Optimization of hybrid robot control system using artificial hormones and fuzzy logic

Abstract

This paper presents a method for hybridizing artificial hormones controller with type-2 fuzzy controller. Artificial hormones robot control system provides the ability to self-control, while the fuzzy controller is appropriate for nonlinear systems with time delay and dynamic systems. This paper presents three feasible scenarios of hybridizing two controllers. Controller performance indicators, such as settling time, overshoot, steady state error, and integrals known as feedback error performance indices (integral absolute error [IAE], integral squared error [ISE], integral time-weighted absolute error [ITAE], integral of time multiplied by the squared error [ITSE]), were studied and compared. The results of the hybrid controller for each of the scenarios show that it has better performance than any of the fuzzy and artificial hormone controllers alone. Energy consumption in the base and hybrid controllers was compared. The results show that the energy consumption for the hybrid controller is 20 to 30% less than the base controller.

Keywords

Robot control system hybrid controller artificial hormone controller fuzzy type-2 controller performance indices

1 Introduction

In recent years, some controllers have been designed based on artificial hormones, and were patterned after the living systems which accord themselves with the environment. These controllers have resulted into the self-control attribute of robots in different environmental situations and even in times when a robot breaks. Fuzzy controllers which are based on fuzzy logic are the kind of controllers appropriate for nonlinear and delayed systems with unclearly known dynamic. Many researchers have used fuzzy systems in control field and have obtained satisfactory results. Considering the advantages of the mentioned controllers, the first idea to use the advantages of both controllers, is to combine them. The constraints of each of the controllers do not exist or are improved in the hybrid controller.

2 Artificial homeostatic hormone system (AHHS)

AHHS was first developed through SYMBRION and RERLICATOR projects [1]. In these projects, the main concentration is to build a number of small automated robots which can join each other automatically and make one or more symbiotic organisms. In a study conducted by [2], artificial evolutionary algorithm was used to self-control a robot control system. AHHS1 and AHHS2 are two of the developed AHHS. AHHS1 was proposed and applied in both robot simulation [3] and real robots [2]. Figure 1 shows an example of AHHS1 application on a simple robot with two wheels.

As shown in Fig. 1, the interior space of the robot is devised into section by a vertical dotted line. The left section contains a sensor and motor, the right section contains right sensor and motor and the middle section does not contain any sensor or motor. The actuated sensors make the hormones secretion to diffuse toward the middle. If the sensors are the distance related sensors, then there are two sensors, S_l (t) for the left and S_r (t) for the right. s¹ is the proportion scale for a unit of hormone and sensor. The diffused hormone in the left, right and middle is shown by $H_{1}^{1}$ , $H_{2}^{1}$ , and $H_{3}^{1}$ . Equations 1 to 3 show each of the hormones secretion. $\begin{matrix} \frac{Δ H_{1}^{1}}{Δ t} & = & + H_{base}^{1} - H_{1}^{1} (t) H_{decay}^{1} \\ + s^{1} S_{l} (t) + D_{1, 2}^{1} (t) \end{matrix}$ (1) $\begin{matrix} \frac{Δ H_{2}^{1}}{Δ t} & = & + H_{base}^{1} - H_{2}^{1} (t) H_{decay}^{1} \\ + D_{2, 1}^{1} (t) + D_{2, 3}^{1} (t) \end{matrix}$ (2) $\begin{matrix} \frac{Δ H_{3}^{1}}{Δ t} & = & + H_{base}^{1} - H_{3}^{1} (t) H_{decay}^{1} \\ + s^{1} S_{r} (t) + D_{3, 2}^{1} (t) \end{matrix}$ (3)

$H_{base}^{1}$ shows the basic amount of hormone and $H_{decay}^{1}$ shows the hormone’s decay rate. Hormone diffusion amount ( $D_{x, y}^{i} (t)$ ) is defined in Equation 4. $D_{x, y}^{i} (t) = \frac{H_{y}^{i} (t) - H_{x}^{i} (t)}{2} d^{i}$ (4)

In Equation 4, dⁱ is the constant hormone diffusion rate. These equations show that the secreted hormone depends on the basic hormone, decay rate for the hormone, sensor amount simulation and the amount of hormone diffusion. Each section of the robots motor should have some inputs according to Equations 5 and 6, where a¹ is the proportion coefficient for a unit of hormone and motor. A_l (t) is related to the left motor and A_r (t) is related to the right motor. $A_{l} (t) = a^{1} H_{1}^{1} (t)$ (5) $A_{r} (t) = a^{1} H_{3}^{1} (t)$ (6)

