This paper presents a novel analytic method to uniquely solve inverse kinematics of 7 degrees-of-freedom manipulators while avoiding joint limits and singularities. Two auxiliary parameters are introduced to deal with the self-motion manifolds: the global configuration (GC), which specifies the branch of inverse kinematics solutions; and the arm angle (ψ) that parametrizes the elbow redundancy within the specified branch. The relations between the joint angles and the arm angle are derived, in order to map the joint limits and singularities to arm angle values. Then, intervals of feasible arm angles for the specified target pose and global configuration are determined, taking joint limits and singularities into account. A simple metric is proposed to compute the elbow position according to the feasible intervals. When the arm angle is determined, the joint angles can be uniquely calculated from the position-based inverse kinematics algorithm. The presented method does not exhibit the disadvantages inherent to the use of the Jacobian matrix and can be implemented in real-time control systems. This novel algorithm is the first position-based inverse kinematics algorithm to solve both global and local manifolds, using a redundancy resolution strategy to avoid singularities and joint limits. 60 are imposed to better imitate the human arm. These limitations, however, also simplify the inverse kinematics solution since they condition the possible configurations. Ultimately, solutions developed for applications under these constraints cannot be directly extended to manipulators with wider working ranges. Also, only Kim and Rosen [21] addressed the joint limits avoidance problem, by using an optimization routine that relies on estimated weight coefficients to distance from joint limits. 65
We consider feed-forward and auto-regulation feed-forward neural (weighted) coupled cell networks. In feed-forward neural networks, cells are arranged in layers such that the cells of the first layer have empty input set and cells of each other layer receive only inputs from cells of the previous layer. An auto-regulation feed-forward neural coupled cell network is a feed-forward neural network where additionally some cells of the first layer have auto-regulation, that is, they have a self-loop. Given a network structure, a robust pattern of synchrony is a space defined in terms of equalities of cell coordinates that is flow-invariant for any coupled cell system (with additive input structure) associated with the network. In this paper, we describe the robust patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks. Regarding feed-forward neural networks, we show that only cells in the same layer can synchronize. On the other hand, in the presence of auto-regulation, we prove that cells in different layers can synchronize in a robust way and we give a characterization of the possible patterns of synchrony that can occur for auto-regulation feed-forward neural networks.
We tested in a robotics experiment a dynamic neural field model for learning a precisely timed musical sequence. Based on neuro-plausible processing mechanisms, the model implements the idea that order and relative timing of events are stored in an integrated representation whereas the onset of sequence production is controlled by a separate process. Dynamic neural fields provide a rigorous theoretical framework to analyze and implement the necessary neural computations that bridge gaps between sensation and action in order to mediate working memory, action planing, and decision making. The robot first memorizes a short musical sequence performed by a human teacher by watching color coded keys on a screen, and then tries to execute the piece of music on a keyboard from memory without any external cues. The experimental results show that the robot is able to correct in very few demonstration-execution cycles initial sequencing and timing errors.
The literature on gait analysis in Vascular Parkinsonism (VaP), addressing issues such as variability, foot clearance patterns, and the effect of levodopa, is scarce. This study investigates whether spatiotemporal, foot clearance and stride-to-stride variability analysis can discriminate VaP, and responsiveness to levodopa. Fifteen healthy subjects, 15 Idiopathic Parkinson's Disease (IPD) patients and 15 VaP patients, were assessed in two phases: before (Off-state), and one hour after (On-state) the acute administration of a suprathreshold (1.5 times the usual) levodopa dose. Participants were asked to walk a 30-meter continuous course at a self-selected walking speed while wearing foot-worn inertial sensors. For each gait variable, mean, coefficient of variation (CV), and standard deviations SD1 and SD2 obtained by Poincaré analysis were calculated. General linear models (GLMs) were used to identify group differences. Patients were subject to neuropshychological evaluation (MoCA test) and Brain MRI. VaP patients presented lower mean stride velocity, stride length, lift-off and strike angle, and height of maximum toe (later swing) (p<.05), and higher %gait cycle in double support, with only the latter unresponsive to levodopa. VaP patients also presented higher CV, significantly reduced after levodopa. Yet, all VaP versus IPD differences lost significance when accounting for mean stride length as a covariate. In conclusion, VaP patients presented a unique gait with reduced degrees of foot clearance, probably correlated to vascular lesioning in dopaminergic/non-dopaminergic cortical and subcortical non-dopaminergic networks, still amenable to benefit from levodopa. The dependency of gait and foot clearance and variability deficits from stride length deserves future clarification.
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