
On a stepladder model walking (with and without a decorator)
Polach, P. ; Prokýšek, R. ; Papáček, Štěpán
This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the realtime movement of the laboratory walking robot, designed and built at the Department of Control Theory of the Institute of Information Theory and Automation of the Czech Academy of Sciences [1, 6, 7]. Underactuated biped robots with an upper body form a subclass of legged robots, see, e.g., [4] for a review on the control of underactuated mechanical systems and [2] for a study of an asymptotically stable walking for biped robots. It is obvious that in general, the walking control of underactuated walking robots is a more challenging problem than walking control of fully actuated walking robots. As follows, we examine the wellknown mechanical system of the stepladder model with and without a decorator, whose role is substituted by an external inertial force according to the D’Alembert principle. It is well known, that stepladder walking is possible due to the periodic movement (pendulating) of an operator – decorator1 The rigorous dynamical analysis of stable cyclic walking of a class of stepladder models is presented in the next section.


COMPUTER SIMULATION STUDY OF THE STABILITY OF UNDERACTUATED BIPEDAL ROBOT MODELS (motivated by Griffin and Grizzle, 2017)
Polach, P. ; Anderle, Milan ; Zezula, Pavel ; Papáček, Štěpán
A key feature for bipedal walkers (robots and humans as well) is their stability or disturbance rejection defined as the ability to deal with unexpected disturbances. The paper by Griffin and Grizzle (2017) have significantly contributed to the shift from flat ground to slopes and steps when evaluating the walking efficiency of their robots. Similarly, in this contribution, based on the appropriate model of robot dynamics and control law, we examine the stability of walkingwithoutfalling for different ground perturbations for a threelink compass gait walker. I.e., we perform the sensitivity analysis of the walking stability of underactuated bipedal walker with respect to certain disturbation using the alaska/MultibodyDynamics simulation tool.


BohlMarek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán ; Matonoha, Ctirad ; Duintjer Tebbens, Jurjen
This study presents an application of one special technique, further called as BohlMarek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the druginduced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzymecatalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the abovesketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasilinear' BohlMarek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.


TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIMESCALE MODELS
Papáček, Štěpán ; Matonoha, Ctirad
Some dynamical systems are characterized by more than one timescale, e.g. two well separated timescales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slowfast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple timescales method, and (ii) the method of averaging. On a case study, being an underdamped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple timescales method is not suitable for our purposes.


On a class of biped underactuated robot models with upper body: Sensitivity analysis of the walking performance
Papáček, Štěpán ; Polach, P. ; Prokýšek, R. ; Anderle, Milan
Biped underactuated robots with an upper body (being a torso) form a subclass of legged robots. This study deals with the walking performance of such class of legged robot models and has been motivated by the need to implement of the previously developed sensor and control algorithms for the realtime movement of the laboratory walking robot, designed and built at the Department of Control Theory of the Institute of Information Theory and Automation (UTIA) of the Czech Academy of Sciences, see Fig. 1 (left). A detailed description of this underactuated walkinglike mechanical system (called further UTIA Walking Robot – UWR) is provided in [2] and [5]. The simplest underactuated walking robot hypothetically able to walk is the socalled Compass gait biped walker, alternatively called the Acrobot, see Fig. 1 (right). For a review of underactuated mechanical systems, i.e. systems with fewer actuators than degrees of freedom, which encounter many applications in different fields (e.g., in robotics, in aeronautical and spatial systems, in marine and underwater systems, and inflexible and mobile systems), see [3]. As follows, we examine the walking performance of parametrized models for different walking regimes and different values of model parameters. More specifically, the sensitivity analysis (i.e., parameter study) of the walking performance with respect to certain design variables (model parameters) is carried out using the software package alaska/MultibodyDynamics. The main attention is attracted to the role of the upper body mass m3 and position lc3, see Fig. 1 (right). Last but not least, having surveyed the mechanics of planar biped robots, our subsequent goal is the analysis of a 3D biped model where lateral balance is either controlled, suppressed or compensated.
