Discrete Mechanics and Optimal Control of Walking Gaits

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
M. W. Koch ◽  
M. Ringkamp ◽  
S. Leyendecker
Keyword(s):  
Optimal Control ◽  
Time Span ◽  
Constrained Systems ◽  
Bipedal Walking ◽  
Interval Length ◽  
Time Interval ◽  
Discrete Mechanics ◽  
Flat Foot ◽  
Flat Feet ◽  
Heel Contact

In this work, we optimally control the upright gait of a three-dimensional symmetric bipedal walking model with flat feet. The whole walking cycle is assumed to occur during a fixed time span while the time span for each of the cycle phases is variable and part of the optimization. The implemented flat foot model allows to distinguish forefoot and heel contact such that a half walking cycle consists of five different phases. A fixed number of discrete time nodes in combination with a variable time interval length assure that the discretized problem is differentiable even though the particular time of establishing or releasing the contact between the foot and the ground is variable. Moreover, the perfectly plastic contact model prevents penetration of the ground. The optimal control problem is solved by our structure preserving discrete mechanics and optimal control for constrained systems (DMOCC) approach where the considered cost function is physiologically motivated and the obtained results are analyzed with regard to the gait of humans walking on a horizontal and an inclined plane.

scholarly journals Discrete mechanics and optimal control for constrained systems

2010 ◽  
Vol 31 (6) ◽  
pp. 505-528 ◽  
Author(s):  
S. Leyendecker ◽  
S. Ober-Blöbaum ◽  
J. E. Marsden ◽  
M. Ortiz
Keyword(s):  
Optimal Control ◽  
Constrained Systems ◽  
Discrete Mechanics

Active Set Algorithm Applied to Discrete Mechanics and Optimal Control for Constrained Systems

2015 ◽  
Vol 723 ◽  
pp. 210-214 ◽  
Author(s):  
Lei Gao
Keyword(s):  
Optimal Control ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Constrained Systems ◽  
Rigid Sphere ◽  
Discrete Mechanics ◽  
Active Set ◽  
Slow Convergence ◽  
Active Set Algorithm ◽  
Nonlinear Equality

Discrete mechanics and optimal control for constrained systems (DMOCC) is a new developed solution for mechanical control. The formulation of DMOCC is attributed to nonlinear equality constraints for the minimization of an appointed cost function. Traditionally, the equations are solved by standard sequential quadratic programming (SQP) algorithm, which suffers for relatively slow convergence speed. In this paper, active set algorithm is introduced to the numerical solution of DMOCC. By comparison of these two algorithms for the example of transferring of the rigid sphere, the efficiency of active set algorithm is validated.

Discrete Mechanics and Optimal Control Applied to Mechanical Systems

2019 ◽  
Author(s):  
Igor Afonso Acampora Prado ◽  
Davi Ferreira de Castro ◽  
Mauricio Andrés Varela Morales ◽  
Domingos Rade
Keyword(s):  
Optimal Control ◽  
Mechanical Systems ◽  
Discrete Mechanics

scholarly journals Optimal Control and Positional Controllability in a One-Sector Economy

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 11
Author(s):  
Nikolai Grigorenko ◽  
Lilia Luk’yanova
Keyword(s):  
Optimal Control ◽  
Production Capacity ◽  
Quality Criterion ◽  
Zero Order ◽  
Suboptimal Control ◽  
Time Interval ◽  
Bounded Control ◽  
Optimal Value ◽  
Current Production ◽  
The Given

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

scholarly journals Longitudinal study of fingerprint recognition

2015 ◽  
Vol 112 (28) ◽  
pp. 8555-8560 ◽  
Author(s):  
Soweon Yoon ◽  
Anil K. Jain
Keyword(s):  
Statistical Models ◽  
Recognition Accuracy ◽  
Temporal Stability ◽  
Poor Quality ◽  
Time Span ◽  
Fingerprint Recognition ◽  
Time Interval ◽  
General Belief ◽  
Probability Of Error ◽  
Fingerprint Database

