The Effect of Pedal Platform Height on Cycling Biomechanics

1990 ◽  
Vol 6 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Maury L. Hull ◽  
Hiroko K. Gonzalez
Keyword(s):  
Cost Function ◽  
Inverse Dynamics ◽  
Problem Solution ◽  
Pedal Force ◽  
Upper Limits ◽  
Inverse Dynamics Problem ◽  
The Cost ◽  
Force Data ◽  
Linkage Model ◽  
Pedaling Rate

Using a five-bar linkage model of the leg/bicycle system in conjunction with experimental kinematic and pedal force data, the inverse dynamics problem is solved to yield the intersegmental moments. Among the input data that affect the problem solution is the height of the pedal platform. This variable is isolated and its effects on the total joint moments are studied as it assumes values over a ±4-cm range. Platform height variation affects the total joint moment peak values by up to 13%. Relying on a cost function derived from the hip and knee moments, it is found that the platform height that minimizes the cost function is +2 cm. The sensitivity of the cost function to the platform height variable is low; over the variable range the cost function increases 2% above the minimum. These results hold for a pedaling rate of 90 rpm. As pedaling rate is varied above and below 90 rpm, the sensitivity of the cost function increases. The platform heights that minimize the cost function are the lower and upper limits for 60 and 120 rpm, respectively. Thus the platform height variable interacts with pedaling rate, requiring a compromise in platform height adjustment. The compromise height depends on the individual’s preferred pedaling rate range.

Static optimal estimation of joint accelerations for inverse dynamics problem solution

2002 ◽  
Vol 35 (11) ◽  
pp. 1507-1513 ◽  
Author(s):  
Violaine Cahouët ◽  
Martin Luc ◽  
Amarantini David
Keyword(s):  
Inverse Dynamics ◽  
Optimal Estimation ◽  
Problem Solution ◽  
Inverse Dynamics Problem

Optimum Trajectory Planning for Redundant and Hyper-Redundant Manipulators Through Inverse Dynamics

2011 ◽  
Author(s):  
Kagan K. Ayten ◽  
M. Necip Sahinkaya ◽  
P. Iravani
Keyword(s):  
Cost Function ◽  
Trajectory Planning ◽  
Inverse Dynamics ◽  
Minimum Energy ◽  
Redundant Manipulators ◽  
Inverse Dynamic ◽  
Dynamic Constraints ◽  
Function Calculation ◽  
The Cost ◽  
Fifth Order

This paper presents a method to develop minimum energy trajectories for redundant/hyper-redundant manipulators with pre-defined kinematic and dynamic constraints. The optimal trajectory planning uses fifth order B-spline functions to represent the Cartesian coordinates of the end-effector and angles of the redundant links. The actuator torques are considered for the formulation of the cost function. Calculation of the cost function is carried out by using an inverse dynamic analysis. The system constraints are handled within the cost function to avoid running the inverse dynamics when the constraints are not satisfied. A novel virtual link concept is introduced to replace all the redundant links to eliminate physicaly impossible configurations before running the inverse dynamic model. The process is applicable to hyper redundant manipulators with large number of links. The proposed scheme is verified with computer simulations based on a 5-link planar redundant manipulator.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Sorting permutations by fragmentation-weighted operations

2020 ◽  
Vol 18 (02) ◽  
pp. 2050006 ◽  
Author(s):  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Approximation Algorithms ◽  
Computational Biology ◽  
Cost Function ◽  
Traditional Approach ◽  
Upper Bounds ◽  
Evolutionary Distance ◽  
Lower And Upper Bounds ◽  
Approximation Factor ◽  
New Type ◽  
The Cost

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species’ genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

Using the cost function to generate Marshallian demand systems

2000 ◽  
Vol 25 (2) ◽  
pp. 209-227 ◽  
Author(s):  
Keith R. McLaren ◽  
Peter D. Rossitter ◽  
Alan A. Powell
Keyword(s):  
Cost Function ◽  
Demand Systems ◽  
The Cost

Optimal actuator placement in adaptive optics systems

2021 ◽  
pp. 107754632110324
Author(s):  
Berk Altıner ◽  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Cost Function ◽  
Adaptive Optics ◽  
Disturbance Attenuation ◽  
Linear Quadratic ◽  
Placement Problem ◽  
Convex Optimization Problem ◽  
Wavefront Aberrations ◽  
The Cost ◽  
Actuator Placement ◽  
Quadratic Cost Function

Adaptive optics systems are powerful tools that are implemented to degrade the effects of wavefront aberrations. In this article, the optimal actuator placement problem is addressed for the improvement of disturbance attenuation capability of adaptive optics systems due to the fact that actuator placement is directly related to the enhancement of system performance. For this purpose, the linear-quadratic cost function is chosen, so that optimized actuator layouts can be specialized according to the type of wavefront aberrations. It is then considered as a convex optimization problem, and the cost function is formulated for the disturbance attenuation case. The success of the presented method is demonstrated by simulation results.

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