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First steps toward formal controller synthesis for bipedal robots with experimental implementation

Ames, Aaron D. and Tabuada, Paulo and Jones, Austin and Ma, Wen-Loong and Rungger, Matthias and Schürmann, Bastian and Kolathaya, Shishir and Grizzle, Jessy W. (2017) First steps toward formal controller synthesis for bipedal robots with experimental implementation. Nonlinear Analysis: Hybrid Systems, 25 . pp. 155-173. ISSN 1751-570X. doi:10.1016/j.nahs.2017.01.002.

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Bipedal robots are prime examples of complex cyber–physical systems (CPSs). They exhibit many of the features that make the design and verification of CPS so difficult: hybrid dynamics, large continuous dynamics in each mode (e.g., 10 or more state variables), and nontrivial specifications involving nonlinear constraints on the state variables. In this paper, we propose a two-step approach to formally synthesize controllers for bipedal robots so as to enforce specifications by design and thereby generate physically realizable stable walking. In the first step, we design outputs and classical controllers driving these outputs to zero. The resulting controlled system evolves on a lower dimensional manifold and is described by the hybrid zero dynamics governing the remaining degrees of freedom. In the second step, we construct an abstraction of the hybrid zero dynamics that is used to synthesize a controller enforcing the desired specifications to be satisfied on the full order model. Our two step approach is a systematic way to mitigate the curse of dimensionality that hampers the applicability of formal synthesis techniques to complex CPS. Our results are illustrated with simulations showing how the synthesized controller enforces all the desired specifications and offers improved performance with respect to a classical controller. The practical relevance of the results is illustrated experimentally on the bipedal robot AMBER 3.

Item Type:Article
Related URLs:
URLURL TypeDescription ItemConference Paper
Ames, Aaron D.0000-0003-0848-3177
Tabuada, Paulo0000-0002-3417-0951
Ma, Wen-Loong0000-0002-0115-5632
Kolathaya, Shishir0000-0001-8689-2318
Grizzle, Jessy W.0000-0001-7586-0142
Additional Information:© 2017 Elsevier Ltd. Available online 14 February 2017. This research is supported by NSF CPS Awards 1239055, 1239037 and 1239085. Experiments were performed at Texas A&M University, College Station, Texas. The robot AMBER 3 was designed and built by Eric Ambrose. The authors would like to thank Aakar Mehra for his assistance with experiments.
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Subject Keywords:Hybrid systems; Formal methods; Nonlinear control; Bipedal robotics
Record Number:CaltechAUTHORS:20170608-073936974
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Official Citation:Aaron D. Ames, Paulo Tabuada, Austin Jones, Wen-Loong Ma, Matthias Rungger, Bastian Schürmann, Shishir Kolathaya, Jessy W. Grizzle, First steps toward formal controller synthesis for bipedal robots with experimental implementation, Nonlinear Analysis: Hybrid Systems, Volume 25, August 2017, Pages 155-173, ISSN 1751-570X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78021
Deposited By: Tony Diaz
Deposited On:08 Jun 2017 21:33
Last Modified:15 Nov 2021 17:36

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