Fuzzy based self-tuned move lengths for enhanced performance of gas source localization algorithm

Abstract

The world has witnessed a lot of catastrophes in recent times due to chemical gas leaks. The core problem is untimely or sudden happenings of calamity for which humans are not prepared to take appropriate actions. Hence robotic gas source localization can be considered as an alternative to prevent such catastrophes. This paper presents an improved approach to an existing chemotactic plume tracing algorithm with self-tuned move length/step size. The technique uses the proposed fuzzy inference model to produce the move lengths for the next walk based on the input of gas concentration magnitude in the present state. The move lengths correspond to either the plume finding or plume tracing stage with which a mobile robot surges for the next step. Dynamic plumes under eight different simulated environments are created to evaluate the proposed approach rather than plumes in laminar flow for a more realistic case. Performance analysis of the algorithm is based on success rate with self-tuned move length compared with fixed move length. In addition, there is an analysis of step size parameters that vary concerning a particular environmental condition. Results show that adaptive step size can increase the success rate of the plume tracing algorithm and consequently improve search performance and efficiency.

Keywords

Gas source localization fuzzy inference autonomous mobile robot environmental monitoring dynamic plumes

1. Introduction

One of the very basic behaviors observed in the animal kingdom is foraging or finding prey. It is important for an animal’s survival and enhances its chances to reproduce in its habitat [1]. But the question arises, how can an animal find its prey or food? May be catching up to the chemical signatures released from food sources [2, 3, 4]. It has let humans understand this act, generally referred to as odor source localization (OSL), gas source localization (GSL), or chemical source localization (CSL).

Gas signatures are present in different drug materials, land mines, and human bodies buried under debris due to any natural calamity or building collapse [5]. Even in industrial setups chemical gas leaks occur frequently, hence GSL can be of utmost importance considering recent disasters in industries. These pose threats to many living beings and humans living in the vicinity of industry setups. In a recent incident, 178 women working at a chemical plant in Andhra Pradesh’s Visakhapatnam fell sick after a gas leak [6]. At least 25 workers fell ill after an ammonia gas leak at balasore factory, in Odisha [7]. These accidents are unalarmed and require continuous monitoring to avoid catastrophes.

GSL can be defined as a three-stage search process that starts with an attempt to contact the odor packet and continues to climb the chemical gradients for a maximum time until the source of release is identified/found/declared at the last [8]. However, the problem of GSL becomes difficult as the odor plumes are patchy and intermittent as they propagate away from the source [9]. Chemical gradients provide markers to find and track the chemical trail while in pursuit. Usually, moths traverse upwind to catch sex pheromones (sporadic chemical gradient) to locate their female counterparts for mating [10]. It exhibits a well-defined behavior of surge-cast that has been extensively used in robotic GSL [11]. Similarly, the behavior of lobsters [12], blue crabs [13], and dung beetle [14] has been well-studied for CPT. These behavior-based modeled bio-inspired algorithms have improved with time. Performance enhancements of bio-inspired algorithms are often achieved with search parameters, surge distance, and casting [15]. It has certain limitations such as likely failure in dynamic environments and improvement scope is constrained. In comparison to this, other classes of algorithms such as multi-robot [16] and engineering-based algorithms [17] can also be improved. Somewhat the exploration and exploitation compensation in the multi-robot approach is evident. Similarly, performance enhancement with machine learning is also viable [18, 19]. Fuzzy controllers are also used for decision-making [20, 21, 22] and maneuvering [23] of mobile robots in OSL. But at the core, move length or surge distance and turn angles decide the chances of getting in contact with plumes or tracing the plume for maximum duration. Hence, the move length in the plume finding and plume tracing stage is important but hardly explored.

