A Hierarchical fuzzy controller for a biped robot. 
 
 
Abstract—In this paper the investigation is placed on the 
hierarchic neuro-fuzzy systems as a possible solution for biped 
control. An hierarchic controller for biped is presented, it 
includes several sub-controllers and the whole structure is 
generated using the adaptive Neuro-fuzzy method. The proposed 
hierarchic system focus on the key role that the centre of mass 
position plays in biped robotics, the system sub-controllers 
generate their outputs taken into consideration the position of 
that key point.   
 
Keywords: biped robot; Neuro-fuzzy systems; hierarchical fuzzy 
systems.   
I. 
 INTRODUCTION  
         The control of a humanoid robot is a challenging task 
due to the hard-to stabilize. In recent years, the control of 
biped robots has made great progress. The control of a biped 
walking robot is to find a control law that allows the 
coordination of movements of the various members of the 
articulated mechanical structure [2]. This enables the 
movement of the robot on a ground. Different methods were 
developed for the control of biped robots with a focus on the 
stabilization of biped locomotion system [3, 4].   
       Biped robots are a typical case of non-linear complex 
system; the control of such systems is addressed using 
classical methodologies such as the PID and also intelligent 
techniques such as PSO, fuzzy sets, neural networks and 
neuro-fuzzy systems [4, 5, 6, 7].   
        The IZIMAN is a research projects that conducting in 
REGIM 
laboratory, 
“Research 
group 
on 
Intelligent 
Machines”. The main challenge of the project is to propose an 
intelligent architecture and controller that are “humanly” 
inspired [8]. Within this project several gait generation 
methodologies focusing on PSO [9, 10, 11, 13], and also 
neuro-fuzzy was investigated [7], PSO based biped control 
was implemented on a small size robot [12]. 
       In this paper the investigation is placed on the hierarchic 
neuro-fuzzy systems as a possible solution for biped control. 
An hierarchic controller for biped is presented, it includes 
several sub-controllers and the whole structure is generated 
using the adaptive Neuro fuzzy method.  
This paper is organized as follows: the first section include 
the description of neuro-fuzzy and hierarchical systems. In the 
second section, the hierarchical fuzzy controller for biped 
robot is presented. In the third section, we present the 
controllers design, obtained results are presented in paragraph 
four.  Finally, paragraph five include the conclusions and 
further work.  
II. 
NEURO-FUZZY AND HIEARCHIC FUZZY SYSTEMS  
A.  Neuro-fuzzy systems 
       Artificial neural networks (ANN) and fuzzy inference 
system (FIS) are generally considered to be complementary 
areas of research. The combination of FIS and ANN define a 
neuro-fuzzy system in such a way that the parameters of FIS 
are determined by using the neural network learning 
algorithms [14].  
       The neuro-fuzzy system uses the linguistic knowledge of 
fuzzy inference system and the learning capability of neural 
network. 
To describe 
the 
architecture a 
neuro-
fuzzy system, consider 
Fig1. For 
simplicity, we 
assume 
that our fuzzy 
system has 
two inputs 
and 
one 
output. 
Furthermore, we 
assume 
that 
the defuzzification of 
the 
variables is a linear combination of the first order of input 
variables [14, 15]. 
 
 
Fig1. neuro-fuzzy system architecture  
 
B.     Hierarchical fuzzy systems 
Hierarchical fuzzy systems have been created to address 
one of the major problems of standard fuzzy systems which is 
essentially the impact of the number of input variables on the 
number of rules of the system [16, 17].  The use of a 
hierarchic structure allowed designing a set of sub-controllers 
with limited number of variables for each one, see Figure 2.  
Complex structures including a hierarchic organization 
are the typical target of the HFLC design concept. In bio-
inspired systems, such as the human locomotion system, a 
Abdallah Zaidi , Nizar Rokbani,   and Adel. M. Alimi, Senior Member IEEE 
REGIM Lab.: REsearch Groups on Intelligent Machines 
National Engineering School of Sfax,  
University of Sfax, BP 1173, Sfax, 3038, Tunisia 
{Abdallah.zaidi, nizar.rokbani, adel.alimi}@ieee.org 
hierarchic design could be directly inspired from the system. 
For such systems the HLFC have a build in justification.   
 
