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Mathematical Problems in Engineering
Volume 2015, Article ID 918301, 13 pages
Research Article

An Optimization-Based Impedance Approach for Robot Force Regulation with Prescribed Force Limits

1Facultad de Ingeniería, Universidad Veracruzana, Boulevard Adolfo Ruiz Cortines S/N, Costa Verde, 94294 Boca del Río, VER, Mexico
2Centro de Investigación y de Estudios Avanzados del IPN, Unidad Zacatenco, Departamento de Ingeniería Eléctrica, Sección de Mecatrónica, Avenida Instituto Politécnico Nacional No. 2508, 07360 San Pedro Zacatenco, México, DF, Mexico

Received 31 October 2014; Accepted 6 January 2015

Academic Editor: Luis Rodolfo Garcia Carrillo

Copyright © 2015 R. de J. Portillo-Vélez 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.


An optimization based approach for the regulation of excessive or insufficient forces at the end-effector level is introduced. The objective is to minimize the interaction force error at the robot end effector, while constraining undesired interaction forces. To that end, a dynamic optimization problem (DOP) is formulated considering a dynamic robot impedance model. Penalty functions are considered in the DOP to handle the constraints on the interaction force. The optimization problem is online solved through the gradient flow approach. Convergence properties are presented and the stability is drawn when the force limits are considered in the analysis. The effectiveness of our proposal is validated via experimental results for a robotic grasping task.