# Improved ‘Infotaxis’ Algorithm-Based Cooperative Multi-USV Pollution Source Search Approach in Lake Water Environment

## Abstract

**:**

## 1. Introduction

## 2. Related Work

- (1)
- Simply overlaying the exploration information of multiple USVs cannot maximize the advantages of the multi-USV system.
- (2)
- Multi-USV systems that lack cooperation make it easy for USVs to search the same area repeatedly. This will lead to the aggregation of multiple USVs in the same area, thus reducing the efficiency of exploration.
- (3)
- How can a reasonable cooperation strategy be designed to minimize the impact of environmental uncertainty?

## 3. Study Foundation

#### 3.1. Topological Logic for Cooperative Multiple USVs-Remote Centre

#### 3.2. ‘Infotaxis’ Algorithm

#### 3.2.1. Probabilistic Map Building Method Based on the Measurement of Binary Sensors

_{0}is the zero-order Bessel function of second kind. $\lambda $ is the characteristic length, and its expression is:

#### 3.2.2. ‘Infotaxis’ Algorithm-Based Exploration Using a Single Robot

#### 3.2.3. ‘Infotaxis’ Algorithm-Based Exploration Using Multiple Robots

#### Information Entropy Prediction of Multi Robot Exploration

## 4. Improved Shared Probability Updating Method Based on Information Confidence Level Judgment

#### 4.1. Method Introduction

- (1)
- The closer the USV’s sampling location nears to the chemical pollution source, the higher its confidence is. The closer the USV is to the chemical pollution source, the greater the probability that it will sample information indicating excessive chemical substances, thus giving it more confidence.
- (2)
- The more pheromones that the USV obtains at the sampling position, the higher the confidence assigned to it. The more times a USV touches cues in its position, or the higher the chemical concentration of the sample, the greater its likelihood of approaching a chemical source, thus giving it more confidence.

#### 4.2. Case Study

_{1}, t

_{2}and t

_{3}. Figure 4, Figure 5, Figure 6 and Figure 7 are probability maps obtained from several cases at three-time moments.

## 5. ‘PSO-Infotaxis’ Algorithm-Based Exploration of Cooperative USVs

#### 5.1. Basic Idea of Standard PSO

^{T}. According to the objective function, the fitness value corresponding to each particle’s position $X$ can be calculated. The velocity of the i-th particle is expressed as V

_{i}= (V

_{1}, V

_{2}⋯ V

_{n})

^{T}, and its individual extreme values denote the optimum historical position of the particle, which is expressed as ${P}_{i}={\left({P}_{1},{P}_{2},\cdots ,{P}_{n}\right)}^{T}$. The extreme value of the population is the optimum historical position of particle populations, which are expressed as ${P}_{g}$. In the t-th iteration, the updating formula of particle velocity and position is as follows:

