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    AuthorTitleYearJournal/ProceedingsReftypeDOI/URL
    Burden, S.A., Revzen, S. & Sastry, S. Dimension reduction near limit cycles of hybrid systems: implications for design and analysis of legged locomotion 2011 IEEE CDC  article  
    Abstract: We consider the geometry of the flow near a periodic trajectory of a hybrid dynamical system. Under a non-degeneracy condition, we demonstrate the existence of an embedded smooth dynamical system that contains the periodic orbit and locally foliates each hybrid domain. Stability of the periodic orbit is determined entirely on this invariant subsystem. Implications for design and analysis of legged locomotors are discussed.
    BibTeX:
    @article{burden2011floq,
      author = {Burden, S A and Revzen, S and Sastry, S},
      title = {Dimension reduction near limit cycles of hybrid systems: implications for design and analysis of legged locomotion},
      journal = {IEEE CDC},
      year = {2011},
      note = {in prep}
    }
    
    Frachtenberg, E. & Revzen, S. Lossless data compression 2003 Patent(20030030575)  patent URL 
    Abstract: Dictionary based data compression apparatus comprising: a library of static dictionaries each optimized for a different data type, a data type determiner operable to scan incoming data and determine a data type thereof, a selector for selecting a static dictionary corresponding to said determined data type and a compressor for compressing said incoming data using said selected dictionary. The apparatus is useful in providing efficient compression of relatively short data packets having undefined contents as may be expected in a network switch.
    BibTeX:
    @patent{Patent-Comp,
      author = {E Frachtenberg and S Revzen},
      title = {Lossless data compression},
      journal = {Patent},
      year = {2003},
      number = {20030030575},
      url = {http://www.freepatentsonline.com/20030030575.html}
    }
    
    Frimerman, A., Revzen, S. & Shani, B. Spatial Relation of QRS-T Vectorcardiogram is a Good Predictor of Coronary Disease in Patients with Normal Rest 12-Leads ECG (poster) 2008 55th Annual Conference of the Israel Heart Society and the Israel Society of Cardiothoracic Surgery  conference  
    BibTeX:
    @conference{Frimerman08,
      author = {Frimerman, A and Revzen, S and Shani, B},
      title = {Spatial Relation of QRS-T Vectorcardiogram is a Good Predictor of Coronary Disease in Patients with Normal Rest 12-Leads ECG (poster)},
      booktitle = {55th Annual Conference of the Israel Heart Society and the Israel Society of Cardiothoracic Surgery},
      year = {2008}
    }
    
    Jusufi, A., Goldman, D.I., Revzen, S. & Full, R.J. Active tails enhance arboreal acrobatics in geckos 2008 Proceedings of the National Academy of Sciences
    Vol. 105(11), pp. 4215-4219 
    article DOI  
    Abstract: Geckos are nature's elite climbers. Their remarkable climbing feats have been attributed to specialized feet with hairy toes that uncurl and peel in milliseconds. Here, we report that the secret to the gecko's arboreal acrobatics includes an active tail. We examine the tail's role during rapid climbing, aerial descent, and gliding. We show that a gecko's tail functions as an emergency fifth leg to prevent falling during rapid climbing. A response initiated by slipping causes the tail tip to push against the vertical surface, thereby preventing pitch-back of the head and upper body. When pitch-back cannot be prevented, geckos avoid falling by placing their tail in a posture similar to a bicycle's kickstand. Should a gecko fall with its back to the ground, a swing of its tail induces the most rapid, zero-angular momentum air-righting response yet measured. Once righted to a sprawled gliding posture, circular tail movements control yaw and pitch as the gecko descends. Our results suggest that large, active tails can function as effective control appendages. These results have provided biological inspiration for the design of an active tail on a climbing robot, and we anticipate their use in small, unmanned gliding vehicles and multisegment spacecraft.
    BibTeX:
    @article{Jusufi03182008,
      author = {Jusufi, A and Goldman, D I and Revzen, S and Full, R J},
      title = {Active tails enhance arboreal acrobatics in geckos},
      journal = {Proceedings of the National Academy of Sciences},
      year = {2008},
      volume = {105},
      number = {11},
      pages = {4215-4219},
      doi = {http://dx.doi.org/10.1073/pnas.0711944105}
    }
    
