A hybridized regression-adaptive ant colony optimization approach for navigation of humanoids in a cluttered environment

Accepted Manuscript Title: A Hybridized Regression-Adaptive Ant Colony Optimization Approach for Navigation of Humanoids in a Cluttered Environment Authors: Priyadarshi Biplab Kumar, Chinmaya Sahu, Dayal R. Parhi PII: DOI: Reference:

S1568-4946(18)30214-X https://doi.org/10.1016/j.asoc.2018.04.023 ASOC 4827

To appear in:

Applied Soft Computing

Received date: Revised date: Accepted date:

12-9-2017 6-4-2018 11-4-2018

Please cite this article as: Priyadarshi Biplab Kumar, Chinmaya Sahu, Dayal R.Parhi, A Hybridized Regression-Adaptive Ant Colony Optimization Approach for Navigation of Humanoids in a Cluttered Environment, Applied Soft Computing Journal https://doi.org/10.1016/j.asoc.2018.04.023 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Hybridized Regression-Adaptive Ant Colony Optimization Approach for Navigation of Humanoids in a Cluttered Environment

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Robotics Laboratory, Mechanical Engineering Department,

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National Institute of Technology, Rourkela-769008, Odisha, India

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Priyadarshi Biplab Kumar1*, Chinmaya Sahu2, Dayal R. Parhi3

[email protected], [email protected], [email protected]

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(Contact No. +91-9853934345)

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* Corresponding Author

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Highlights

Determination of navigational parameters for humanoid path planning.

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Design of the RA and AACO navigational controllers.

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Design of hybrid RA-AACO controller using the logic of both RA and AACO.

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Design of a Petri-Net system for inter-collision avoidance.

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Testing of the navigational controller in both simulated and experimental environments.

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Abstract

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Humanoids are preferred over their wheeled counter parts because of their ability to replace human efforts. Navigation and path planning of humanoids is very much important and challenging area of investigation for robotic researchers to enable the humanoids for accomplishing tedious and repetitive tasks. In this paper, a novel hybridization scheme is attempted for the path planning and navigation of humanoids in a cluttered environment. Here, hybridization has been attempted on NAO humanoid robots using regression technique

and adaptive ant colony optimization. In the hybridization scheme, the navigational parameters of the humanoids are fed to the regression controller initially in terms of obstacle distances, and the interim output from the regression controller is again fed to the adaptive ant colony optimization controller to obtain the final output. By using V-REP software, navigation simulations are performed, and the simulation results are also tested against real experimental set-up developed under laboratory conditions. The simulation and experimental results reveal that the humanoids are successful in avoiding the obstacles and reach their

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destinations safely with path optimization. The results obtained from both the environments are compared against each other and are in good agreement with minimal percentage of

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errors. The navigational controller is tested for both single as well as multiple humanoids, and it works well for both the cases. Finally, the proposed controller is validated against other

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navigational approaches, and a significant enhancement of results is obtained.

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Keywords: Navigation, Path Planning, RA-AACO, Petri-Net, V-REP.

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1. Introduction

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With the development of science and technology, robots are becoming an integral part of human life. Among the different forms of robots, humanoids are popular because of their ability to mimic the human behaviour and replace human efforts in repetitive and tedious

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tasks. Humanoids are very much integrated to workplace in several industries such as medical assistance, manufacturing sectors, industrial automation, etc. To accomplish smooth

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operation of humanoids in a human workplace, navigation and path planning is very much important. By designing a proper navigational intelligent controller for the humanoids enables them in avoiding the obstacles that are present in the path and negotiate with humans in the workplace. Navigation and path planning approaches are primarily categorized as local

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or sensor based approaches and global or model based approaches. In sensor based approaches, the robot is unaware of the environmental conditions, and it negotiates with the obstacles by immediate detection and planning. In model based approaches, the robot is aware of the environmental conditions with obstacle locations, and thus it plans the path by mapping the environment from the beginning itself. Similarly, based on the type of obstacles used, path planning can be divided as static path planning and dynamic path planning. In

static path planning, only static obstacles are used in the environment, and in dynamic path planning, dynamic obstacles (either in forms of moving obstacles or other fellow robots) are present in the environment. Dynamic path planning is way more challenging than static path planning as needs careful design of the control architecture considering conflicting situations that may arise in deciding the priority among multiple robots when they navigate in a common platform and encounter same obstacle. The use of artificial intelligent algorithms in humanoid navigation is a relatively new area of investigation among robotics researchers.

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Therefore, the current investigation is devoted towards the use of a hybrid navigation

architecture for path planning of humanoids in complex environments. Over the last few

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decades, humanoid navigation and robotics research have been the center of attraction for many researchers. Some of them can be cited over here.

Parhi et al. [1-3] have used several artificial intelligent (AI) approaches for navigation of

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mobile robots. They have tested the effectiveness of their proposed controllers through proper simulation and experimental environments. Deepak et al. [4-6] modified the controlling

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parameters of different intelligent algorithms and observed an enhanced efficiency with the

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adaptive parameters. Hugel and Jouandeaue [7] developed a 3D LIP model without any

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torque in the support phase for the walking pattern of humanoid robots. Sadedel et al. [8] incorporated genetic algorithm (GA) to hip and foot trajectories for an offline path planning

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approach for 2D humanoid robots. Karkowski et al. [9] used A* algorithm and adaptive 3D action set to develop a real time path planning approach for humanoids considering step by step height information. Ido et al. [10] used motion capture data as an input to a view based

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sequence and analyzed the walking pattern of humanoids. Mohanty and Parhi [11-17] used fuzzy and cuckoo search based hybrid system for navigation of mobile robots in complex

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environments and validated the proposed controllers in practical environments. Dalibard et al. [18] developed a collision free path for the dynamic walking of humanoids by a randomized algorithm. Clever and Mombaur [19] proposed an optimal inverse control scheme for motion transfer from humans to humanoids. Mirjalili et al. [20] developed an inverted pendulum

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model to propose an online path planning approach for SURENA-III humanoid robot. Pradhan et al. [21] used fuzzy logic for navigation of both single and multiple mobile robots with path optimization. Shakiba et al. [22] proposed a modified particle swarm approach by adding Ferguson splines to generate a collision free path for soccer playing humanoids. Perrin et al. [23] compared among different footstep planning approaches applicable to humanoid path planning to generate a classical motion planning approach. Ryu et al. [24] developed a

way point based path for humanoids. Parhi et al. [25-27] developed different adaptive optimization techniques for navigation of mobile and underwater robots. Shimizu and Sugihara [28] used the transitional sequence of the double support phase to propose a path planning approach for the humanoids. Fen et al. [29] generated a collision free path for a humanoid manipulator by modifying the basic ant colony optimization (ACO) algorithm. Kanoun et al. [30] used a virtual kinematic tree as an inverse kinematics problem to generate a path for humanoids. Schmid and Woern [31] generated smooth and collision free path for

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humanoids by using NURBS curve. Pham and Parhi [32] used neural network as a potential navigation strategy for mobile robots by designing the control architecture considering the

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environmental constraints. Niskiwaki et al. [33] proposed a laser range finder based path

planning approach for humanoids in a complex environment. Yoo and Kim [34] developed a gaze control based architecture for navigation of humanoid robots in complex environments.

