Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations

IFAC PapersOnLine 55-5 (2022) 1–6 ScienceDirect ScienceDirect Available online at www.sciencedirect.com 2405-8963 Copyright © 2022 The Authors. This is an open access article under the CC BY-NC-ND license . Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2022.07.630 10.1016/j.ifacol.2022.07.630 2405-8963 Copyright © 2022 The Authors. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0/ ) Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source Water Quality Map Extraction from Field Measurements Targetting Robotic Simulations A. Anderson ∗,∗∗ J.G. Martin ∗∗∗ J. Mougin ∗∗∗∗ N. Bouraqadi ∗ E. Duviella ∗L. Etienne ∗L. Fabresse ∗K. Langueh ∗G. Lozenguez ∗ C. Alary ∗G. Billon ∗∗∗∗ P.J. Superville ∗∗∗∗ J.M. Maestre ∗∗∗ ∗IMT Nord Europe, Univ. Lille, F-59000 Lille, France ∗∗ Instituto de Desarrollo Tecnol´ ogico para la Industria Qu´ ımica (INTEC), Consejo Nacional de Investigaciones cientficas y tecnicas (CONICET) and Universidad Nacional del Litoral (UNL), Santa Fe, Argentina ∗∗∗ Departamento de Ingenier´ ıa de Sistemas y Autom´ atica, Universidad de Sevilla, C/ Camino de los Descubrimientos, s/n., 41092 Sevilla, Spain ∗∗∗∗ Univ. Lille, CNRS, UMR 8516 - LASIRE - Laboratoire Avanc´ e de Spectroscopie pour Les Int´ eractions La R´ eactivit´ e et L’Environnement, 59000, Lille, France Abstract: The assessment of the quality of water can be shortly defined as the analysis of its physical, chemical and biological characteristics in order to determine the degradation of freshwater resources. In this context, one of the latest technological methods for real-time data acquisition comes from the use of unmanned vehicles (aerial, surface and underwater). Therefore, the development of control strategies to perform environmental missions is crucial to manage water resources in an efficient and effective way. Prior to the actual implementation, some in-silico experiments are needed to test the proposals, which is one of the purposes of this work. This proposal, based on real experiments in a lake, presents a novel method for the construction of a water quality map based on polygons. The result is compared with a classical data generation method showing positive outcomes. The generated limnological map has a twofold purpose: to test set-based predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a source of contamination in the analyzed region of the lake. Keywords: Unmanned Surface Vehicle, Environmental Monitoring, Water Quality, Kriging 1. INTRODUCTION Water resource management is an integral aspect of the preventive management of aquatic ecosystems health and drinkingwater quality. A comprehensive monitoring program is becoming a necessity in order to safeguard public health and to protect the freshwater resources as required by the Water Framework Directive (WFD) (Edition, 2011; Kannel et al., 2007). Water quality assessment requires real-time measurement of many physical and chemical parameters. Usually, the monitoring of these parameters exploits highly reliable instrumentation which is deployed only in few locations. Nevertheless, the vast collection of data necessary to define the conservation status of a region represents a set of challenges to be solved. For instance, the size of the monitored area will require the deployment of a number of detection devices ranging from a single device to a fleet of unmanned vehicles covering several points. The second challenge comes from the remoteness of the sites to be monitored. In this case, the sensing devices must be provided with some kind of data transmission system. Finally, to be efficient, human intervention must be kept to a minimum (Madeo et al., 2020). To fulfill all the previous objectives, recent works propose the use of Unmanned Surface Vehicles (USV) for the collection of data (Sinisterra et al., 2017; Siyang and Kerdcharoen, 2016). The implementation of autonomous vehicles offers the flexibility for a variety of intervention plans and it provides an energy efficient and robust solution for specific tasks in sophisticated environments (see Wang et al. (2021) and the references therein). In this preliminary work, the SPYBOAT® vessel - equipped with specific sensors to monitor turbidity, dissolved oxygen (DO), pH, conductivity, temperature from water surface - was tested in several environmental scenarios. Some of these scenarios were intended to guarantee the quality of the data by means of a proper validation using data provided by a Laboratory deployed in the field (Mougin, 2021) in coordinated experiments. Another experimental scenario was performed on the wider area of the Heron lake in Villeneuve d’Ascq, France. The monitored area is located close to the arrival of contaminated waters from storm overflows and was expected to show interesting gradients. The main purpose of this paper is to provide a novel data approximation method to extract the maximum amount of information possible from a minimum amount of data. This approximation method is used to generate a limnological profile of the complete monitored region of the Heron lake aforementioned. The result is compared with a classical data generation method showing positive outcomes. The generated map has a two-fold purpose, to create a structural reliability framework to test predictive controllers in simulation scenarios with an aquatic