Therefore, in this paper, the focus is on improving the search performance of a plume tracing algorithm rather than proposing or devising a new algorithm. The methodology targets the move length as an important factor that can affect the success rate of the source-seeking algorithm and eventually improve search performance. Hence the author would like to highlight the importance of two search parameters namely plume finding and plume tracing move length. It is proposed in this paper that auto-tuned plume finding and plume tracing move length can increase the success rate as compared to fixed move lengths. The main contributions of this paper are:

1.
Enhancing the plume tracing algorithm for better search performance
2.
Fuzzy-based self-tuned move lengths to improve success rate
3.
Analysis of parameters based on step size

The remainder of the paper is organized as follows: Section 2 gives the research background of the stated problem; Section 3 discusses the problem formulation; Section 4 is about the materials and methods; Section 5 gives details about the results and discussions; Section 6 discusses the conclusions of the paper. Section 7 discusses the future work of the present work.
2. Literature survey

Many organisms inspired robotic GSL with their source-seeking behavior. Its adaptation into amalgamated algorithms and hardware resulted in gas-locating robotic platforms. Similarly, there have been attempts to formulate mathematical and physics-based approaches to locate chemical sources. The multi-robot approach has emerged as a promising method to successfully locate sources and eradicate the drawbacks of single source-seeking mobile robots. Irrespective of any source-seeking method, different algorithm advancements have been reported. It required improvements in algorithms and hardware design owing to the ephemeral nature of chemical plumes. Over the years source-seeking algorithms have been modified considering turbulence as one of the main factors.

Liberzon et al. proposed an odor-based navigation strategy in a windy environment for the flier to locate a pulsating source upwind. This strategy exploited the physical characteristics of turbulent flow having intermittent puffs of odor. It used an instantaneously measurable quantity “puff crossing time” in turbulent plumes which enables a single threshold-based detection sensor. This approach was found to improve the success rate as compared to zig-zag strategy using intermittent contact [24]. Okajima et al. built an odor-sampling device to introduce a flicking mechanism in a self-developed differential drive mobile robot that mimicked the programmed behavior of male silkmoth. A pair of odor-sampling devices resembled dual antennae and were placed on left and right sides of the mobile robot. The inter-antennal angle (IAA), the angle between the pair of odor sampling devices can be varied from minimum (70 ${}^{\circ}$ ) to maximum (140 ${}^{\circ}$ ) corresponding to phases of the programmed behavior namely surge, zigzag and loop. The flicking mechanism improved the CPT performance [25]. Rahbar et al. proposed a bio-inspired 3D odor navigation algorithm. It was inspired by spiraling movement and upwind-surge behavior of moths that were fitted to the plume tracing stage of OSL. For the plume acquisition stage crosswind levy walk was selected. The success rate was found to improve for the proposed bio-inspired 3D algorithm (surge-spiral) as compared to 2D algorithm (surge-cast). Experiments were performed both in simulation and with a real Khepera IV robot [26].

Yan et al. introduced modified particle swarm optimization (PSO) algorithms for multi-robots for gas source seeking. They introduced “Request and Reset” strategy to guaranteed convergence PSO (GC-PSO) and Dissipative PSO (D-PSO) algorithms. The proposed modified algorithm was found to perform better in terms of success rate and iteration time [27]. Duisterhof et al. used a swarm of nano quadcopters for gas-seeking applications. They introduced a novel particle swarm optimization (PSO)-powered bug algorithm called “Sniffy Bug”. The parameters of “Sniffy Bug” were also optimized by “AutoGDM” (fully automated end-to-end environment generation and Gas Dispersion Modeling pipeline) [28]. Search and rescue system (SAR) was designed for unmanned aerial vehicles (UAVs) to maximize the probability of target detection and minimize the search time. Re-configuring the UAVs to counter failures and continue the mission was targeted in the work with a focus on the minimum amount of control information shared among them [29].

Song et al. proposed collaborative infotaxis that was relatively fast and low-cost. The particle filter in conjunction with gaussian fitting enhanced the search efficiency in cluttered environments with a smaller number of particles and utilizing a narrow communication bandwidth [30]. Yungaicela-Naula et al. compared different metaheuristic algorithms for pollutant source localization for unmanned aerial vehicles (UAVs). Improved simulated annealing was used to trace the plume and Bayesian method generated the probabilistic map of the source location [31]. Jabeen et al. proposed gradient adaptive extremum seeking control (GA-ESC) for OSL. It was an improvement to basic ESC that has three-point gradient estimation technique to approximate odor gradient. Adaptive feedback gain was also introduced to link the estimated gradient with output quantity. Global searching capability was enhanced with perturbation amplitude adjustment (PAA). The proposed approach improved the success rate and average searching time [32].