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The extensive survey of the available literatures suggest that navigation and path planning is very much popular in case of mobile robots. A very few citations are available for humanoid

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navigation. Although some of the researchers have attempted humanoid navigation up to

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some extent, most of their approaches are not destination directed, and they apply to limited

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environments also. Along with that, navigation of multiple humanoids on a common platform has not been reported in any of the literatures as per author’s knowledge. Based on the

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limitations available in the literatures regarding the navigation of humanoids, the current work is focused on the development of a sensor based navigation strategy for single as well as multiple humanoids in a cluttered environment. To optimize the path followed by the

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humanoids, a novel hybrid technique comprising of regression analysis (RA) and adaptive ant colony optimization (AACO) has been proposed. Here, the basic control parameters of Ant

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Colony Optimization (ACO) have been changed to enhance the effectiveness of the original algorithm. Several researchers have tried to control the parameters of the ACO technique, and some of them can be highlighted over here. Castillo et al. [35-37] proposed a navigation strategy for autonomous mobile robots by modifying the controlling factors of fuzzy logic by

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ant colony optimization and similarly modifying the factors of ant colony optimization by fuzzy logic. They have experienced a performance improvement by the modification of controlling factors. Zhong and Ai [38] modified the basic ant colony algorithm for balancing a multi-objective assembly line. They observed a minimized workload variation among workstations. Mohammed [39] used a modified approach of ant colony optimization for solution of a travelling salesman problem. Brand et al. [40] used ACO for navigation of

mobile robots. They tested their approach in both static and dynamic environments. Purian and Sadeghian [41] used ACO for optimizing the controlling factors of a fuzzy logic and used it in navigation of mobile robots. Wang et al. [42] modified the basic ACO approach by focusing on the solution to pheromone overlapping and used it in a network coding resource optimization. Habib et al. [43] used a combined approach of Voronoi diagram and modified ACO for path planning of mobile robots on point to point motion planning scheme. Krentz et al. [44] proposed a navigation strategy for multiple mobile robots by modifying the basic

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ACO and considering the challenges involved in shifting the arena from simulation to

experimental ones. Han et al. [45] developed a navigation strategy for mobile robots by

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considering the critical obstacles as the initial pheromone trails in a basic ACO algorithm. By modifying the basic scheme of the algorithm, path length could be optimized as the ants search for the optimal path near the critical obstacles rather than searching the entire space. Reshamwala and Vinchurkar [46] reviewed about the use of ant colony technique in different

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engineering applications. It can be noticed from the survey of earlier researches that ACO

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and its modified versions have been mostly applied for mobile robot navigation and industrial

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applications. The use of the same in humanoid navigation is not yet reported.

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The application of a humanoid robot in a complex and dynamic environment demands use of hybrid AI techniques as the individual approaches may not always be self-sufficient for the

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stated purpose. Sometimes, the navigation problem may also experience trapping in a local optima and unable to deal with navigation of multiple humanoids in a common platform. To avoid the limitations of the standalone methods as navigational approcahes, hybridization is

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attempted. Several researchers [47-51] have attempted hybridization in the past for navigation of mobile robots. However, the application of the same in humanoid robots is very rare to

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find. Based on the above research gap available, the objective of the current investigation is set as the design and implementation of a novel navigational controller that can be used to navigate single as well as multiple humanoid robots in a complex environment with optimization of path and time taken to reach the desired destination. Here, regression analysis

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is chosen as a classical technique; AACO is chosen as an artificial intelligent algorithm, and a scheme of hybridization is attempted between them to navigate the humanoids. Classical approaches are known to produce converged results within a limited time; however, they are mostly dependent upon the training pattern data and the results produced may lack accuracy in comparison to AI approaches. AI approaches may take somewhat more time to converge; however, they produce more accurate results. Therefore, the hybridization between classical

and AI techniques is supposed to take the positive aspects from both the techniques and provided refined outputs. 2. RA Control Architecture Regression analysis is a well-known statistical method of data forecasting by relating dependent variables with independent ones. By regulating the basic navigational parameters of a humanoid walking pattern, regression technique can be effectively used to generate a

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suitable solution for the path planning problem.

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2.1. Basic Overview

In a basic regression technique, the dependent parameters are not directly related to the independent ones; rather they are made dependent on some governing parameters that can directly be dependent on the independent variables. A general equation of regression can be

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i=1, 2, 3…n

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yi  a1  a 2 xi  ei

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represented as follows.

In the above equation, yi is a dependent variable and xi is an independent variable with

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parameters as a1 and a2 and ei represents an error form. Figure 1 represents an example for

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understanding the scheme of a basic linear regression.

Figure 1: Basic linear regression

(1)

In Figure 1, it can be noticed that ranges have been taken from 0 to 10 and 0 to 3 in the x-axis and y-axis respectively. Here, the parameters represented in the x-axis are the independent ones, and those represented in the y-axis are the dependent ones. After locating the corresponding values of the dependent variables with the independent ones, a straight line equation is generated by the regression equation. The straight line shows the basic equation of regression. Accumulation of scattered data into a common straight line equation is the

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most significant feature of regression. Similarly, by taking into consideration the governing parameters of humanoid navigation, a basic control scheme can be proposed by using the logic of regression. In the following

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section, a basic control architecture for humanoid navigation using RA has been presented. 2.2. Control Architecture

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Path planning problems are primarily aimed at avoiding the obstacles present in the path and reach the destination position smoothly. In the humanoid navigation, four controlling

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parameters such as front obstacle distance (FOD), left obstacle distance (LOD), right obstacle

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distance (ROD) and turning angle (TA) are chosen for solving the path planning problem.

