going on here and uh one program through the state of new york is a genius new york program which is like a world largest business incubator competition for unmanned systems specifically for drone based technologies so it's an international competition so all startups and middle companies can participate in this one with their unique inventions and some technology so in the very first edition of this genius new york competition like i applied like uh just to with all my ideas like whatever i was doing as part of my academy research and development i wanted to kind of bridge that gap because the industry is looking for something and at the academy the people the researchers in academy they were doing something so there need to be a bridge between these two things then i found this a good opportunity to take all these uh the hardcore research and development happening in these universities to the industry because the industry is in much need in looking the very big demand for this actual science behind this autonomy the unmanned system and take flight so i found that a good opportunity and i have a couple of patents and tons of papers uh regarding the guidance navigation control of the system so with all these things i submitted my application and uh my company got selected uh kind of out of 250 other competitors and we are incubating here in the circuit take that and so this is also a government incubator and accelerator for small business and so this office is under their hood so we are directly funded by the state to start all these things and it's all going so now we are bridging the gap between the sign and the engineering that's that's fantastic and you and i first met about six months ago in san diego at the ns faa ipp kickoff meeting and appreciate the enthusiasm you had there and the ideas and what you're doing now and showing us the background and and describing more how the company came into being that's pretty a pretty good testimony to the to the to the sincerity that the state of new york is applying to the drone situation and i think we all applaud the way the 50 mile corridor test range has been generated in new york and that was happening right here and it was but it's done to save the state money that was the part that really struck me it's an investment that's already paying off because they don't need to have the uh the chase aircraft uh trailed behind the national guard aircraft as their UAVs as they're going from site to site so the training got better the cost went down don't need the manned aircraft to support and a hot spare to carry for the one that is doing training or doing it the following so cost savings by virtue of investment that is a really interesting story and to know you and what you're doing about it is is is quite incredible what i what i and the fact is you're working on guidance navigation and control that's like the core of the whole aspect of the UAV if you don't have that you don't have a UAV you certainly don't have an autonomous one and so what i had wanted to do was have you lead us through a conversation that we could use with teachers and and students in school i'm talking about high school even elementary perhaps in that regard and and of course university and postdocs as well but the whole core of the drone system is is a lot of mathematics and you know you pick up something like this and you look at it and you can see right away we've got mechanical issues like we've got structure we've got materials we've got fabrication we've got propulsion we've got fuel mechanisms we've got uh some form of control we've got electronics we've got radio communication we've got sensors we've got uh need to be reliable and durable we've got on the on the ground station we've got the need to do a lot of computation and analysis of what's being recorded we need to do emission planning there's so much in here that when you look at it you see some but what you don't see is what's inside and what you're dealing with is totally uh under the cover under the hood uh what's inside and i would say we're at a fairly elementary level of that right now moving into a much more advanced domain and is math that's going to lead us there and and math i came out of aeronautical engineering we all deal with triple-intervals and things like this on aerodynamic forces but uh that isn't what's needed here we need here the dynamic math the the various forms of pattern recognition uh covariance and some of the more exotic factors of math that lead to a different state of thinking a different state of connect we're not talking about arithmetic calculation we're talking about insight generated through computation so uh if we wanted to approach high schoolers and tell them what domain of math to think about or even approach our folks at the university and generate a math for drones curriculum or uh sub-curriculum tell us what you think we would need to do to start down that direction oh yeah it's a a much needed thing now because everybody's like fascinated about drones and applications who can do this can delivery pizzas it can delivery anything and it can't but there are so many bugs doing around these things but it's really good to have all these high school and elementary school kids especially like involved in the science behind this one so so i normally define and understand science using mathematics because i may not know german i may not know spanish i may not know uh uh any other form language but i know this particular language called mathematics and using that language i can communicate with science the nature so there is a natural scientific causes that need to be like encoded mathematically and then that will be translated to programming code assembly language and that mission uh had the drone the the mechatronics device can understand these things so so this is the basic foundation so as a high school and elementary school kids like they always have this question even i had the same question when i was going to high school so i'm doing all these linear algebra some arithmetic uh how i'm going to