So, so far we have been looking at some of the fundamentals of Lyapunov theory, some preliminary background and some physical insights into how Lyapunov has to come up with different different theorems and we saw some kind of a you know intuitive understanding about it ok. So, if you recall we had seen this stability proofs based on some definition of some functions which are energy based functions and the derivatives along the system trajectories ok. So, we define some mathematical preliminaries and you know come up with this idea which what we Lyapunov has come up with ok. And now we will see more formally some mathematical kind of a stability theorems we will not get into the proof of them, but we will just see the mathematics a little bit more in detail and apply it to the case of you know development of control and you know providing the proof for stability proof for any control that is proposed ok. So, that process we will go through ok. So, let me get to the slides now to so see this first theorem we will just recap that we saw was about the stability ok. So, stability of a system. So, we are considering this system which is x dot is equal to f of t comma x where x is a state you know x is a. So, if you have n state system ok. Typically say if you take a 2 r manipulator robotic system that robotic system would have 4 states ok 2 degree of freedom typically will have 4 states. So, that kind of a system if we have then this x will be a 4 vector ok. So, 4 by 1 kind of a vector like that f will be 4 by 1 kind of a vector ok. And it is a function of so it takes r and r n and r to space r n again ok. So, that is how this is f is defined. Now, for this system this first stability theorem says that the equilibrium x is equal to 0 ok. This is a this is a x vector 0 vector of a system is stable if there exist this is now locally positive definite function C 1 ok. C 1 means continuously differentiable at one time. And locally positive definite function we have seen what are the definitions of that. So, LPDF C 1 function which is like typically designated as V ok. So, V is like you know Lyapunov function some function ok. If it satisfies this property LPDF and C 1 then we call it Lyapunov function candidate ok. This V is Lyapunov function candidate if it is satisfying these properties ok. So, this V is taking r plus means this is a time you know positive value to and r n to r space ok. So, so this is a real valued function this is a LPDF function V and constant small r greater than 0 ok. So, this is defined to have some kind of a finite radius ball of finite radius r here. So, we are defining a local definitions here we are not kind of considering like a global stability of a system we are considering local stability of a system. So, we it is sufficient to have these properties hold true in small kind of a you know hyper ball of this radius r ok. So, when this V dot of this function ok which is Lyapunov function candidate V dot is less than or equal to 0 ok. So, and this is this should be valid for all t greater than 0 or greater than t 0 and within this ball of radius r ok x belonging to this ball of radius r ok. And V dot is a function which is again real valued kind of a function is evaluated along the trajectories of a system ok. So, trajectories of a system you remember like you know V dot will be actually del V by del t plus del V by del x into x dot ok. So, this is like you know typically given as expression for V dot. So, we have seen what is this derivative along the trajectories and where this x dot is substituted as this function here ok. So, we will see through some examples how this is done and all those processes, but this is how this stability theorem is defined. And if this is valid for like entire R n space then it becomes like a globally stable system. And this also needs to be valid entire R n space ok. Then you have this notion of asymptotic stability we have seen. So, now this is a asymptotic stability theorem for. So, we need now you know we say for the same system same equilibrium is uniformly asymptotically stable. If there exists even decrescent now this is a decresency is additional property that is put here ok. So, decresency is this upper bound by class k function ok. And then you have this LPDF V this conditions are same. So, is that minus V dot is an LPDF function now this is not just less than or equal to 0 that equal to sign is not valid now it is this needs to be strictly like you know locally positive definite function minus V dot ok. So, it can be 0 only at 0 no other point it can be 0, but in the previous stability definition this was lesser or equal to 0 kind of a sign. So, now we want V dot to be strictly less than 0 for asymptotic stability ok. So, this is a more stringent condition this is one kind of a condition decresency and then there is another stringent condition LPDFness ok.  So, we will not again as I said we will not get into the proof of this theorem, but we are more interested in application. There is a there is a entire different course can be given on about like you know theory and its proofs and you know all the mathematical nitty gritties and details about the Lyapunov theory for utility in many many different applications. What we are looking at is there application in the in the mechatronics systems alone right now. So, let us say with the example ok. So, we have this example of you want to control this mass which is on the resting on the surface and applied by the force F. This force F is considered to be a control force I can change it you know whatever way I want it to be changed and we want to know what is this force if it is specified like say in this case like a PD control then whether this is going to stabilize my system or not that is what my interest and I want to use Lyapunov theory to prove that ok. So, to say whether it is asymptotically stable or it is stable or what kind of a proof I can get that is what I want to know. So, what is the equation that is governing the system dynamics is mx double dot is equal to F very simple. So, this is a two state kind of a system in terms of like you know if you want to see it in terms of x dot is equal to F of t comma x you can convert the system into that form by saying x 1 and x 2 where x 1 is equal to x and x 2 is equal to x dot. So, x 1 dot will be equal to x 2 and x 2 dot will be equal to f by m. So, this is how I can define that system, but I can also work with see for such a simple systems we can directly work with this basic system itself and understanding that our state has x and x dot ok. So, your the system can be transformed into into the error equation by considering like a x t minus c we want to take the system to x t. So, x t minus x is a error and then we can convert this m e double dot is equal to f will be the new system like that you do like lot of this little bit of you know intermediate steps to see that m e double dot is finally, your equation f and f is defined in terms of e as k p times e minus k d times x dot x dot is also if you write x is equal to e is equal to x t minus x then x dot becomes equal to e dot rather x e is equal to x minus x t that is what you need to write then e dot will become equal to x dot. So, this small integrities are there to be worked out and see for yourself then now for such a system if we define Lyapunov function candidate. So, typically for mechanical systems we resort to the energy of our total energy of a system as a indicator of this Lyapunov function candidate it is not a must, but many times it works very well. So, given some system you try to see in terms of this control and in terms of like