Optimal Control of a 5-Link Biped Using Quadratic Polynomial Model of Two-Point Boundary Value Problem

Ernesto Hernandez-Hinojosa, Aykut Satici, Pranav A. Bhounsule

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

To walk over constrained environments, bipedal robots must meet concise control objectives of speed and foot placement. The decisions made at the current step need to factor in their effects over a time horizon. Such step-to-step control is formulated as a two-point boundary value problem (2-BVP). As the dimensionality of the biped increases, it becomes increasingly difficult to solve this 2-BVP in real-time. The common method to use a simple linearized model for real-time planning followed by mapping on the high dimensional model cannot capture the nonlinearities and leads to potentially poor performance for fast walking speeds. In this paper, we present a framework for real-time control based on using partial feedback linearization (PFL) for model reduction, followed by a data-driven approach to find a quadratic polynomial model for the 2-BVP. This simple step-to-step model along with constraints is then used to formulate and solve a quadratically constrained quadratic program to generate real-time control commands. We demonstrate the efficacy of the approach in simulation on a 5-link biped following a reference velocity profile and on a terrain with ditches. A video is here: https://youtu.be/-UL-wkv4XF8.

Original languageAmerican English
Title of host publicationProceedings of the ASME 2021 International Design Engineering Technical Conference and Computers and Information in Engineering Conference
StatePublished - 1 Jan 2021

Keywords

  • boundary-value problems
  • ditches
  • feedback
  • optimal control
  • polynomials
  • real-time control

EGS Disciplines

  • Biomedical Engineering and Bioengineering
  • Mechanical Engineering

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