Stability optimization of open-loop controlled walking robots (Q2781529)

The goal of this doctoral dissertation is to devise controls such that the resulting periodic motions of several types of walking robots possess a certain degree of stability.NEWLINENEWLINENEWLINEThe idea is to find parameters (controls, initial conditions) such that first a periodic solution is obtained (within a finite horizon optimal control framework) and second solve an optimization problem (with respect to some model parameters) for the largest singular value associated to the monodromy operator \(M\) obtained from the linearization along the periodic trajectory. Here, one plays with norms and suitable powers of \(M\). It is important to realize that in this work, stability is obtained ad hoc and not specifically through the control; in the conclusion, the author states that stability may not be obtained.NEWLINENEWLINENEWLINEThe first half of the development formulates the main problem and associated subproblems for the solution, presents the equations of motion from mechanics, recalls known results on stability theory and describes the optimization problems. The second half consists of simulation results for three types of walking or hopping robots. Finally, one finds in the remaining pages a conclusion, some implementation considerations and a bibliography with 105 entries.NEWLINENEWLINENEWLINEThe reviewer does not find a substantial mathematical contribution in this work. There is no study on the existence of the solutions to the given problems, nor on issues of convergence or computational complexity.NEWLINENEWLINENEWLINEFrom the control point of view, there seem to be misconceptions concerning fundamentals: the author writes that in open-loop control, ``In contrast to closed-loop control, there is no need\dots for any on-line computation'' (p. 11). Also, she writes expressions like ``open-loop stable walking'' or ``open-loop control or self-stabilization'' (the latter seen as equivalent), which should be explained precisely in general and which are not consistent with the lack of established stability results in the context of this study.NEWLINENEWLINENEWLINELet us observe that initial conditions are part of the solution to the problem studied, which is a weakness from the practical point of view. Also, the focus is on a nominal trajectory design without perturbations (in order to save the open-loop philosophy), and at the end perturbations are introduced for checking robust stability. Moreover, one expects that solutions to the problems exist because of daily observations, but the actuators have a quite erratic behaviour in the simulations. One may wonder if this happens in the natural situation of an articulation operating when a man is walking.NEWLINENEWLINENEWLINEThis work presents mainly engineering experimental work on walking robots.