ROBO SPRING

 

        

      

        

    

         

  

   

     

 

 




 

       

 
   

 

   
  



 





  



Robots today have been used successfully in many domains, from exploring Mars and finding evidence of water, to mapping the health of coral reefs, to assisting long-distance drivers, to assembling cars. In our course we will pursue a Grand Challenge approach to robotics and create new robot bodies and brains. We are motivated by tasks at the frontier of today's robotic capabilities. We will develop solutions for these tasks that are grounded in state-of-the-art algorithms and systems science for robots. We will implement these solutions and test them using a challenge format.
Our robots will employ sophisticated techniques for perception, navigation, and manipulation to cope with unknown environments, negotiating intricate paths, adapting their next move to obstacles, finding useful objects in the environment, and using them to build a structure. This work will provide our students with the foundations for creating computer systems that interact with the physical world, leading the way from PCs to PRs (personal robots).
The grand challenge for this course is to Gather Materials and Build a Shelter on Mars. Imagine a robot delivered to an uncertain location in a remote and unknown environment such as the surface of Mars, and given an uncertain prior map of the local terrain. Imagine further that construction materials, in the form of distinctively colored blocks in a few discrete sizes, have been similarly delivered and are scattered around the landscape. Some blocks have ended up where intended (i.e., in known locations), whereas others have ended up in unknown locations or may have been lost or destroyed.
Your goal is to design and implement a robot (both its body and its code) that can move about within its new domain, collect blocks, transport them (all at once, in small batches, or even one at a time) to some autonomously-determined construction location, and assemble them into a primitive shelter. The shelter may range from a simple low wall, to a multi-level (stacked) wall, to an "L" or "V" shape, to a room-like structure.

One or more of elements needed to solve the Challenge arise in many other robotic mobile manipulation applications, ranging from autonomous navigation with dynamic obstacles, coordinated manufacturing, searching for and rescuing victims at a disaster area, tidying up a room, clearing the dishes in a cafeteria, delivering packages in an office environment, and fetching items from a stockroom or mailroom. 

ROBO SPRING   MISSION   :

Learning Objectives:

1. Specify the requirements for an integrated hardware and software design and implementation of an autonomous system performing a specified task;
2. Critically evaluate choices of design and architectures;
3. Use kinematics, control theory, state estimation and planning to implement controllers, estimators and planners that satisfy the requirements of specified tasks;
4. Operate the system for an extended and specified time;
5. Communicate, orally and in writing, the results of the project design process and the key aspects of the overall project (from concept to end goal).
6. Collaborate more effectively, for example by having more choices of action, flexibility, and resilience with team process such as decision-making, negotiation and conflict resolution.

Measurable Outcomes

1. An integrated hardware-software system that performs the desired task;
2. A written design proposal that specifies and presents the integrated software and hardware design that satisfies design requirements;
3. Lab reports and briefings that demonstrate mastery of key design skills;
4. Development and delivery of an oral presentation suitable for a professional audience;
5. Development and delivery of a debate that evaluates design choices and demonstrates ability to use evidence to argue for conclusions;
6. Completion of a final report that analyzes the design and its success or failure, and reflects upon learning.

rope wrapped around and spinning motion capture missions steady string stability for spring AMNIMARJESLOW AL

 

String Theory For Dummies 

String theory, often called the “theory of everything,” is a relatively young science that includes such unusual concepts as superstrings, branes, and extra dimensions. Scientists are hopeful that string theory will unlock one of the biggest mysteries of the universe, namely how gravity and quantum physics fit together.

String Theory Features

String theory is a work in progress, so trying to pin down exactly what the science is, or what its fundamental elements are, can be kind of tricky. The key string theory features include:

• All objects in our universe are composed of vibrating filaments (strings) and membranes (branes) of energy.
• String theory attempts to reconcile general relativity (gravity) with quantum physics.
• A new connection (called supersymmetry) exists between two fundamentally different types of particles, bosons and fermions.
• Several extra (usually unobservable) dimensions to the universe must exist.