Whenever the distance sensor detects a barrier, the related hormone is secreted. The more the hormone is secreted the more the machine speeds away from the barrier. These articles [4] and [5] have proposed some revisions of AHHS1 and AHHS2, in which AHHS1’s genome has been improved using evolution algorithms and with the same goal as AHHS1. If we consider the increase and decrease rates as linear and also between 0 and 1, then the momentary hormone concentration c_g (t) and the momentary speed V_xx (t) for each cycle is obtained asfollows: $C_{g} (t) = (α_{g} \dot{ActLevel} (t)) + (β_{g} {\dot{C}}_{g} (t - 1))$ (7) $V_{xx} (t) = V_{xx} command (t) * (1 - (0.9 * (C_{g} (t))))$ (8)

3 Fuzzy systems

Fuzzy logic is the kind of mathematics which formulates mankind’s knowledge and was invented by Prof. Zadeh [6]. Fuzzy controllers which are based on fuzzy logic are the kind of controllers that are appropriate for nonlinear systems, dynamic systems and the systems with delay time. In recent years, many researchers have used fuzzy systems to control nonlinear processes and have obtained satisfactory results [7, 8]. The process step is called the inference motor in fuzzy systems and it operates based on a set of “If-Then” fuzzy rules. There are two main fuzzy inference methods; these methods are known as Mamdani and Sugeno methods. Fuzzification of the inputs and fuzzy operators are the same for these two methods, but the outputs are different. Mamdani fuzzy inference method defines the outputs as fuzzy membership function, but the outputs of Sugeno inference method are linear or constant. A control loop could be used in fuzzy systems. In this loop, fuzzy set database connects E and U to each other and the “If-Then” rules are formed based on it (Fig. 2). The performance of fuzzy method is better than other methods for the complex systems, where the relationship between inputs and outputs could not be described or are hardly described. Fuzzy systems could be used as opened loop controller or closed loop controller. When using it as an opened loop controller, the fuzzy systems usually determine some control parameters and then the systems work based on these parameters.

Many fuzzy system applications in electronics belong to this type of loops. When using the fuzzy system as a closed loop controller, the outputs are measured and controlled simultaneously. Fuzzy systems applications in industrial sites are of this type. Researchers have shown that type-1 fuzzy systems are not appropriate for modeling and minimizing uncertainly, because of single membership degree for the input [9]. Type-2 fuzzy systems could be used to solve this problem (the problem of type-1 fuzzy system), because the membership degree is a fuzzy set [10]. Type-2 fuzzy systems were used in some studies [11, 12]. The main difference between type-1 fuzzy inference systems and type-2 fuzzy inference systems is the type-reducer block. The output of the fuzzy inference which is a fuzzy set enters the type-reducer block and type-2 fuzzy set changes info type-1 fuzzy set during the operations known astype-reducer.

4 Fuzzy control model

A closed loop fuzzy control is as shown in Fig. 3.

Feedbacks which are the measured variables from sensors are fuzzificated and thereafter are defuzzificated when passing the rules’ database and the proper orders are made. The fuzzy control used in this paper is known as fuzzy controller under direct operation or fuzzy control based on error. The inputs are error or system error derivatives and the output is the control signal in this type of controller. In this paper, type-2 fuzzy controller is used. Error and error derivatives are the two inputs of the controller and the output signal is the only output variable for this fuzzy controller.Gaussian membership functions are used in the input and output. The two inputs are defined by three membership functions N, Z and P and the output is defined by five membership functions GN, N, Z, P and PG (Figs. 4 and 5). The proposed controller used set reducer to type-reduce and center of gravity to defuzzificate.

The rules’ database which is used in this paper is shown in Table 1. The method is designed considering type-2 fuzzy logic toolbox in MATLAB.

5 Hybridizing artificial hormone controller and fuzzy controller

Hybridizing artificial hormone and fuzzy controllers is the first idea that comes to mind to take advantages of both controllers. One of the first studies in hybrid controller’s field is reported by [13]. In this study, after discussing the constraints of each type of controllers, a switching mechanism is proposed to hybridize two fuzzy controllers of type (PI) and PD. The fuzzy rules increase exponentially when the inputs of the fuzzy controller increase. Therefore, the two controllers (PD and PI) with two inputs are hybridized and the result is a more simple rules’ database containing less rules. In a research study by [14], a fuzzy controller was used instead of the term P and proportional integral derivative (PID) controller and the stability of the controller was proven using small gain theorem. In the study by [15], a fuzzy control and PID controller are hybridized based on a pre-defined steady state error to exploit the beneficial sides of both categories. In this study, three scenarios were proposed to hybridize artificial hormone and fuzzy controllers. In order to hybridize these two controllers, the switching system should decide about the percentage of the controllers’ outputs which are entered into the system. The decisions are made based on the criteria error square or the absolute value of error. Suppose the system has a step set point in the beginning that the error is high, then the controller which has more output, gains a higher share in guiding the system towards the set point. Therefore, in the switching block, the controller with more output is first selected, then the first controller is multiplied by e² and the other control output is multiplied by (1-e²); hence, either Equations 9 or 10 will take place: $U_{hybrid} = e^{2} U_{AHS} + (1 - e^{2}) U_{fuzzy}$ (9) $U_{hybrid} = e^{2} U_{fuzzy} + (1 - e^{2}) U_{AHS}$ (10)

6 Three scenarios used to make the hybrid artificial hormone controller and fuzzy controller models

6.1 Determining the basic values of the artificial hormone control system by the fuzzy controller

As shown in the following figures, process ‘feedbacks are transferred with both the fuzzy and artificial hormone controllers. Therefore, the fuzzy controller determines the best set-point for each control hormone based on the knowledge database. Figure 6 shows a simple model of this hybrid scenario and Fig. 7 shows the closed loop control system for this scenario.