robot and to determine if there is a significant source 2 A. Anderson et al. / IFAC PapersOnLine 55-5 (2022) 1–6 of pollution in the analyzed region of the lake by considering the spatial direction in which the parameters rises most quickly. The structure of this paper is as follows. Section 2 provides the architecture of the USV used on the real measures and a proper data validation analysis. Section 3 describes the main experiment on the Heron lake, including the region of interest, the analyzed parameters and the sampling procedure. The main result of the paper is presented in Section 4. This section presents an estimated limnological map of the region based on data collected on the field. Two different approaches were proposed to build the map, the strategy knowing as Kriging and a novel proposal based on the specific features of the experiment. A comparison between the results and a discussion about the methods are further presented. Lastly, Section 5 presents the conclusions and perspectives of the paper. 2. THE USE OF ROBOTS FOR REAL-TIME MEASUREMENT The official SPYBOAT® system used in the present study is an USV equipped with a Hyperion optical sensor from Valeport 1, for the measurement of the turbidity. It is also equipped with Tripod sensors from AquaLabo 2to measure the temperature, DO, pH, and conductivity. The first experiment scenario - performed in the Marque River (close to Lille in France) - attempted to validate the SPYBOAT® sensors measurements. This was carried out with an intercomparison between the USV on a fixed location and a field Laboratory (static station on the side of the river) (Mougin, 2021), performing an online analysis of the physicochemical parameters of the water with a multiparameter probe (Manta+, Eureka Water Probes). The comparison was performed during a one hour monitoring period, with a one second delay between measurements for the USV and a two and a half minute delay for the laboratory. Table 1. Comparison between sensors from USV and from field Laboratory. Temperature pH Conductivity Turbidity O2 Shift 3% 6% 5% 17% 5% Correlation 0.98 0.95 0.93 0.42 0.96 The results show a small shift in absolute value for most of the parameters between the USV and the laboratory (see Table 1). 3. DESCRIPTION OF ENVIRONMENTAL EXPERIMENTATION Pollution of surface water occurs when too much of an undesirable or harmful substance flows into a water body, exceeding its natural ability to remove it (dilute or convert it to a harmless concentration). The study area (see Fig. 1) of the experiment is a part of the Heron Lake in Villeneuve d’Ascq, France. It is an artificial lake, dug in the 70s to drain the marshy area, to receive rain water from roads and other artificialized ground and from storm overflows from mixed drainage system (rain and to a lesser extent domestic wasterwater). The water arrives at the east of the lake and when the level is too high, water is pumped out to 1https://www.valeport.co.uk/content/uploads/2021/05/0901814i-Hyperion- Optical-Sensors-Operating-Manual.pdf 2https://en.aqualabo.fr/ a nearby river in the far western point. A natural remediation of the water occurs in lake so a gradient can be expected between the entrance with a high biodegradable input and the exit (Ivanovsky et al., 2018). Fig. 1. Region Ωon the Heron lake, Villeneuve d’Ascq, where measurements are carried out. The measures were focused in the region Ω(pink region in Fig. 1) where the gradient should be the strongest, at the interface between the small canal bringing the contaminated water and the main part of the lake where dilution and decontamination occurs. The region has been explored with the USV during close to 1hour, getting sample each 1second (Fig. 2). Fig. 2. Trajectory of the hand-operated vessel in region Ωwith decimal GPS coordinates. 4. MAIN RESULTS In this section we discuss an approach to sort the challenges to improve the collection of data. In order to account for the regularization of the survey, we perform an approximation of every missing data. This is accomplished thanks to a regular map of the region of interest (set Ωfrom Fig. 1), where every point of Ωis now associated with an estimation of its physical parameters (turbidity, DO, pH, conductivity and temperature). In what follows, the limnological map is constructed in such a way it can be used in simulation scenarios in order to test different control strategies (for a single and a fleet of USV) to address these challenges. 4.1 Map meshing The boundaries of the region Ωare determined thanks to the Matlab function boundary. This function returns a vector of points indices PBthat represents a compact boundary around this area. It is possible to obtain less detailed boundaries by A. Anderson et al. / IFAC PapersOnLine 55-5 (2022) 1–6 3 of pollution in the analyzed region of the lake by considering the spatial direction in which the parameters rises most quickly. The structure of this paper is as follows. Section 2 provides the architecture of the USV used on the real measures and a proper data validation analysis. Section 3 describes the main experiment on the Heron lake, including the region of interest, the analyzed parameters and the sampling procedure. The main result of the paper is presented in Section 4. This section presents an estimated limnological map of the region based on data collected on the field. Two different approaches were proposed to build the map, the strategy knowing as Kriging and a novel proposal based on the specific features of the experiment. A comparison between the results and a discussion about the methods are further presented. Lastly, Section 5 presents the conclusions and perspectives of the paper. 