you know system dynamics what is total energy of a system. For example, here we know that for this system half m x dot x dot square will be its energy of this mass in terms of e it is will be half m e dot square this is the first term in this v and then we will have this potential energy coming up because this proportional control here is acting as if we are connecting a spring here. So, this spring potential energy is k p times e square that is what we are doing this k p e when we put then we are kind of putting a spring which is getting deformed by the value of the error and that spring will have this e will be 0 when this mass reaches the final value x t. So, like that this term comes from the proportional control term. So, you will find this term you can take it similarly for many other kind of systems as well when you are using proportional control you can take this half k p e square as a term for the for the energy corresponding to that proportional control ok. So, this is like becomes like a total energy now this is this can be verified to be locally positive definite function ok by applying all the different conditions that we had put for locally positive definiteness of a function. So, it has both e dot and e both the states are coming here and that is why this is like a locally positive definite function. I mean it is actually a globally positive definite function with respect to e belonging to r 2 space. Then we differentiate this to get e dot and then we get this e double dot here. Now, this e double dot is to be substituted from the system dynamics equation here and whatever control choice that we have. So, this m e double dot will become k p e. So, this is x double dot is nothing, but e double dot is equal to minus k p e into k d e dot x dot is also same as e dot ok. So, this e double dot is substituted here from the system directories m e double dot is this value and then we substitute that and simplify you get b is equal to minus k d is e dot square. Now, this is not having any term corresponding to e that is why this is less than or equal to 0 not strictly less than 0 ok. That is why we can conclude that this you know this control PD control gives this system stability ok only we can say the system is stable or this equilibrium x is equal to x t is a stable equilibrium it is not asymptotically stable ok. This is important here see with this we cannot get it is to be asymptotically stable, but is it that the system is that way that only e dot is going to 0 and e cannot be going to 0 no. We know from the from the linear system analysis and our actually a perfect solution that both e dot and e are going to go to 0 when the PD control is applied ok. So, then but Lyapunov theory is not yet able to establish that ok. So, this is how like you know we can look at these results. So, Lyapunov analysis is not saying that it is not asymptotically stable it is just saying that we it is stable system for now ok. For asymptotic stability we need to do some something more to prove ok and remember again this real this rules of the Lyapunov theorem are only like you know the sufficient conditions ok. So, then if these conditions are satisfied then you say the system is stable if they are not satisfied that does not mean anything ok you cannot conclude nothing about that. If these conditions are satisfied then like you know you you have this result available ok. So, this is very important thing to know that because you are not able to find out any V which will satisfy these conditions that then the system is not stable or you cannot conclude that otherwise result is there only sufficient conditions. Now, we can apply this to entire domain of this you know mechanical systems. So, to say which are obtained by using our Lagrange formulation applied to like you know fully actuated mechanical system ok. Mechanical system I mean the rigid body mechanical system. We can restrict our discussion to rigid body systems alone here although some parts can be extended to flexible bodies also later, but right now for this course let us focus on only the rigid body systems, multi body systems and fully actuated systems ok. So, number of degrees of freedom are equal to the number of actuators in the system ok. So, this was the equation if you remember that was obtained by the Lagrange formulation and we introduce the motor dynamics into it ok. So, motor dynamic equations if you remember they are also in the in this form, but now this torque k or this is kth joint whatever we are considering here. This is actually coming from this equation or this is this is what is a connection between the Lagrange formulation which is giving us the external force in the generalized in the direction of generalized coordinate as torque will be provided by the motor ok. So, this is coming as a load torque on the motor dynamics ok. So, with this some kind of a gear reduction here ok. So, R k is some kind of a gear reduction ok. So, theta this is the theta is a motor angle and then these are some of the motor parameters and this model can be incorporated through this kind of a connection tau k. Now, this tau k if you substitute from this you get some simplification here and you get some kind of a equation ok or we can convert this motor dynamics also into into. So, this theta m can be substituted by 1 over R k into q k as a as a. So, everything will be in terms of the generalized coordinates of your Lagrange formulation that we have and this tau k can be substituted here and now everything becomes into the generalized coordinate q k ok. And this equation will look something of this sort ok. So, this has some kind of a complications coming up here additional kind of a inertia terms are getting added and that is what is happening to this equation here. Now, in the matrix form these equations will finally, look like this ok. So, this entire thing can be put into some kind of a matrix vector form ok. Then it will like you know it looks the complication that you usually get by using this C i j k kind of a terms and this is kind of gone here ok. So, you see that this is one kind of a n by n matrix where n is a degree of freedom of the system or n is number of actuators in the system same fully actuated system. And you get this D matrix little bit modified because of the motor parts coming in and then this u vector is basically all the inputs to the input voltage to the motor which is in defined this way. So, v is actually more voltage going to the motor, but this constant is getting multiplied we get our u or controlling input u in the actuator that is represented as a vector up here. Then this g vector is coming b vector is coming and then C was a big you know many different terms here that will be kind of collected in some kind of a matrix form C q and q dot C is a function of q and q dot multiplied by q dot here ok. So, this D plus j this is similar to our inertia matrix kind of a term here ok. So, now this so, this one can have another approximation to this system by saying that you have the motor equation alone, but all the terms which are coming on the motor equation you remember the motor equation was something of this sort here is a motor equation in terms of theta and in terms of this. Now, this can be considered as a disturbance and we can directly write you know some control here that is another kind of a possibility that can exist. If you want to avoid like or we are not interested in too many very high performances in the robotic system or mechanical system, then we can do that that we are just kind of considering this as a all the non-linearities as a motor as a disturbances and