use all these things in my life and how i can get some kind of uh like inside about like what it is going to do in the real world application so for example just if you take a simple like a mathematical equation like like a linear velocity or linear acceleration so in a high school level the students can get some understanding and some feeling about that particular thing the acceleration the velocity and there's also like other terms the higher order terms called the jerk the snap these are mathematical things and they are actively like working in all the drones that we use when we try to fly a drone like we need to activate the drone so there is a gravity parameter so the the thrust will be generated against the gravity so all these things so but to understand all these statistics the science behind these things the mathematics is the really really very uh that's the only way that we can understand all these things for example if you want to take a drone from a point A to point B then one of the things that we need then we can use the biomimetry inside that one the students can observe how naturally things are like carried out like they can see the flight of a back and they can also see the flight of a bird or some other insect or some flying thing and they can't observe from that one for example a bird a bird uh users like uh it's a vision sensor with its eyes and the echolocation that is like an ultrasonic sensor then they can find the people and the uh the mechanical clots of those things the electronical analogous of those things the eyes can be replicated with a camera so in general uh kind of the bad eye they can try to see how the camera can be used to do the same thing and also for the echolocation they can use ultrasonic sensor so when they fuse these two things then that is the navigation part of a drone so so this is the high level physics but the understanding the mathematics behind that one so for the very beginning of these uh college students college students will be introduced to these uh elementary level of this control problem like the Kalman filtering and why do we need a filter and what a filter is doing what the mechanical filter and what of an electronic filter and what about a sense governor so those things they build some kind of understanding about all these uh uh in the elementary school about the specifics of this drone or any other mechanical system then with that inside they can really do better in the college so they can easily connect all these things in their future educational career and understanding all these things but as far as the math is concerned like uh all about like uh algebra so for anyone who is not uh happy learning linear algebra they cannot have build a system like this like they cannot build the brain of the system so it all starts with that really fundamental linear algebra and most importantly the physics so I would emphasis all the students to get some idea about all these physical things is what's the mass what is the weight what is the difference between the mass and weight so they need to know all these things and what is the press and what is the torque so drone is some easily available platform that anybody can just go buy in a market and can just get some feeling about all these things so there is a mass okay there then we need to generate a fresh to lift that mass okay so just go to the textbook the high school textbook and see what is the equation that is relating the mass and the press and how this propeller is going to generate that one then there will be some little bit of aerodynamics coming in and so as a high school student they'll be getting all opportunities they will be learning biology they'll be learning physics chemistry pretty much everything is going inside the drone so for example the flight of the drone can be mimicked from a bag or from a bird and on the other hand like uh so there is a linear and angular momentum terms like for example you cannot stop the drone just like that if you just apply the brake or something it won't stop in the air so it'll just take something so the students can think about that why it is not stopping like that so what I was thinking about is how we would construct or think through a one semester program that would touch on all these aspects without getting into a lot of depth but show the application but let's let's take a we take a one minute break in the middle of the show let's come back after that one break and talk about how we would think of a one semester class that would bring in bits and pieces of all this to give people that instant insight can we one minute later yep looked in a shoe she had so many children she didn't know what to do she gave them some broth without any bread and kissed them all soundly and put them to bed hunger is a story we can end end it at feeding america.org Hi I'm Dave Stevens the host of Cyber Underground every Friday here at 1pm on thinktechkawaii.com and then every episode is uploaded to the Cyber Underground that library of shows that you can see of mine on youtube.com and I hope you'll join us here every Friday we have some topical discussions about why security matters and what could scare the absolute bejesus out of you if you just try to watch my show all the way through hope to see you next time on Cyber Underground stay safe it is still noontime folks noontime hour here in in honolulu and six fifteen time period over in the syracuse new york where sassy is standing by with us again from acrobatics uh sassy dr sassy pabaga han did i get it pretty close and anyway sassy yeah yeah you're okay with that i like that so we were talking before the break about the incredible role that math has in something as small and as complex but as as effective as the drone such as the ones you have behind you there and you went through in your discussion some of the aspects of math again we're not talking about just the pure calculational aspects but about the uh inspirational inspirational i guess you might say and and actually drones and stem could be a fantastic inspiring factor for