The move length and turn angle modifications can also be important criteria to enhance an algorithm for better search performance. One of the benchmarks reported by Lu, considered the office-like environment with chemical release from a source kept in one of the rooms. The primary investigation was on the advantageous start positions and the role of surge distance while in pursuit of the chemical source. It was concluded that there are no advantageous start positions and variable surge distances perform better than fixed in general [33]. There was a novel thought of accumulation of micro steps for underground odor sources with an autonomous mobile robot on the ground with gas sensor. It improved the search performance of the classical zigzag path algorithm and hexagon-path algorithm proved through computer simulations. It avoided some basic defects of real chemical sensors and also the difficult task of step size selection [34]. An algorithm was proposed namely time varying moth-inspired (TVMI) by Shigaki et al. [18]. It was formulated using the electromyograms (EMGs) data of flight muscle of male silkmoth and input to the trained support vector machines (SVM) to estimate the surge state. Depending upon the number of chemical stimuli the surge state can change. They further introduced the TVMI algorithm. Shigaki et al. further introduced a fuzzy controller for decision-making on switching between one of the three states namely ‘surge’, ‘stop’ and ‘casting’ according to environmental conditions [35]. For plume finding spiral movements had been incorporated as an algorithm and validated with a self-developed mobile robot [36]. However, the variation in straight paths for plume finding has been also considered which can provide better results. A novel plume-finding strategy namely levy-taxis was proposed that performed better than levy walk, correlated random walk and systematic zigzag [37]. It was further improved, and the key parameters of levy-taxis were tuned concerning odor gradient. It was named adaptive levy taxis and found to perform better than well-established moth-inspired algorithms [38]. Chen et al. proposed a fuzzy model to adaptively tune the parameters of a probability distribution of turning angle and move length in different environmental conditions. It was found to perform better than adaptive levy taxis [39]. The fuzzy model was also used for decision-making based on the fused information of the source probability map and plume distribution map. A path-planning algorithm was generated with model-based reinforcement learning [40]. A fuzzy controller was proposed for a mobile robot to auto-adjust the trajectory parameters according to environmental conditions [41].

Therefore, the tuning of plume finding and plume tracing has been hardly explored, and too with a non bio-inspired approach. In this paper, the existing chemotaxis plume tracing algorithm (veco-taxis) has been adopted for further improvement which worked well in the laminar flow. It’s now used in turbulent environments and has shown that better success rate can be achieved with fuzzy based self-tuned move lengths.

Figure 1.

The gas molecules are dispersing in the positive x direction and a mobile robot is pursuing the chemical cues upwind with A: fixed move lengths, B: Variable move lengths.

3. Problem formulation

Gas source localization can be performed by plume tracing algorithm namely veco-taxis. However, the improvement scope still exists as the algorithm performed poorly in turbulent flow as reported in previous work [42]. Maybe the performance enhancements depend on move lengths and turn angles as discussed in Section 2. Here two cases are taken into consideration. The first case belongs to fixed move lengths in both plume tracing and plume finding stages. It is shown in Fig. 1(A). The second case belongs to variable move lengths for the two stages which is shown in Fig. 1(B).

It is hypothesized in this paper based on literature review that tuned/variable move lengths can result in higher success rate as compared to fixed move lengths. Hence, in the present work fuzzy inference model is proposed to adapt the move lengths based on concentration values.

4. Materials and methods

4.1 Simulated robot and its environment

The simulation framework uses a simulated differential drive mobile robot with gas sensors (Refer first point in Appendix A: Supplementary data). The arena considered for simulation is 50 m by 25 m and the source is kept at (5,12.5) m. To realize the same in a simulation environment (SE) a representative figure of 720 by 360 pixels was used enclosed by black pixels considered to be a bounded wall. The SE with five different start locations is shown in Fig. 2.

The dimensions are equivalent to 14.4 pixels equal to 1 m in real conditions. As a special case, two MATLAB windows are used. The reason is that the first MATLAB window is engaged in running the plume data at a rate of 1 data/0.5 sec and the second MATLAB window is dedicated to triggering the action of gas source localization. The two MATALB windows can communicate with each other and consider the continuous plume run and gas source localization as independent events [42].

