A Caltech Library Service

Coupled Control Systems: Periodic Orbit Generation with Application to Quadrupedal Locomotion

Ma, Wen-Loong and Csomay-Shanklin, Noel and Ames, Aaron D. (2021) Coupled Control Systems: Periodic Orbit Generation with Application to Quadrupedal Locomotion. IEEE Control Systems Letters, 5 (3). pp. 935-940. ISSN 2475-1456. doi:10.1109/LCSYS.2020.3006963.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


A robotic system can be viewed as a collection of lower-dimensional systems that are coupled via reaction forces (Lagrange multipliers) enforcing holonomic constraints. Inspired by this viewpoint, this letter presents a novel formulation for nonlinear control systems that are subject to coupling constraints via virtual “coupling” inputs that abstractly play the role of Lagrange multipliers. The main contribution of this letter is a process—mirroring solving for Lagrange multipliers in robotic systems—wherein we isolate subsystems free of coupling constraints that provably encode the full-order dynamics of the coupled control system from which it was derived. This dimension reduction is leveraged in the formulation of a nonlinear optimization problem for the isolated subsystem that yields periodic orbits for the full-order coupled system. We consider the application of these ideas to robotic systems, which can be decomposed into subsystems. Specifically, we view a quadruped as a coupled control system consisting of two bipedal robots, wherein applying the framework developed allows for gaits (periodic orbits) to be generated for the individual biped yielding a gait for the full-order quadrupedal dynamics. This is demonstrated on a quadrupedal robot through simulation and walking experiments on rough terrains.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Ma, Wen-Loong0000-0002-0115-5632
Csomay-Shanklin, Noel0000-0002-2361-1694
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2020 IEEE. Manuscript received March 17, 2020; revised May 25, 2020; accepted June 16, 2020. Date of publication July 3, 2020; date of current version July 20, 2020. This work was supported by National Science Foundation under Award IIS 1724464. Recommended by Senior Editor L. Menini. (Corresponding author: Wen-Loong Ma.)
Funding AgencyGrant Number
Subject Keywords:Robotics, cooperative control, optimization
Issue or Number:3
Record Number:CaltechAUTHORS:20200707-110517874
Persistent URL:
Official Citation:W. Ma, N. Csomay-Shanklin and A. D. Ames, "Coupled Control Systems: Periodic Orbit Generation With Application to Quadrupedal Locomotion," in IEEE Control Systems Letters, vol. 5, no. 3, pp. 935-940, July 2021, doi: 10.1109/LCSYS.2020.3006963
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104248
Deposited By: Tony Diaz
Deposited On:07 Jul 2020 18:12
Last Modified:16 Nov 2021 18:29

Repository Staff Only: item control page