The basin of attraction for running robots: Fractals, multistep trajectories, and the choice of control

Tom Cnops, Zhenyu Gan, C. David Remy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

If the control authority of a running system is insufficient to reach a target state in a single step, i.e. if deadbeat control is not possible, then a stabilizing controller is faced with the decision on how to plan intermediate steps. In this work, we compare the performance of a simple greedy control policy (that computes deadbeat inputs and simply caps them) with the optimal performance found by an exhaustive search through decision space. The performance criterion used in this study is the basin of attraction: the set of all states from where the target state will be reached in a finite number of steps. Using the planar spring-loaded inverted pendulum (SLIP) as a model for a running robot, we compare the two control schemes and a fully passive behavior. To this end, we extended the passive slip model to include a controllable, yet limited variation of the touchdown angle and of the damping in the leg spring. We quantified the number of steps that it would take for the model to fall or converge from arbitrary initial states. The paper highlights how the passive stabilization, that is inherent to the SLIP model, greatly influences the dynamics of the controlled system. Furthermore, it reveals some new insights into the structure of basins of attractions of SLIP-like running models.

Original languageEnglish (US)
Title of host publicationIROS Hamburg 2015 - Conference Digest
Subtitle of host publicationIEEE/RSJ International Conference on Intelligent Robots and Systems
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1586-1591
Number of pages6
ISBN (Electronic)9781479999941
DOIs
StatePublished - Dec 11 2015
Externally publishedYes
EventIEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2015 - Hamburg, Germany
Duration: Sep 28 2015Oct 2 2015

Publication series

NameIEEE International Conference on Intelligent Robots and Systems
Volume2015-December
ISSN (Print)2153-0858
ISSN (Electronic)2153-0866

Conference

ConferenceIEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2015
CountryGermany
CityHamburg
Period9/28/1510/2/15

Keywords

  • Damping
  • Fractals
  • Mathematical model
  • Robots
  • Robustness
  • Springs
  • Trajectory

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Vision and Pattern Recognition
  • Computer Science Applications

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  • Cite this

    Cnops, T., Gan, Z., & Remy, C. D. (2015). The basin of attraction for running robots: Fractals, multistep trajectories, and the choice of control. In IROS Hamburg 2015 - Conference Digest: IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 1586-1591). [7353579] (IEEE International Conference on Intelligent Robots and Systems; Vol. 2015-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/IROS.2015.7353579