ORIGINAL ARTICLE Artif Life Robotics (2006) 10:69–72 © ISAROB 2006 DOI 10.1007/s10015-005-0357-5 Tae-Yong Choi · So-Yeon Park · Ju-Jang Lee A hybrid SOF-PID controller for a MIMO biped robot Received and accepted: December 6, 2005 Abstract The application of the hybrid self-organizing fuzzy (SOF) PID controller to a multiinput multioutput nonlinear biped robot is studied in this article. The SOF- PID controller was initially studied by H.B. Kazemian in 1998. Actually, his SOF-PID controller has limits. The su- pervisory capacity of the SOF-PID controller can adjust only certain kinds of parameters. Here the hybrid SOF-PID controller is introduced to tune some kinds of parameters, and it was tested on a MIMO biped robot. In the experi- ment, the hybrid SOF-PID controller shows a better perfor- mance than the SOF-PID. Key words Self-organizing fuzzy · Biped · PID controller 1 Introduction Over the past few decades, many industrial processes have been controlled using PID. Despite extensive use of PID in conventional control problems, its performance in indus- trial applications is limited. For instance, in case of a step input problem, it cannot show the best performance. For a fast response it shows a bad overshoot property. Even if you succeeded in tuning PID gain to show a fine overshoot and ripple, you must have some steady-state error. For this rea- son, a few replacement algorithms appeared, but it is not necessary to discard an existing controller such as a conven- tional PID, which works well and is already in operation with good performance even if it is not the best. A supervi- sory controller which can adopt a conventional PID control- ler is enough, and can be a good solution. Kazemian 1–3 studied the SOF-PID to adjust a PID con- troller which was applied to a complex nonlinear system, and showed a fine performances. He tuned only propor- tional gains. For other gains, e.g., differential gains and integral gains, he used the Ziegler–Nichols tuning method because only one kind of parameter, proportional gains, can be tuned using his method. Here, I suggest the hybrid SOF- PID to adjust all three kinds of PID gain. All through the hybrid SOF-PID can tune all three PID gains, in experi- ments, proportional gains and differential gains are tuned because the PD controller can control a nonlinear MIMO robot. Section 2 describes the structure of the SOF-PID con- troller suggested by Kazemian. Section 3 describes the structure of the hybrid SOF-PID controller. Section 4 ex- plains the experimental results of the MIMO biped robot’s trajectory following, and compares the results with the SOF-PID. Finally, Sect. 5 discusses and concludes the re- sults of this work. 2 Basic structure of the SOF-PID Controller The block diagram in Fig. 1 shows the basic structure of the SOF-PID controller. This diagram shows the SOF at a su- pervisory level readjusting the PID gains at an actuator level. An error from the actuator level is fed into the super- visory level to enable the SOF to analyse the process out- put. There is also an input from the PID controller block to the history of the past states block via the PID input section to continuously fuzzily the values of the PID gains. Finally, the SOF adjusts the PID gains during operation, and feeds the results from the output section block into the actuator block. Details of the SOF block follow. – Error input section: error and error change are defined on Eqs. 1 and 2, respectively. Error e setpo s system output po i i i ( ) = ( ) - ( ) int (1) Error change ce error e errror e i i i ( ) = ( ) - ( ) -1 (2) T.-Y. Choi (*) · S.-Y. Park · J.-J. Lee Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea e-mail: ermzace@odyssey.kaist.ac.kr This work was presented in part at the 10th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2005