4.2 Dynamic plume generation and test cases

Table 1
Simulation environment description with parameters

Simulation Environment	Kx	Ky	Noise gain ( $\eta$ ) ${}^{*}$	Drel
SE1	10	10	2	0
SE2	10	10	2	2
SE3	10	10	20	0
SE4	10	10	20	2
SE5	20	20	2	0
SE6	20	20	2	2
SE7	20	20	20	0
SE8	20	20	20	2

${}^{*}$ Input gain constant for boundary condition noise generation. Drel is the scaling coefficient of diffusion of puffs. Kx and Ky are the diffusion constants in X and Y directions respectively.

Figure 2.

Different release points of mobile robot with gas source in experiment arena.

Figure 3.

Plume generation for 250 ${}^{\text{th}}$ sample (a) SE1 (b) SE2 (c) SE3 (d) SE4 (e) SE5 (f) SE6 (g) SE7 (h) SE8.

A simulated mobile robot (Refer Appendix A) uses data and figure files of dynamic plumes based on a filament-based atmospheric dispersion model [43]. To generate the data an open-source code was used [44] and the same was imported into MATLAB software. There are four parameters to generate eight different simulation environments (SEs). The four parameters are furnished in Table 1. Eight different SEs are shown in Fig. 3. Maximum simulation time is 300 secs. Wind velocity is 1 m/s along the x-axis.

4.3 Algorithm improvement methodology

Veco-taxis algorithm is selected as a plume tracing algorithm for improvement (Refer first point in Appendix A: Supplementary data). A detailed description of the simulated mobile robot with the arrangement of gas sensors can be also found in previously published work [45]. This subsection outlines the methodology used to improve the adopted veco-taxis algorithm.

4.3.1 Self-tuned move length/Variable move lengths

Plume finding and plume tracing move length is an improvement factor in algorithm performance. Tuning of these move lengths is implemented using the fuzzy inference method. There are three membership functions and decisions were taken based on plume concentration as input. There were several trials to get the appropriate move length range of plume finding and plume tracing according to the environment area. Attributes of fuzzy logic controller are provided in Table 2 and logic rules are provided in Table 3.

Table 2
Attributes of fuzzy-based adaptive step size controller

S. N	Attributes		Membership functions
1	FIS type	Mamdani	$-$
2	Defuzzification	Centroid	$-$
3	Rules	Four	$-$
4	Input	One, Normalized concentration, range (0 to 45)	Four
5	Output	Two; plume finding step size ( $L_{\text{min}}$ ), range (0.1 m to 0.5 m), and plume tracing step size (0.1 m to 3 m)	Three and three respectively

According to Table 2, the $L_{\text{min}}$ generated as the output of fuzzy block will help to calculate the actual plume finding step size by the following Eq. (1)

$\displaystyle M_{l}=L_{\text{min}}.r^{\frac{1}{1-\mu}}$ (1)

Where $M_{l}$ is plume finding length, ‘ $r$ ’ a random variable uniformly distributed $r\in\left[{0,1}\right]$ , $L_{\text{min}}$ the minimum move length, and $\mu$ (levy-index) the move length’s key parameter (1 $<\mu\leqslant$ 3). $\mu$ has been set to maximum value i.e., equal to 3.

Table 3

Fuzzy Logic rules

Rule	Normalized concentration	Plume finding step	Plume tracing step
1	Very low	High	Low
2	Low	Middle	High
3	Middle	Low	Middle
4	High	Low	Low

Figure 4.

Flowchart of the proposed methodology.

However, in the initial step, as there are no chemical cues (below the odor threshold), a random walk begins and tries to contact the odor cue. Upon reaching the odor threshold veco-taxis algorithm locally calculates the direction of maximum concentration and magnitude (Refer Appendix A: Supplementary Data for its working mechanism). These values are input to the fuzzy inference model which outputs the plume tracing step and plume finding step size. Then accordingly the simulated robot surges based on the odor threshold and the iteration continues. The proposed methodology is shown in Fig. 4.