then like you know collect them all together as these d k terms is nothing, but this tau k term ok. And we can use linear control on this equation also ok, but now right now we are interested in like you know doing some non-linear analysis with this equation ok. Now, we want to see that ok, we propose this PD control on the joints ok. So, q is a generalized coordinate in terms of typically if it is a n degree of freedom robot it takes the robot joints ok or generalized coordinates. So, in the direction of generalized coordinate you define this u where k p and k d are matrices they are kind of typically diagonal matrices and q tilde is defined as q d minus q here. So, desired kind of a generalized coordinate minus actual generalized coordinate that is a error term that we are defining here ok. So, this u is equal to k p times error and k d times error dot is what we are defining here and these are now in the vector matrix form. So, this u is again a vector which is used here ok. So, this u is here and now we are interested in looking at how do we do this analysis using Lyapunov analysis ok. So, what is what is to be proposed as a Lyapunov function candidate here, can you think about that ok. So, see what we did for the simple kind of a mass resting on the surface we used some kind of a energy based Lyapunov function. Now, we can think of on the similar lines ok. So, what is the energy of such a system where like now you have fully non-linear dynamics of n degree of freedom robotic system happening here right now ok. So, this kinetic energy of this is based on the d j k terms or d matrix in this equation ok. So, this will give you kinetic energy ok. So, typically the kinetic energy will be given as q dot q dot transpose you know this d matrix now we have additional term coming from the motor inertia also and q dot ok q transpose d q ok q dot transpose d q dot will be your kinetic energy. And a potential energy term similar to the potential energy that we defined for this for the proportional control consider as a spring we have now because this is a matrix form this is q tilde transpose q k p times q tilde that will be the total energy corresponding to all you know variables or all the errors q tilde this is a vector here this is a matrix and this is again vector ok. So, first term here this is a kinetic energy and the second term is accounting for the proportional feedback in the in the form of a spring elastic energy ok. So, now, we have these terms corresponding to q dot also and q tilde also now this can entire be converted into q tilde alone by using this relationship q d dot minus. So, q d is is a say a fixed quantity we want to be able to a fixed desired position ok. So, so, we we consider for this discussion right now that q d is not a function of time it is a fixed point where we want to go ok. So, this is a as we saw that is a this is a regulation kind of a control not a tracking control ok. So, for this q d is constant. So, q tilde dot will be equal to minus q dot ok that is that is what we can do here substitute for this here ok. Now, if you see this time derivative of v. So, we can use this q tilde according to like you know wherever we need. So, finally, it is right now kept in q dot terms only ok.  So, it will have this terms which are derivative of these times this plus this times derivative of this. So, this is like a chain rule that we are applying here ok. So, this chain rule when you apply what is the derivative that results here is this ok. So, this is q dot transpose d q plus j q double dot here. So, first derivative of this term is taken and then half q dot transpose d dot q and then there will be a term which is same as this term. So, this half will actually go away ok. So, this half is come half should go away here the way you have this q dot transpose k p q tilde ok.  And so, so you can see this negative sign will come based on the you know transformation between q tilde and q dot ok q tilde and q actually or q tilde dot and q tilde ok. Now solving for this we know that now from the equation of dynamics here that d q plus j q double dot this part of the term will be equal to this whole thing shifted on the other side and substituted for you ok you will get this term here as u minus c q q c of q and q dot times q dot the plus b q dot ok. Now we are setting g q to be 0 here for this discussion right now ok. So, we can add and we will have some compensation to be done in control for that term ok, but right now we will not worry about that term ok to make our first understanding easier here. Then you have this term. So, this is this half is not there. So, I am not put that half here. So, you get this term first then this term as it is and so, you have derivative of the happening here and then here you will have this same term coming up here ok. Now if you see that we collect this terms in a very specific manner ok what we do see still we have not used u here u is kept as it is and then this b q dot term and k p q tilde ok. So, this c term is moved out of this place ok. So, this c term is taken out and this k p q tilde term is put here in ok and here like now u minus this c q dot minus b q dot this should be minus sign here ok. So, this is that is why this will become minus b q then you use this d dot minus 2 c term here this 2 is coming because this is half outside here. So, d dot minus 2 c q dot then q dot transpose ok. So, we are collecting this term here for a reason because we know that d dot minus 2 c is a skew symmetric matrix for the mechanical system as we have seen in Lagrange formulation and that is why this is quadratic form will yield 0 here ok. So, we do that and we get this expression for b dot as q dot transpose u times b q dot and minus k p into q tilde is coming.  So, this remember this k d is a diagonal matrix b is a damping matrix in a system that also can be a diagonal matrix here and then you get this final expression ok and this is again has only q dot kind of a terms here. So, you if you see this this relationships happening are exactly similar to what is happening in the scalar form for our simple mass on the on the surface kind of a system ok. So, again we get this is less than or equal to 0 ok then because there is no term corresponding to q. So, for some values of q this q which is nonzero this term is still going to be 0 ok. So, if q dot is equal to 0 ok. So, that means, it is violating this you know pdf-ness of minus b dot kind of a term that is why this is less than or equal to 0 ok. So, this q dot will be this will this condition we can make q dot is equal to 0, but q is not equal to like you know q desired yet ok. So, this is not proven yet. So, q dot is equal to 0 means q tilde dot also will be equal to 0 ok. So, this to prove this we need some more kind of a tools ok. So, this is this equation is giving just a stability in the sense of Lyapunov and no asymptotic stability here ok. So, so we need some additional tool and that tool is is basically Lassala's theorem ok. What is this theorem telling us is given here ok. So, this suppose the system x dot is equal to f of x is there now see that is removed here. So, this system is autonomous ok there is no explicit time dependence happening here now ok. So, this system is is x dot is equal to f of x only and there exists see this function this again our Lyapunov function candidate and this v is pdf and radially unbounded. So, there is a new property coming here for this thing is should be pdf and radially unbounded and then v dot is less than or equal to 0 ok as we are getting in this case here that p dot is less than or equal to 0 for all t greater than 