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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 963496, 17 pages
Research Article

Modeling and Finite-Time Walking Control of a Biped Robot with Feet

Centro de Investigación en Matemáticas (CIMAT), A.C., Jalisco S/N, Colonia Valenciana, 36240 Guanajuato, GTO, Mexico

Received 11 August 2015; Accepted 18 October 2015

Academic Editor: Guangming Xie

Copyright © 2015 Juan E. Machado 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.


This paper addresses the problem of modeling and controlling a planar biped robot with six degrees of freedom, which are generated by the interaction of seven links including feet. The biped is modeled as a hybrid dynamical system with a fully actuated single-support phase and an instantaneous double-support phase. The mathematical modeling is detailed in the first part of the paper. In the second part, we present the synthesis of a controller based on virtual constraints, which are codified in an output function that allows defining a local diffeomorphism to linearize the robot dynamics. Finite-time convergence of the output to the origin ensures a collision between the swing foot and the ground with an appropriate configuration for the robot to give a step forward. The components of the output track adequate references that encode a walking pattern. Finite-time convergence of the tracking errors is enforced by using second-order sliding mode control. The main contribution of the paper is an evaluation and comparison of discontinuous and continuous sliding mode control in the presence of parametric uncertainty and external disturbances. The robot model and the synthesized controller are evaluated through numerical simulations.