people to think more about the math of the future but we've got to think about the math of the the static item structure uh and such the dynamic aspects come out of control the the operational aspects like safety and reliability and dependability those can be modeled mathematically as well we do that all in the aerospace domain today this needs to be injected into our thinking process at the elementary at the high school and then in the college level so as i was saying during the break that i remember two years before you got through enough time to was to be able to handle aeronautical engineering in in days gone by and it seems like we have to work a lot faster today so if we were to think of a one semester the math of drones curriculum of some kind and maybe you know a semester is what uh 18 weeks these days that's like nine two week segments uh what could we realistically do to illustrate the essence of these multiple branches of math in a quick sense without actually training them but then the application side without actually having the learning we got matlab these days for example a lot can be done in sim these days so we we seem to have generated the tools to allow us to go much faster forward what would you think of a one semester class a uvsi sponsoring or something like that that is one thing like even like uh yeah schools need to have that such kind of curriculum because it's drones it's not a single major or something it's a multi-disciplinary approach so one of the things going inside is like uh that is a lot of mechanical engineering to make all the spectral designing the couplers and uh that uh add drag interaction so that is a lot of aerodynamics and going with that one and some chemistry guys can exploit those things like they can do the molecule structure like uh what is it how the black coefficient is going to be changed over the temperature and in different medium because there are nooses and they want to fly drones in venus or in mars so they don't have the same atmospheric condition as we do so these kind of there is a lot of chemistry that's a totally different atmosphere with different like add into the different molecules so how these and so that is the chemistry major people can jump into this one they can learn and they can probably contribute into that one and there is a lot of electrical and electronics going in this one a software development a hardware development firmware development so that is a high level like a control algorithm and that will be running on the very higher outer loop and that will be a lower level motor controller that will be taking all the control inputs and translating everything through the motor language so there is a lot of firmware in that going so compare one student then jump into this one and they need to know the fundamentals like uh so there are multiple like kind of disciplinary things and the main important thing is like the controls groups so the controls uh students measuring the controls that can do come out with a simple linear PID controller and when they graduate and join the phd or the advanced degree then they can just expand the same thing so i did all these things in my undergrad a PID controller but this is having this kind of problem so and what i need to do now is come up to come up with a non-linear controller so the non-linear controller on manifold so this is a totally evolving process so if someone is really passionate about this drone and if they start everything from the elementary school then during their college the entry of the first second year of the college they will be to combine all these things together so a proper curriculum will be having a one-year probe will be having uh fundamentals about uh the mathematics like it's nothing more than linear algebra so how do you invert a matrix how do you take uh like a vector measurement sensor will just give you vector measurement if you want to measure the uh the altitude of the drone how are we going to do just going to put a laser lighter sensor in the bottom single point source lighter sensor and that will be giving everything as a float of kind of a bit and pieces so how to kind of acquire the data and how to process that one of mathematics not advanced mathematics not any mathematical it's a simple like pre-level mathematics but how to kind of acquire the data how to process the data then again simply use a simple butterworth filter so there is some kind of control kind of engineering going in so the fundamental course should talk more about linear algebra the linear algebra is very fundamental for all the kind of but a simple like a toy drone it's just linear algebra you don't need to know anything other than that it's just if you're good with linear algebra then you can start to build your own like a toy drone but if you want to make an autonomous like a sophisticated drone then on top of the linear algebra you need to know some kind of uh kind of uh non-linear dynamics and control approach so you need to know what a hamiltonian is what a like granjean is so that is for the higher level but for a beginner course or crash course linear algebra with some programming skills and it's not even super complicated it's like the adeno level the adeno one-on-one level programming a simple how to put two vectors and how to subtract two vectors how to implement a simple uh butterworth filter you know these kind of things should cover the programming side and when it comes to the controller side it's a very simple like a PID controller a linear PID that is more than enough for a toy drone so so he'll be covering the linear algebra part a simple programming the introduction to programming level and then some kind of another important thing that I forgot to mention is like a mechanical understanding it's they know need to do a course in this one but they need to have some kind of understanding so if I want to select a material it's some kind of common sense like whether it should be made of iron steel aluminum or like a carbon fiber so that makes them to think about what is the weight to