0 and such that this x belongs to R n space here ok for all R it is for all x it is valid. Then we define this set R here ok how this set is defined in this set is defined such that x is belonging to this R n space and for all t equal to 0 v such that v dot is equal to 0. So, this x is such that v dot of t comma x is equal to 0 ok. This is how this set is defined so we look at this v dot is equal to 0 condition now. So, we v dot is equal to 0 condition now we need to look at ok so v dot is equal to 0 condition means like q dot is equal to 0 ok. So, we look at this q dot is equal to 0 condition and see that x is belonging to this R n space or this q or q or like you know this x is belonging to this R n space such that v dot of x comma t is equal to 0. Now, this x is nothing but q in our case now ok. So, we will see with the example later, but understand that we put this condition such that v dot is equal to 0 and x is belonging to this R n space ok. So, we collect all such x together and observe them ok and this such all this x or this set R does not contain any other trajectory of the system other than the trivial trajectory x is equal to 0 then the equilibrium x equal to 0 will be a globally uniformly asymptotic stable system ok. This is what is Lenssela's theorem saying ok. So, this theorem is what we need to make use of in our case ok. So, for PD control we apply this theorem if you see that v dot is equal to 0 like you know means like you know v dot is this is equal to 0 that means like you know q dot is equal to 0 ok. Then q double dot q when q dot is equal to 0 I differentiate it once and I say that q double dot is equal to also 0 and this is because this q dot is equal to not instantaneous it is for all time ok. So, we need to see that for all time t is equal to 0 v dot is equal to 0 ok that is a condition that is coming. So, then I see this in the system equation ok. See in system equation wherever q double dot is there I will put that to be 0 and wherever q dot is there I put that also to be 0 and then what remains is this control term here ok and in that q dot again this is equal to 0 ok. This means that k p times q tilde is equal to 0 ok and this implies that our q tilde should be equal to 0 and q tilde is like you know the error between the desired and actual directory ok. So, this is how we establish like you know in the full mathematical sense that PD control indeed will take position and you know the velocity both to the final desired kind of a value ok. So, this lesser as theorem implies that then the system is asymptotically stable and this is what like we make sure that our system is taken to the final position also and final velocities are also to be desired value which is 0 for the final position.  So, you do this control computation and you introduce this term in control to compensate for that ok. So, this is u minus if you without compensation it will come like this here ok. So, in u if suppose there is a term which is g of q then that will get cancelled out in.  So, this how like you know we go ahead and handle that ok. So, overall conclusion is that PD control can asymptotically stabilize a general rigid body mechanical system this is very very important kind of a conclusion here. So, if you use simple PD control on many systems it will it will they are fully actuated it will work ok. It will take the system to its final value in the presence of gravity if there is a gravity compensation to be done that you do that and then this PD control will work ok. So, even without having all these kind of analysis one can definitely like control any rigid body mechanical system fully actuated by just using PD control and it should it should work ok. That is why this PRD controllers are kind of quite powerful tools that are available in the in the market and you know they they work quite well. So, so in the presence of so even if we do not know whether the system is a non-linear or linear or as long as it is a fully actuated mechanical system there are no under actuation in the system then this PD control is going to going to work quite well. Now, the problem comes when we have want to do the trajectory tracking ok. This trajectory tracking is an is an important issue here. So, for that we need a lot more kind of a thing to be done ok. So, so the trajectory tracking problem is is simply like the suppose you have a two-link manipulator say just explained by using this two-link manipulator, but we want to track this trajectory like say the problem is given that we want like to go from PS to PF in 3 seconds along the along this path a straight line path. This becomes like a motion or path planning problem ok and this the solution to this path planning problem will give you theta 1 desired and theta 2 desired as a function of time which will which will make this happen.  If I if I know x position I know what is the y position and if I know x position in time I know what is the y position in time that is the kinematics of the path that is solved. Then I can convert that x of t and y of t into theta 1 of t and theta 2 of t ok. And then I get these are like my desired theta which will take me along that path. So, I want to now track the trajectory for theta 1 to go along theta 1 desired as a function of time ok. This is like a like a inverse kinematic problem ok. Given end effector position in terms of time how do I get like you know my joint coordinates in terms of time ok. That is a motion or path planning problem that is typically used in robotics kind of a literature ok. And similar kind of a thing exists like you know for any mechatronic system for example, if I want to go if I want to have some desired kind of a you know operation done in time as a trajectory thing then what should be my joint or my motor motor angles in terms of time. And once we know this theta 1 desired t and theta 2 desired t or q 1 desired t q 2 desired t how do I now track this desired trajectory ok that is a problem. So, then computed torque controller is one of the ideas that can be used. So, this computed torque is basically idea where you know this trajectory you know this joint angles based on the derivative now. So, the joint angle desired are known the desired joint angle derivatives will be known and those one can use from this equation of dynamics. So, this is a equation of dynamics here you know this say suppose joint angles q are known their derivatives are known q double dots are known q dots are known. So, everything here is known then you know what is a like you know control that any without any other disturbances you know you will know what is the desired control that is to be there right because q when I know the trajectory q ok I know q dot q double dot ok all the all are desired of course, they are desired you put in this equation and you will get to know what is a torque that will maintain those desired trajectory in the absence of any other disturbances ok any other kind of. So, this is how you find its computed torque and use that torque in addition you use that the control now should be that you desired plus this feedback you or you feed forward and you feedback and then like you know this controller will work typically ok. So, that is what is written here like analysis of computer torque controllers can be then then one can use this computer torque control and see whether we can use you know our Lyapunov theory to kind of get something from there ok. So, the problem here is that Lasalas theorem will not be you will not be able to apply. So, I would leave this analysis you carry out this analysis then something will make sense you do this computer