Human identification by fingerprints is based on the fundamental premise that ridge patterns from distinct fingers are different (uniqueness) and a fingerprint pattern does not change over time (persistence). Although the uniqueness of fingerprints has been investigated by developing statistical models to estimate the probability of error in comparing two random samples of fingerprints, the persistence of fingerprints has remained a general belief based on only a few case studies. In this study, fingerprint match (similarity) scores are analyzed by multilevel statistical models with covariates such as time interval between two fingerprints in comparison, subject’s age, and fingerprint image quality. Longitudinal fingerprint records of 15,597 subjects are sampled from an operational fingerprint database such that each individual has at least five 10-print records over a minimum time span of 5 y. In regard to the persistence of fingerprints, the longitudinal analysis on a single (right index) finger demonstrates that (i) genuine match scores tend to significantly decrease when time interval between two fingerprints in comparison increases, whereas the change in impostor match scores is negligible; and (ii) fingerprint recognition accuracy at operational settings, nevertheless, tends to be stable as the time interval increases up to 12 y, the maximum time span in the dataset. However, the uncertainty of temporal stability of fingerprint recognition accuracy becomes substantially large if either of the two fingerprints being compared is of poor quality. The conclusions drawn from 10-finger fusion analysis coincide with the conclusions from single-finger analysis.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Clinical and functional outcomes of tarsal coalition resection to correct rigid flat foot

2021 ◽  
Vol 15 (2) ◽  
pp. 115-119
Author(s):  
Rodrigo Guimarães Huyer ◽  
Mário Sérgio Paulillo Cillo ◽  
Carlos Daniel Cândido Castro Filho ◽  
Hallan Douglas Bertelli ◽  
Marcelo Morelli Girondo ◽  
...  
Keyword(s):  
Case Series ◽  
Categorical Variables ◽  
Continuous Variables ◽  
Tarsal Coalition ◽  
Retrospective Case ◽  
Aofas Score ◽  
Level Of Evidence ◽  
Flat Foot ◽  
Flat Feet ◽  
The Mean

Objective: This study used the AOFAS score to assess the clinical functional results of patients who underwent tarsal coalition resection. Methods: This was a retrospective case series of patients who underwent tarsal coalition resection to correct rigid flat foot. Clinical and functional assessment was performed with the AOFAS score before and 6 months after surgical treatment. Descriptive analysis was performed for 7 patients (11 operated feet) using measurements of position and dispersion (mean, standard deviation, minimum, median and maximum value) for continuous variables and frequency tables (absolute and relative) for categorical variables. Results: The mean patient age was 10 years, 7 months, and the majority (71.43%) were male. The most affected joint was the calcaneonavicular. The right side was affected in 54.55% of the cases. The most frequent type of coalition was osseous (81.82% of the cases). The mean pre- and postoperative AOFAS scores were 32.7 and 70.2 points, respectively, which was a significant increase. Conclusion: The increased scores after coalition resection was considered the main change between the two assessments. Thus, it can be concluded that in rigid flat feet without severe hind- or forefoot deformities for which conservative treatment failed, bar resection should be the surgical procedure of choice. Level of Evidence IV; Therapeutic Studies; Case Series.

scholarly journals Discrete Mechanics and Optimal Control for Image Registration

2007 ◽  
Vol 48 ◽  
pp. 1 ◽  
Author(s):  
Robert McLachlan ◽  
Stephen Marsland
Keyword(s):  
Optimal Control ◽  
Image Registration ◽  
Discrete Mechanics

A PROPOSED FORMULA FOR HORIZONTAL REVENUE ALLOCATION IN NIGERIA

2012 ◽  
Vol 29 (06) ◽  
pp. 1250033
Author(s):  
VIRTUE U. EKHOSUEHI ◽  
AUGUSTINE A. OSAGIEDE
Keyword(s):  
Optimal Control ◽  
Federal Government ◽  
Optimal Control Theory ◽  
Fixed Time ◽  
Tax Revenue ◽  
Time Interval ◽  
Fixed Time Interval ◽  
Hypothetical Data ◽  
Revenue Allocation ◽  
The Individual

In this study, we have applied optimal control theory to determine the optimum value of tax revenues accruing to a state given the range of budgeted expenditure on enforcing tax laws and awareness creation on the payment of the correct tax. This is achieved by maximizing the state's net tax revenue over a fixed time interval subject to certain constraints. By assuming that the satisfaction derived by the Federal Government of Nigeria on the ability of the individual states to generate tax revenue which is as near as the optimum tax revenue (via the state's control problem) is described by the logarithmic form of the Cobb–Douglas utility function, a formula for horizontal revenue allocation in Nigeria in its raw form is derived. Afterwards, we illustrate the use of the proposed horizontal revenue allocation formula using hypothetical data.

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