in this paper, stability analysis of walking gaits and robustness analysis are developed for a five-link and four-actuator biped robot. stability conditions are derived by studying unactuated dynamics and using the poincarã© map associated with periodic walking gaits. a stable gait is designed by an optimization process satisfying physical constraints and stability conditions. also, considering...

Nogueira, in 1995, presented a study of the Poincaré map and the related ParryDaniels map. In this note some variants of this algorithm are presented which seem to have quite different ergodic behavior.

Poincaré maps often prove to be invaluable tools in the study of long-term behaviour and qualitative properties of a given dynamical system. While the analytic theory of these maps is fully explored, finding numerical algorithms that allow the computation of Poincaré maps in concrete problems is far from trivial. For the verification it is desirable to approximate the Poincaré map over as large...

Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay ...

the focus of studies in the field of passive walking has often been on straight walking, while less attention has been paid to the field of turning motions. in this paper, the passive motions of a finite width rimless wheel as the simplest 3d model of passive biped walkers was investigated with a focus on turning motions. for this purpose, the hybrid model of the system consisting of continuous...

Statistics of Poincaré recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the statistics of the return times.

We prove two new identities in scattering theory in Hamiltonian mechanics and discuss the analogy between these identities and their counterparts in quantum scattering theory. These identities involve the Poincaré scattering map, which is analogous to the scattering matrix. The first of our identities states that the Calabi invariant of the Poincaré scattering map can be expressed as the regula...

In this paper we investigate the relation between robustness of periodic orbits exhibited by systems with impulse effects and robustness of their corresponding Poincaré maps. In particular, we prove that input-to-state stability (ISS) of a periodic orbit under external excitation in both continuous and discrete time is equivalent to ISS of the corresponding 0-input fixed point of the associated...