    Moore, T.Y., Revzen, S., Burden, S. & Full, R.J. Adding inertia and mass to test stability predictions in rapid running insects (abstract only) 2010 Integrative and Comparative Biology  conference  
    Abstract: A spring-mass model for the horizontal plane dynamics of sprawled running animals (Lateral Leg Spring Model) predicts that added inertia reduces stability and increases the time required to recover from a perturbation. To empirically test this model, we perturbed cockroaches while running across a platform inserted into a track. Cockroaches (Blaberus discoidalis; N=9, 2.17 g mass, 2.18 g cm^2 moment of inertia) ran along the surface of the platform at 31+/-6 cm/sec with a stride frequency of 12.5+/-1.7 Hz. We accelerated the platform (10 cm x 25 cm) laterally at 0.6+/-0.1 g in a 0.1 sec interval providing a 50+/-3 cm/sec velocity change from the impulse. We affixed one of three backpacks on the cockroach to change its inertia distribution and mass. We used a computer vision-based tracking of body roll, pitch, yaw, leg position, and velocity on the translating platform. The control backpack increased the animal's mass by 36% and moment of inertia by 25%; the mass backpack increased mass by 84% and moment of inertia by 26%; the inertia backpack increased mass by 93% and moment of inertia by 865%. Animals equipped with the inertia backpack were not less stable than controls, thereby rejecting the prediction of the horizontal plane Lateral Leg Spring Model. Animals running with the mass backpack were least stable, showing greater body angular changes than other conditions. Larger angular body exercisions of the animals with mass backpacks were delayed by approximately one to two steps. Consistent with this delay was a lag in the change of lateral foot placement relative to the body axis along with its recovery to the pre-perturbation values. Results suggest that a three dimensional model is necessary even in sprawled- posture animals to test hypotheses of self-stabilization, and the role of both mechanical and neural feedback.
    BibTeX:
    @conference{moore-SICB10,
      author = {T Y Moore and S Revzen and S Burden and R J Full},
      title = {Adding inertia and mass to test stability predictions in rapid running insects (abstract only)},
      booktitle = {Integrative and Comparative Biology},
      year = {2010}
    }
    
    Revzen, S. Neuromechanical control architectures in arthropod locomotion 2009 School: Univeristy of California, Berkeley  phdthesis PDF 
    BibTeX:
    @phdthesis{RevzenPhD09,
      author = {S Revzen},
      title = {Neuromechanical control architectures in arthropod locomotion},
      school = {Univeristy of California, Berkeley},
      year = {2009}
    }
    
    Revzen, S. Phase estimation from kinematic data 2008 Tutorial 2 presentation, Workshop 4, Mathematical Biosciences Institute  misc PDF 
    BibTeX:
    @misc{RevzenTut2,
      author = {S Revzen},
      title = {Phase estimation from kinematic data},
      year = {2008}
    }
    
    Revzen, S. Paging on access graphs of minimal degree 3 2001 School: Hebrew University, Jerusalem  mastersthesis  
    Abstract: This paper presents two related results in the field of Paging Algorithms and in graph theory. It begins in presenting a generalization of the Access Graph model of paging, dubbed Abstract Access Graphs. This model is applicable to online problems in general, and its study motivated my research. Then it is shown that on access graphs (in the usual sense) with a minimal vertex degree of 3 or more the competitive ratio is at least k/4 for all deterministic algorithms and H_k/4 for randomized algoorithms. This is derived from a graph theoretical result showing that such trees contain many leaves. In attempting to extend this result to abstract access graphs it is found that such trees (arboresences) do not exist in some directed graphs, even with arbitrarily high minimal in- and out- degree. Such an example is constructed, thereby disproving the existence of linearly small strongly connected directed dominating sets in such graphs.
    BibTeX:
    @mastersthesis{RevzenMSc01,
      author = {S Revzen},
      title = {Paging on access graphs of minimal degree 3},
      school = {Hebrew University, Jerusalem},
      year = {2001},
      note = {unpublished}
    }
    
