Stride Reduction Research Articles

Development of a three-dimensional dynamic biped walking via the oscillation of telescopic knee joint and its gait analysis

The purpose of this study is to extend the three-dimensional (3-D) passive dynamic biped walker to a 3-D dynamic biped walker, i.e., a walker that can walk on a horizontal surface based on a passive dynamic walking. A new prototype of 3-D biped walker called RW04, which has telescopic knee joints, was developed and its ability for walking was validated through some experiments. A sinusoidal oscillation, which is regarded as a central pattern generator with no sensory feedback, was provided to the knee joints to achieve the biped walking. The results showed that the biped gait of RW04 was possible only via a sinusoidal oscillation of the knee joint. Moreover, the 3-D dynamic walking gait via frequency response and zero moment point (ZMP) trajectory was also analyzed. The biped locomotion had a resonance, i.e., the frequency matched the natural frequency of the locomotion in the gain property. An “8” shaped ZMP trajectory was observed, which was found to be similar to that of the human gait. However, the simple sinusoidal oscillation had limitations such as stride reduction or discontinuation by phase difference. Therefore, in future work, more adaptable control strategy such as a sensory feedback using ZMP should be provided.

Eigenvalue clustering of coefficient matrices in the iterative stride reductions for linear systems

Solvers for linear systems with tridiagonal coefficient matrices sometimes employ direct methods such as the Gauss elimination method or the cyclic reduction method. In each step of the cyclic reduction method, nonzero offdiagonal entries in the coefficient matrix move incrementally away from diagonal entries and eventually vanish. The steps of the cyclic reduction method are generalized as forms of the stride reduction method. For example, the 2-stride reduction method coincides with the 1st step of the cyclic reduction method which transforms tridiagonal linear systems into pentadiagonal systems. In this paper, we explain arbitrary-stride reduction for linear systems with coefficient matrices with three nonzero bands. We then show that arbitrary-stride reduction is equivalent to a combination of 2-stride reduction and row and column permutations. We thus clarify eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction method. We also provide two examples verifying this property.

Lifting the “FOG” With Laser Generated Visual-Cueing

To ascertain whether freezing of gait (FOG) and stride reduction (SR) may be relieved by the use of an attachable, adjustable laser (the Mobilaser). Seven parkinsonian patients with FOG and SR were randomized in an open-label, randomized, cross-over clinical study at a tertiary referral center. The Mobilaser was attached to a 4-wheeled walker by Velcro and switched on, producing an adjustable red line, which the subjects stepped on or over while ambulating a standardized course. The length of time each subject took, and the number of freezes they experienced traversing the course, using a 4-wheeled walker with the device turned on and off, were compared. A total of 7 patients were investigated; however, one was excluded from the study due to severe deconditioning, prohibiting completion of the testing. Of the 6 enrolled, all subjects took less time to ambulate the course using the attachable, adjustable laser than without it (Wilcoxon signed-rank test, P=0.03). In addition, the total number of freezes was less in all 6 subjects when using the device than without it. No adverse events occurred during the trial. The Mobilaser is potentially an effective and safe device for alleviating parkinsonian FOG and SR.

Solving separable elliptic equations by the block stride reduction algorithm

A comparison of the Buneman version of the block cyclic reduction (BCR) algorithm and Stride Reduction (BSR) based on polynomial factorization for separable elliptic equations with Dirichlet boundary conditions is presented. This study was initiated by an interest in the parallel computing techniques that can be used to increase the computational efficiency of these model problems

Cyclic and stride reduction methods for generalised tridiagonal matrices

In this note a comparison of the cyclic and stride reduction methods for general tridiagonal matrices is outlined and a omparison of the computational work involved is presented.

The Block Stride Reduction (B.S.R.) AlgorithmWith Application To Domain DecompositionMethods

In this paper we consider the application of the Block Stride Reduction algorithm for the solution of separable self-adjoint elliptic equations on rectangular domains. Non-overlapping domain decomposition techniques are applied to reduce the differential operator to block diagonally bordered linear systems which can then be solved by the Preconditioned Conjugate Gradient method. Finally, a new preconditioner for such systems is outlined.

Strides reduction algorithms for block tridiagonal linear systems

A new formulation of the Stride of 3 reduction algorithm for block tridiagonal systems is presented. Partial fractions expansions are used for decoupling the tridiagonal systems occurring during the forward reduction and backward substitution processes. As a result enhanced parallelism is obtained in the algorithm. A hybrid combination of Stride reduction and block alternating group explicit method (BLAGE) is shown to have a superior convergence rate than BLAGE and the cyclically reduced BLAGE system.

A comparison of the computatlonal complexities of the stride reduction methods

In this paper the 'Stride of 3' reduction method is compared with the wtfell known cyclic reduction method for solving tridiagonal systems derived from the discretiped steady state convection diffusion equation. The Stride of 3 algorithm is shown to be superior for moderate to large linear systems (e.g., of order > 20).

The Parallel Solution Of Banded LinearSystems By The Block Stride ReductionAlgorithm

A comparison of the Buneman version of the block cyclic reduction (BCR) algorithm and Stride Reduction (BSR) based on polynomial factorization for separable elliptic equations with Dirichlet boundary conditions is presented. This study was initiated by an interest in the parallel computing techniques that can be used to increase the computational efficiency of these model problems.