4.3.2 Algorithm assessment metrics

Performance metrics of the simulation experiments are based on the success rate of the mobile robot. It defines the number of successful identifications of the source out of 100 trials. So-called ‘successful identifications’ are defined when the mobile robot reaches close to or in the vicinity of the gas source. There are three boundaries of the closest reach namely 0.5 m, 1 m, and 2 m. Hence, the source vicinity reach (SVR) is defined by the values of 0.5 m, 1 m, and 2 m as the radii having a point source as the center. Figure 5 shows the SVR as the mobile robot touches the circumference with a radius of 0.5 m, 1 m, and 2 m emanating from a point source.

Figure 5.

SVR with circumference of circles having radii 0.5 m, 1 m, and 2 m.

There are three terms other than success rate that help in the assessment of algorithm performance. These are namely the number of steps taken to reach the source (STR) for the first time, a total number of steps in a successful simulation run is TNS, and the time taken to reach the source for the first time (TTR) in secs. STR is cumulative of plume finding steps and plume tracing steps which is shown in Fig. 6. Its corresponding distance traveled adds clarity to the analysis. TNS is a combination of STR and extra steps (after source declaration for the first time) till the simulation experiment terminates. All these parameters have been analyzed for each simulation environment.

Figure 6.

The description of STR, TNS and TTR in a chemical source search.

5. Results and discussions

Under this heading, important results are furnished with discussions outlined in four subsequent subsections. These subsections correspond to results of the success rate with SVR criterion, analysis of TTR, STR, and TNS, analysis of plume finding and plume tracing move length, and comparison of success rate based on variable vs. fixed move length respectively. The first three subsections have the results for self-tuned move lengths only. The results of success rate with SVR criterion are presented for start locations SL1 (10 m, 14.5), SL2 (10 m, 12.5 m), SL3 (20 m, 12.5 m), SL4 (20 m,14.5 m), and SL5 (25 m, 12.5 m) in the first subsection. The second subsection presents the analysis of all the SEs based on TTR, STR and TNS for only successful runs out of 100 trials. Also, the third subsection depicts a comparison of only plume finding and plume tracing move lengths. The second and third subsection includes the results for SL1, SL2, SL3 and SL4. The fourth subsection includes the comparison of success rate with SVR criterion based on variable vs. fixed move length. The success rate varies along different SEs having different environmental conditions, therefore comments for the same are also provided under the appropriate subsection.

Figure 7.

Success rate with SVR criterion a) SL1 b) SL2 c) SL3 d) SL4 and e) SL5.

5.1 Success rate with SVR criterion

The success rate with SVR criterion has been shown in Fig. 7 for all the start locations. Figure 7 also depicts the success rate across all SEs.

SL1 (10 m, 14.5 m) location is 2m above the plume centerline. It is situated 5 meters approximately downwind from the source. The highest number of successful runs are observed for SVR $=$ 2 m having values 62, 60, and 60 for SE4, SE6, and SE8 respectively. The SVR decreases to 1 m then the number of successful runs decreases and recorded 49 for SE4 and SE5. Further decreasing it to 0.5 m the number of successful runs recorded highest for SE1 at 39 followed by SE2 at 38 and SE5 at 37. The success rate for SL1 is shown in Fig. 7(a).

It is difficult to comment upon the SE, that facilitated the maximum success rate, but it can be observed that SE7 gave the lowest success rate irrespective of SVR. It may be caused due to high noise gain ( $\eta$ ) and less puff diffusion.

For SL2 (10 m, 12.5 m) the coordinates are in the plume centerline and approximately 5 meters from the source at a downwind position. As it is in the plume centerline hence the probability of encountering the plume concentration is more. Even higher success rate was recorded for SL2 as compared to SL1. If to consider SVR as a criterion, the maximum success rate is 71% (SE1), 63% (SE5), and 51% (SE2) for (SVR $=$ 2 m), (SVR $=$ 1 m), and (SVR $=$ 0.5 m) respectively. The lowest success rate has been observed for SE7 for all SVRs. The success rate is shown in Fig. 7(b).