 
 
Fig2.  Hierarchical fuzzy systems architecture as in [20] 
 
III. 
AN HIEARCHICAL FUZZY SYSTEM FOR BIPED ROBOT 
CONTROL  
A planar biped model is used, the model includes a knee 
rotation, a hip rotation, and the remaining of the body is 
represented by a punctual mass with a motion, see figure3, 
such a model is close to the “Bipsim” proposed in [22].  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig4. Structure of the biped robot 
 
The training Data-set needed to generate the controllers 
using the Adaptive Neuro-Fuzzy System method is obtained 
from a classical dynamic model similar to [18].  Separated 
Data-sets of 10, 30, 40, 60 and 120 samples are created in 
order to evaluate the impact of the training set size on the 
quality of the controllers. Test data set relative to training data 
sets are separately managed.  
The overall architectural design is given in figure 4, 
where a set of neuro-fuzzy controllers integrated into a 
Hierarchical structure centered on the COM position of the 
biped robot. The system generates the needed joints rotations 
for a given COM reference position, a supervision system is 
then used to compute the estimated position of the COM.  
Due to the symmetry of the walking system, the design of 
the left and right legs are the same, a leg include four 
controllers. The left leg controllers are HFLC1, HFLC3, 
HFLC5 and HFLC7, the right leg controllers are HFLC2, 
HFLC4, HFLC6 and HFLC 8.  Since the controllers design is 
similar only the left leg controllers are described in this paper. 
The overall design appears in figure5, a brief description of 
the sub-controllers is given bellow:    
 
For HFL1, the controller inputs are the vector 
(x0, y0) coordinates of the center of mass and the 
angle angel (beta_left), the output is the same leg 
angle (gamma_left).  
 
For HFL3, the controller inputs are the vector 
(x0, y0) coordinates of the center of mass and the 
angle angel (gamma_left), the output is the 
vector (xcl,ycl) coordinates of left ankle.  
 
For HFL5, the controller inputs are the vector 
(x0, y0) coordinates of the center of mass the 
vector (xcl,ycl) coordinates of left ankle. The 
output is the angel (beta_left). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig5. Hierarchic fuzzy controller for biped robot 
IV. 
RESULTS      
A. Controllers Responses  
In this paragraph we presented the controllers response 
surface, representing controller output in accordance with its 
inputs. The controller’s behavior corresponding to the left leg 
and using a training data set of 10 samples appears in figure 6.   
γ 
β 
α 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig6. Controllers Design, from top to bottom HFLC1, HFLC2 and HFLC3 
controllers responses.  
B.     Effect of the training data size 
The controllers are generated using a set of training Data 
including respectively 10, 30, 40 and 120 samples; t
are evaluated using a set of test Data. The cumulative scare 
error for all test data is computed, it is used as an evaluation 
0
0.1
0.2
0.3
0.35
0.4
0.45
0
0.5
1
1.5
2
in1
in2
out1
0.1
0.2
0.3
0.4
0.14
0.16
0.18
0.2
0.22
0
0.5
1
1.5
in1
in2
out1
0
0.2
0.4
0.6
0.2
0.4
0.6
0
0.1
0.2
0.3
0.4
0.5
in1
in2
out1
 
 
, HFLC2 and HFLC3 
The controllers are generated using a set of training Data 
including respectively 10, 30, 40 and 120 samples; then they 
are evaluated using a set of test Data. The cumulative scare 
error for all test data is computed, it is used as an evaluation 
criteria of the HFLCs. Results are presented 
9.   
. 
 
 
 
 
Fig7. representation of the error 
Fig8. Representation 
Fig9. Representation of the
The results show that the best training set size for all 
controllers is made of 30 samples
(25) for a training set of (40) samples, a similar result is 
observed in HFLC5 when trained with (60) samples its error is 
about (3.5).  
0.3
0.5
0.8
Results are presented in figures 7, 8 and 
 
 
 
 
 
 
 
 
 
 
error of the proposed HFLC1 
 
 
 of the error of HFLC3 
 
 
Representation of the error of HFLC5 
 
The results show that the best training set size for all 
controllers is made of 30 samples. HFLC1 had an error of  
25) for a training set of (40) samples, a similar result is 
observed in HFLC5 when trained with (60) samples its error is 
For a training set of 30 samples the error is about (0.001)  
for HFLC1, (0.00001) for HFLC3 and (0.0001) in the case of 
HFLC5.  
V. 
DISCUSSION AND FURTHER WORK 
  In this paper, we have proposed a hierarchical fuzzy 
controller of the biped robot. The generation methodology as 
well as the test procedure is explained. An investigation on the 
effect of the number of training samples is also conducted and 
allowed to fix the optimal size to (30) experimentally.  
The paper detailed only the generation and test of the left-
leg since the right leg has a symmetric Behavior. The obtained 
results are interesting with a limited error for the main 
controllers of the left leg.  
A comparative test between the full controller and a 
classical one such in [18] will be developed soon.   
 
ACKNOWLEDGMENT 
The authors would like to acknowledge the financial 
support of this work by grants from General Direction of 
Scientific Research (DGRST), Tunisia, under the ARUB 
program. 
 
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