The results in relation to the output signal of the basic controller (artificial hormone) are as shown in Fig. 8 and the results for the output signal of hybrid controller (fuzzy artificial hormone) are as shown in Fig. 9. These figures show that the efficiency of the controller in the hybrid controller is improved.

6.2 Revising the control results of the artificial hormone network by the fuzzy controller

In this scenario, the output of the artificial hormone controller is used as the input of the fuzzy controller. Processes with changed characteristics during this time, take this method into account to automatically set the artificial hormone controller. A simple model of this hybrid scenario is as shown in Fig. 10 and the fuzzy closed loop control system of the scenario is as shown in Fig. 11.

The results for the output signal of the basic controller (artificial hormone) are as shown in Fig. 12. The results for the output signal of the hybrid controller (fuzzy artificial hormone) are as shown in Fig. 13. These figures indicate improvements in the efficiency criteria of the hybrid controller.

6.3 Parallel performance of the artificial hormone and fuzzy controllers

Another hybridization of the fuzzy and artificial hormone controllers is as shown in the following figure. In this method, the fuzzy and artificial hormone controllers work parallel and the output is added together. In normal situation, the fuzzy output is supposed to be zero and the hormone controller controls the robot, but the fuzzy system is activated in the times which abnormal situations, such as severe instabilities are detected. Figure 14 shows a simple model of this scenario and the fuzzy closed loop control system is as shown in Fig. 15.

The results in relation to the output signal of the basic controller (artificial hormone) are as shown in Fig. 16 and the result for the output signal of the hybrid controller (fuzzy artificial hormone) is as shown in Fig. 17. These figures show that the efficiency of the controller in the hybrid controller is improved.

7 Design of experiment

In this section, the controller efficiency indicators are evaluated. Usually, the objective function in control system is considered in a way that there is no steady state error and the output of the system is propelled towards the desired value. In order to do this, the kind of functions used is based on the system error. In this paper, mean absolute error (MAE) is used as the objective function (Equation 11). $MAE = \frac{1}{M} \sum_{i = 1}^{M} | e (i) |$ (11)

For a more accurate comparison of the controller, the related efficiency indicators, such as settling time (ts), overshoot (mp% ), steady state error (ESS), rise time (tr), and the prominent integrals of the feedback error are surveyed and compared together. Error integrals in this article are integral squared error (ISE), integral absolute error (IAE), integral time-weighted absolute error (ITAE), integral of time multiplied by the squared error (ITSE) which are calculated according to Equations 12 to 15. $ISE = \int e^{2} dt$ (12) $IAE = \int | e | dt$ (13) $ITAE = \int t | e | dt$ (14) $ITSE = \int {te}^{2} dt$ (15)

Table 2 shows the results of the comparison between the efficiency indicators of the basic artificial hormone controller and the hybrid fuzzy artificial hormone controller. The results show that the indicators of the hybrid controller are improved as compared to the basic controller. The diagrams of the control signal for the artificial hormone, fuzzy and hybrid controllers and the step response if these controllers are plotted in MATLAB software are as shown in Figs. 18 and 19. These figures show that the hybrid controller is better than the artificial hormone and fuzzy controllers when considering the efficiency indicators.

Finally, three situations are simulated in V-REP-PRO-ED simulator and the energy consumption of the basic controller (AHS) and the fuzzy hybrid controller (FAHS) are measured. In situations where the simulations are normal, then there is low and high disturbances. The simulation result shows that the hybrid controller is more efficient and the energy consumption of this controller is 20 to 30% less than the basic controller (Table 3).

8 Conclusions and future research

In this paper, a hybrid model of artificial hormone controller and type-2 fuzzy controller is proposed. The energy consumption of a robot is lowered about 20 to 30% in the proposed controller. Table 2 shows the improvement in the hybrid controller as compared to the basic controller when considering the controller efficiency indicators. Also, the hybrid controller shows 3 to 4% improvement in the overshoot from another aspect, because of the uncertainly in the fuzzy membership function. Type-2 fuzzy system is a robust system for the situation. Therefore, a flexible intelligent system for complex situations is proposed when hybridizing artificial hormone and fuzzy controllers. Hence, the advantages of the controller are robustness to the environmental alterations, improvements in speed oscillations and improvements in energy consumption. It is recommended to use the proposed hybrid controller to avoid a collision with moving barriers for the future research.

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