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FOD, LOD and ROD are selected as the input parameters, and TA is selected as the output parameter. NAO is equipped with a large set of sensors such as ultrasonic sensors, infrareds,

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etc. Based on the sensory information received from the sensors of the humanoid, the RA controller is fed with input distances and the controller provides the required output by

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performing some computations. Figure 2 represents the control scheme used in RA algorithm.

Figure 2: Navigational parameters of the humanoid NAO

The RA controller is designed in such a way that as long as there is no obstacle present within the threshold range of the sensory network of the humanoid, the humanoid would move towards the destination without activation of the controller. Once the sensors detect any obstacles in the environment, the controller acts as per the training pattern and provides the output. Different environmental conditions are fed to the RA controller in forms of training data. Table 1 represents some of the training parameters.

Sl. No 11 12

FOD in cm 50

60

TA in degree 0 10

30

40

3

35

70

50

20

13

50

4

30 70 40

55 30 40

30 40 30

-15

14

45

35

50

0 -25 20

15 16 17

30 40 30

8

35

55

40

-15

18

9 10

80 38

45 59

55 42

0 10

19 20

5 6 7

60

50 40 55 42

LOD in cm 60

ROD in cm 30

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ROD in cm 50

TA in degree -14

30

40

16

35

70

12

30 70 40

55 30 40

15 -17 -25

45

35

-18

35

55

20

80 38

45 59

-22 18

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LOD in cm 30

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FOD in cm 60

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Sl. No 1 2

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Table 1: Examples of some training pattern data for the RA controller

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In Table 1, the input parameters FOD, LOD and ROD are measured in centimeters of distance of robot from the obstacle and the output parameter TA is measured as the degrees

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of turning. By taking one example of the training data, the navigational parameters can be understood. By taking the 15th data from the Table 1, it is observed that FOD, LOD and ROD

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are 40 cm, 70 cm and 30 cm respectively. As the ROD is minimum for this case, the turning angle is set as -17 degrees. It has to be noted that negative turning angle only symbolizes

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turning to an opposite direction. To understand the same, a particular sign convention has been followed in this case. Figure 3 represents the sign convention that has been followed for

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RA controller.

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Figure 3: Sign conventions used in the RA controller It can be noticed from the Figure 3 that a positive turning angle represents a right turn for the humanoid. A negative turning angle represents a left turn, and a zero turning angle represents

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that the humanoid is moving in a straight path without any turning. After deciding the specific sign conventions and training pattern for the regression navigational controller, the training data are fed to the regression toolbox of a Minitab software. The primary aim of using the Minitab software is to formulate a solution in an equation format that can be used in the output of the system. The Minitab software generated the equation that can be represented as follows.

K4 = -23.0228 – 0.006183 K1 - 0.28508 K2 + 0.78636 K3

(2)

Where K1= Front Obstacle Distance, K2= Left Obstacle Distance, K3= Right Obstacle Distance, K4= Turning Angle The values of these parameters of equation 2 can also be refined by using more number of training pattern data. In the current analysis, 1000 numbers of training pattern data have been

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used to formulate the regression equation. 3. AACO Control Architecture

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M. Dorigo [52] has proposed ACO algorithm based on food searching behaviour followed by ants. ACO is preferred among other nature-inspired metaheuristic algorithms such as Bee Colony Optimization (BCO). ACO works on pheromone deposition by the ants and BCO works on dancing behaviour of bees. Therefore, when the number of ants is outnumbered by

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number of bees, ACO becomes advantageous than BCO in terms of systematic path

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optimization. ACO produces more converged results within a threshold limit than BCO as the

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bees proceed towards their destination in a dancing and random manner, and also they do not follow the same path in returning; while the ants follow to and fro path and if necessary, they

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alter the path systematically. ACO is more robust and adaptive than other approaches, and the convergence is guaranteed. It works faster than other approaches also. Therefore, in the

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3.1. Basic Overview

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current work, ACO has been preferred for navigational purpose than other techniques.

The basic idea behind the ACO algorithm is that the first ant leaves behind a pheromone trail

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in search of food and the trail is followed by other ants. Once a better path is available, the ants change their path and over the time, the path in which the pheromone density increases is

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considered as the optimized path. Figure 4 represents the basic search behaviour of ants.

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Figure 4: Basic search behaviour of ants

It can be noticed from Figure 4 that, initially the ants were distributed over two routes around

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the obstacle present in the path. However, with the due course of time, only one path which

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was the shortest was chosen as the optimal one. This peculiar behaviour of the ant colony

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system can be modelled mathematically as explained below.

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Let there are m numbers of ants building a tour for a travelling salesman problem. Initially, ants are in random position (all are at a particular city). For each step, ant k will apply a

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probabilistic rule, i.e., known as proportional rule to decide the next city to travel. So now the probability of ant k to choose city j from city i is 

 ij  ij 

 il  il  

lNik



, j  Nik

(3)

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



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p  k ij

Where  ij is the amount of pheromone between city i and city j.

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ij 

1 and d ij is the distance between ith and jth city (a heuristic value), α and β are two dij

parameters depending on pheromone trail and heuristic information, k

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is the feasible neighbourhood of ant k, when k is at city i, and the probability of choosing a

city outside

k

Ni

is 0.

As per this probabilistic rule, the probability of choosing a path length ( i, j) will increase with the value  ij and ij . If   0 , the chance of selecting the closest city will increase.

  1 leads to a stagnation level after that all the ants will follow the same path and construct the same tour.

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If   0 , only pheromone level will increase (without being biased by heuristic value)

The pheromone trail is updated in two steps after all the ants finish their tour. In the first step,

on the paths in which the ants have crossed during their tour.

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The pheromone level is updated by the following equation

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the pheromone level is decreased on all the paths by a constant factor, and then it is increased

(4)

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 ij  1    ij   i, j   L

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Where,  is the pheromone evaporation rate and 0    1

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 is implemented here to avoid unwanted or extra accumulation of pheromone trail and helps

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the algorithm to rectify the bad decision taken previously. After evaporation of the pheromones, all the ants will deposit pheromone on the paths they

m

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have passed in their tour as per the rule explained below.

 ij   ij    ijk   i, j   L

(5)

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k 1

Where,  ijk is the amount of pheromone deposited by the ant k on the paths visited by it.

 

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k ij



1/Ck if path i , j  T k 0 else

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where C k represents path length of the T k travelled by kth ant, i.e., the summation of all path lengths belongs to T k .