There are also other possible string theory features, depending on what theories prove to have merit in the future. Possibilities include:

• A landscape of string theory solutions, allowing for possible parallel universes.
• The holographic principle, which states how information in a space can relate to information on the surface of that space.
• The anthropic principle, which states that scientists can use the fact that humanity exists as an explanation for certain physical properties of our universe.
• Our universe could be “stuck” on a brane, allowing for new interpretations of string theory.
• Other principles or features, waiting to be discovered.
  
  

  Superpartners in String Theory

  String theory’s concept of supersymmetry is a fancy way of saying that each particle has a related particle called a superpartner. Keeping track of the names of these superpartners can be tricky, so here are the rules in a nutshell.
  
• The superpartner of a fermion begins with an “s,” so the superpartner of an “electron” is the “selectron” and the superpartner of the “quark” is the “squark.”
• The superpartner of a boson ends in “–ino,” so the superpartner of a “photon” is the “photino” and of the “graviton” is the “gravitino.”

Use the following table to see some examples of the superpartner names.

Some Superpartner Names

Standard Particle	Superpartner
Higgs boson	Higgsino
Neutrino	Sneutrino
Lepton	Slepton
Z boson	Zino
W boson	Wino
Gluon	Gluino
Muon	Smuon
Top quark	Stop squark									Keeping Track of String Theory’s Many Names String theory has gone through many name changes over the years. This list provides an at-a-glance look at some of the major names for different types of string theory. Some versions have more specific variations, which are shown as subentries. (These different variants are related in complex ways and sometimes overlap, so this breakdown into subentries is based on the order in which the theories developed.) Now if you hear these names, you’ll know they’re talking about string theory! Bosonic string theory Superstring theory (or Supersymmetric string theory) Type I, Type IIA, Type IIB, Heterotic string theories (Type HE, Type HO) M-theory Matrix theory Brane world scenarios Randall-Sundrum models (or RS1 and RS2) F-theory Extra Dimensions Space is three As we indicated before, one of the key consequences of string theory is that there are more dimensions to our world than we imagined. We normally think of our world as four-dimensional. The count goes as follows. We can think of a point in space as being specified by its left-right position, its height, and its depth. Space is therefore three-dimensional. We need three numbers to specify a point in space. We can redo the count in another way. Consider the surface of the earth. When we specify the parallel and great circle of a position on the globe, we can pinpoint the position. The surface of the earth is two-dimensional. But if we had buried a treasure under its surface, we would need to know also how deep it is buried to locate it precisely. Space is again three-dimensional according to this count. A similar count is of course valid for the localization of stars. (Exercise: Count !) A special dimension Time is the fourth dimension. Indeed, to localize an event, we not only have to specify its precise position in space, but we also need to know when it happened. The extra number we need is the time at which the event happened. That fourth number indicates that space-time is actually four-dimensional. Recall that it was one of the big achievements of special relativity to treat the three dimensions of space and the one dimension of time in the same mathematical framework. Of course, the time dimension still plays a special role, and its role in string theory is similar to its role in our everyday lives, or in the theory of special relativity. The extra dimensions we consider in the following are of the usual spatial sort. -- There are theories that try to make sense of two different times, but we do not consider them here, since they have little or nothing to do with string theory. (Note: crackpots tend to underestimate how seriously professionals have already investigated the ideas they come up with.) We concentrate on extra dimensions in space. More than 3+1 Many scientists had played around with extra dimensions before string theory came along. The idea is natural, since an extra dimension gives some room to play around in, and circumvent theorems that tell you that something is impossible in the 3+1 dimensions that we know off. But people had considered only one extra dimension, since they didn't need more than one. String theory actually tells us there is more than one extra direction. How many more ? Now, that's a tricky question. For years we have thought that string theory needs precisely six extra spatial dimensions -- we will assume this to be true for now, and will explain some more subtly points about how to count the extra dimensions later, when we introduce the concept of M-theory. 