International Journal of Advanced Robotics
and Automation

Real-time navigation in the partially unknown environment is an interesting task for mobile robotics. This article presents the cascade neuro-fuzzy (CN-Fuzzy) architecture for intelligent mobile robot navigation and obstacle avoidance in static and dynamic environments. The array of ultrasonic range finder sensors and sharp infrared range sensors are used to read the front, left and right obstacle distances. The cascade neural network is used to train the robot to reach the goal. Its inputs are the different obstacle distance received from the sensors. The output of the neural network is a turning angle between the robot and goal. The fuzzy architecture is integrated with the cascade neural network to control the velocities of the robot. Successful simulation and experimental results verify the effectiveness of the proposed architecture in both static and dynamic environments. Moreover, the proposed CN-Fuzzy architecture gives better results (in terms of path length) as compared to previously developed techniques, which verifies the effectiveness of the proposed architecture.

Keywords: Cascade neuro-fuzzy; Fuzzy logic; Neural networks; Mobile robots; Obstacle avoidance; Velocity

The applications of the intelligent robot in many fields such as industry, space, agriculture, defense and transportation, and other social sectors are growing day by day. The mobile robot performs many tasks such as rescue operation, patrolling, underwater exploration, disaster relief and planetary exploration, etc. Therefore, the author is trying to put the effort in the field of the intelligent robot using CN-Fuzzy architecture, which can avoid the obstacle autonomously and reach the goal safely in the given environment. Autonomous mobile robot navigation is one of the challenging tasks for any soft computing techniques. Fuzzy logic and neural network have been widely used for mobile robot navigation and control because these methods are capable of handling the system uncertainty. Generally, the fuzzy logic is the combination of fuzzy rules and membership functions (inputs and outputs), which are constructed by human knowledge. And the neural network may be applied to a linear or nonlinear system, which can solve the real system problems using empirical data set (experimental or predicted). The neural network with fuzzy logic [1] improves the decision speed of the mobile robot for target seeking and obstacle avoidance.

Target seeking and obstacle avoidance are the two important tasks for any mobile robot in the environment. Godjevac and Steele [2] have integrated the Takagi-Sugeno type fuzzy controller and Radial Basis Function Neural Network (RBFNN) to solve the mobile robot path planning. Where the fuzzy logic is used to handle the uncertainty of the environment, and the neural network is used to tune the parameters of membership functions. Rai and Rai, [3] have designed the Arduino UNO microcontroller-based DC motor speed control system using multilayer neural network and Proportional Integral Derivative (PID) controller. Yang and Meng [4] have applied the biologically inspired neural network to generate a collision-free path in a nonstationary environment. In [5], the authors have designed the Reinforcement Ant Optimized Fuzzy Controller (RAOFC) and applied it for wheeled mobile robot wall-following control under reinforcement learning environments. The inputs of the proposed controller are rangefinding sonar sensors, and the output is a robot steering angle. Algabri, et al. [6] have combined the fuzzy logic with other soft computing techniques such as Genetic Algorithm (GA), Neural Networks (NN), and Particle Swarm Optimization (PSO) to optimize the membership function parameters of the fuzzy controller for improving the navigation performance of the mobile robot. Fuzzy reinforcement learning sensor-based mobile robot navigation has been presented by Beom and Cho [7] for complex environments. In [8], the authors have constructed behaviour-based neuro-fuzzy control architecture for mobile robot navigation in an unstructured environment. Rossomando and Soria, [9] have designed an adaptive neural network PID controller to solve the trajectory tracking control problem of a mobile robot. In [10], the authors have developed a genetic algorithm to choose the best membership parameters from the fuzzy inference system and implemented it to control the steering angle of a mobile robot in the partially unknown environment. In [11], the authors have presented the navigation method of the two robots (a leader robot and a follower robot) using Fuzzy Controllers (FC). In [15-16], the authors have designed the sensor based adaptive neuro-fuzzy inference controller for mobile robot navigation and obstacle avoidance in the various environments.