3.2. Adaptive Control of ACO Parameters With an ease of solving real engineering problems and predicting accurate results, ACO has become very much popular among researchers. Therefore, to enhance the performance of the basic ACO algorithm, some controlling parameters are modified to formulate AACO algorithm. From the extensive search of the literature, it can be noticed that  ,  and  act as the controlling parameters of basic ACO algorithm. Several researchers [53-55] have

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attempted to modify the controlling parameters of the basic algorithm. In the current investigation, initialization and updating of pheromone trail are selected as the two

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controlling parameters for modifying the basic algorithm. 3.2.1 Initialization of pheromone trail

The existing literature regarding ACO modification suggests that decreasing the value of 

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would also decrease the convergence rate of the algorithm. And by increasing the value of 

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the convergence rate will increase to lead to a local optimum. As our aim here is to find out

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the global optimum, we have to balance the  value by changing it dynamically by the help

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of the following equation.

(7)

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Pj  a1  l j / l0   b1  t j / t0 

Where, l j is path length travelled by the ant in jth tour just completed.

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t j is time required by the ant in jth tour just completed.

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a1 is proportion of priority of path length b1 is proportion of priority of time required

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And a1  b1  1

l0 is average value of all path length travelled in the tour, i.e.



j 1,2,....m

t0 is average value of time required to travel in the tour, i.e.



j 1,2,....m

lj / M

tj / M

Here M is total number path travelled. After this adaptive control, the initial pheromone of the algorithm is calculated as

 j  1    j  Pj

(8)

3.2.2. Updating of pheromone trail

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The proposed parameter to update the pheromone is as follows

Ui  a2  Li / L0   b2 Ti / T0   a2b2

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(9)

Where, Li is path length travelled by the ant in ith tour just completed.

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Ti is time required by the ant in ith tour just completed.

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And a2  b2  1

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b2 is proportion of priority of time required.

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a2 is proportion of priority of path length.

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L0 is average value of all path length travelled in the tour, i.e.

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T0 is average value of time required to travel in the tour, i.e.



i 1,2,....m



i 1,2,....m

Li / M

Ti / M

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Here M is total numbers of arc or path travelled. After this adaptive control, the initial pheromone of the algorithm is calculated as (10)

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 i  1    i  Ui

Based on the above control scheme, the navigational parameters of the humanoid path planning can be correlated to the AACO architecture, and the desired obstacle avoidance and goal following behaviour can be achieved.

3.3. Control Architecture It can be noted that all the artificial intelligent approaches are used to optimize a mathematical function rather than an engineering problem itself. Therefore, according to the need of the user, a mathematical function is formulated based on the governing parameters of the chosen problem and the algorithm optimizes the function itself. To implement the AACO algorithm in path planning problem of humanoids, a fitness function has to be defined using

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the necessary conditions of path planning which has to be optimized by the algorithm. Obstacle avoidance and target seeking are considered as the two important aspects in developing the fitness function for humanoid navigation. The working of the AACO

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algorithm and the implementation of the same in the current problem can be understood from Figure 5.

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OBSTACLE

ROBOT SENSING RANGE

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A

(XG,YG)

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Activation of AACO algorithm

(XR,YR)

Target

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C

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Starting point of the Robot

Figure 5: Working of AACO algorithm Let the humanoid robot is at point ‘A’ to begin the journey towards the target ‘C’. Here, the

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objective of the humanoid robot is to search an optimal step/position towards the target by using the AACO algorithm. The robot starts its journey from A towards C and reaches point B without using any navigational algorithm as there was absence of any obstacle. The controller of the robot is so designed that it is provoked only after detection of any potential obstacle by the sensory network. After getting sensor information that there is an obstacle near the position ‘B’, it starts processing and implementing the proposed algorithm to decide

its next step. In the first step, a number of ants belonging to an ant colony are virtually created around the obstacle, and the goal acts as the source which they are looking for food. After detection of the food source, the ants move towards the goal by avoiding the obstacle which is present ahead. They follow random paths while doing so; but always leave a pheromone trail. In between the pheromone deposition, the trail is updated considering the best position of the ants, and eventually all the ants finally come to an optimized path. After detection of the optimal path by the virtual ant colony, the robot proceeds towards its next

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step in the direction of the goal. It is clearly mentioned in the illustration that how safely the humanoid robot is avoiding the obstacle as well as obtaining its optimal steps/positions

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towards the goal ‘C’. After point ‘B’, many possible points are marked in the figure which

can be a next possible position for the humanoid, but it goes through the optimised one with the help of AACO navigational technique. In the colony, the ant having minimum value of objective function is taken as the optimal position, and that will be the next best step for the

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humanoid robot. Here, the optimization is a minimization problem as the primary aim is to

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maintain maximum distance from the obstacle and minimum distance from the goal. The

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fitness function is so designed that it takes care of both the above mentioned objectives. As mentioned earlier, obstacle avoidance and target seeking are the two primary issues those

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need to be resolved for safe navigation of humanoids. Therefore, the objective function is

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designed considering these two aspects primarily. 3.3.1. Objective function for obstacle avoidance behaviour

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The Euclidean distance between the nearest obstacle and the ant having global optima position can be formulated by the following equation in terms of objective function and is

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represented as:

DistOAnt Obs 

x

Obs

 xOAnti

 y 2

Obs

 yOAnti



2

(11)

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Where, xOAnti and yOAnti represents the x and y coordinates of the position belonging to the ant having global optima, xObs , yObs represents the x and y coordinates of the nearest obstacle and

DistOAnt Obs is the Euclidean distance between the position of the ant (having global optima) and the nearest obstacle.

By taking the reference of above objective function equation, the distance between the humanoid robot and the nearest obstacle can be evaluated by the following equation:

DistHRob NObs 

 xNObs  xHRob    yNObs  yHrob  2

2

(12)

Where xNObs , yNObs represents the x and y coordinates of the nearest obstacle and xHRob , yHRob

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represents the x and y coordinates of the humanoid robot. 3.3.2. Objective function for target seeking behaviour

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In the target seeking behaviour, we should keep a minimum distance between the ant (having global optimum value) and the target point. One robot has to move towards target means it

has the aim to go to the next best position from the previous position. The Euclidean distance between the best ant (having global optimum value) and the target can be calculated in terms

T arg et  xOAnti

 y 2

T arg et  yOAnti



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x

2

(13)

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DistOAnt T arg et 

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of objective function, by the following equation:

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Where, xT arg et , yT arg et are the at x and y coordinates of target position. xOAnti , yOAnti represents

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the x and y coordinates of the position belongs to the ant having global optima. Based on the two behaviours discussed above for the humanoid robot, the objective function

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equation of the individual ants having local optimum can be represented as:

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Objective function  Ofi   C1

1  C2  DistOAnt T arg et  Minimum  DistOAnt Obs 

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Obs j Obss

Let’s there are ‘m’ numbers of obstacles present in the environment, and they are represented as Obs1 , Obs2 , Obs3 , .................Obsm and their centre coordinates are

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 xObs1, yObs1  ,  xObs 2 , yObs 2  ,  xObs3 , yObs3  ..............  xObsm , yObsm 

respectively.