    Revzen, S., Berns, M.S., Koditschek, D.E. & Full, R.J. Determining neuromechanical control architecture using kinematic phase response to perturbations (abstract only) 2008 Integrative and Comparative Biology  conference  
    Abstract: We define several neuromechanical control architectures that represent rhythmic motion. The first class is a mass-spring system interacting with the environment whose motions are triggered by specific events. The second class is a mass-spring system driven by the feedforward signal of a CPG-like clock. The third class is a mass-spring system coupled to a clock, but with proprioceptive feedback that tracks a trajectory without altering the dynamics of the clock. The fourth class is similar to the third, but allows feedback to modulate the clock dynamics. We propose that a battery of perturbations to an animal can provide outcomes that allow identification of an architecture. To define these architectures, we selected a vertical hopping model that has received analytical treatment in both robotics and biomechanics, because it is a simple model that captures the essential phase and frequency responses of a neural pattern generator coupled to a mechanical oscillator. We assume that kinematically derived measurements of mechanical phase reflect the coupled internal neural clock phase and can be used to capture aspects of the various motor systems' phase response curves during rhythmic behavior. We subjected the four models to three perturbations that include a bump, a step, and an incline. In the first class phase and frequency change continuously. In the second, frequency is preserved by the clock and phase exhibits several discrete values. Both phase and frequency are preserved by the third class, whereas the fourth is similar in outcomes to the first, but at much longer time scales. Experiments on polypedal running animals will reveal the true empirical power of these architectural hypotheses.
    BibTeX:
    @conference{Revzen-SICB08,
      author = {Revzen, S and Berns, M S and Koditschek, D E and Full, R J },
      title = {Determining neuromechanical control architecture using kinematic phase response to perturbations (abstract only)},
      booktitle = {Integrative and Comparative Biology},
      year = {2008},
      note = {(abstract only)}
    }
    
    Revzen, S., Bishop-Moser, J., Spence, A.J. & Full, R.J. Testing control models in rapid running insects using lateral ground translation 2007 Integrative and Comparative Biology
    Vol. 47(suppl 1), pp. e1-152 
    article DOI  
    Abstract: Perturbation of simple passive, dynamic models of legged locomotion suggest the possibility of self-stabilization with minimal neural feedback. Rapid recovery from brief impulses to the body of fast, sprawled-posture runners and the absence of muscle activation pattern changes while traversing rough terrain support the hypothesis of recovery by mechanical feedback alone. Large and complex perturbations to rapid running insects imposed by a single, hip-high hurdle do produce significant leg phase and frequency changes showing that sensory feedback must play a role in recovery. To better determine the interrelationship between neural and mechanical feedback, we designed a trackway with a 10 x 25 cm platform insert that could translate laterally to a maximum acceleration of 10g in 50 msec. Cockroaches (Blaberus discoidalis; n=14) running at 30±8 cm/sec at a step frequency of 11.5±2.7 Hz onto a movable platform were accelerated laterally at 1g in a 100 msec interval providing a 56±3 cm/sec specific impulse. By automatically tracking body position and orientation and leg (tarsus) positions, we found no change in leg motion timing for at least 50 msec. Following this delay, animals decreased step frequency for one stride, and then partially recovered frequency thereafter. Results are consistent with previous research showing that the initial rapid recovery is accomplished by mechanical feedback promoting self-stabilization followed by neural feedback modulation of a central pattern generator at a slower rate occurring after a delay comparable to the duration of a step. Funded by NSF FIBR Grant.
    BibTeX:
    @article{Revzen-SICB07,
      author = {S Revzen and J Bishop-Moser and A J Spence and R J Full},
      title = {Testing control models in rapid running insects using lateral ground translation},
      journal = {Integrative and Comparative Biology},
      year = {2007},
      volume = {47},
      number = {suppl 1},
      pages = {e1-152},
      note = {(abstract only)},
      doi = {http://dx.doi.org/10.1093/icb/icm104}
    }
    
    Revzen, S., Burden, S.A., Moore, T.Y. & Full, R.J. Interplay of Neural and Mechanical Control in Insects Journal of Experimental Biology  article  
    Abstract: Animals running at intermediate speeds likely depend on both neural and mechanical feedback to maintain stability. When perturbed, changes in instantaneous kinematic phase and frequency of rhythmic movements can provide evidence for neural feedback with a time resolution not possible with traditional approaches. To induce a perturbation, we ran cockroaches (Blaberus discoidalis) at their preferred speed onto a movable cart that was accelerated laterally with respect to the animals' motion. The specific impulse imposed on animals was 0.50±4 ms -1 (mean, s.d.), nearly twice the
    forward speed (0.25±6 ms-1) of the animals. Animals corrected by decreasing stride frequency, thereby demonstrating neural feedback to their neural pattern generator. Trials fell into two classes in terms of forward ground velocity changes, while exhibiting statistically indistinguishable frequency changes. The class of a trial could be predicted based on the posture of the body at the onset of perturbation. Trials during which the animals had front and hind feet of a tripod in stance on the side towards which the animals were pulled were in a more stable posture, suggesting that eight or more legged animals might be more robust to lateral perturbations. In both classes frequency decreased at a delay of over 0.110 s from onset of perturbation. Results are consistent with previous research on fast running showing that the
    recovery begins with self-stabilizing mechanical feedback. Here, at intermediate speeds, we discovered that mechanical stabilization is followed by neural feedback modulation of the central pattern generator at delays comparable to the duration of one stride.
    BibTeX:
    @article{revzen2010lat,
      author = {S Revzen and S A Burden and T Y Moore and R J Full},
      title = {Interplay of Neural and Mechanical Control in Insects},
      journal = {Journal of Experimental Biology},
      note = {(in review)}
    }
    