The SL3 (20 m, 12.5 m) under consideration gives a low success rate as the source-to-start distance has increased. There is no vertical shift in the position in comparison to the previous location SL2. It is equal to approximately 15 meters downwind from the source. The success rate for the SL3 is shown in Fig. 7(c). As per the observed trends, the maximum success rate is for SE5 in all cases of SVR and the lowest for SE7 in cases of SVR equals 1 m and 0.5 m.

This SL4 (20 m, 14.5 m) is the same as in the previous section except for a shift in the vertical direction. Its position is 2 meters above the plume centerline and the distance to the source is 15.36 meters. The number of successful runs is 16 for SE2 when SVR is 2m. No clear distinction has been observed for the success rate among respective SEs. But in all the cases a lower success rate is observed for SE3 and SE7 which is consistent with 4 and 2 respectively. Figure 7(d) shows the success rate of SL4.

SL5 (25 m, 12.5 m) is located farthest from the source position with the y-axis coinciding. The difference is only x coordinate. The approximate distance from the source is 20 meters. The number of successful runs is very low as shown in Fig. 7(e). For each SVR corresponding to 2 m, 1 m, and 0.5 m, the success rate varies from 0 to 3. Hence the success rate has been affected substantially due to the increased distance from the source.

Figure 8.

Box plot showing the time taken to reach source (TTR), steps taken to reach source (STR), and the total number of steps (TNS) for SL1 (SVR $=$ 0.5 m) (w.r.t variable move length).

5.2 Analysis of TTR, STR, and TNS for all start locations

For SL1, TTR, STR, and TNS data have been shown in box plots of Fig. 8 for all eight environments. It contains only successful runs out of 100 for variable move length.

As per Fig. 8, the boxplot provided details for TTR, the median of which is the least for SE7 and highest for SE8. Here it is important to note that Drel $=$ 0, $\eta=$ 20, and Kx $=$ Ky $=$ 20 for SE7 and Drel $=$ 2, $\eta=$ 20, and Kx $=$ Ky $=$ 20 for SE8 respectively. The least spread of data has been observed for SE7 and the highest for SE8 in cases of TTR and STR. The median for STR is minimum for SE7 and maximum for SE8. The median higher than SE7 is for SE6 followed by SE3. An important observation suggests that for SE7 success rate is the lowest, but the mobile agent has taken the least STR and spent the least TTR. The values of STR and TTR are slightly higher for SE6 as compared to SE7, but its success rate is much higher than SE7. The median of TNS is minimum for SE5 followed by SE1.

Figure 9.

Box plot showing the time taken to reach source (TTR), steps taken to reach source (STR), and total number of steps (TNS) for SL2 (SVR $=$ 0.5 m) (w.r.t variable move length).

Figure 9 gives an overview of the three parameters TTR, STR, and TNS for SL2. For TTR, the median is lowest for SE7 and slightly higher for SE8. The median is highest for SE5 and followed by SE2. The variation in TTR values has been observed highest for SE2 followed by SE3. For STR the least median is for SE7 and slightly higher for SE8 like TTR. But the median is highest for SE2 i.e., 84, and slightly lower for SE5 i.e., 82. The data variation of STR is like TTR and observed highest for SE2 followed by SE3. For TNS median is highest for SE8 and lowest for SE1. The variation is observed highest for SE2 and slightly lower for SE6.

The parameters TTR, STR and TNS discussed above for SL1 and SL2 change concerning the cumulative effect of three environmental conditions taken into consideration (Drel, $\eta$ , and Kx $=$ Ky).

Figure 10.

Bar plot showing the time taken to reach source (TTR), steps taken to reach source (STR), and total number of steps (TNS) for SL3 (SVR $=$ 0.5 m) (w.r.t variable move length).

As the number of successful runs is comparatively lower than in the previous SLs, the bar graph provides information about TTR, STR, and TNS in Fig. 10 below for SL3. For TTR the minimum value, maximum value, and average value are the least for SE1 among all SEs. The same is true for STR. For SE2 and SE3 the minimum values of TTR and STR is comparatively higher than all minimum values of other SEs.

Figure 11.

