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- Aaron M. Hoover, Samuel Burden, Xiao-Yu Fu, S. Shankar Sastry, Ronald S. Fearing
- 2010 3rd IEEE RAS & EMBS International Conference…
- 2010

Rapidly running arthropods like cockroaches make use of passive dynamics to achieve remarkable locomotion performance with regard to stability, speed, and maneuverability. In this work, we take inspiration from these organisms to design, fabricate, and control a 10cm, 24 gram underactuated hexapedal robot capable of running at 14 body lengths per second and… (More)

- Joshua D. Bishop, Samuel Burden, +4 authors T. Nguyen
- 2005 IEEE/RSJ International Conference on…
- 2005

In this paper, we introduce a robotic implementation of the theory of graph grammars (Klavins et al., 2005), which we use to model and direct self-organization in a formal, predictable and provably-correct fashion. The robots, which we call programmable parts, float passively on an air table and bind to each other upon random collisions. Once attached, they… (More)

- Nils Napp, Samuel Burden, Eric Klavins
- Proceedings 2006 IEEE International Conference on…
- 2006

We describe how a graph grammar program for robotic self-assembly, together with measurements of kinetic rate data yield a Markov process model of the dynamics of programmed self-assembly. We demonstrate and validate the method by applying it to a physical testbed consisting of a number of "programmable parts", which are able to control their local… (More)

- Eric Klavins, Samuel Burden, Nils Napp
- Robotics: Science and Systems
- 2006

We consider the control of programmable selfassembling systems whose dynamics are governed by stochastic reaction-diffusion dynamics. In our system, particles may decide the outcomes of reactions initiated by the environment, thereby steering the global system to produce a desired assembly type. We describe a method that automatically generates a program… (More)

- Samuel Burden, Jonathan Clark, Joel Weingarten, Haldun Komsuoglu, Daniel E. Koditschek
- Proceedings 2007 IEEE International Conference on…
- 2007

Legged robots are by nature strongly non-linear, high-dimensional systems whose full complexity permits neither tractable mathematical analysis nor comprehensive numerical study. In consequence, a growing body of literature interrogates simplified "template" (Full and Koditschek, 1999; Ghigliazza et al., 2005) models - to date almost exclusively confined to… (More)

- Samuel Burden, Shai Revzen, S. Shankar Sastry
- IEEE Trans. Automat. Contr.
- 2015

We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous–time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical system, nearby executions generically contract superexponentially to a constant– dimensional subsystem.… (More)

- Aaron M. Johnson, Samuel Burden, Daniel E. Koditschek
- I. J. Robotics Res.
- 2016

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and… (More)

Though hybrid dynamical systems are a powerful modeling tool, it has proven difficult to accurately simulate their trajectories. In this paper, we develop a provably convergent numerical integration scheme for approximating trajectories of hybrid dynamical systems. This is accomplished by first relaxing hybrid systems whose continuous states reside on… (More)

- Lillian J. Ratliff, Samuel Burden, S. Shankar Sastry
- IEEE Trans. Automat. Contr.
- 2016

We present a unified framework for characterizing local Nash equilibria in continuous games on either infinitedimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient firstand second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions… (More)

- Nils Napp, Samuel Burden, Eric Klavins
- Auton. Robots
- 2009

We present an integral feedback controller that regulates the average copy number of an assembly in a system of stochastically interacting robots. The mathematical model for these robots is a tunable reaction network, which makes this approach applicable to a large class of other systems, including ones that exhibit stochastic self-assembly at various… (More)