Cascade Neural Network (CNN) is similar to feed Forward Neural Network (FNN). Both neural networks use back propagation algorithm for updating the weights and biases [12]. This article describes the cascade neural network based fuzzy architecture for mobile-robot navigation and obstacle avoidance in static and dynamic environments. The cascade neural network is used to train the robot to reach the goal. Its inputs are different obstacle distance received from the sensors. The output of the neural network is a turning angle between the robot and goal. The fuzzy logic architecture is used to control the right motor velocity and left motor velocity of the mobile robot. In the last two decades, many researchers have implemented different neurofuzzy techniques for solving the navigation problem of the mobile robot. Motivated by the above literature survey, the primary objective of this paper is to improve the navigation accuracy and efficiency of the mobile robot using the cascade neuro-fuzzy controller. The remainder of this article is structured as follows: Section 2 introduces the design and implementation of the CNFuzzy architecture for mobile robot navigation and obstacle avoidance in various environments. Section 3 demonstrates the computer simulation results in different unknown environments. Section 4 describes the simulation result comparison with developed techniques. Section 5 presents the experimental results and discussion for validating the proposed controller. Finally, Section 6 depicts the summary.

This section introduces the design and implementation of the CN-Fuzzy architecture for navigation of mobile robot and obstacle avoidance in various environments. The cascade neural network is used to train the robot to reach the goal in the environment, and the fuzzy logic architecture is used to control the right motor velocity and left motor velocity of the mobile robot. Figure 1 shows the proposed architecture of CN-Fuzzy for navigation of mobile robot and obstacle avoidance in unknown environments.

The neural network is one of the important techniques for the mobile robot navigation. In this section, the Cascade Neural Network (CNN) is used to train the robot to reach the goal in the environment. The neural network is the combination of many layers such as input layer, hidden (intermediate) layers, and the output layer; all the layers are connected with each other by the neurons. The CNN is the similar to the feed Forward Neural Network (FNN). Both CNN and FNN use back propagation algorithm for updating the weights and biases. The two back propagation algorithms, namely Levenberg-Marquardt (LM) and Bayesian Regularization (BR) are used to adjust the network weights and biases. Figure 2 illustrates the general structure of a Cascade Neural Network (CNN). In Figure 2, u, w , b and v addresses the input variables, synaptic weights, neuron bias, and output variable, respectively.

The inputs of the CNN are the obstacle distance received from the various sensors, and the output of the CNN is a turning angle between the robot and goal. Table 1 describes the different training patterns for the cascade neural network, which helps the robot to reach the goal in the environment. The proposed CNN uses three inputs, two hidden layers (six and four neurons, respectively) and single output layer for the mobile robot navigation. The CNN has three inputs: F.O.D. (Front Obstacle Distance), L.O.D. (Left Obstacle Distance), and R.O.D. (Right Obstacle Distance), respectively. The output of this CNN is a Turning Angle (T.A.) between the robot and goal. The input and output of the CNN can be written as follows: -

Where = 1, 2, 3. (Three inputs F.O.D., L.O.D., and R.O.D., respectively)
Input layer (first layer):

Two hidden layers (second and third):
$q_t^{[s]}=\phi \left(NE{T}_t^{[s]}\right)$                                                                                                            (2)

$NE{T}_t^{[s]}={\displaystyle \sum _i(w_{t\cdot i}^{[s]}\cdot q_i^{[s-1]}+b_t^{[s]})}$                                                                              (3)
Where s = 2, 3. (Second and third layers)
Output layer (fourth layer):
$v_{(p)}=q^{[4]}=\phi \left(NE{T}^{[4]}\right)$                                                                                               (4)

$NE{T}^{[4]}={\displaystyle \sum _i(w_i^{[4]}\cdot q_i^{[3]}+b_i^{[4]})}$                                                                                   (5)

Where $u_i$ is the input variables, $v_{(p)}$ is the predicted output variable (turning angle). The $w_{t\cdot i}^{[s]}$ is the synaptic weight on connection joining the th neuron in the layer $[s-1]$ to the t th neuron in the layer $[s]$ ; $b_t^{[s]}$ is a bias of the $t$ th neuron in the layer $[s]$ and ${\phi }_t\left(d\right)$ is the Log-sigmoid transfer function. $$\phi (d)=\frac{1}{\left(1+\exp (-d)\right)}\text{ (6)}$$

The proposed CNN is verified through the mean squared error (MSE) and root mean square error (RMSE) method: -

Where $v_{(a)}$ is the actual output variable, $v_{(p)}$ is the predicted (network) output variable, and $r$ is the number of observations. $u$ , $w$ , $b$ and $v$ addresses the input variables, synaptic weights, neuron bias, and output variable, respectively.

