Departmental Papers (ESE)



This paper explores the applicability of a Linear Quadratic Regulator (LQR) controller design to the problem of bipedal stance on the Minitaur [1] quadrupedal robot. Restricted to the sagittal plane, this behavior exposes a three degree of freedom (DOF) double inverted pendulum with extensible length that can be projected onto the familiar underactuated revolute-revolute “Acrobot” model by assuming a locked prismatic DOF, and a pinned toe. While previous work has documented the successful use of local LQR control to stabilize a physical Acrobot, simulations reveal that a design very similar to those discussed in the past literature cannot achieve an empirically viable controller for our physical plant. Experiments with a series of increasingly close physical facsimiles leading to the actual Minitaur platform itself corroborate and underscore the physical Minitaur platform corroborate and underscore the implications of the simulation study. We conclude that local LQR-based linearized controller designs are too fragile to stabilize the physical Minitaur platform around its vertically erect equilibrium and end with a brief assessment of a variety of more sophisticated nonlinear control approaches whose pursuit is now in progress.

Sponsor Acknowledgements

This work was supported by the ARL/GDRS RCTA project, Coop. Agreement #W911NF-10-2-0016.

Document Type

Conference Paper

Subject Area

GRASP, Kodlab

Date of this Version


Publication Source

Proceedings of SPIE





Copyright/Permission Statement

Copyright 2016 Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Bib Tex

T. Turner Topping, Vasileios Vasilopoulos, Avik De, Daniel E. Koditschek, "Towards bipedal behavior on a quadrupedal platform using optimal control", Proc. SPIE 9837, Unmanned Systems Technology XVIII, 98370H (13 May 2016); doi: 10.1117/12.2231103;



Date Posted: 28 November 2017