#### 5.2. ‘Infotaxis’ Algorithm of Multi-USV Exploration Based on Improved PSO

#### 5.3. The Overall Process of the Method

## 6. Experimental Study

#### 6.1. Construction of Test Platform

#### 6.2. Source Location Tracking Experiment

#### 6.3. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Wang, Y.N.; Xiao, Z.; Chen, Y.H. Multifunctional Data Acquisition System for Intelligent Autonomous Mobile Robot. Control Eng. China
**2013**, 11, 1005–1013. [Google Scholar] - Schwarz, M.; Rodehutskors, T.; Droeschel, D. NimbRo Rescue: Solving Disaster-Response Tasks through Mobile Manipulation Robot Momaro. J. Field Robot.
**2017**, 34, 400–425. [Google Scholar] [CrossRef] [Green Version] - Patic, P.C.; Mainea, M.; Pascale, L. Designing a Mobile Robot used for Access to Dangerous Areas. In Proceedings of the 2017 International Conference on Control, Artificial Intelligence, Robotics & Optimization (ICCAIRO), Prague, Czech Republic, 20–22 May 2017. [Google Scholar] [CrossRef]
- Li, J.C.; Meng, Q.H.; Liang, Q. Simulation Study on Robot Active Olfaction Based on Evolutionary Gradient Search. Robot
**2007**, 29, 234–238. [Google Scholar] - Zarzhitsky, D.; Spears, D.; Thayer, D. Agent-based chemical plume tracing using fluid dynamics. Form. Approaches Agent-Based Syst.
**2004**, 3228, 146–160. [Google Scholar] - Edwards, S.; Rutkowski, A.J.; Quinn, R.D. Moth-Inspired Plume Tracking Strategies in Three-Dimensions. IEEE Int. Conf. Robot. Autom.
**2005**, 1669–1674. [Google Scholar] [CrossRef] - Porter, M.J.; Vasquez, J.R. Bio-Inspired Navigation of Chemical Plumes. In Proceedings of the Bio-Inspired Navigation of Chemical Plumes, Florence, Italy, 10–13 July 2006. [Google Scholar] [CrossRef]
- Vergassola, M.; Villermaux, E.; Shraiman, I. ‘Infotaxis’ as a strategy for searching without gradients. Nature
**2007**, 445, 406–409. [Google Scholar] [CrossRef] [PubMed] - Guerrero, J.; Oliver, G.; Valero, O. Multi-Robot Coalitions Formation with Deadlines: Complexity Analysis and Solutions. PLoS ONE
**2017**, 12, e0170659. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Budinska, I.; Havlik, S. Task allocation within a heterogeneous multi-robot system. In Proceedings of the 2016 Cybernetics & Informatics (K&I), Levoca, Slovakia, 2–5 February 2016. [Google Scholar] [CrossRef]
- Yan, Z.; Jouandeau, N.; Ali, A. A Survey and Analysis of Multi-Robot Coordination. Int. J. Adv. Robot. Syst.
**2013**, 10, 399. [Google Scholar] [CrossRef] - Prorok, A.; Bahr, A.; Martinoli, A. Low-cost collaborative localization for large-scale multi-robot systems. Proc. ICRA
**2012**, 12, 4236–4241. [Google Scholar] [CrossRef] [Green Version] - Gintautas, V.; Hagberg, A.A.; Bettencourt, L.M.A. Leveraging synergy for multiple agent infotaxis. Los Alamos
**2008**, 7, 1–12. [Google Scholar] - Masson, J.B.; Bailly Bechet, M.; Vergassola, M. Chasing information to search in random environments. J. Phys. A Math. Theor.
**2010**, 42, 434009. [Google Scholar] [CrossRef] - Zhang, S.Q.; Xu, D.M. Odor source search employing multi-robots with limited perception in turbulence environments. Control Decis.
**2015**, 8, 88–92. [Google Scholar] - Song, C.; He, Y.Y.; Lei, X.K.; Yang, P.P. Multi-robot collaborative infotaxis searching for plume source based on cognitive differences. Control Decis.
**2018**, 33, 48–55. [Google Scholar] - Liu, N.X.; Pan, J.S.; Wang, J.; Nguyen, T.T. An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks. Sensors
**2019**, 19, 4112. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Tian, A.Q.; Chu, S.C.; Pan, J.S.; Cui, H.Q.; Zheng, W.M. A Compact Pigeon-Inspired Optimization for Maximum Short-Term Generation Mode in Cascade Hydroelectric Power Station. Sustainability
**2020**, 12, 767. [Google Scholar] [CrossRef] [Green Version] - Pan, J.S.; Hu, P.; Chu, S.C. Novel Parallel Heterogeneous Meta-Heuristic and Its Communication Strategies for the Prediction of Wind Power. Processes
**2019**, 7, 845. [Google Scholar] [CrossRef] [Green Version] - Kennedy, J.; Eberhart, R.C. The Particle Swarm: Social Adaptation in Information-Processing Systems New Ideas in Optimization; McGraw-Hill Ltd.: London, UK, 1999; pp. 303–308. [Google Scholar]
- Yang, W.; Li, Q.Q. Survey on Particle Swarm Optimization Algorithm. Eng. Sci.
**2004**, 6, 87–94. [Google Scholar] - Peng, Z.Z. Mathematical Model of Water Environment and Its Application; Chemical Industry Publishing House: Beijing, China, 2007; pp. 24–33. [Google Scholar]

**Figure 1.**Communication link and cooperative decision topology diagram of the USV remote monitoring center.

**Figure 7.**Shared probabilistic map set up by two cooperative USVs considering cognitive differences.

**Figure 9.**The calculated probabilistic map of the source detected by three robots. (

**a**) t = 0 s, (

**b**) t = 50 s, (

**c**) t = 80 s, (

**d**) t = 182 s.

**Figure 11.**Comparison of optimal shared probability curves. (

**a**) Optimal sharing probability curve using the ‘PSO-Infotaxis’ algorithm, (

**b**) Optimal sharing probability curve using the basic ‘Infotaxis’ algorithm.

**Figure 12.**Comparison of information entropy curves. (

**a**) Information entropy curve using the ‘PSO-Infotaxis’ algorithm, (

**b**) Information entropy curve using the basic ‘Infotaxis’ algorithm.

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Huang, X.
Improved ‘Infotaxis’ Algorithm-Based Cooperative Multi-USV Pollution Source Search Approach in Lake Water Environment. *Symmetry* **2020**, *12*, 549.
https://doi.org/10.3390/sym12040549

**AMA Style**

Huang X.
Improved ‘Infotaxis’ Algorithm-Based Cooperative Multi-USV Pollution Source Search Approach in Lake Water Environment. *Symmetry*. 2020; 12(4):549.
https://doi.org/10.3390/sym12040549

**Chicago/Turabian Style**

Huang, Xiaoci.
2020. "Improved ‘Infotaxis’ Algorithm-Based Cooperative Multi-USV Pollution Source Search Approach in Lake Water Environment" *Symmetry* 12, no. 4: 549.
https://doi.org/10.3390/sym12040549