Bar plot showing the time taken to reach source (TTR), steps taken to reach source (STR), and the total number of steps (TNS) for SL4 (w.r.t variable move length).

The bar pot for SL4 is shown in Fig. 11. For TTR the minimum value, maximum value, and average value are the least for SE8 among all SEs. The same is true for SE8 when STR is observed for all SEs. The range for TTR and STR i.e. (minimum-maximum) is maximum for SE2. The range is minimum for TTR and STR for SE7.

The analysis for TTR, STR, and TNS for all four start locations suggests that these parameters vary with initial search locations and also depend on the the environmental conditions. However, based on the Drel, $\eta$ , and Kx $=$ Ky there is no clear trend, and prediction about the parameters TTR, STR, and TNS is difficult owing to the turbulence effect.

Figure 12.

Box plot showing bifurcation of STR into plume finding steps and plume tracing steps for SL1 (SVR $=$ 0.5 m) (w.r.t variable move length).

Figure 13.

Box plot showing distance traveled during plume finding and plume tracing in meters till it reaches source for the first time; for SL1 (SVR $=$ 0.5 m) (w.r.t variable move length).

5.3 Comparison of plume finding and plume tracing move length

To break down STR into plume-finding steps and plume-tracing steps Fig. 12 can be referred to for SL1. For SE8 the median is highest with 147 and more data variation in plume finding step values. Plume tracing steps are concentrated toward lower values. It has a median of 14. Like SE8 for other SEs such as SE2, SE4, and SE6 the median of plume finding steps is more as compared to plume tracing steps. It is important to note that for all the SEs mentioned Drel is 2. In the case of SE3, the median of plume finding steps is slightly higher than plume tracing steps which is odd one in this group. Box plots of SE1, SE5, and SE7 are similar i.e., variation in plume finding steps and plume tracing steps is similar. Here Drel is zero. There are several outliers for SE1, SE5, and SE7. Similar is the trend observed for distance traveled for plume finding steps and plume tracing steps to which Fig. 13 can be referred.

There is one important observation that for some cases in respective SEs plume finding steps are higher as compared to plume tracing steps. For example, in a successful experiment in SE1, plume finding steps are 106 as compared to the plume tracing step which is only 1. There are at least nine occurrences of successful experiments in which plume tracing steps are only in single digits ranging from 0 to 10. It suggests that random searching leads the mobile robot near the gas source, and it has been found without any gradient climbing. Hence it can be considered as one of the disadvantages of the start position being so close to the gas source.

Figure 14.

Box plot showing bifurcation of STR into plume finding steps and plume tracing steps for SL2 (SVR $=$ 0.5 m) (w.r.t variable move length).

Figure 15.

Box plot showing a comparison of plume finding steps and plume tracing steps in reaching source for the first time for SL3 (SVR $=$ 0.5 m) (w.r.t variable move length).

Box plots of plume finding steps and plume tracing steps are shown for SL2 in Fig. 14. These are different as compared to SL1. Here it can be observed that for SE1 and SE5 the median of plume finding steps is much smaller as compared to plume tracing steps. For all the other SEs median of plume finding steps is higher as compared to plume tracing steps. In other words, for all the cases except Drel $=$ 0 and $\eta=$ 2, the median of plume tracing steps is lower in comparison to plume finding steps. This may be due to the position of the mobile robot which is already inside the plume as the search starts.

Figure 16.

Box plot showing a comparison of plume finding steps and plume tracing steps in reaching source for the first time for SL4 (SVR $=$ 0.5 m) (w.r.t variable move length).

For SL1 and SL2 there are variations observed in plume finding and plume tracing move lengths with different SEs. But as these locations are close to the source the trend is similar in some specific SEs. For both SL1 and SL2, SE1 has a higher median of plume tracing steps compared to plume finding steps. Even for SE5, the median of the plume tracing step is just lower for SL1 (plume finding steps $=$ 33 and plume tracing steps $=$ 30) and higher for SL2.