strength ratio so that is a kind of introduction to mechanical engineering but all the components are already available in the market so they know need to do anything they can just find some carbon fiber and they need to know how to whatever manufacturing process involved in missioning such things and they need to know like what a lathe mission is what a drilling mission is and but most of the things are already available if they want to do something on top of that one a simple 3d printer can do most of the things for them and again the same skill set whatever they have learned in this linear algebra and in the the basic physics it will be helping them to kind of form the foundation for printing or getting some insight of how to develop a word a 3d model and all these kind of parameters so the comprehensive course on this 101 of this drone will be and this is not about the applications that this is about internally if you without knowing the internal components of the drone it cannot like kind of be a successful like a researcher in this aspect and the future needs a lot more of these kind of people it's not someone with mathematics skill it's not someone with electronic skill it's like a combination so drone is a very good platform and a very good approach to attack this multi-disciplinary aspect if you want to build a drone you have to be an electrical engineer you have to be a mechanical engineer you have to be a kind of an aerospace engineer a computer scientist a programmer and also a pilot so you can all these things you've kind of covered the complete waterfront from from mechanical systems chemical systems and and all the way to non-linear control systems and you've tied that into plain old linear algebra all the way to some mathematics you haven't mentioned yet such as calculus of variations and Markov chain modeling and some of these exotic aspects so you've you've tied the whole thing together in a very nice way and I really appreciate that if we could get that story to some folks who do academic curriculum development and think of a piece that fits at the high school level a piece that fits at the undergraduate level I think we would do a favor to the business because I think as you said this is multi-disciplinary multi-functional and and a strong capability in just one area isn't going to get you there isn't going to advance the state of the art as as we need but I was intrigued by your comment about the non-linear that's something that our aspect our our our our industry doesn't understand very well and I think a lot of people don't understand I mean aeronautics emerged by linearizing everything and the whole idea of an airplane is is it's totally linearized and you have prevention devices to keep you from getting into the Lonnie Lonnie linear response areas because you can't handle them so you've broken through that code and and you you've moved into the non-linear domain which is a major advance in that direction so tell us a little bit in the two or three minutes we have left you tell us a little bit about how do you explain that to our audience okay so now we are moving to the graduate level of the control column that we are doing especially in approve audits we are trying to bridge the gap as Ted mentioned just now like the industry still working the linear space but that is actually happening so the traditional system uses eek of a extended carbon filter for centrifuging and it uses linear PID for kind of attitude and patient control and it's a simple like a kind of a greater circle or a geo busy problem for all the guidance thing but that is not for a graduate who can understand to make the exploit the system to get the maximum out of it without harming anybody to make it in the same region so what we are trying to do is like we are coming up with an engineer like a state estimation team they call the variational force estimator that is based on the state Lagrangian principle that uses that uses the energy model and that is converge to the real time so and we are using a finite time stable controller so whenever I mention all these non-linear things I always stress this stability so what we are trying to do is making that non-linear system stable and flexible so it should be a system should be stable flexible and robust so if you can achieve these two things these three things then the system is considered to be safe and reliable no linear mathematics can do these things so you need to do your calculus on a manifold because all these system all the drone everything is evolving on a non-linear state space not a linear Cartesian phase it's evolving on a non-linear state space and the way to represent the non-linear state space is by using this manifold approach so we do all our calculus on a geometric group called the special including group the C3 there is a combination of these rotation matrix and position vectors and that is on a manifold so that that's a lead group of rotation actually and position let me just intercept that for me because we're going to I think we're going to be out of time here in a minute but the concept of manifold operations, manifold calculations super because that allows the non-linear to be managed then the other piece we won't be able to talk about here but that's the issue of fault accommodation and how we're going to handle all that with there's failures of some kind sense of failures or or equipment failures and that would be Markov chain modeling and things like this that manage the propagation of fault forward so but at this point in time Saucy I truly appreciate your your incredible expression of this future and how we have to get kids going in this direction of non-linear mathematics in order to push the state of the art to where it has to be so thank you very much for coming on it's a very it's only half an hour a very short show it's hard to get all the information in there we'll have you on again and we'll talk about the next steps of what you're doing at AK Robotics and where this is going in math and again folks we'll see you next time on where the drone leads