As per the limitations of the sensors implemented in the humanoid robot, it can recognize a limited numbers of obstacles in each move. Suppose the numbers of obstacles being sensed by the humanoid robot in some stages are represented as

Obss   Obs1 , Obs2 , Obs3 , .................Obsm  .

From the objective function equation written above, it can be easily perceived that when

OAnti is nearer to the target, the value of function DistOAnt T arg et will be reduced. And when

OAnti is away from the obstacle, the value of function Minimum  DistOAnt Obs  is increased. So Obs j Obss

from the above discussion, conclusion can be drawn that the path planning problem for the humanoid robot by the proposed technique is a minimization problem.

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In the objective function, there are two parts namely obstacle avoidance and target seeking. The first part is dependent upon the distance between the nearest obstacle and the robot, and the second part is dependent upon the distance between the robot and the destination. The

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primary objective in humanoid navigation is to maintain a maximum possible distance from

the obstacle and minimum possible distance from the target. Here, the optimization is chosen as a minimization problem. Therefore, the obstacle distance is kept in the denominator side,

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and target distance is kept in the numerator side. C1 and C2 act as the weightage given to both the individual parts of the final objective function. A threshold limit is set for the sensors of

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the humanoid to provoke the AACO algorithm. In this case, the threshold limit is set as 30

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cm. Once any object is detected within the threshold limit, the robot perceives it as a potential

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obstacle, and the algorithm is provoked. By this, a virtual ant colony is generated around the obstacle, and the target is perceived as the food source. The objective of the ant colony is to

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find a next best position for proceeding towards the goal by avoiding the obstacle present in the path. In between, many possible solutions are generated as the next best position. If the obstacle distance is more in initial position than the next possible position for an ant, then less

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weightage is given to the first part of objective function (C1). Similarly, if the target distance is more in the initial position than the next possible position, then less weightage is given to

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the second part of objective function (C2). In their respective movements, each ant deposits pheromone in the path which is updated according to the previously discussed criteria. In AACO algorithm, the output of the ant colony is a next best position to move. The final turning angle is calculated by simple geometric calculations as the angle between the initial

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and final position.

4. Proposed RA-AACO Hybrid Controller As already discussed, classical approaches are known to produce more converged results within a limited time with less accuracy while their counterparts AI approaches need relatively higher time to converge with a better accuracy. Humanoid navigation is a

challenging area of robotic investigation, and it requires both accuracy and convergence. The use of standalone intelligent approaches may not always be self-sufficient to solve complex engineering problems. They may also experience a problem of trapping at some local optima. Also, the navigation of multiple humanoids in a common platform requires higher end computing of the navigational parameters. Therefore, to increase the efficiency of the standalone algorithms, hybridization techniques are employed. In the current work, RA is hybridized with AACO algorithm. To do the same, sensory information regarding the

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obstacle distances are first fed to the RA controller. The output from the RA controller which is Interim Turning Angle (ITA) is again fed to the AACO controller to obtain the final

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turning angle. Figure 6 represents the hybridization scheme used in the present study.

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Figure 6: Scheme of hybridization

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The steps of the RA-AACO hybrid controller for humanoid navigation can be listed as below. Step 1: Initialize the start and goal position of the humanoid robot.

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Step 2: Navigate the robot towards its target until it is encountered by any obstacle. Step 3: Call RA algorithm when any obstacle comes in the target path. Step 4: Sensory data regarding FOD, LOD, and ROD are implemented to the controller and ITA is evaluated. Step 5: Initialize the parameters and the pheromone trail of the AACO algorithm.

Step 6: Determine the best local position of each ant and keep it in ascending order. Assign the ITA value to the best position. Step 7: Determine the best global position (optimum value of ITA) of the ant colony. Step 8: Update the pheromone trail. Step-9: Repeat the step-4 to step-8 until the humanoid robot reaches to the target by avoiding

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all the obstacles. Figure 7 represents the pseudo code for the RA-AACO technique that has been implemented

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in the current investigation. Start

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Feed the input parameters to the RA controller Calculate the ITA Feed ITA to AACO algorithm and activate AACO Controller Initialize the parameters  ,  ,  , i, j

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Initialize the pheromone trail Pj

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Generate m numbers of ants as population size

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Calculate  ij

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Calculate fitness of each individual ant Determine the best local position of each ant

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Determine the best global position of the ant colony Update the pheromone trail U i

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Stop when maximum iteration is reached or minimum error condition satisfied Calculate the FTA. Stop

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Figure 7: Pseudo code for the proposed RA-AACO controller 5. Petri-Net Control Architecture for Inter-Collision Avoidance

The Petri-Net Controller was first proposed by Peterson [56] for dynamic obstacle avoidance. Figure 8 represents a Petri-Net System that has been designed to avoid inter-collision among multiple humanoids when they navigate in a common platform.

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Figure 8: Proposed Petri-Net model for avoidance of inter-collision

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By attempting navigation of multiple humanoids in a common platform, each humanoid acts as a dynamic obstacle for the other ones. The Petri-Net model consists of six tasks or states.

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The position of the token defines the present state of the humanoid. First, it is considered that the humanoids are in an unknown environment where their positions and that of the obstacles and targets are not known. Initially, each of the humanoid is at state-1 for performing task T1, which implies the waiting signal for start. A current state is represented by a token. After

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receiving the command, the humanoids start finding their respective targets. Now the humanoids are in state-2 performing the task T-2 which is movement of the humanoids towards the goal by avoiding the obstacles. During the motion of the humanoids, a situation of conflict arises if two humanoids come in the influence of each other by their path towards the goal. This state is defined by the task T-3 which is the task of conflict detection among the robots. Now two robots which are in conflict for navigation will negotiate between

themselves and take a decision for navigation according to the priority. Here, the state-4 represent the task of negotiation represented as task T-4. In this case, the robot having less distance to reach the goal is given higher priority than the other one. When the conflict is solved, the robots will go for checking any other conflict and will execute their motion represented by task T-5. Suppose there is a third robot which finds two robots in a conflicting situation in its path then the priority of the third robot will be less as it has taken late entry towards the conflict and it will be treated as a static obstacle as represented by T-6 and will

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wait for resolve of the conflict. After the solution, the robot will be able to enter for task T-2. In this way, by the proposed Petri-Net model, all the humanoids can move simultaneously

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without becoming a hindrance in each other’s path.