Concerning Fig. 15, successful experiments are plotted on the x-axis whereas the plume finding step and plume tracing steps are shown on the y-axis for SL3. It shows that for SE3, SE4, SE7, and SE8 plume tracing steps are lower as compared to plume finding steps. In all these SEs noise gain is 20. For SE6 it is also true but it is the odd one in the group because its noise gain is 2. For SE1 and SE5 comparison suggests no clear trend. SE2 has only two successful experiments in which alternate cases are true i.e., for the first experiment plume tracing steps are higher than plume tracing steps and vice versa.

As far as the comparison of plume finding and plume tracing steps of SL4 are concerned, Fig. 16 shows the box plot. It shows that SE3, SE4, SE7, and SE8 have plume tracing steps lower than plume finding steps for noise gain ( $\eta$ ) equal to 20. For all other SEs, no clear trend is observed.

5.4 Success rate for fixed vs. variable move lengths

Figure 17.

The success rate for SL1 with comparison of variable and fixed move length (w.r.t SVR).

Experiments are also conducted keeping the plume finding move length equal to 0.3 m and plume tracing move length equal to 0.8 m fixed throughout the experiments. The recorded data of SL1 and SL2 has been compared with those of self-tuned move length to evaluate the effect on success rate. Depending upon the SVR the success rate varies considerably for both variable move length and fixed move length and is discussed under this subsection.

Figure 18.

The success rate for SL2 with comparison of variable and fixed move length (w.r.t SVR).

For SL1, the success rate is higher for variable move lengths as compared to fixed move lengths for all the SEs except for SE5 (SVR $=$ 2 m) and SE7 (SVR $=$ 0.5 m). Therefore, the success rate is a maximum 62%, 49% and 39% for SVR $=$ 2m, SVR $=$ 1 m and SVR $=$ 0.5 m respectively for variable move length. A similar trend is observed for fixed move length having maximum success rates as 57%, 41% and 29% for SVR $=$ 2 m, SVR $=$ 1 m and SVR $=$ 0.5 m respectively. Therefore, the self-tuned move lengths increase the success rate of veco-taxis. It is shown in Fig. 17.

For SL 2, the success rate is also higher for all SEs for variable move length as compared to fixed move length. Hence, the adapted move lengths have contributed to higher success rate. It has been shown in Fig. 18. Similarly, for fixed move length, SE5 has the maximum success rate with 63%, 54%, and 39% for (SVR $=$ 2 m), (SVR $=$ 1 m), and (SVR $=$ 0.5 m) respectively.

6. Conclusions

The present work proposes a fuzzy inference model that auto-tunes the move length of plume finding and plume tracing for a mobile searcher for GSL. The proposed approach strengthens the chemotaxis plume tracing algorithm and improves the search performance. Experiments have been carried out in eight different SEs as test cases. The success rate varies for five different start locations and is recorded higher for self-tuned move lengths as compared to fixed move lengths. The three parameters of assessment namely TTR, STR, and TNS are affected by the change in start locations. Environmental conditions also have a cumulative effect on these parameters that leads to variations across different SEs. As per findings, a median of plume tracing steps is higher for SE1 and SE5 for start locations SL1 and SL2. But for other start locations, no clear trend is observed. Hence self-tuned move lengths have increased the success rate of the plume tracing algorithm compared to fixed move lengths with enhanced search performance.

7. Future work

The author will propose a robust fuzzy inference model to self-tune move lengths as well as turn angles. The fuzzy model will also include turbulence parameters that can optimize the search trajectory. Simulation experiments followed by hardware-based experiments will validate the results in further studies.

Footnotes

Acknowledgments

The author is grateful for the research facilities provided by Manipal University Jaipur.

Supplementary data

The supplementary files are available to download from https://dx-doi-org.web.bisu.edu.cn/10.3233/IDT-230225.

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Fuzzy based self-tuned move lengths for enhanced performance of gas source localization algorithm

Abstract

Keywords

1. Introduction

4. Materials and methods

4.1 Simulated robot and its environment

4.2 Dynamic plume generation and test cases

Table 1 Simulation environment description with parameters

4.3.1 Self-tuned move length/Variable move lengths

Table 2 Attributes of fuzzy-based adaptive step size controller

7. Future work

Footnotes

Acknowledgments

Supplementary data

References

Table 1
Simulation environment description with parameters

Table 2
Attributes of fuzzy-based adaptive step size controller