    Revzen, S., Full, R.J. & Koditschek, D.E. Using kinematic phase to test neuromechanical control hypotheses: Running in cockroaches disrupted by a hurdle Journal of Experimental Biology  article  
    Abstract: Using hypotheses derived from a dynamical system approach, we tested whether the control of running uses neural feedback to recover from a perturbation. If feedforward neural signals are unmodified by the perturbation, then the timing (phase) of tarsal (foot) kinematics should remain phase-locked to the pre-perturbation rhythm. We video recorded Blaberus discoidalis cockroaches traversing a hurdle and processed the kinematic data from the fore-aft excursions of all tarsi to produce a single kinematic phase variable. Kinematic phase may be used to reliably predict future leg motions based on the preceding strides. The time derivative of kinematic phase provides a frequency which must remain unchanged if neural patterns are unaffected by sensory feedback. Results of forty trials showed that the kinematic phase was reset, while running frequency was closely maintained to within +/-5%. Kinematic phase changes were distributed bi-modally with modes 180 degrees or half a stride apart (in an axial distribution)- a difference of one step, which corresponds to a left-right reflection of the kinematic state of the body. Neither mode had significant weight at zero phase change, decreasing the likelihood of feedforward control and supporting the use of neural feedback for this task. Phase changes did not depend on visual or antennal sensory ability. We propose a controller that expresses the timing of the two tripods as two coupled phase oscillators, which in turn, may also be coupled to a master clock. Our controller informs and is informed by controllers operating in legged robots.
    BibTeX:
    @article{Revzen-bump09,
      author = {S Revzen and R J Full and D E Koditschek},
      title = {Using kinematic phase to test neuromechanical control hypotheses: Running in cockroaches disrupted by a hurdle},
      journal = {Journal of Experimental Biology},
      note = {(working title; in prep)}
    }
    
    Revzen, S. & Guckenheimer, J.M. Finding the dimension of slow dynamics in a rhythmic system 2010 J R Soc Lond Interface
    Vol. (under review) 
    article  
    Abstract: Dynamical systems with asymptotically stable periodic orbits are generic models for rhythmic processes in dissipative physical systems. This paper presents a method for reconstructing the dynamics near a periodic orbit from multivariate time series data. It is used to test the ories about the control of legged locomotion, a context in which time series are short compared to previous work in nonlinear time series analysis. The method presented here identifies appropriate dimensions of reduced order models for the deterministic portion of the dynamics. The paper also addresses challenges inherent in identifying dynamical models with data from different individuals.
    BibTeX:
    @article{revzen2010fdsd,
      author = {Revzen, S and Guckenheimer, J M},
      title = {Finding the dimension of slow dynamics in a rhythmic system},
      journal = {J R Soc Lond Interface},
      year = {2010},
      volume = {(under review)}
    }
    
    Revzen, S. & Guckenheimer, J.M. A dynamical systems analysis of running cockroaches 2008 Mathematical Biosciences Institute, Workshop 4  conference  
    Abstract: We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion. We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.
    BibTeX:
    @conference{RevGuk-MBI08,
      author = {S Revzen and J M Guckenheimer},
      title = {A dynamical systems analysis of running cockroaches},
      booktitle = {Mathematical Biosciences Institute, Workshop 4},
      year = {2008},
      note = {(abstract only)}
    }
    