torque based control and try to kind of like you know see similar kind of a PD control plus feed forward the computer torque control term you can use as a control and start working out Lyapunov analysis and you will find that this Lasalas theorem may not be applied in this case ok. There are some other kind of a stability proofs that will be needed ok. So, so we will this is out of scope of this course ok, but there is a very high performance tracking controller that can be possible ok. We will this expression of this controller is given here ok. So, this DC terms are coming from the system equation of dynamics that we have seen before and you know these other terms are new and A are defined in this manner here ok. This is called least lot in controller and this is a controller this can do the trajectory tracking also. So, this q this q desired is not constant here it is can be function of time also and how this is able to kind of do the job we can prove by Lyapunov stability analysis you know that will be happening in the in the future classes to come ok. But you can ponder over this controller and see whether you are able to kind of carry out the analysis of this by using Lyapunov theory you know and the this control is applied in this in the equation of this kind ok. So, this this u is basically given by this u is basically given by that expression that you see as a tau expression in the control here ok. This expression ok and gravity is not there here ok. Again you assume that gravity is 0 g term is 0 in the equation of dynamics and see whether you are able to kind of do something about proof of that ok. And the the the hint is like you know you express everything in in this variable r ok and try to express everything in terms of variable r although your generalized coordinates are q ok you express everything in terms of r and you will find some interesting thing happens in that coordinate dimension ok. So, we will do that analysis in the future classes to come ok. Thank you we will stop here for now ok.


So, you saw his brother speak earlier about pooping and almost dying.   So I met Nate, like I said, 18 years ago. And shortly thereafter, when I came over after a serious battle, I met his little brother, Eli, as this guy over here. So Eli was in fifth grade when I met him. And their little sister, Hannah, was in second grade when I met him. I've had the good fortune of having these three dukes in my life for quite a while now. Eli is, I think, the most interesting resume I've ever seen. He has a series of entry-level jobs with the greatest wage I've ever seen on the resume. So he's got a lot of breath, but not a lot of depth. The past four years, he's gone to Antarctica for a few minutes, and he's going to share some stories about that. Hey, everybody. Can you hear me? No. Is my mic checked up? All right. So, yeah, Shane and I go back to Indiana. And we certainly have a connection in programming. We started in the PHP world and dove into Ruby together. Got neck deep in the depot. It was good. And then I lived in Indiana most of my life in the move to Seattle. I went and stayed with my aunt and uncle, who live out there. And I just happened to time it perfectly so that a friend of the family was coming over for dinner party and a photo slideshow because he had just come back from Antarctica. And it was unbelievable to me. I didn't even think that such a thing was possible. You sort of have an idea that some people go there for research and stuff like that, but you don't really know the breadth of it. And so he came to the slideshow and I became sort of infatuated with it. And it took about a year or so for me to actually land a job there. And then I've been going back every summer there, winter here for the past four years. And so I'm just going to sort of kind of give an overview of the process. It kind of works out to my advantage here because a lot of times in my life now, sort of going through my non-anartica time, the question always comes up, what do you do?  It's like, oh, cool. That's nice. But it's like, I work in Antarctica. And then people, it's like, are there roads there? Are there cars there? Do people live underground? You know, it's like there's no real concept. Until recently, a documentary came out that some people have seen. And I forget what it's called right now. Close Encounters. Yeah, Close Encounters at the end of the world. So that was Werner Herzog and he filmed that movie the year before I went down there. So I know some of the people that were in that movie, but myself wasn't in it. So I've been four times now. I was a dishwasher in my first season. I was a plumber assistant. I was an electrical helper. And this last year I was a fuels operator. So I'm going to kind of like meld everything into one. And it works out because I can tell all of you the same story at once instead of having to repeat myself a bunch of times because that never really happens with a group of people. And someone's like, oh, you work in Antarctica? Wow, are there roads there? Are there cars that people live underground? And then like five minutes later, someone else comes over and they start hearing. They're like, well, you live in Antarctica? Wow, that's crazy. Are there roads there? Are there cars that people live underground? It's just like the same thing over and over again. So one of the first things that people ask is how do you get that job? And it's a really boring answer that you just apply online.  And if they say you got a job instead of going downtown, you go to Antarctica. So everything happens to the National Science Foundation and the United States Antarctic Program. And there's three bases primarily. There's McMurdo Station, which is near New Zealand, South Pole, South Pole. And Palmer Station, which is south of Chile, which John has to be wearing a shirt right now. The John M. Gould is a boat. Did you know that John? Yeah, I did. Nice. So everything happens under the umbrella of the National Science Foundation and the United States Antarctic Program. But there's a contract. And currently the contract is Raytheon, which is an evil military arms dealer sort of. But they have one section of their company, which is the Raytheon Puller Services. So you apply online.  And in Denver it's excruciatingly boring.  And then you all load up in a plane and you fly to Christchurch. And you're there for about two days. And you sort of hang out in the town, but you also get outfitted with lots of cold weather gear. They give you a coat and a few other things depending on your job. So they know you're going to be working outside to get more cold weather gear than if you were going to be a dishwasher, for instance. So from there you load up into a C-17, which is a military cargo plane. And the crew that does those flights is actually out of Tacoma, Washington. And they fly you down to McMurdo, which is the largest station on the continent. In the summertime there's about a thousand people there. And it's a small town. It's kind of dirty. Some people describe it as kind of like a mining town. There's probably a hundred buildings or so. And there's everything from dishwashers and janitors to doctors and dentists and garbagemen and plumbers and just firefighters. Everything that is needed for a small town to run along with all of the research people. And there's sort of a strange divide between the workers and the scientists. And I don't really know why that is, but it's just sort of how it was when I was there. I think there's just not as much interaction between those two groups because the scientists come in and they do their work and then they go out to the field or something like that. And so once you get to McMurdo, it takes a little while to get into it, but the really nice thing is that it's a pretty awesome sort of small community there. There's a thousand people, so you don't get to know everyone, but you do get to know some people and you work very closely with a lot of people and so you become fast friends.   