2. THE USE OF ROBOTS FOR REAL-TIME MEASUREMENT The official SPYBOAT® system used in the present study is an USV equipped with a Hyperion optical sensor from Valeport 1, for the measurement of the turbidity. It is also equipped with Tripod sensors from AquaLabo 2to measure the temperature, DO, pH, and conductivity. The first experiment scenario - performed in the Marque River (close to Lille in France) - attempted to validate the SPYBOAT® sensors measurements. This was carried out with an intercomparison between the USV on a fixed location and a field Laboratory (static station on the side of the river) (Mougin, 2021), performing an online analysis of the physicochemical parameters of the water with a multiparameter probe (Manta+, Eureka Water Probes). The comparison was performed during a one hour monitoring period, with a one second delay between measurements for the USV and a two and a half minute delay for the laboratory. Table 1. Comparison between sensors from USV and from field Laboratory. Temperature pH Conductivity Turbidity O2 Shift 3% 6% 5% 17% 5% Correlation 0.98 0.95 0.93 0.42 0.96 The results show a small shift in absolute value for most of the parameters between the USV and the laboratory (see Table 1). 3. DESCRIPTION OF ENVIRONMENTAL EXPERIMENTATION Pollution of surface water occurs when too much of an undesirable or harmful substance flows into a water body, exceeding its natural ability to remove it (dilute or convert it to a harmless concentration). The study area (see Fig. 1) of the experiment is a part of the Heron Lake in Villeneuve d’Ascq, France. It is an artificial lake, dug in the 70s to drain the marshy area, to receive rain water from roads and other artificialized ground and from storm overflows from mixed drainage system (rain and to a lesser extent domestic wasterwater). The water arrives at the east of the lake and when the level is too high, water is pumped out to 1https://www.valeport.co.uk/content/uploads/2021/05/0901814i-Hyperion- Optical-Sensors-Operating-Manual.pdf 2https://en.aqualabo.fr/ a nearby river in the far western point. A natural remediation of the water occurs in lake so a gradient can be expected between the entrance with a high biodegradable input and the exit (Ivanovsky et al., 2018). Fig. 1. Region Ωon the Heron lake, Villeneuve d’Ascq, where measurements are carried out. The measures were focused in the region Ω(pink region in Fig. 1) where the gradient should be the strongest, at the interface between the small canal bringing the contaminated water and the main part of the lake where dilution and decontamination occurs. The region has been explored with the USV during close to 1hour, getting sample each 1second (Fig. 2). Fig. 2. Trajectory of the hand-operated vessel in region Ωwith decimal GPS coordinates. 4. MAIN RESULTS In this section we discuss an approach to sort the challenges to improve the collection of data. In order to account for the regularization of the survey, we perform an approximation of every missing data. This is accomplished thanks to a regular map of the region of interest (set Ωfrom Fig. 1), where every point of Ωis now associated with an estimation of its physical parameters (turbidity, DO, pH, conductivity and temperature). In what follows, the limnological map is constructed in such a way it can be used in simulation scenarios in order to test different control strategies (for a single and a fleet of USV) to address these challenges. 4.1 Map meshing The boundaries of the region Ωare determined thanks to the Matlab function boundary. This function returns a vector of points indices PBthat represents a compact boundary around this area. It is possible to obtain less detailed boundaries by (a) Square Entity Esqr with Sp = 10m. (b) Square Entity Esqr with Sp =5m. (c) Hexagonal Entity EHwith Sp =5m. (d) Hexagonal Entity EHwith Sp = 12.5mand overlapping. Fig. 3. Map meshing of Ω. tuning the parameter FaceAlpha of the function, with a value less than one. The following step aims at meshing the map. A regular map meshing of the region Ωcould be done by different shapes of different sizes (see Fig. 3), which particularities are discussed in Section 4.5. Matlab software offers the library Generate Mesh for triangular mesh for a 2-D geometry. Another option is to perform map meshing thanks to the Multiparametric Toolbox 3.0 3library (Herceg et al., 2013), that allows adjusting the size and choosing the shape of each finite element. From this library, the functions Polyhedron, meshGrid or isInside are available. Hence, according to the function Polyhedron and the previous determined vector PB, an entity Zone is created from the area of interest. The elementary entity Eis created with the relative coordinates of the polyhedron’s vertices VE. For a square entity Esqr with a side length Sp, it is necessary to code: Esqr =Polyhedron(′lb′,[−Sp/2,−Sp/2],′ub′,[Sp/2, Sp/2]). For any other polyhedron with a side length Sp, the code is: Ep=Polyhedron(VE), with VEthe coordinates of vertices. As an example, to define the entity EHas a hexagon, the