Dynamics of Bipedal Gait: Part II—Stability Analysis of a Planar Five-Link Biped

1993 ◽  
Vol 60 (2) ◽  
pp. 337-343 ◽  
Author(s):  
Y. Hurmuzlu
Keyword(s):  
Stability Analysis ◽  
Parameter Space ◽  
Graphical Representation ◽  
Rigid Bodies ◽  
Bipedal Locomotion ◽  
Dimensional Parameter ◽  
Bipedal Gait ◽  
Stable Gait ◽  
Mapping Techniques ◽  
The Stability

A general approach based on discrete mapping techniques is presented to study stability of bipedal locomotion. The approach overcomes difficulties encountered by others on the treatment of discontinuities and nonlinearities associated with bipedal gait. A five-element bipedal locomotion model with proper parametric formulation is considered to demonstrate the utility of the proposed approach. Changes in the stability of the biped as a result of bifurcations in the four-dimensional parameter space are investigated. The structural stability analysis uncovered stable gait patterns that conform to the prescribed motion. Stable nonsymmetric locomotion with multiple periodicity was also observed, a phenomenon that has never been considered before. Graphical representation of the bifurcations are presented for direct correlation of the parameter space with the resulting walking patterns. The bipedal model includes some idealizations such as neglecting the dynamics of the feet and assuming rigid bodies. Some additional simplifications were performed in the development of the controller that regulates the motion of the biped.

A Geometrical Approach Assessing Instability Trends for Galloping

1991 ◽  
Vol 58 (3) ◽  
pp. 784-791 ◽  
Author(s):  
P. Yu ◽  
N. Popplewell ◽  
A. H. Shah
Keyword(s):  
Wind Speed ◽  
Parameter Space ◽  
Degrees Of Freedom ◽  
Critical Conditions ◽  
Geometrical Approach ◽  
Two Dimensional ◽  
Electrical Conductor ◽  
Geometrical Method ◽  
Dimensional Parameter ◽  
The Stability

Although the galloping of an iced electrical conductor has been considered by many researchers, no special attention has been given to the galloping’s sensitivity to alternations in the system’s parameters. A geometrical method is presented in this paper to describe these instability trends and to provide compromises for controlling an instability. The conventional but uncontrollable parameter of the wind speed is chosen as the basis for obtaining the critical conditions under which bifurcations occur for a representative two degrees-of-freedom model. Variations in these critical conditions are found in a two-dimensional parameter space in order to determine the trends for the initiation of galloping as well as to evaluate the stability of the ensuring periodic vibrations.

STABILITY ANALYSIS AND ROBUST CONTROL OF A PLANAR UNDERACTUATED BIPED ROBOT

2010 ◽  
Vol 07 (04) ◽  
pp. 535-563 ◽  
Author(s):  
REZA DEHGHANI ◽  
ABBAS FATTAH
Keyword(s):  
Stability Analysis ◽  
Robust Control ◽  
Sliding Mode ◽  
Center Of Mass ◽  
Biped Robot ◽  
Gait Pattern ◽  
Research Area ◽  
Parameter Uncertainties ◽  
Stable Gait ◽  
The Stability

Stability analysis is one of the main issues in the research area of biped robots with point feet. This article develops stability analysis and robust control of a planar biped robot with point feet with one degree of underactuation. A stability analysis is presented for the bipedal motion comprising single support and impact phases by using Poincaré map for nonlinear systems. Then, the stability conditions of periodic orbits are derived and stable gait pattern is determined using an optimization process. Thereafter, a robust sliding mode control with a time-invariant feedback is proposed to track stable gait in the presence of parameter uncertainties of the biped. Proposed approach is carried out for two types of bipeds, namely, a normal model and a balanced model in which the biped center of mass located at the hip using a novel model. Energy efficiency of biped is investigated for both models. Moreover, the stability of biped motion is studied in the presence of an unexpected stair. Simulation results show the biped motion quickly converges to cyclic motion during the first gait in both models.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

scholarly journals Measure of Similarity between GMMs by Embedding of the Parameter Space That Preserves KL Divergence

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 957
Author(s):  
Branislav Popović ◽  
Lenka Cepova ◽  
Robert Cep ◽  
Marko Janev ◽  
Lidija Krstanović
Keyword(s):  
Computational Complexity ◽  
Parameter Space ◽  
Recognition Accuracy ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Dimensional Manifold ◽  
Dimensional Parameter ◽  
Trade Off ◽  
Measure Of Similarity ◽  
Lower Dimensional

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Sign in / Sign up

Export Citation Format

Share Document