And it sort of, for a lot of people, becomes the world and they keep going back and going back. And as it happened to me, this is my fourth time down. It's possible I'm not going to go back next season, but there's sort of an intention in mind to not get totally stuck into it because I know people that have been down there going straight every year for 30 years. And it seems insane to me. But the community is amazing. Like I said, there's music. There's a band room and there's lots of live music because people want to fill their time. They want something interesting to do while they're there. And there's the holidays are big celebrations every year. And on New Year's there's an outdoor music festival called Ice Stop. And it's just a big outdoor party and it's lots of fun and the whole community gets into it. And it's sort of like because there isn't much to do, the things that there are to do, everyone does them. And everyone wants to make them as interesting and as awesome as they can. So my first season, like I said, I was a dishwasher and that was pretty cool, but not amazing. As you can imagine. It's sort of a common sort of entry level job. And a lot of people do it their first year and a lot of people do it just to get there. There's sort of a pattern in the dishwasher world that it's like from 18-year-old kids to 50-year-old men and women, sometimes even older that just that's a job they can get and so they go for it. So my first season there was a woman working down there, she was maybe in her mid-thirties and she had been a lawyer with Arthur Anderson during the Enron scandal. And she was in the trenches as Shane was saying. And at one point they said, you might want to think about just sort of bailing out now while you still can. And so she said okay and so she left and went traveling and ended up down there working as a dishwasher. She was awesome and there were some younger people working there, some older people, but it's a wide range of people working that job versus my second year when I was a plumber. And that is basically very, for the most part, old, crotchety tradespeople. And it's a really hilarious world for me because I went down there, this was my second season, and I kind of thought, I know what I'm doing now, I've been here before, I understand what's going on. And so I got down there, it was my first day. I woke up in the morning and the of these card overalls and everything, and I took my first shirt off the pile. And it turned out to be a pink shirt. And that's just sort of a coincidence because I happen to like that color. But as I walked into the shop on my first day as a plumber, I walked in and I realized that I probably had made a mistake because to one of my favorite guys that I worked with, his name is Walter, and he was a hilarious, he was like 75, 70 years old or so from Maine. And to him, any one characteristic of me makes me gay. But if you combine all of them into one person and I not be gay, it's an impossibility in his mind. You can see the gear is just like grinding in his head and just like every day he would like learn one more thing. So I walked in my first day, kind of shaggy hair, my ears are pierced, and I'm wearing a pink shirt. And so he started calling me Pinky. And that nickname really took. And as time went along, you know, he'd find out that I was vegetarian. And he was just like, oh my gosh, who is this human? How does such a thing exist like this? And the name really stuck and people kind of ran with it and it was a good time. But in that world, it was basically this world of kind of older, kind of conservative trades people, but it was amazing. They were still wonderful people. He had the best of intentions. I mean, he came by it honestly in a way, you know, he couldn't help it. And I like to think that maybe I sort of changed his worldview a little bit, I don't know.  I don't think there's a color that a girl can wear that is like incompatible with her gender. But like, I can wear a pink shirt and it just doesn't match with people. And people sit and they're like, hey, cool shirt, man. Well, okay. And so I like that. I had a good time. My first season I was working in the, just in the galley, you know, washing dishes for 10 hours a day, 6 days a week. And it kind of gets old. That year I worked with the plumbers and it was nice. We got to move around town. We got to go to different buildings, got to go to the airfields. And that's sort of the, sort of on a base level, that's sort of the farthest that I got out of town. Because town is maybe a square mile. I'm just kind of guessing right now. It's kind of hard to say how big the town is. And then the airfields are out on the ice shelf because McMurdo Station is on Ross Island, which is just south of New Zealand. It's not actually on the continent of Antarctica. It's a small island just off the continent. And so it's a big rocky space and they couldn't build an airfield on the island. And the best place to do it was out on the endless sheet of flat ice that just goes on forever out off the, like, off the island onto the ice shelf. So I would go with Walter frequently out onto the ice shelf. We would take a shuttle because there's a lot of people going out to the airfields back and forth every day. We would get on a shuttle and it's a big 15 passenger van with big, you know, big knobby tires on it and go out to the airfield and do sort of just general maintenance on the buildings out there and make sure everything was running okay. And so it was a nice sort of change of pace from the season before I got to work outside and I got to work with my hands and I got to build things and stuff like that. So that was nice. And then my second season I was an electrical helper and so sort of the same vibe as the season before, but I was working with electricians instead. And so similar thing working outside. And then I got to sort of the golden ticket of working in Antarctica is getting off station. That's like people sort of, that's everyone's goal because it's cool to go to Antarctica and you're washing dishes and stuff like that. But then you start to see the, you see off into the distance and you see that there's more exciting things off on the horizon. And so from McMurdo, which is, you know, sort of the hub of most scientific activity that occurs on the continent, people, the science groups go from there out into different field camps. They go from there to the South Pole. They go from there to different points of interest of research around the continent. And so I got to go with the electricians to the dry valleys, which is a helicopter ride over to this special area where there's a series of valleys that for some reason don't have any snow in them. Sort of unknown why that's the case but it is and they're being studied and so I went with the electricians to work on some electrical work there. And so each season has been progressing, each season has been a little bit more interesting than last, each season has been moving along and so I keep enjoying it. And this last year I worked in fuels and in the McMurdo word the fuels operators are fuelies and we smell like diesel 100% of the time basically. You spill it on you, it's like you're just around it enough and so there's a sort of a stigma of fuelies and how we smell and we sort of sit together at lunch, you know.  