A screw syzygy with applications to robot singularity computation

A syzygy is a relation between invariants. In this paper a syzygy is presented between invariants of sequences of six screws under the action of the Euclidean group. This relation is useful in simplifying the computation of the determinant of a robot Jacobian and hence can be used to investigate the singularities of robot manipulators. © Springer Science+Business Media B.V. 2008

Introduction to Polynomial Invariants of Screw Systems

Screw systems describe the infinitesimal motion of multi–degree-of-freedom rigid bodies, such as end-effectors of robot manipulators. While there exists an exhaustive classification of screw systems, it is based largely on geometrical considerations rather than algebraic ones. Knowledge of the polynomial invariants of the adjoint action of the Euclidean group induced on the Grassmannians of screw systems would provide new insight to the classification, along with a reliable identification procedure. However many standard results of invariant theory break down because the Euclidean group is not reductive. We describe three possible approaches to a full listing of polynomial invariants for 2–screw systems. Two use the fact that in its adjoint action, the compact subgroup SO(3) acts as a direct sum of two copies of its standard action on R3. The Molien–Weyl Theorem then provides information on the primary and secondary invariants for this action and specific invariants are calculated by analyzing the decomposition of the alternating 2–tensors. The resulting polynomials can be filtered to find those that are SE(3) invariants and invariants for screw systems are determined by considering the impact of the Pl¨ucker relations. A related approach is to calculate directly the decomposition of the symmetric products of alternating tensors. Finally, these approaches are compared with the listing of invariants by Selig based on the existence of two invariant quadratic forms for the adjoint action

Development of a biomechanical energy harvester

© 2009 Li et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Traffic Instabilities in Self-Organized Pedestrian Crowds

In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in opposite directions spontaneously segregate into lanes of uniform walking directions. This phenomenon is often referred to as a smart collective pattern, as it increases the traffic efficiency with no need of external control. However, the functional benefits of this emergent organization have never been experimentally measured, and the underlying behavioral mechanisms are poorly understood. In this work, we have studied this phenomenon under controlled laboratory conditions. We found that the traffic segregation exhibits structural instabilities characterized by the alternation of organized and disorganized states, where the lifetime of well-organized clusters of pedestrians follow a stretched exponential relaxation process. Further analysis show that the inter-pedestrian variability of comfortable walking speeds is a key variable at the origin of the observed traffic perturbations. We show that the collective benefit of the emerging pattern is maximized when all pedestrians walk at the average speed of the group. In practice, however, local interactions between slow- and fast-walking pedestrians trigger global breakdowns of organization, which reduce the collective and the individual payoff provided by the traffic segregation. This work is a step ahead toward the understanding of traffic self-organization in crowds, which turns out to be modulated by complex behavioral mechanisms that do not always maximize the group's benefits. The quantitative understanding of crowd behaviors opens the way for designing bottom-up management strategies bound to promote the emergence of efficient collective behaviors in crowds.Comment: Article published in PLoS Computational biology. Freely available here: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.100244

Mechanical Work as an Indirect Measure of Subjective Costs Influencing Human Movement

To descend a flight of stairs, would you rather walk or fall? Falling seems to have some obvious disadvantages such as the risk of pain or injury. But the preferred strategy of walking also entails a cost for the use of active muscles to perform negative work. The amount and distribution of work a person chooses to perform may, therefore, reflect a subjective valuation of the trade-offs between active muscle effort and other costs, such as pain. Here we use a simple jump landing experiment to quantify the work humans prefer to perform to dissipate the energy of landing. We found that healthy normal subjects (N = 8) preferred a strategy that involved performing 37% more negative work than minimally necessary (P<0.001) across a range of landing heights. This then required additional positive work to return to standing rest posture, highlighting the cost of this preference. Subjects were also able to modulate the amount of landing work, and its distribution between active and passive tissues. When instructed to land softly, they performed 76% more work than necessary (P<0.001), with a higher proportion from active muscles (89% vs. 84%, P<0.001). Stiff-legged landings, performed by one subject for demonstration, exhibited close to the minimum of work, with more of it performed passively through soft tissue deformations (at least 30% in stiff landings vs. 16% preferred). During jump landings, humans appear not to minimize muscle work, but instead choose to perform a consistent amount of extra work, presumably to avoid other subjective costs. The degree to which work is not minimized may indirectly quantify the relative valuation of costs that are otherwise difficult to measure