    Revzen, S. & Guckenheimer, J.M. Estimating the phase of synchronized oscillators 2008 Physical Review E
    Vol. 78(5), pp. 051907 
    article DOI  
    Abstract: The state of a collection of phase-locked oscillators is determined by a single phase variable or cyclic coordinate. This paper presents a computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors. Measurements are assumed to be a collection of multidimensional time series. Each series consists of several cycles of the same or similar systems. The oscillators within each system are not assumed to be identical. Using measurements of the noise covariance for the multivariate input, data from the individual oscillators in the system are combined to reduce the variance of phase estimates for the whole system. The efficacy of the algorithm is demonstrated on experimental and model data from biomechanics of cockroach running and on simulated oscillators with varying levels of noise.
    BibTeX:
    @article{RevGuk08,
      author = {S Revzen and J M Guckenheimer},
      title = {Estimating the phase of synchronized oscillators},
      journal = {Physical Review E},
      year = {2008},
      volume = {78},
      number = {5},
      pages = {051907},
      doi = {http://dx.doi.org/10.1103/PhysRevE.78.051907}
    }
    
    Revzen, S., Guckenheimer, J.M. & Full, R.J. Subtle differences in gaits: the perspective of data driven Floquet analysis 2011 Yearly meeting of the Society for Integrative and Comparative Biology  conference  
    Abstract: Most rapid forms of animal locomotion involve producing a gait - a rhythmic sequence of body motions that propels the body through space by acting on the environment. Gaits are stable with respect to environmental perturbations. Data driven Floquet analysis promises a quantitative model of gait derived purely from kinematic measurements. The model encompasses familiar concepts such as averaged cycles, phase response curves and stability eigenvalues, as well as the less familiar Floquet modes. Our models of gait provide a prediction of future animal motions against which neuromechanical control hypothesis may be statistically tested. By computing Floquet modes of seemingly similar gaits, we can expose the fact that these gaits are sensitive to perturbations in very different ways -- producing testable hypotheses can that separate these gaits empirically.
    BibTeX:
    @conference{revzen2011sicb,
      author = {Revzen, S and Guckenheimer, J M and Full, R J},
      title = {Subtle differences in gaits: the perspective of data driven Floquet analysis},
      booktitle = {Yearly meeting of the Society for Integrative and Comparative Biology},
      year = {2011}
    }
    
    Revzen, S., Guckenheimer, J.M. & Full, R.J. Data Driven Floquet Analysis for Biomechanics and Robotics 2010 Dynamic Walking  conference URL 
    Abstract: Abstract: Floquet theory describes the linearization of an oscillator around its orbit. We convert this familiar classical result to an empirical form, allowing Floquet models to be constructed directly from experimentally obtained trajectories of periodic gaits. The Floquet model can be used to derive dimensionally reduced "templates" that predict responses to transient stimuli and be used as maneuvers through transient destabilization. The ability to express maneuvers in these reduced models holds promise for robot design and tuning, and for biomechanical research. We report on ongoing work applying our methods to human and cockroach data, and illustrate their use on some gaits of the Clock-Torqued Spring Loaded Inverted Pendulum (CT-SLIP) model.
    BibTeX:
    @conference{revzen-dw2010,
      author = {S Revzen and J M Guckenheimer and R J Full},
      title = {Data Driven Floquet Analysis for Biomechanics and Robotics},
      booktitle = {Dynamic Walking},
      year = {2010},
      url = {http://techtv.mit.edu/collections/locomotion:1216/videos/8022-dynamic-walking-2010-shai-revzen-data-driven-floquet-analysis-for-biomechanics-and-robotics}
    }
    
    Revzen, S., Guckenheimer, J.M. & Full, R.J. Study of the neuromechanical control of rhythmic behaviors by floquet analysis 2009 Integrative and Comparative Biology  conference  
    Abstract: The control of rhythmic behaviors like locomotion is difficult to study when compared with control of fixed-point behaviors such as standing. The problem is largly due to dynamics: perturbations away from the typical cycle may have surprising and counter-intuitive consequences later on the in the same cycle or even several cycles in the future. These causal relationships between seemingly different perturbations at different phases of motion can make conclusions drawn from PCA and other matrix factorization methods misleading or erroneous. Dynamical systems theory describes the interrelation of perturbations in different parts of a cycle using Floquet Theory. The theory guarantees the existence of a change of coordinates that rectifies the dynamics to the simple linear form found in fixed-point systems. We developed our method for estimating a Floquet structure from kinematics to test the ``Templates and Anchors Hypothesis.'' This hypothesis states that rapid locomotion is controlled by restricting the many degrees of freedom of the animal's morphology, as represented by an ``anchored'' model, to follow low dimensional ``template'' dynamics. The presence of a template would express itself in the Floquet structure as having a few weakly damped modes that decay over multiple strides and span the template, and many strongly damped modes that decay within a stride or a step, and span the remainder of the degrees of freedom of the anchor. Our preliminary results suggest that running death's-head cockroaches (Blaberus discoidalis) posses a template that can be distinguished in the Floquet structure of the animals' kinematics. We believe our methodology can be applied to the study of neuromechanical control in a broad range of rhythmic behaviors.
    BibTeX:
    @conference{Revzen-SICB09,
      author = {S Revzen and J M Guckenheimer and R J Full},
      title = {Study of the neuromechanical control of rhythmic behaviors by floquet analysis},
      booktitle = {Integrative and Comparative Biology},
      year = {2009},
      note = {(abstract only)}
    }
    
