The key theme of my work is bio-inspired control of physical interactions. My research activities include experimental biology, experimental robotics, robotic theory and applied mathematics.
Electrical Engineering and Computer Science (EECS)
University of Michigan
Dimension reduction near limit cycles of hybrid systems
|Burden, S. A.; Revzen, S. & Sastry, S.|
|IEEE CDC, 2011|
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. [ARXIV preprint]
Finding the dimension of slow dynamics in a rhythmic system
|Revzen, S. & Guckenheimer, J. M.|
|J R Soc Lond Interface, 2010 (published online before print)|
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 theories 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. [preprint]
A general stiffness model for programmable matter and modular robotic structures
|Robotica, 2010, vol. 29, pp. 103 - 121|
The paper presents an algorithm for rapidly computing the approximate deformation of a modular structure under load, and shows various analytic and experimental methods for identifying the parameters required. By using our algorithm, the structural load bearing implications of various module configurations can be quickly evaluated, allowing the design space of module layouts to be explored computationally.
Insects running on elastic surfaces
|Spence, A. J.; Revzen, S.; Seipel, J.; Mullens, C. & Full, R. J.|
|J Exp Biol, 2010, vol. 213(11):1907|
The paper shows that cockroaches use fundamentally different means from humans when responding to a change in substrate stiffness. In the process, our results reject SLIP (the Spring Loaded Inverted Pendulum) as a model of cockroach running - the animals were shown to run under conditions for which no SLIP gait could exist - and instead lends support to the more elaborate "CT-SLIP" model. The paper also presents a method of 5DOF pose estimation using a single high-speed camera and an Unscented Kalman Filter.
Subtle differences in gaits: the perspective of data driven Floquet analysis.
|Revzen, S.; Guckenheimer, J. M.; & Full, R. J.|
|Integrative and Comparative Biology (SICB), Jan 2011|
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.
Data driven Floquet analysis for biomechanics and robotics
|Revzen, S.; Guckenheimer, J. M.; & Full, R. J.|
|Dynamic Walking 2010|
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 manoeuvres through transient destabilisation. The ability to express manoeuvres 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.
Linear iterative strategies to identify and overcome malicious links in wireless networks
|Sundaram, S.; Revzen, S. & Pappas, G.|
|Automatica 2011 (IN PRINT)|
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 neighbours that is a linear combination of its previous value and the values received from its neighbours. 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 behaviour 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.
Tutorials and Non-academic Publications
MBI 2008 Tutorials
In 2008 I gave several tutorials for mathematical biologists:
CKBot Tutorials for ICRA 2010
In 2010 Jimmy Sastra (ModLab) and I gave two video tutorials on using the new software interface we developed for the CKBot modular robots.