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Aaron Johnson

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A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

The International Journal of Robotics Research, Vol. 35, No. 11, September, 2016

Aaron M. Johnson*, Samuel A. Burden† and D. E. Koditschek*
*: Electrical and Systems Engineering, University of Pennsylvania
†: Electrical Engineering and Computer Science, University of California, Berkeley

Full PDF | Web Link | arXiv:1502.01538 | Penn ScholarlyCommons

Figure 1: Keyframes from RHex simulation leaping onto a 20cm ledge. Blue arrows show contact forces while the red arrow shows body velocity.
       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 even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice exact quantitative accuracy for qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.
This work was supported by the ARL/GDRS RCTA project under Cooperative Agreement Number W911NF-10–2−0016.
BibTeX entry
  author       = {Aaron M. Johnson and Samuel E. Burden and D E Koditschek},
  title        = {A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems},
  year         = {2016},
  month        = {September},
  volume       = {35},
  number       = {11},
  pages        = {1354--1392},
  journal    = {The International Journal of Robotics Research}

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