9+1 = 10 String theory tells us we live in ten dimensions. How does it tell us that, and, importantly, why don't we need to specify ten coordinates when we want to specify the location of a treasure ? The first question is the more difficult one. The mathematics of string theory is such that it leaves us with a dilemma. We either choose to have ten dimensions, or we can choose to accept that there are particles that have a negative probability to be in the universe. The last option (and its formulation in the last sentence) is entirely nonsensical. In other words, nobody has made sense of the notion of "negative probability" up until now, and it is doubtful whether anybody ever will. We now what it means to have a particle somewhere with a small or high likelihood, but not what it means to have it exist with a "negative" likelihood We choose therefore for the lesser evil, and interpret the conundrum as the fact that string theory simply predicts that there are ten dimensions. The problem actually turns out to be a blessing in disguise. We get one more spectacular prediction from string theory. Little balls everywhere Let's tackle the second question then: where are the six extra dimensions that string theory predicts ? There are different answers to this question, and for starters I discuss only the old one -- I'll come back to an exciting new possibility later. -- The first part of the first answer is that the six extra dimensions are very small, or compact. They do not extend very far, in contrast to the three spatial directions that we know of. The extra dimensions are curled up, and in such a way that they are extremely tiny. Since we haven't seen them yet in particle accelerators, we know that they are smaller than 0,000000000000001 meter. The second part of the first answer is that these extra dimensions are everywhere. Indeed, we can think of every point in our space (or kitchen) as not actually being a point, but as being a tiny six-dimensional ball. We do not need to specify the six extra coordinates of a knife in our kitchen, say, because the ball is so tiny that we can easily locate the knife without this extra information. If these dimensions were bigger, we would have seen them long time ago, of course. We would have moreover been able to think much easier in 3D, 4D, or even 9D. (Note that the trick of hiding the extra dimensions is very similar in spirit to hiding the stringy features of strings -- both make use of the fact that the resolution of our measuring devices is too small to make out the new features, as yet.) Consequences We first of all saw that there is no real problem to having six extra dimensions, as predicted by string theory. That is not to say that they do not have observable consequences. Indeed, once we probe small enough distances, we should be able to see many new interesting phenomena, depending on the shape and size of these extra dimensions. For one thing, we will be able to distinguish particles that run around in these extra dimensions from the ones that don't. Moreover, we will be able to see particles that are actually strings or membranes that are wrapped around some directions of the six-dimensional compact space. And many more interesting phenomena would appear and they might be observed in the next accelerator, depending on how small the six-dimensional compact space is precisely. Let's hope it is not so small that we will never be able to see it in our lifetime. Brane worlds We treated some aspects of a first answer to the question of where these extra dimensions are hiding. There are other, more modern answers to this question, of which we will treat one in more detail in the chapter on branes. But to introduce branes properly, and to understand how they provide an alternative answer to that question, we first need to introduce a few more properties of string theory. Illustrative footnote: An expert points out to me: "Dear J, I was wandering around the net, and encountered your web site on string theory. It looks very nice, a really thoughtful service. One comment: I would quibble with your characterization that string theory predicts 10 dimensions. It is not known to predict this--string theory can be formulated in any dimensionality; it is just that one does not have a classical solution with exactly flat space in any dimensionality. The leading effect of venturing away from the critical dimension is that one finds a tree level dilaton potential, which forces us to solve the dilaton and graviton equations of motion nontrivially rather than finding a constant-dilaton Min kow ski space solution. Other contributions to the dilaton potential from branes, fluxes, orientifolds, etc. allow us to find compensating forces on the dilaton that fix it. (Or one can consider the linear dilaton background in cases it makes sense, as in the 2d string.) Since we don't live in precisely flat space, the critical dimension is not a condition we know to impose even phenomenologically. It might transpire that YE POSTING FOR PIT  provides a reason to focus on the critical dimension (I also find this a very plausible possibility), but this is not known at the moment either experimentally or theoretically. Best regards, E" To translate: when I say string theory predicts 9+1 dimensions, my colleague believes I make quite a few hidden assumptions (that I may need to explain in lay terms). My colleague is right, of course, and she refers to established technical results to support her case. I include the comment as a footnote, not merely as a fair correction to the above, but also to illustrate that we discuss about how to present string theory results to the layman, and that when we argue, we can use a technical language not accessible to all. To truly do justice to her comment, the task set out for me is to explain the content of the comment (on which experts agree) in understandable terms. I may implement this later on ...