    Revzen, S., Ilhan, B.D. & Koditschek, D.E. Dynamical reference generators for uncertain environments 2011 Q3 (in-prep)  article  
    BibTeX:
    @article{Revzen-drg2011,
      author = {S Revzen and B D Ilhan and D E Koditschek},
      title = {Dynamical reference generators for uncertain environments},
      journal = {(in-prep)},
      year = {2011 Q3}
    }
    
    Revzen, S., Koditschek, D.E. & Full, R.J. Towards Testable Neuromechanical Control Architectures for Running 2008 Progress in Motor Control - A Multidisciplinary Perspective, ch. 3, pp. 25 - 56 inbook DOI  
    BibTeX:
    @inbook{Revzen-TestArch07,
      author = {S Revzen and D E Koditschek and R J Full},
      title = {Progress in Motor Control - A Multidisciplinary Perspective},
      publisher = {Springer Science+Business Media, LLC - NY},
      year = {2008},
      pages = {25 - 56},
      doi = {http://dx.doi.org/10.1007/978-0-387-77064-2}
    }
    
    Revzen, S., Koditschek, D.E. & Full, R.J. Selecting among neuromechnical control architectures using kinematic phase and perturbation experiments 2007 American Society of Biomechanics  conference  
    Abstract: We use an experimental paradigm grounded in dynamical systems (DS) theory to select which among several competing neuro-mechanical control architectures (NCA) could be in use in a given rhythmic motor behavior by using kinematic data alone. Our method allows us to extrapolate animal motions based on a few consecutive video frames, and compare the predicted motion to perturbation experiment outcomes. We apply the method to the study of control of running in the cockroach Blaberus discoidalis, and discuss its broader utility in a variety of biomechanical problems, e.g. in potential clinical application of motor learning tasks
    BibTeX:
    @conference{Revzen-ASB07,
      author = {S Revzen and D E Koditschek and R J Full},
      title = {Selecting among neuromechnical control architectures using kinematic phase and perturbation experiments},
      booktitle = {American Society of Biomechanics},
      year = {2007},
      note = {(poster)}
    }
    
    Revzen, S., Koditschek, D.E. & Full, R.J. Testing feedforward control models in rapid running insects using large perturbations (abstract only) 2006 Integrative and Comparative Biology
    Vol. 46(suppl 1), pp. e1-162 
    article DOI  
    Abstract: Sensory feedback dominates limb coordination in walking. By contrast, insects are capable of stable running over rough surfaces with no detectable change in motor output to major leg muscles. Passive, dynamic models suggest self-stabilization. A central pattern generator forcing a mass-spring system can model these observations. RHex, a rapid running, bio-inspired hexapedal robot is a physical realization of these models. The robot can self-stabilize over simple terrain when its leg motors are driven with feedforward ``clock'' (CPG-like) signals only. However, RHex requires sensory feedback to its clock to attain comparable speeds over complex terrain. With such feedback, traversal of significant obstacles induces phase shifts in motor timing to coordinate legs. We examined high-speed running in cockroaches to determine whether neural feedback shifts leg phase and/or frequency after encountering an obstacle. Cockroaches were tripped with a hip-high hurdle while running at 25 cm/s on a treadmill. High-speed video tracked the body and distal portion of all six legs versus time. Perturbations struck different legs in different locations, but always caused a significant disruption to the mechanical system for the several strides traversing the obstacle. Cockroaches incurred significant phase and frequency changes. When the pattern of leg motions was extrapolated from before the obstacle to after the obstacle, it failed to match the animals' pattern after recovery in 17 of 22 trials. Results suggest that sensory feedback is likely sent to a CPG-like clock driving leg movements, as required by our physical model. We reject the hypothesis that animals use a feed-forward clock without neural feedback when challenged with large perturbations in rapid running.
    BibTeX:
    @article{Revzen-SICB06,
      author = {S Revzen and D E Koditschek and R J Full},
      title = {Testing feedforward control models in rapid running insects using large perturbations (abstract only)},
      journal = {Integrative and Comparative Biology},
      year = {2006},
      volume = {46},
      number = {suppl 1},
      pages = {e1-162},
      note = {(abstract only)},
      doi = {http://dx.doi.org/10.1093/icb/icl056}
    }
    
