Next Article in Journal
The Chemistry of Polydopamine Film Formation: The Amine-Quinone Interplay
Previous Article in Journal
Fiber Embroidery of Self-Sensing Soft Actuators
Article Menu
Issue 3 (September) cover image

Export Article

Open AccessArticle
Biomimetics 2018, 3(3), 25; https://doi.org/10.3390/biomimetics3030025

Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping

Robotics and Motion Laboratory, Department of Mechanical Engineering, The University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA
*
Authors to whom correspondence should be addressed.
Received: 29 July 2018 / Revised: 30 August 2018 / Accepted: 1 September 2018 / Published: 6 September 2018
Full-Text   |   PDF [13491 KB, uploaded 14 September 2018]   |  

Abstract

Inspired by biological control synergies, wherein fixed groups of muscles are activated in a coordinated fashion to perform tasks in a stable way, we present an analogous control approach for the stabilization of legged robots and apply it to a model of running. Our approach is based on the step-to-step notion of stability, also known as orbital stability, using an orbital control Lyapunov function. We map both the robot state at a suitably chosen Poincaré section (an instant in the locomotion cycle such as the mid-flight phase) and control actions (e.g., foot placement angle, thrust force, braking force) at the current step, to the robot state at the Poincaré section at the next step. This map is used to find the control action that leads to a steady state (nominal) gait. Next, we define a quadratic Lyapunov function at the Poincaré section. For a range of initial conditions, we find control actions that would minimize an energy metric while ensuring that the Lyapunov function decays exponentially fast between successive steps. For the model of running, we find that the optimization reveals three distinct control synergies depending on the initial conditions: (1) foot placement angle is used when total energy is the same as that of the steady state (nominal) gait; (2) foot placement angle and thrust force are used when total energy is less than the nominal; and (3) foot placement angle and braking force are used when total energy is more than the nominal. View Full-Text
Keywords: synergies; legged locomotion; stability; region of attraction; orbital control Lyapunov function; limit cycle; SLIP model; Poincaré map synergies; legged locomotion; stability; region of attraction; orbital control Lyapunov function; limit cycle; SLIP model; Poincaré map
Figures

Graphical abstract

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Zamani, A.; Bhounsule, P.A. Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping. Biomimetics 2018, 3, 25.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Biomimetics EISSN 2313-7673 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top