6. Implementation of the Proposed RA-AACO Controller in Humanoid Navigation After designing the logic of the proposed hybrid navigational controller and the Petri-Net

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model for the avoidance of inter-collision among them, the testing of the controller was

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performed in both simulation and experiment platforms. It can be noted that the use of Petri-

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Net model is only required for the navigation of multiple humanoids and for single humanoid navigation, it is not required. Humanoid NAO has been chosen as the humanoid platform on

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6.1. Humanoid NAO

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which the testing of the proposed hybrid navigational controller is intended.

Being a small sized programmable robot designed by Aldebaran Robotics group, France,

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humanoid NAO has gained immense popularity by replacing Sony’s AIBO. NAO of version V4 has been used in the current work. NAO has a height of 58 cm and weight of about 5 kg. NAO is equipped with several sensors [57] such as sonars, infrared sensors, accelerometers,

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gyroscope, force sensitive resistors, etc. Encoders are also fitted with the NAO so that the value of the joint torques and the force exerted on the ground can be recorded in any time. NAO can be coded and controlled with Python language with the help of choregraphe

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interface developed by the designers of NAO. The sensory network of the humanoid NAO is capable of detecting and measuring the obstacles present in the environment. 6.2. Navigation of a Single Humanoid NAO in a Complex Environment V-REP has been chosen over several simulation software that are available for analysis of humanoid navigation because of the ease of performing humanoid simulations and better obstacle detection and avoidance. V-REP works on LUA language which is based on ANSI C

language. An environment of size 200 x 250 units with random numbers of static obstacles (5 for scene 1 and 6 for scene 2) has been created in the simulation window of the software. By considering the logic of RA-AACO navigational controller, a program has been written and implemented in the NAO humanoid. Specific start and destination positions were also defined, and the humanoid was set to navigate through the obstacles present in the arena to reach the destination position. Figure 9 and Figure 11 represent the simulation results obtained from the V-REP software for the navigation of single NAO in scene 1 and scene 2

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respectively.

IP T SC R U N A M ED PT CC E A Figure 9: Simulation results for navigation of single humanoid NAO in scene 1

It can be observed from Figure 9 (a) and Figure 11 (a) that initially, the NAO was set at a source point and a specific destination point was provided. The two blue boxes represent the source point and destination point. Five number of static obstacles were set at random positions in scene 1, and six number of obstacles were present in scene 2. It was noticed that the humanoid was successful in avoiding the obstacles present in the arena and reached safely to the goal by the use of the proposed controller. The humanoid has also followed the shortest path during its navigation. The path length covered by the humanoid from the start to the

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destination position and the time taken to cover this path length were noted from the V-REP simulation window itself and recorded for further analysis.

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To validate the effectiveness of the proposed RA-AACO controller, the simulation results

were also tested against real time experiments. An actual environmental set-up was designed under laboratory conditions to test the results obtained from the simulation analysis. To

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maintain the same environment size, the actual platform to conduct the experiment was chosen as 200 x 250 centimeters. Specific numbers of static obstacles were selected and

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placed at same positions as that of the simulation environment. Specific start and goal

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positions were defined for the humanoid. The humanoid was coded by using the logic of the

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RA-AACO controller. In the actual environment, the NAO was operated by a Wi-Fi control. After the environment was set up, the navigation of NAO was observed and analyzed. Figure

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10 and Figure 12 represent the snapshots taken during the actual experiment that was

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performed in the laboratory for scene 1 and scene 2 respectively.

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Figure 10: Experimental result for the navigation of single humanoid NAO in scene 1

IP T SC R U N A M ED PT CC E A Figure 11: Simulation results for navigation of single humanoid NAO in scene 2

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Figure 12: Experimental result for the navigation of single humanoid NAO in scene 2 It can be noted from Figure 10 (a) and Figure 12 (a), that the environmental conditions are kept exactly same as was done in case of the simulation software. The two blue boxes represent the start and destination position for the humanoid. Specific numbers of static obstacles are kept at similar positions as was in case of simulations. After the environment was set up, the NAO was started for its navigation. It was observed that the humanoid NAO was able to avoid all the obstacles that were present in the path and reach the desired target

safely. The humanoid has also followed the shortest path during its travel. In the actual environment, the path length from source to destination was measured by using a measuring tape, and a stopwatch was used to measure the time taken to reach the target. The purpose of recording path length and time required to travel the path is that a comparison can be performed between the simulation and experimental results. As stated earlier, the effectiveness of the proposed navigational controller can only be checked by the proper comparison between the simulation and experimental results regarding the navigational

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parameters, which are the path length and time taken to reach the target. After recording the

navigational parameters for respective environments, the comparison for path length and time

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taken was done and is represented in Table 2 and Table 3 respectively. It is to be noted that

quite large number of experiments were performed for the navigational control of humanoid NAO using RA-AACO controller and only a few have been shown here.

Table 2: Comparison of the path length between simulation and experiment for navigation of

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304.9 306.9 306.1 304.7 305.8 306.7 305.5 305.3 304.4 306.2 305.65

4.43 5.21 4.54 4.79 4.58 5.58 4.84 5.18 4.20 5.13 4.85

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Error in %

Simulation Path Length (cm)

Experimental Path Length (cm)

Error in %

295.6 295.9 296.5 297.1 295.1 296.7 297.2 296.4 296.9 295.8 296.32

309.4 310.4 311.7 313.5 311.6 310.6 311.8 310.2 309.9 309.8 310.89

4.46 4.67 4.87 5.23 5.30 4.48 4.68 4.45 4.19 4.52 4.69

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Experimental Path Length (cm)

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1 2 3 4 5 6 7 8 9 10 Average

Scene 2

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Number of Runs

Scene 1 Simulation Path Length (cm) 291.4 290.9 292.2 290.1 291.8 289.6 290.7 289.5 291.6 290.5 290.83

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single humanoid NAO

Table 3: Comparison of the time taken between simulation and experiment for navigation of single humanoid NAO

Error in % 4.53 5.56 7.12 4.32 5.97 6.81 4.87 7.31 5.29 4.34 5.61

Scene 2 Time Taken in Simulation (sec) 35.81 35.9 36.35 36.82 35.7 36.5 37.15 36.48 36.71 35.96 36.338

Time Taken in Experiment (sec) 37.92 38.21 38.85 39.3 37.74 38.9 39.78 39.07 38.92 37.98 38.667

Error in % 5.56 6.05 6.44 6.31 5.4 6.17 6.61 6.63 5.68 5.32 6.02

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Time Taken in Experiment (sec) 37.08 39.04 37.93 36.82 38.5 37.3 38.6 37.19 37.8 38.25 37.851

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Number of Runs

Scene 1 Time Taken in Simulation (sec) 35.4 36.87 35.23 35.23 36.2 34.76 36.72 34.47 35.8 36.59 35.727

It can be observed from Table 2 and Table 3 that the experimental results for path length and

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time taken always show higher values than their simulation counter parts. The cause for the

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same is that, during simulation, the results obtained are the ideal ones without any external hindrance. However, during the real time experiment, several factors such as frictional forces,

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slippage between the foot of humanoid and the environment floor, loss of data during

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transmission through Wi-Fi control may come into account. The average percentage of errors for both path length and time taken are within 6% which is well within the acceptable limit.