    Shani, B., Revzen, S. & Frimerman, A. Analysis of electrocardiogram signals 2006 Patent(WO/2006/123334)  patent URL 
    Abstract: Apparatus for graphical representation of a train of ECG complexes, said ECG complexes comprising an R wave and a T-P interval and having variable isoelectric levels, the apparatus comprising: an isoelectric alignment unit for aligning the complexes in terms of isoelectric level by aligning respective T-P intervals, thereby to provide a graphical representation of said train of ECG complexes; and a temporal alignment unit for aligning said complexes temporally using a predetermined point of respective R waves. The aligned units are superimposed to provide a distribution of a normalized ECG signal over a series of pulses or heartbeats.
    BibTeX:
    @patent{Patent-ECG,
      author = {B Shani and S Revzen and A Frimerman},
      title = {Analysis of electrocardiogram signals},
      journal = {Patent},
      year = {2006},
      number = {WO/2006/123334},
      url = {http://www.freepatentsonline.com/WO2006123334.html}
    }
    
    Spence, A.J., Revzen, S., Seipel, J., Mullens, C. & Full, R.J. Insects running on elastic surfaces 2010 J Exp Biol
    Vol. 213(11), pp. 1907 
    article DOI  
    Abstract: In nature, cockroaches run rapidly over complex terrain such as leaf litter. These substrates are rarely rigid, and are frequently very compliant. Whether and how compliant surfaces change the dynamics of rapid insect locomotion has not been investigated to date; largely due to experimental limitations. Here we test the hypothesis that a running insect can maintain average forward speed over an extremely soft elastic surface (10 N/m) equal to 2/3 of its virtual leg stiffness (15 N/m). Cockroaches Blaberus discoidalis running from a rigid surface onto an elastic surface were able to maintain forward speed (39.6 0.7 cm/s, rigid substrate, versus 43.3 1.1 cm/s, elastic substrate; p = 0.0064). Step frequency was unchanged (25.5 0.3 steps/sec, rigid surface, versus 26.1 0.5 steps/sec, elastic surface; p = 0.28). To uncover the mechanism we measured the animal's COM dynamics using a novel miniature backpack, consisting chiefly of a 3-axis MEMs accelerometer attached very near the COM. Vertical acceleration of the COM on the elastic surface had smaller peak-to-peak amplitudes (13.95 0.41 m/s2, rigid, vs. 10.07 0.50 m/s2 on the elastic surface; p < 0.0001). The observed change in COM acceleration over an elastic surface requires no change in effective stiffness when duty factor and ground stiffness are taken into account. Due to the lowering of the COM towards the elastic surface the swing leg lands earlier and increases the period of double support. A simple feedforward control model explains the experimental result and provides one plausible model mechanism. We find no evidence for active neural control of effective leg stiffness.
    BibTeX:
    @article{Spence-Memb09,
      author = {A J Spence and S Revzen and J Seipel and C Mullens and R J Full},
      title = {Insects running on elastic surfaces},
      journal = {J Exp Biol},
      year = {2010},
      volume = {213},
      number = {11},
      pages = {1907},
      doi = {http://dx.doi.org/10.1242/jeb.042515}
    }
    
