KIŠA, D. Matematické modelování kráčejících robotů [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020.

Posudek vedoucího

Tomášek, Petr

The thesis deals with modelling of walking robots, in particular the rimless wheel and the compass gait biped. After a mathematical background introduction Section 3 deals with the rimless wheel robot, where the analysis of its motion along an inclined plane is introduced. Several regimes of the motion must be considered and analysed. A long term behaviour is studied and stability of stationary states is investigated utilizing the Poincaré map. The results are clearly summarized in Table 1 on page 37. A more general model, the compass gait biped, is introduced in Section 4, which is much more complicated and extra possible control term is considered (see eq. (4.5)). The analysis using Poincaré map is limited just to a passive walking case in this section (without any control term). There are quite a lot of grammar or factual mistakes in the thesis, e.g. p.8: missing "dt" in the functional A introduction, p17: missing number at Subsection reference; question mark within the second row of eq. (3.12) p. 27: procede -> proceed punctuation throughout the thesis, the recommended bibliography was not referred. The student has designed the thesis topic himself and he duly consulted the problems during the winter semester. Then he worked mostly individually and he was finally pressed for time, which concluded to incomplete analysis in the case of compass gait biped. Improving of text and corrections were scanty for a lack of time, which influenced the final quality of the thesis. A more general analysis was considered to be done in the case of compass gait biped. Nevertheless, the nontrivial rimless wheel analysis was realized properly and partial analysis was done also in the case of compass gait biped. The analysis of the both robots is supported by two original Python programs: the first one is a phaseportrait generator for the compass gait (suitable also for the rimless wheel), and the second one is a numerical search for passive gaits of the compass gait biped. Both programs are integral to the thesis. Although the intended goals were achieved partially, I appreciate the student's self-reliance, his insight into considered models and his Python programming abilities.

Posudek oponenta

Opluštil, Zdeněk

The master's thesis deals with mathematical models of walking robots. The text is divided into three main parts. Firstly, a mathematical apparatus relevant to the considered models are introduced. Then the rimless wheel model is analyzed by means of Poincaré map's fixed points. Finally, the author studies the compass gait model. In this case, a numerical solver was implemented in the programming language Python. The main goals have been achieved with the exception that the compass gait biped model is not numerically solved with the control term in the dynamical system. The text is clear and logically structured. The analysis of the considered models is based on the lectures of Russ Tedrake (see [5]). A detailed analysis of the behavior of the rimless wheel model, including assertions and their proofs, has been done in Section 3. Unfortunately, some of the justifications contain mathematical inaccuracies, e.g., - page 32 line 16: Inclusion does not follow from the lemma 3.7. - page 34, line 7: Lemma 3.2 cannot be used directly because its assumption is not satisfied for i = 0. The text also contains typos e.g. -page 5, line 3: there is "to" twice -page 11, line 15: "between" instead of "between" -page 17, line 24: there is extra "?" etc. In the thesis, I appreciate the following. Mathematical modeling of walking robots is very applicable in practice. Models are described in detail and clearly, including illustrative pictures. The author also programmed non-trivial compass gait biped solver and numerical searching for passive gaits in Python (functional source codes are attached in the text). I recommend the thesis for the defense with classification satisfactory.

eVSKP id 124460