Legged Self-Manipulation

IEEE Access. Vol. 1.

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Abstract
This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactions. The term denotes a set of modeling choices that permit a uniform and body-centric representation of the equations of motion — essentially a guide to the selection and configuration of coordinate frames. We present the hybrid system kinematics, dynamics and transitions in the form of a consistently structured representation that simplifies and unites the account of these otherwise bewilderingly diverse differential algebraic equations. Cleaving as closely as possible to the modeling strategies developed within the mature manipulation literature,self-manipulation models can leverage those insights and results where applicable, while clarifying the fundamental differences. Our primary motivation is not to facilitate numerical simulation but rather to promote design insight. We instantiate the abstract formalism for a simplified model of RHex, and illustrate its utility by applying a variety of analytical and computational techniques to derive new results bearing on behaviors, controllers, and platform design. For each example, we present empirical results documenting the specific benefits of the new insight into the robot’s transitions from standing, to moving in place, to leaping.

Abstract

This paper introduces self-manipulation as a new formal design methodology for legged robots with varying ground interactions. The term denotes a set of modeling choices that permit a uniform and body-centric representation of the equations of motion — essentially a guide to the selection and configuration of coordinate frames. We present the hybrid system kinematics, dynamics and transitions in the form of a consistently structured representation that simplifies and unites the account of these otherwise bewilderingly diverse differential algebraic equations. Cleaving as closely as possible to the modeling strategies developed within the mature manipulation literature,self-manipulation models can leverage those insights and results where applicable, while clarifying the fundamental differences. Our primary motivation is not to facilitate numerical simulation but rather to promote design insight. We instantiate the abstract formalism for a simplified model of RHex, and illustrate its utility by applying a variety of analytical and computational techniques to derive new results bearing on behaviors, controllers, and platform design. For each example, we present empirical results documenting the specific benefits of the new insight into the robot’s transitions from standing, to moving in place, to leaping.

This work was supported by the ARL/GDRS RCTA project under Cooperative Agreement Number W911NF-10–2−0016

Fig. 1: Selected coordinate frames for self-manipulation.

BibTeX entry
@article{paper:johnson_selfmanip_2013, title = {Legged Self-Manipulation}, author = {Aaron M. Johnson and D. E. Koditschek}, journal = {IEEE Access}, year = {2013}, month = {May}, volume = {1}, _doi = {10.1109/ACCESS.2013.2263192}, pages = {310--334}, url_Info = {http://www.andrew.cmu.edu/user/amj1/LeggedSelfManipulation}, url_Publisher = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6516555}, url_PDF = {http://kodlab.seas.upenn.edu/uploads/Aaron/Johnson_Legged_Self-Manipulation.pdf}, url_Errata = {http://www.andrew.cmu.edu/user/amj1/LeggedSelfManipulation/Legged_Self_Manipulation_Errata.pdf}, url_Video = {https://www.youtube.com/watch?v=ON5B4ILcF-8} }

BibTeX entry

@article{paper:johnson_selfmanip_2013,
  title     = {Legged Self-Manipulation},
  author    = {Aaron M. Johnson and D. E. Koditschek},
  journal   = {IEEE Access},
  year      = {2013},
  month     = {May},
  volume    = {1},
  _doi      = {10.1109/ACCESS.2013.2263192},
  pages     = {310--334},
  url_Info  = {http://www.andrew.cmu.edu/user/amj1/LeggedSelfManipulation},
  url_Publisher = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6516555},
  url_PDF   = {http://kodlab.seas.upenn.edu/uploads/Aaron/Johnson_Legged_Self-Manipulation.pdf},
  url_Errata   = {http://www.andrew.cmu.edu/user/amj1/LeggedSelfManipulation/Legged_Self_Manipulation_Errata.pdf},
  url_Video = {https://www.youtube.com/watch?v=ON5B4ILcF-8}
}

Errata -- Download as PDF
Page 310, the citation to prior publication of section IV-A should read `[13]`.
Page 315, Eqn. (14), the adjoint matrices `A` should read `Ad`.
Page 316, Eqn. (17), the subscript on `R` should read `wp`.
Page 317, Eqn. (29) should be the line just after Eqn. (28).
Page 328, Eqn. (68), the length terms in the denominator of the first line should be squared, as in Eqn. (67), and the font for ε in Result C.5 should match this line.
Page 330, Appendix D, first column, the sixth line of equations in this section should not include the symbol × (this should be interpreted as the usual matrix multiplication with the previous line).
Page 331, Appendix E, first column, the fourth line of equations on this page should not include the symbol × (this should be interpreted as the usual matrix multiplication with the previous line).
Page 332, second column, the reference to the mass matrix and Corilis matrix in Fig. 15 should have no equation numbers (81 and 82 are unrelated).