    Spence, A.J., Revzen, S., Yeates, K., Mullens, C. & Full, R.J. Insects running on compliant surfaces 2007 Integrative and Comparative Biology
    Vol. 47(suppl 1), pp. e1-152 
    article DOI  
    Abstract: Human runners and hoppers attempt to adjust their leg stiffness to maintain similar center of mass (COM) dynamics when confronted with a compliant substrate. Dynamic materials testing of cockroach legs shows that their behavior in the sagittal plane is largely determined by passive exoskeletal properties. We tested the hypothesis that rapid running cockroaches maintain their COM mechanics by compensating for a compliant substrate. Cockroaches Blaberus discoidalis ran from a rigid Plexiglas surface onto an elastic substrate of stiffness (8-13 N/m) equal to 2/3 its virtual leg spring stiffness (15 N/m for all three legs of a tripod). We directly measured the animal’s COM dynamics using a novel 3-axis, MEMs accelerometer configured as a backpack placed near its COM. Vertical acceleration of the COM on the elastic surface had smaller peak-to-peak amplitudes (9.3 ± 0.012 m/s2, n = 374 steps on elastic substrate, vs. 12 ± 0.007 m/s2, n = 879 steps on rigid substrate; p<0.0001). Step duration was slightly longer (44.7 ± 0.044 ms, elastic versus 42.6 ± 0.016 ms rigid; p = 0.019) and forward velocity was actually faster on the elastic substrate (35.6 ± 0.004 cm/s on elastic substrate, versus 33.4 ± 0.002 cm/s on rigid substrate; p < 0.0001). We conclude that the cockroach does not maintain similar vertical accelerations and therefore COM trajectories when encountering an elastic substrate. Despite their inability to maintain constant COM dynamics, cockroaches moved effectively on complaint substrates. Funded by NSF FIBR.
    BibTeX:
    @article{Spence-SICB07,
      author = {A J Spence and S Revzen and K Yeates and C Mullens and R J Full},
      title = {Insects running on compliant surfaces},
      journal = {Integrative and Comparative Biology},
      year = {2007},
      volume = {47},
      number = {suppl 1},
      pages = {e1-152},
      note = {(abstract only)},
      doi = {http://dx.doi.org/10.1093/icb/icm104}
    }
    
    Sundaram, S., Revzen, S. & Pappas, G. Linear iterative strategies to identify and overcome malicious links in wireless networks 2011 Automatica  article  
    Abstract: We consider a network where every node has a value that we wish to disseminate to all other nodes. A certain number of communication links between nodes are allowed to be under the control of an attacker who maliciously chooses the messages carried by these links. We study linear iterative strategies that disseminate information despite such attacks. In such strategies, at each time-step each node in the network broadcasts a value to its neighbors that is a linear combination of its previous value and the values received from its neighbors. As long the number of incoming links to any node and the total number of other nodes with incoming malicious links is no greater than f , we show that linear strategies are almost always resilient to malicious behavior provided that vertex-connectivity of the network is at least 2f + 1. Furthermore, we show that each node can identify the exact set of malicious links that directly enter that node, and can communicate this information to the other nodes via the linear strategy.
    BibTeX:
    @article{sundaram2011lis,
      author = {S Sundaram and S Revzen and G Pappas},
      title = {Linear iterative strategies to identify and overcome malicious links in wireless networks},
      journal = {Automatica},
      year = {2011},
      note = {(in review)}
    }
    
    White, P.J., Revzen, S., Thorne, C.E. & Yim, M. A general stiffness model for programmable matter and modular robotic structures 2010 Robotica
    Vol. 29, pp. 103 - 121 
    article DOI  
    Abstract: The fields of modular reconfigurable robotics and programmable matter study how to compose functionally
    useful systems from configurations of modules. In addition to the external shape of a module configuration, the internal
    arrangement of modules and bonds between them can greatly impact functionally relevant mechanical properties such as
    load bearing ability. A fast method to evaluate the mechanical property aides the search for an arrangement of modules
    achieving a desired mechanical property as the space of possible configurations grows combinatorially. We present a
    fast approximate method where the bonds between modules are represented with stiffness matrices that are general
    enough to represent a wide variety of systems and follows the natural modular decomposition of the system. The method
    includes nonlinear modeling such as anisotropic bonds and properties that vary as components flex. We show that the
    arrangement of two types of bonds within a programmable matter systems enables programming the apparent elasticity
    of the structure. We also present a method to experimentally determine the stiffness matrix for chain style reconfigurable
    robots. The efficacy of applying the method is demonstrated on the CKBot modular robot and two programmable matter
    systems: the Rubik’s snake folding chain toy and a right angle tetrahedron chain called RATChET7 mm. By allowing
    the design space to be rapidly explored we open the door to optimizing modular structures for desired mechanical
    properties such as enhanced load bearing and robustness.
    BibTeX:
    @article{white2010stiffness,
      author = {P J White and S Revzen and C E Thorne and M Yim},
      title = {A general stiffness model for programmable matter and modular robotic structures},
      journal = {Robotica},
      year = {2010},
      volume = {29},
      pages = {103 - 121},
      doi = {http://dx.doi.org/10.1017/S0263574710000743}
    }
    

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