This section describes the design of Mamdani-type fuzzy logic [17] architecture for navigation of mobile robot and obstacle avoidance in unknown environments. The Fuzzy Logic Architecture (FLA) is used to control the right motor velocity and left motor velocity of the mobile robot. The proposed FLA has four inputs and two outputs. The FLA receives first three inputs (obstacle distance) from the various sensors of the mobile robot. The first three inputs are denoted by F.O.D., L.O.D., and R.O.D., respectively. The fourth input is the turning angle (goal angle) between the robot and goal, and which is received from the CNN. The outputs of the FLA are the velocities of the motors of robot. The outputs are addressed by RMV (Right Motor Velocity) and LMV (Left Motor Velocity), respectively. The range of first three inputs is divided into two linguistic variables, namely CLOSE and AWAY, respectively, and it is located between 20cm to 150cm. The two linguistic variables NEGATIVE and POSITIVE, respectively, are used for turning angle. The range of outputs is divided into two linguistic variables, namely LOW and HIGH, respectively. The two generalized bell-shaped (Gbell) membership functions are used for inputs and outputs. Figure 3 shows the input and output variables of the FLA. Figure 4 illustrates the fuzzy logic architecture. The fuzzy rule set of the FLA is described in Table 2. The FLA is composed through Mamdani-type fuzzy model in the following form: -

Where $m$ =1, 2, 3…12 (twelve rules), the $x_1$ , $x_2$ , $x_3$ and $x_4$ are the input variables. Similarly $y_1$ and $y_2$ are the outputvariables. The $A_{j1}$ , $A_{j2}$ , $A_{j3}$ and $A_{j4}$ are the fuzzy sets of the input variables. Similarly, $B_{j1}$ and $B_{j2}$ are the fuzzy sets of theoutput variables. The $j$ =1, 2 because each input and output have two Gbell membership functions. The fuzzy set (inputs and outputs) uses the following Gbell membership function: - $${\mu }_{jk}(x_k;a,b,c)=\frac{1}{1+{\left|\frac{x_k-c_{jk}}{a_{jk}}\right|}^{2b_{jk}}}\text{ (10)}$$
$${\mu }_{jl}(y_l;a,b,c)=\frac{1}{1+{\left|\frac{y_l-c_{jl}}{a_{jl}}\right|}^{2b_{jl}}}\text{ (11)}$$

Where $k$ =1…4 (four inputs), and $l$ =1, 2 (two outputs). The symbols $a$ , $b$ and $c$ are adjusting parameters of the Gbell membership function; called as the half width, slope control, and centre respectively.

The defuzzification of the output variables $(y_1 and{y}_2)$ are accomplished by the weighted average method: - $$y_1=\frac{{\displaystyle \sum _{m=1}^{12}\left({\mu }_{j1}(x_1)\cdot {\mu }_{j2}(x_2)\cdot {\mu }_{j3}(x_3)\cdot {\mu }_{j4}(x_4)\right)\cdot y_1}}{{\displaystyle \sum _{m=1}^{12}\left({\mu }_{j1}(x_1)\cdot {\mu }_{j2}(x_2)\cdot {\mu }_{j3}(x_3)\cdot {\mu }_{j4}(x_4)\right)}}\text{ (12)}$$ $$y_2=\frac{{\displaystyle \sum _{m=1}^{12}\left({\mu }_{j1}(x_1)\cdot {\mu }_{j2}(x_2)\cdot {\mu }_{j3}(x_3)\cdot {\mu }_{j4}(x_4)\right)\cdot y_2}}{{\displaystyle \sum _{m=1}^{12}\left({\mu }_{j1}(x_1)\cdot {\mu }_{j2}(x_2)\cdot {\mu }_{j3}(x_3)\cdot {\mu }_{j4}(x_4)\right)}}\text{ (13)}$$