Thus, we could test them on a real working robot and inform the robotician to avoid those locations of the points on the object as well as that of the camera so that they could control the robot without any problems. We recently succeeded with the help of CAG tools that if there are 4 points, there are at least 2 positions of the camera that are singular and at most 6. For instance, if the three points on the object are collinear, the robot can rotate about that line while it thinks that it is stationary since the projections of those points on the image plane of the camera will be stationary. The problem is that there are some configurations in which you cannot control the robot (called as singularities of the control model). For some serial robots (that resemble an arm), a camera is placed at the free end which is used to track some points (could be other gemetric features) on an object, which is then used to control the motion of the robot. If you are interested, you can find more details in my PhD thesis: Īlso, at the moment, I am working on a control problem in robotics. Although we built a 3d printed prototype, I believe that this gripper can be manufactured for different applications. We used these singularities to build a compliant gripper that can have angular and parallel grasping capabilities. We can thus deduce that the mecanism has singularities between these modes (which are nothing but the singularities of the algebraic variety corresponding to its motion). Concepts from algebraic geometry (such as prime decomposition of ideals) tell us that this mechanism can have three different kinds of degrees of freedom (called operation modes in the kinematics lingo): two rotations and a translation. One of the examples that I can give you is the kinematic analysis of a simple four-bar linkage with equal link lengths. I used computational algebraic geomtery (CAG) to analyse them. I finished my PhD last year and it was on the kinematic analysis of some special robots. I'm really trying to do some soul searching here and you could really help me with it. Thank you so much! I really appreciate your help. I don't think I have the knowledge of AG to understand the details, so I am more interested in the statement of the "real"-life problem and the non-trivial result of its mathematical modelling using concepts in algebraic geometry. I think you would really answer my question if you could give me an example of a real life problem (not in excessive detail) that was solved thanks to techniques of algebraic geometry. I'm very much interested in algebraic geometry (and I am being honest when I say that it is one of the rare things that makes me truly giddy thinking about it). My question is: If I changed my mind, applied to do a graduate degree in mathematics and decided to work in a field outside of academia, would I have useful applications of what I studied (and not just a tiny fraction of what I studied, e.g. something is a "group", but the recognition that it is was completely useless since the application did not produce a result that would have been otherwise unknown. Galois theory, I got two sorts of answers:Īn application of the concept in another area of mathematics.which is not what I was looking for.Ī trivial application where a physical/computational/etc system is "modelled" with the concept, e.g. ![]() One of the reasons was that, seeing my professors, it seemed that mathematicians were very much living in a world of their own and every time I asked for an application of what I was studying, e.g. However, every once in a while I have doubts about my decision because it was made on more than one basis, i.e. I decided not to proceed with math and am continuing on to a professional degree. ![]() I did my undergraduate degree in mathematics, taking a pretty heavy course load in theoretical math and doing really well in it. Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. If V W ‾ ≅ X Y ‾ \overline J K ∥ N O start overline, J, K, end overline, \parallel, start overline, N, O, end overline.
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