It's like I had stink lines just sort of like coming off of me at all times. And the fuels world was definitely bigger than the world's before because it was much more responsibility. I wasn't just a helper or an assistant or something like that, I was a fuels operator and the fuel system at McMurdo is huge and intense and sort of mind boggling at times. I mean the basic system is that a fuel tanker comes down every year, offloads 7-8 million gallons of fuel into different bulk tanks and then that comes out of those tanks and is distributed to buildings to run heaters. It's distributed to the airfields and to get out to the airfield which is 13 miles away out on the ice shelf. We have to run a 6-inch fuel line, 13 miles. And 13 miles of 6-inch fuel line is about 100,000 gallons of fuel if it's just sitting in the line. And so every couple days we would do transfers out to the airfields to fuel the planes primarily so that they could fly to field camps but also so that they could deliver fuel to the South Pole. Because if the South Pole runs out of fuel just like McMurdo but if the South Pole runs out of fuel then it would be bad. And fortunately like I said each season keeps kind of progressing this season I got to go to the South Pole to work with the fuel just as part of the fuels crew because there's three people that work at the South Pole permanently every year in the fuels department and there's one rotator from McMurdo every year. And so I worked at the airfield of McMurdo fueling planes that were flying to the South Pole throughout the year and then at the end of the season I got to go down there and work with them. And so the fuel comes in in a tanker, goes into a tank, gets pumped 13 miles out to the airfield, gets pumped into a plane that then flies to the South Pole and then gets pumped out of that plane into tanks that then run the generators. And they fill up a plane with about 8,000 gallons of fuel, they fly to the South Pole, offload about 3,000 gallons and then fly back. So it takes about a gallon of fuel to get a gallon of fuel to the South Pole. And so it's pretty efficient in the grand scheme of things and there's a push over the last five or six years for and it's continuing now for a South Pole traverse which is where we fill up giant bladders of fuel and people and tractors drive them to the South Pole. And so they're trying to work more on that but working at the South Pole was pretty cool. It was cool to see the whole sort of link in the system, the whole sort of process. And I was there at the very end at the South Pole working before closing because you have to get just the right amount of fuel there before they close for the winter. Because the South Pole is open for about three and a half months in the summertime. And during that time people are coming and going, flights are coming and going and moving through. And then it starts to get too cold because the planes can only operate above minus 55 degrees Fahrenheit. And when it gets below that they just don't work anymore, they have failures and they fall apart and the engines shut down. And so they push and push and push to get as much fuel in as they can. And then at a certain point they just have to stop because it starts getting too cold. So we just barely got in. I think as we were leaving it was just getting to about 400,000 gallons that they need at the South Pole to run the station for the winter. And that's primarily for the generators and for the larger telescope science projects that happen down there. So we finished the last offload of fuel was the plane that we flew out on. So I was at the tanks where the fuel gets offloaded too. And I opened the valve so the fuel would flow in and then I grabbed my stuff and walked up to the airfield. The plane finished offloading and then we just got on that plane and flew out. And everyone that was at the South Pole that was staying for the winter, it was about 50 people or so that will be there for eight months or so. They all came out to the airfield and as we were flying away they kind of like, it's sort of a deal that they, it's like, well there it goes. That didn't happen again for a while, you know. So flew back to McMurdo and then that 13 miles of fuel line that we laid out to the airfield we had to roll up. Because you can't leave it over the winter or it will get buried and then you won't be able to find it. So the very sort of the second to last flight out of McMurdo flew out. There was a tank that was left there at the airfield that had enough fuel to fuel the last plane that came in. And then it was just the winter population and then the fuels people that were staying to tear down the fuel line. And so we broke into two crews, we worked like, within the two crews a little overlap about 20 hours a day just rolling up fuel line. And it took six days I think, total, to roll up 13 miles. At the most we would roll up maybe two to three miles a day I think. And once that was done then the last plane came in before the McMurdo winter. And I was on that last plane and flew out to Christchurch. From there basically you are normally just put up in a hotel for air too. And then you can sort of, you can go home, you can see New Zealand, you can sort of travel from there. But right at the moment when the most, basically the most possible Antarctic related people can be in Christchurch that is possible, was when the earthquake hit. And so there was about 600 United States Antarctic program people sort of around the Christchurch area when the earthquake hit. And it was kind of a big deal for the people that we were still down in Antarctica because we didn't know, I mean buildings were crumbling and collapsing and it was like we had friends in the city and didn't know what was going on. And somehow not a single Antarctic related person was injured. And so then when we were on our way out we were not encouraged to stay in the city at all. We had to basically put us up for one night and then we were heavily encouraged to get on a plane to fly to Auckland to just leave because they didn't want us getting in the mix of things. I stayed on the South Island anyway and sort of just didn't hang out in the earthquake area. And made my way home and in the process of being down in Antarctica, Shane had told me about the conference and told me about this going on and I was hoping it would work into my plans but it didn't sound like it was and I'm really glad that it did because I got to come out here and hang out and I got here on Monday and helped mow the backyard. It's deceiving right now but it was a jungle just a few days ago. And do some other things and it's been fantastic. And so I just want to thank Shane and I think we should all give him a little applause. It certainly takes sort of some, you know, what's that like? Balls. There we go. You sort of like can't be afraid to fail, I think. It's pretty cool. So thanks for your time. If anybody has any questions, be happy to answer them. Mike, sorry over here. I have two questions. Although you sort of answered it with McMurdo but do people at the South Pole all celebrate New Year's at the same time where there are even other from different countries or do they celebrate with their own country? That's kind of one. And the other is how the hell do you roll up a two mile long or whatever? Two miles a day. Is the geometry of it like where does it go? Is there a giant spool? Okay, so McMurdo and the South Pole are all on New Zealand time. So that's just sort of the general rule. Is there all US workers? Yeah, mainly US workers. What about the South Pole? What time do they celebrate New Year's Day and the South Pole? Same as New Zealand time. Yeah, because it's sort of like New Zealand is the logistical hub. So it makes sense to be on the same time as that so they can just orchestrate things. And rolling up the hose, it's in 600 foot sections. Well, there's 600 foot sections but then there's three 600 foot sections that are considered to be one reel and there are about 40 reels.  