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The results signify that the proposed hybrid controller works well in both simulation and experimental platform under complicated environmental conditions.

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6.3. Navigation of Multiple Humanoid NAOs in a Complex Environment Three humanoid NAOs are considered for the navigation of multiple humanoids in a common

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platform in the current work. The environment size is kept same as the one used for single humanoid navigation. Random numbers of static obstacles (4 for scene 1 and 6 for scene 2) are considered in the analysis at several positions. Each humanoid has its own predefined

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source and destination position. It can be noted that the rules of RA-AACO navigational controller can avoid the obstacles but not decide regarding the priorities if a conflicting situation arise. Therefore, along with the RA-AACO navigational controller, the logic of the Petri-Net controller is also considered in the current problem. The environment size for multiple humanoid navigation is kept as 200 x 250 units. Along with the static obstacles, each humanoid acts as a dynamic obstacle for the other two. The three humanoid NAOs (denoted as N1, N2, and N3) have their predefined source or start positions (denoted as S1, S2 and S3)

and goal or target positions (T1, T2 and T3). A program has been written in the LUA language using the combined logic of both RA-AACO navigational controller and Petri-Net controller, and it was implemented in all the three humanoids. After the setting of the environment, all the three humanoids were set to move towards their respective destinations. Figure 13 and Figure 15 illustrate the results obtained from the simulation of multiple humanoid navigation in a common platform for scene 1 and scene 2 respectively. It can be observed from the results obtained from the simulation software; all the humanoids were

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successful in avoiding the obstacles present in the path and also the fellow humanoids which acted as the dynamic obstacle for each other. The path length and time taken for all the

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humanoids were recorded separately for further analysis.

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experiment regarding the navigation of multiple humanoid NAOs under laboratory conditions for scene 1 and scene 2 respectively. It can be observed from the results that similar to the navigation of single humanoids, the navigation of the multiple humanoids was also successful using the proposed technique. All the humanoids avoided the obstacles that were present in the path and reached their respective destinations without colliding with fellow humanoids and also tackling conflicting situations. The path length and time taken for each humanoid

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were recorded for further analysis.

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Figure 14: Experimental results for the navigation of multiple humanoid NAOs in scene 1

IP T SC R U N A M ED PT CC E A Figure 15: Simulation results for the navigation of multiple humanoid NAOs in scene 2

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Figure 16: Experimental results for the navigation of multiple humanoid NAOs in scene 2

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The results obtained from the simulation and experiments for path length and time taken for each humanoid were compared against each other for each scene separately. Table 4 and Table 5 represent comparison of path length and time taken for scene 1 and Table 6 and Table 7 represent the same for scene 2 respectively.

Table 4: Comparison of the path length between simulation and experiment for navigation of multiple humanoid NAOs in scene 1

N3 286.3 285.4 288.1 287.5 286.5 286.3 287.1 286.2 285.8 285.9 286.51

Experimental Results

Errors in %

N1 259.5 259.2 260.5 261.6 262.1 260.7 261.9 262.4 263.5 263.8 261.52

N1 4.78 4.75 5.07 5.59 5.65 5.18 6.26 5.37 6.34 6.18 5.51

N2 238 238.1 237.9 238.2 237.8 236.6 237.8 239.1 239.2 237.4 238.01

N3 304.1 305.2 304.7 305.8 302.6 303.4 304.9 302.8 303.4 306.5 304.34

N2 4.83 4.45 4.04 5.46 4.42 3.04 4.79 5.56 4.74 4.42 4.57

N3 5.85 6.49 5.45 5.98 5.32 5.64 5.84 5.48 5.80 6.72 5.86

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1 2 3 4 5 6 7 8 9 10 Average

Simulation Results Time required in sec N1 N2 247.1 226.5 246.9 227.5 247.3 228.3 247 225.2 247.3 227.3 247.2 229.4 245.5 226.4 248.3 225.8 246.8 227.9 247.5 226.9 247.1 227.12

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No of runs

Table 5: Comparison of time taken between simulation and experiment for navigation of multiple humanoid NAOs in scene 1

N3 37.5 37.1 37.51 39.66 37.78 36.24 39.4 36.2 36.3 37.5 37.519

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N2 29.68 29.85 30.9 27.8 30.5 28.9 29.7 28.9 30.34 28.81 29.538

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N1 31.9 31.73 32.5 32.4 32.5 32.45 31.5 34.32 32.5 33.8 32.56

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Experimental Results

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Simulation Results Time required in sec N1 N2 N3 30.5 28.3 35.6 30.2 28.65 34.7 30.6 29.4 34.5 30.25 26.5 37.2 30.7 28.6 35.9 30.65 27.5 34.1 29.5 28.15 36.95 32.5 27.3 34.2 31.2 28.9 34.9 31.5 27.85 35.05 30.76 28.115 35.31

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No of runs

Errors in % N1 4.39 4.82 5.85 6.64 5.54 5.55 6.35 5.3 4 6.8 5.53

N2 4.65 4.02 4.85 4.68 6.23 4.84 5.22 5.54 4.75 3.33 4.82

N3 5.07 6.47 8.02 6.2 4.98 5.91 6.22 5.52 3.86 6.53 5.89

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Table 6: Comparison of the path length between simulation and experiment for navigation of multiple humanoid NAOs in scene 2 Simulation Results Time required in sec N1 N2 290.5 296.42 291.2 297.16 292.64 295.68 290.85 296.58 291.36 296.15 292.15 296.8 291.68 295.63 290.92 295.9 291.61 297.18 292.43 296.24 291.53 296.37