A half spring O max spring not semi ring

Variable Force

( DElta )

Suppose F acting on a mass m depends on x; e.g., F = kx We divide x into little increments, Dxi, where Fi is the average force over that interval:

  

Total work going from x1 to x2 = Wtotal = S FiDxi = area under curve!! (C word = integral of F from x1 to x2) and DKE = Wtotal.

For linear force, F= kx, Area under curve from 0 to xf = .

                       

A mass m is moving in a straight line at velocity vo. It comes into contact with a spring with force constant k. How far will the spring compress in bringing the mass to rest?

A spring exerts F proportional to x in both compression and extension (for reasonable x).

Change in KE = KEf - KEi = 0 - mvo^2. Work done by F on mass, W = - kxf^2. Therefore, kxf^2 = mvo^2 or .
IF we use object and compress spring this same distance (xf = xo) and let go, what is final KE and v? Work done by F on mass, W = +kxo^2.
Change in KE = KEf - KEi = mvf^2 + 0. Therefore, mvf^2 = kxo^2. Since xf = xo, we see that: || = ||. Since we take a , ± does not give direction. Have to go to PICTURE; conclude that . 

Running the Stairs to the Stars (Part rangers Bldg -- Basement to 14th floor); Consider POWER.
1. Who could generate the highest instantaneous power?
2. Who could generate the highest average power?
What are "significant" output levels?
Person in good physical shape -- 1/10 hp (75 W) at steady pace. O2 consumption -- 1 liter (1000 cm3)/minute.
Top athlete -- (long distance sports-runners, skiers, bikers) 0.6 hp (~400 W); O2 consumption -- 5.5 liter/minute. Gossamer: (1979) human powered airplane, piloted by world class biker, crossed English Channel -- averaged 190 W (0.3 hp).
FOR approx. 1 minute spurts - 450 - 500 watts.
For fraction of a second -- several kW.
A 70 kg student runs up 2 flights of stairs (Dh = 7.0 m) in 10 s. Compute the student’s output in doing work against gravity in
(a) watts, (b) hp.
(a) W = FDh/t = mgDh/t = (70 kg) (9.81 m/s2) (7 m)/10s = 480 W
(b) W (in hp) = W (in W)/746 = 480/746 hp = 0.64 hp

The express elevator in M Tower A (MISSI) averages a speed of 550 m/minute in its climb to the 103rd floor ( 408.4 m) above ground. Assume a total load of 1.0 x 103 kg, what is the average power that the lifting motor must provide?
vavg = 550 m/minute x 1 min./60 s = 9.144 m/s.
At constant v, Force to lift = F = mg;
Pavg = Fvavg = (1.0 x 103 kg)(9.144 m/s) = 89.57 kW = 90 kW.
(takes ~44 s to make trip).

You want to loose weight; You therefore want to:
a)Run the stairs once/day as hard as you can, then hit the chips!, or
b) Sustain an activity that burns ~ 1CALORIE/Minute almost every day for 30-60 minutes and don’t hit the chips!
1 CALORIE = 1 Kilocalorie (4.186 kJ). 1 Kcal/minute = 70 Watts (substantial effort). To loose weight have to exercise and diet!!!