Locomotor changes in length and EMG activity of feline medial gastrocnemius muscle following paralysis of two synergists

The mechanism of the compensatory increase in electromyographic activity (EMG) of a cat ankle extensor during walking shortly after paralysis of its synergists is not fully understood. It is possible that due to greater ankle flexion in stance in this situation, muscle spindles are stretched to a greater extent and, thus, contribute to the EMG enhancement. However, also changes in force feedback and central drive may play a role. The aim of the present study was to investigate the short-term (1- to 2-week post-op) effects of lateral gastrocnemius (LG) and soleus (SO) denervation on muscle fascicle and muscle–tendon unit (MTU) length changes, as well as EMG activity of the intact medial gastrocnemius (MG) muscle in stance during overground walking on level (0%), downslope (−50%, presumably enhancing stretch of ankle extensors in stance) and upslope (+50%, enhancing load on ankle extensors) surfaces. Fascicle length was measured directly using sonomicrometry, and MTU length was calculated from joint kinematics. For each slope condition, LG-SO denervation resulted in an increase in MTU stretch and peak stretch velocity of the intact MG in early stance. MG muscle fascicle stretch and peak stretch velocity were also higher than before denervation in downslope walking. Denervation significantly decreased the magnitude of MG fascicle shortening and peak shortening velocity during early stance in level and upslope walking. MG EMG magnitude in the swing and stance phases was substantially greater after denervation, with a relatively greater increase during stance of level and upslope walking. These results suggest that the fascicle length patterns of MG muscle are significantly altered when two of its synergists are in a state of paralysis. Further, the compensatory increase in MG EMG is likely mediated by enhanced MG length feedback during downslope walking, enhanced feedback from load-sensitive receptors during upslope walking and enhanced central drive in all walking conditions

Is the metabolic cost of walking higher in people with diabetes?

People with diabetes walk slower and display biomechanical gait alterations compared with controls, but it remains unknown whether the metabolic cost of walking (CoW) is elevated. The aim of this study was to investigate the CoW and the lower limb concentric joint work as a major determinant of the CoW, in patients with diabetes and diabetic peripheral neuropathy (DPN). Thirty-one nondiabetic controls (Ctrl), 22 diabetic patients without peripheral neuropathy (DM), and 14 patients with moderate/severe DPN underwent gait analysis using a motion analysis system and force plates and treadmill walking using a gas analyzer to measure oxygen uptake. The CoW was significantly higher particularly in the DPN group compared with controls and also in the DM group (at selected speeds only) compared with controls, across a range of matched walking speeds. Despite the higher CoW in patients with diabetes, concentric lower limb joint work was significantly lower in DM and DPN groups compared with controls. The higher CoW is likely due to energetic inefficiencies associated with diabetes and DPN reflecting physiological and biomechanical characteristics. The lower concentric joint work in patients with diabetes might be a consequence of kinematic gait alterations and may represent a natural strategy aimed at minimizing the CoW

Effects of an attention demanding task on dynamic stability during treadmill walking

