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Mathematical Problems in Engineering
Volume 2017, Article ID 6725427, 15 pages
Research Article

Constrained Quadratic Programming and Neurodynamics-Based Solver for Energy Optimization of Biped Walking Robots

1Department of Electronic Engineering, Shunde Polytechnic, Foshan, Guangdong 528300, China
2School of Automation, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
3College of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China

Correspondence should be addressed to Liyang Wang; moc.621@90gnayilgnaw

Received 17 February 2017; Revised 16 July 2017; Accepted 3 August 2017; Published 17 September 2017

Academic Editor: Dan Simon

Copyright © 2017 Liyang Wang et al. 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.


The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP) problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO) strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i) the force-moment equilibrium equation of biped robots, (ii) frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii) physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.