Yeah, it's that time of the season. There's lots of help from lots of other departments. So there's like the heavy equipment operators. There's like a couple of heavy equipment operators that are assigned to us. And it's like a constant thing of like this reel is full, take it away, bring another one. And so it's a big operation to get it done in time. I have two really serious questions. The first one is do you think it's cold right now? I'm freezing. It's a little chilly. Yeah, you adapt pretty quickly. It's surprising. The second one is did they keep calling you pinky after that second year? Yeah, there's some people that only knew me as that. They're like just never learned my name.  Like I don't know what their actual name is, I just know their name. Some people stuck with it, some people still do. So I was wondering the entire time, does anyone live underground? Are there roads? Are there cars? There are roads and there are cars, but people don't live underground. You mentioned that you guys at outdoor concerts sometimes. How cold is it when you had your outdoor concerts? So the warmest time of the year is right at New Year's. Yeah, the warmest time of the year is right at New Year's because that's sort of like the middle of the summer. And so it is not uncommon for it to be like 40 degrees. And when the sun is shining and you've been accustomed to 20 below, it's like 40 degrees, it's lovely, it's glorious. And the sun is shining, you could be outside in a t-shirt, you'd feel comfortable, you'd be okay with that. What do you have to do about like visas or anything for outdoor? Well that's fortunately taken care of through the company that we work for. I get a special letter that's like to the New Zealand visa people. When you go through customs, that gets us a nine month visitor visa in New Zealand because technically while we're in Antarctica, we're in New Zealand. Because when you go to Antarctica, you're not going to another country. The last country you were in was New Zealand, so that's where you were the whole time technically. And so you get a nine month visa, which works out because the longest stint is usually about like August to February, which is six months. And so when you leave, you still have three months left in your visa. So if you wanted to, you could, without doing anything, you could stay in New Zealand for the three months if you wanted to. John wants to know about background checks and we should also talk about PQ. About what? PQ. Oh, okay. So background checks, yes there are some. I don't know. Yeah, I mean they go through like higher rate with some company that makes phone calls and pokes around. And yes, there's a pretty involved like medical checkup process that once you get hired, you have to go through the problem. You have to have a physical. You have to get blood work done. You have to have a dental checkup. So it's involved and some people get really close to going and then right the last minute something happens and they don't, they fail. They're like, medical says you're not good enough. You don't, you're not healthy enough or something like that. So. So in Antarctica during our winter, your summer. Yep. Is it pretty much day like? Yeah, it is. Yep. Is that? The daylight is less of an issue than you'd think because it's really easy to make darkness.  I've never done a winter. So winter would be very difficult because then you can't really synthesize daylight and sunshine. So people that winter said that that's much more difficult. But the constant daylight is actually nice because you can always do stuff outside. It's like if it's late and you feel like going on a hike doesn't matter because it's sunshine. I remember a few years ago there was a rescue mission for someone that needed emergency surgery. Was that on the winter crew? Yeah, I think I've heard that was the winter crew at the winter South Pole. And I think the story I remember was that it was a woman who found out she had advanced some stage of breast cancer. And she was actually the doc and she had to give herself surgery. So she had attendants, like they trained and they sent down through the internet special things for other people. She did most of the work, but there were people there that had some understanding. Who did they get to play ice hockey? Those are all local bands. It's just bands that have formed during the season. I was in a sort of a blues funk rock sort of cover band this year. And we did for iStock, the lead singer who is really obsessed with having a really awesome stage performance. He gets really into it. And so he made the paper mache heads for us to be the Muppet Band this year. So I got to be animal, which is pretty cool. And it's pretty much anyone who wants to do anything. It's really kind of a cool moment for people to just throw bands together and do... There was a group that kind of opened up there with the ukuleles. These two girls that played ukulele and sang. So just whatever anybody can throw together is pretty awesome. I don't know if this makes any sense or not, but I've heard that there's a club, an article where you get a badge for running streaking into a sauna. Is there an official run that you do? It's possible. It's at the South Pole in the winter. I've never done it, but it's called the 300 Club. Where the sauna is 200 degrees and the ambient outside temperature is minus 100. So it's like a 300 degree temperature difference.  And you have to run around the pole. I think you have to run outside and run around the pole and run back inside. This question is probably kind of lame, but... Sorry. Yeah. What do they do about like weights? Garbage? That's a good one. Poop, yeah. I know all about that. My brother Nate over here was down there. We went down together our first season and he worked at the wastewater treatment plant. Disgusting. So it used to be, and not so distant past, that waste was just flushed into the ocean.  But in recent times they put in a wastewater treatment plant and so that pulls out the waste and whatever. All the other waste is, including the solid human waste, is like contained in these sort of try wall kind of pallet boxes. There's food waste.  There's like ten different divisions of your trash.   And then there's a resupply vessel that comes down every year and brings in new supplies.    I have a couple of footnotes to the, I've heard the Anarca stories for a few years, so. And it's too bad Mickey had to leave early because they have a sort of recycle program there called SCUA. SCUA's are the little birds in Anarca. Basically like, I'm done with these shoes, you can't really throw them away or like take them to Goodwill.  That's a pretty cool little program that got going on there. And I've heard a lot of these stories and it wasn't until Eli started putting all his photos on Flickr that it really started to make sense. And we were talking about the other day, books and I think that Eli has the most published photos of Anarca. So it's seriously, it paints a picture, you know, fuller than what he could say. And his Flickr handle is Eli's fan club.  That's the last thing we have for Eli, so thanks Eli. Yep.