<p>Abstract</p> <p>Background</p> <p>People exhibit increased difficulty balancing when they perform secondary attention-distracting tasks while walking. However, a previous study by Grabiner and Troy (<it>J. Neuroengineering Rehabil</it>., 2005) found that young healthy subjects performing a concurrent Stroop task while walking on a motorized treadmill exhibited <it>decreased </it>step width variability. However, measures of variability do not directly quantify how a system responds to perturbations. This study re-analyzed data from Grabiner and Troy 2005 to determine if performing the concurrent Stroop task directly affected the dynamic stability of walking in these same subjects.</p> <p>Methods</p> <p>Thirteen healthy volunteers walked on a motorized treadmill at their self-selected constant speed for 10 minutes both while performing the Stroop test and during undisturbed walking. This Stroop test consisted of projecting images of the name of one color, printed in text of a different color, onto a wall and asking subjects to verbally identify the color of the text. Three-dimensional motions of a marker attached to the base of the neck (C5/T1) were recorded. Marker velocities were calculated over 3 equal intervals of 200 sec each in each direction. Mean variability was calculated for each time series as the average standard deviation across all strides. Both "local" and "orbital" dynamic stability were quantified for each time series using previously established methods. These measures directly quantify how quickly small perturbations grow or decay, either continuously in real time (local) or discretely from one cycle to the next (orbital). Differences between Stroop and Control trials were evaluated using a 2-factor repeated measures ANOVA.</p> <p>Results</p> <p>Mean variability of trunk movements was significantly reduced during the Stroop tests compared to normal walking. Conversely, local and orbital stability results were mixed: some measures showed slight increases, while others showed slight decreases. In many cases, different subjects responded differently to the Stroop test. While some of our comparisons reached statistical significance, many did not. In general, measures of variability and dynamic stability reflected different properties of walking dynamics, consistent with previous findings.</p> <p>Conclusion</p> <p>These findings demonstrate that the decreased movement variability associated with the Stroop task did <it>not </it>translate to greater dynamic stability.</p

Differences in Walking Pattern during 6-Min Walk Test between Patients with COPD and Healthy Subjects

BACKGROUND: To date, detailed analyses of walking patterns using accelerometers during the 6-min walk test (6MWT) have not been performed in patients with chronic obstructive pulmonary disease (COPD). Therefore, it remains unclear whether and to what extent COPD patients have an altered walking pattern during the 6MWT compared to healthy elderly subjects. METHODOLOGY/PRINCIPAL FINDINGS: 79 COPD patients and 24 healthy elderly subjects performed the 6MWT wearing an accelerometer attached to the trunk. The accelerometer features (walking intensity, cadence, and walking variability) and subject characteristics were assessed and compared between groups. Moreover, associations were sought with 6-min walk distance (6MWD) using multiple ordinary least squares (OLS) regression models. COPD patients walked with a significantly lower walking intensity, lower cadence and increased walking variability compared to healthy subjects. Walking intensity and height were the only two significant determinants of 6MWD in healthy subjects, explaining 85% of the variance in 6MWD. In COPD patients also age, cadence, walking variability measures and their interactions were included were significant determinants of 6MWD (total variance in 6MWD explained: 88%). CONCLUSIONS/SIGNIFICANCE: COPD patients have an altered walking pattern during 6MWT compared to healthy subjects. These differences in walking pattern partially explain the lower 6MWD in patients with COPD

Energy extraction from the biologic battery in the inner ear

Endocochlear potential (EP) is a battery-like electrochemical gradient found in and actively maintained by the inner ear [superscript 1, 2]. Here we demonstrate that the mammalian EP can be used as a power source for electronic devices. We achieved this by designing an anatomically sized, ultra-low quiescent-power energy harvester chip integrated with a wireless sensor capable of monitoring the EP itself. Although other forms of in vivo energy harvesting have been described in lower organisms [superscript 3, 4, 5], and thermoelectric [superscript 6], piezoelectric [superscript 7] and biofuel [superscript 8, 9] devices are promising for mammalian applications, there have been few, if any, in vivo demonstrations in the vicinity of the ear, eye and brain. In this work, the chip extracted a minimum of 1.12 nW from the EP of a guinea pig for up to 5 h, enabling a 2.4 GHz radio to transmit measurement of the EP every 40–360 s. With future optimization of electrode design, we envision using the biologic battery in the inner ear to power chemical and molecular sensors, or drug-delivery actuators for diagnosis and therapy of hearing loss and other disorders.Focus Center Research Program. Focus Center for Circuit & System Solutions. Semiconductor Research Corporation. Interconnect Focus CenterNational Institutes of Health (U.S.) (Grant K08 DC010419)National Institutes of Health (U.S.) (Grant T32 DC00038)Bertarelli Foundatio