RAMASUBRAMANIYAN, S. Geometrické řízení neholonomních systémů [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2023.

Posudek vedoucího

Návrat, Aleš

This thesis deals with the control of nonholonomic systems using geometric methods. The student has studied the necessary basics of differential geometry and geometric control theory, especially the so-called nilpotent approximation of the control system. In his work, he demonstrates all concepts and methods immediately with simple examples, showing that he really understands the substance. The highlight of the work is the computation of an approximation of a complex nonholonomic system, namely a 3-body space robot. The student worked very hard and within the limited time for the project, he became familiar with the subject matter. I was very satisfied with his work. However, probably due to time constraints, unfortunately, not all objectives were fully achieved and therefore I grade this paper with a B.

Posudek oponenta

Vašík, Petr

The topic in the thesis is very advanced and is currently one of the research directions at the Institute of Mathematics. It exceeds the content of master studies at most universities. This may be the reason why the introductory part lacks logical continuity and sometimes suffers from mathematical inaccuracy. The second part containing the examples on privileged coordinates, nilpotent approximation and exponential coordinates of the first and second kind is excellent, descriptive and self - explanatory. The last part, ie. the application to the problem of a satellite control, somehow lacks any form of calculations and/or simulations. I believe that there is some attachment missing in the system by mistake. Therefore, I am asking the student to provide such a material (Maple output) during their defense. Some specific problems: Mathematical inaccuracy: - Introduction: do really trigonometric controls facilitate precise control? - Definition 2.1: what is "v"? How do you guarrantee that f is diffentiable in t? - the tangent vector on a manifold v_p[f] is defined in very different way. Furthermore, your v_p[f] is a function to reals, not a vector. Can you explain this? - Corolary 2.6: undefined symbol f_{\ast p} - page 19, proof without a proposition - Definition 2.8: U should be an open subset of X - page 20 - you are using diffeomorphism but before you described homeomorphism - Degfinition 2.10: why differentiable manifold whenthe transition functions are smooth? - Example 2.11: wrong definition of SO(3) - Section 2.1.2: distribution should be of constant dimension - Section 2.1.2:  notion of a bundle not defined - Section 2.2: why the one-parameter group of diffeomorphisms is mentionned before the flow of vector fields and, the exponential form of the flow is not mentionned until the examples in Section 3.4.1, where it is not established correctly? - Example 3.5: why \Delta^2 contains "e_3" when X_3=-e_3 and then you have (-1)^n e_n as the element of \Delta^{n-1}? - Section 3.4.1, page 37, what is L(1,2)? - page 42: what do you mean by the Jacobian between tensors? - page 48, last line: if x_1(t)=z_1t, then x_1(0)=0, but you should have x_1(0)=z_1t - Example 5.10: you are describing kinematics, not dynamics Typographically, the text is on very high level with just minor issues, eg., page 44 - wrong reference (4.8). The thesis is written in excellent English containing acceptable number of typos and grammar mistakes.  Overall the goals have been achieved (although I recall the need for a simulation or calculations in Maple for the satellite ) and the thesis may serve as a guide for other educated students. Therefore I recommend the thesis for the defense and suggest evaluation by grade B.

eVSKP id 150035