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No of runs

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N3 255.7 256.4 257.91 256.92 256.73 257.36 257.19 255.94 256.92 256.46 256.75

Experimental Results

Errors in %

N1 303.6 304.5 306.5 303.9 305 306.8 304.8 303.7 305.7 306.9 305.14

N1 4.31 4.37 4.52 4.29 4.47 4.78 4.3 4.21 4.61 4.71 4.46

N2 310.5 311.8 309.6 310.9 311 311.5 310.2 310.3 311.6 310.6 310.8

N3 268.8 270.1 270.9 269.8 269.4 271.4 271 269.1 270.2 269.8 270.05

N2 4.53 4.7 4.5 4.61 4.77 4.72 4.7 4.64 4.63 4.62 4.64

N3 4.87 5.07 4.8 4.77 4.7 5.17 5.1 4.89 4.91 4.94 4.92

Table 7: Comparison of time taken between simulation and experiment for navigation of multiple humanoid NAOs in scene 2 Experimental Results

Errors in %

N1 38.2 38.65 38.9 38.24 38.86 39.1 38.79 38.26 39.04 39.11 38.72

N1 4.97 5.25 5.22 4.94 5.76 5.09 5.28 5.04 6.17 5.01 5.27

N2 39.56 40.06 39.57 39.72 39.84 39.81 39.85 39.64 39.93 39.6 39.76

N3 33.6 33.87 34.05 33.76 33.85 34.28 34.16 33.9 33.98 33.83 33.93

N2 5.16 4.79 5.76 5.34 6.12 4.9 6.68 5.95 4.58 5.35 5.46

N3 4.91 5.23 4.02 3.97 4.02 5.05 4.95 5.6 4.15 4.26 4.62

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Simulation Results Time required in sec N1 N2 N3 36.3 37.52 31.95 36.62 38.14 32.1 36.87 37.29 32.68 36.35 37.6 32.42 36.62 37.4 32.49 37.11 37.86 32.55 36.74 37.19 32.47 36.33 37.28 32 36.63 38.1 32.57 37.15 37.48 32.39 36.67 37.59 32.36

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No of runs

The results obtained from the experimental data show a higher value as was the case for navigation of single humanoid. The reason for the same has been already described in the

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previous subsection. In the navigation of multiple humanoids also, the average error is within

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7 % which is well inside the acceptable range. The agreement of results between simulation

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and experimental platforms for navigation of single as well as multiple humanoids in complex environments give a significant insight into the effectiveness of the proposed

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controller. The controller is also tested against other approaches in the following section.

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7. Comparison of the Proposed RA-AACO Controller with other Existing Navigational Controllers

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The effectiveness of the proposed RA-AACO navigational controller was validated through multiple simulations and experiments with minimal percentage of errors. However, it is

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simultaneously important to test the controller with other existing navigational methods. To do the same, a Fuzzy-Wind Driven Optimization (FWDO) [58] and Adaptive Neuro Fuzzy Inference System (ANFIS) [59] based navigational controllers developed by Pandey et al. was considered. Here, the navigation of a single robot was compared with FWDO method

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and navigation of multiple robots was compared with ANFIS method. Figure 17 and Figure 18 represent the comparison of the proposed RA-AACO method with FWDO method in terms of path trajectory and Table 8 demonstrates the path length comparison.

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Figure 17: Path obtained by FWDO method for single robot [58]

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Figure 18: Path obtained by RA-AACO method for single robot Similarly, Figure 19 and Figure 20 represent the comparison among ANFIS method and RAAACO method in terms of path trajectory and Table 9 demonstrate the path length

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comparison.

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Figure 19: Path obtained by ANFIS method for multiple robot [59]

Figure 20: Path obtained by RA-AACO method for multiple robot

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Table 8: Comparison of FWDO and RA-AACO method in terms of path length for single

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Technique used

Path length in cm

FWDO [58] (Figure 17)

243.9

RA-AACO (Figure 18)

233.7

Deviation in %

4.18

Table 9: Comparison of ANFIS and RA-AACO method in terms of path length for multiple robot Path length in cm

Technique used

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Robot 3

ANFIS [59] (Figure 19)

394.5

288.7

432.6

RA-AACO (Figure 20)

374.2

271.3

407.9

Deviation in %

5.15

6.03

5.71

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From the comparison of the proposed controller with other existing navigational methods, an

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enhancement of about 4-6% was obtained. Here, RA-AACO achieves better results than FWDO and ANFIS methods. The reasons for the same can be discussed as follows. The proposed hybridization scheme combines a classical technique with a computational intelligent method. It inherits the advantages of quick convergence from the regression

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method and better accuracy from the AACO method. The two step hybridization provides a

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refined result than the standalone one. AACO method operates in parallel mode for

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optimization using the pheromone deposition. Online positive feedback by updating pheromone accounts for rapid discovery of good solutions. This is somewhat lacking in

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FWDO and ANFIS methods. FWDO lacks in population diversity. For a problem of multiple parameters with multiple variables, implementation of RA-AACO is simpler compared to

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FWDO and ANFIS as the latter two techniques require fine-tuning of parameters for robot path planning in a very complex unknown environment. Due to parallel feedback in dynamic

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environments, RA-AACO is better suited to unforeseen changes in the environment as observed from the results. Hence, the efficiency of the proposed RA-AACO navigational

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controller is on an enhanced mode than the existing methods. 8. Conclusions

With the gaining popularity of the humanoids over several fields of application, path planning

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and navigation of humanoids has emerged as one of the most promising area of research. In this paper, a novel scheme of hybridization was proposed for navigational control of humanoid robots. Here, a regression controller was hybridized with an adaptive ant colony optimization controller. To test the effectiveness of the proposed controller, it was tested in both simulated and experimental environments. To navigate multiple humanoid robots in a common platform, a Petri-Net controller was designed for avoidance of inter-collision. The

results obtained from both the environments were compared against each other, and a good agreement between them was found. The proposed controller was successful in navigation of single as well as multiple humanoid robots. The proposed RA-AACO navigational controller can be used as a robust technique for navigation of humanoids as well as other forms of robots. This research would definitely be beneficial for researchers dealing with navigational

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aspects of humanoids and other similar kind of robots.

References 1. Parhi, D.R. and Singh, M.K., 2009. Real-time navigational control of mobile robots using an artificial neural network. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 223(7), pp.1713-1725. 2. Singh, M. K., Parhi, D. R., Bhowmik, S., & Kashyap, S. K., 2008, October. Intelligent controller for mobile robot: Fuzzy logic approach. In The 12th International Conference

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