Articles

Sagittal stability PD controllers for a biped robot using a neurofuzzy network and an SVR

João P. Ferreira^a1a2 c1, Manuel Crisóstomo^a2 and A. Paulo Coimbra^a2

^a1 Department of Electrical Engineering, Superior Institute of Engineering of Coimbra, Rua Pedro Nunes-Quinta da Nora, Coimbra 3030-199, Portugal

^a2 Department of Electrical and Computer Engineering, Institute of Systems and Robotics, University of Coimbra, Polo 2-Pinhal de Marrocos, Coimbra 3030-290, Portugal. E-mail: mcris@isr.uc.pt, acoimbra@deec.uc.pt

SUMMARY

The real-time balance PD control of an eight-link biped robot using a zero-moment point (ZMP) dynamic model is implemented using two alternative intelligent computing control techniques that were compared: one based on support vector regression (SVR) and another based on a first order Takagi–Sugeno–Kang (TSK) -type neural-fuzzy (NF). Both methods use the ZMP error, and its variation as inputs and the output is the correction of the robot's torso necessary for its sagittal balance. The SVR and the NF were trained based on simulation data, and their performance was verified with a real biped robot. Two performance indexes are proposed to evaluate and compare the online performance of the two control methods.

The ZMP is calculated by reading four force sensors placed under each robot's foot. The gait implemented in this biped is based on ankle and hip human trajectories that were acquired and adapted to the robot's size. Some experiments are presented and the results show that the implemented gait combined either with the SVR controller or with the TSK NF network controller can be used to control this biped robot. The SVR and the NF controllers exhibit similar stability, but the SVR controller runs at 0.2 ms, about 50 times faster than the NF controller and much faster than a controller based on full ZMP dynamic model equations.

(Received September 15 2010)

(Online publication October 12 2010)

KEYWORDS:

• Neural-fuzzy (NF) networks;
• Support vector regression (SVR);
• Biped robot;
• Balance;
• Zero-moment point (ZMP)

Correspondence:

^c1 Corresponding author. E-mail: ferreira@isec.pt