vertices are defined as: VEH={(−Sp ∗cosd(30)/2; Sp ∗cosd(60)/2),(0; Sp/2), (Sp ∗cosd(30)/2; Sp ∗cosd(60)/2), (Sp ∗cosd(30)/2; −Sp ∗cosd(60)/2), (0; −Sp/2),(−Sp ∗cosd(30)/2; −Sp ∗cosd(60)/2)}. Note:Esqr is dedicated to an elementary entity with a square shape, EHto a hexagonal shape, and Epto a polyhedral shape. The centers for Esqr can be easily determined thanks to the function meshGrid. However, the coordinates of centers for any other polyhedron has to be determined, based on the shape of the entity Ep. Hence, the set of these centers Cp that belong to Zone is determined thanks to the function isInside. The final step consists in computing for each center ci∈Cp, a new entity Epi=ci+Ep. As a result we get one entity Epifor each center ci. Figure 3 shows different meshes with constructed by varying the entity shape (square &hexagonal), in a. Sp = 10m(meters), in b. Sp =5m, and with hexagonal Entity without overlapping in c. Sp =5m, and with in d. Sp = 10m. 3https://www.mpt3.org/ CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO CF Co CE CD CA CB CC AO BO CO FO DO EO Fig. 4. Blue dots {A, B, ..., F}, represent already taken measurements, {CA,C B, ..., CF}, and the red dot, O, is the point where the value is being interpolated. Thus, since distances from the measurements to the interpolated point are available, we can use kriging to interpolate CO. (a) Theoretical variogram (circular model). 0 50 100 Distance (h) 0 2 4 6 8 10 (h) (b) Experimental variogram (red dots) and fitting to a theoretical model. Fig. 5. Kriging Variograms. Based on the map meshing, the next step is to create the limnological map of Zone,i.e. to associate an estimated value of each physico-chemical parameter (turbidity, DO, pH, conductivity and temperature) to each of the entity Epi, and to determine the variance of these estimations if any. This represent a challenge that will be tackle in the next Section. Basically, the USV has explored the Zone with different velocities and several trajectories. Hence, first the USV has not taken the same number of samples for each entity Epi, second some entities Epjcould not be explored because of their size of entities. In the next Sections, two methods to attribute one value of each physical parameter to each entity Epiis presented. The first approach is the Kriging strategy, which results will be compared with the proposed strategy presented in Section 4.3. The two methods have been used to estimate all parameters (turbidity, DO, pH, conductivity and temperature). However, for sake of simplicity and due to the limitation of space, only DO is depicted in this paper. 4.2 Map construction: Kriging approach Kriging is a geostatistical interpolation method that was developed for the mining field at the end of the decade of 1960 (see Fig. 4). This method has been widely extended in the literature to the interpolation of environmental variables, such as soil quality (Snepvangers et al., 2003), wheater temperature (Shtiliyanova et al., 2017), solar irradiance (Yang et al., 2013), and water quality (Chen et al., 2012). To perform these interpolations, Kriging strategy uses Variograms to relate the distance, h, between the measurements and the semivariance, γ(h), and that can be computed from the known measurements. However, these empirical variograms do not provide information for all possible h(needed for kriging). Thus, they are often approximated by model function, 4 A. Anderson et al. / IFAC PapersOnLine 55-5 (2022) 1–6 (a) Final Kriging map of DO. (b) Variance of measures of DO based on Kriging map. Fig. 6. Kriging Map Generation. as circular variogram (see Fig. 5a), ensuring validity (Chiles et al., 1999). Fig. 5b shows as red dots empirical variogram computed from the measurements taken in Ω. The theoretical model used to fit the data is represented as blue dashed line. Note that in Fig. 5b there is a large divergence between the experimental and the theoretical variagrams, specially for small distances. The reason of this divergence is that there are many measurements which, disregarding being very close in distance, are very far in time. Thus, the real value of the parameter can have changed a lot during the time between them. Making use of this theoretical Variogram we can interpolate the mesh of points inside Ω, carried out with hexagonal shape of Sp =5m. Fig. 2 shows the explored area in red. Note that in the top left corner, it can be seen that the USV explored several times the same entities. Meanwhile, in the bottom right corner there are some non-explored entities. With the center of each entity EHi, a limnological map is obtained for every physical parameter analyzed in this work. Fig. 6a shows the map for the DO. Furthermore, by assessing Fig. 6a, it can be seen that the maximal rate of DO in this region comes from 1.1mg/l (dark blue) to 9.09mg/l (yellow). The DO concentration presents smaller values in the top left corner of the set Ω, which corresponds to the river mouth where there is a suspicion of a source of pollution. By means of the generated maps, the gradient of each parameter can be assessed in order to determine if there is a significance pollution source. Lastly, the variance of the measures are depicted in Fig. 6b, with values from 0to 0.51. The variance takes the maximum values at the non-explored area of Ω(see Fig. 2), i.e., the farthest points to the trajectory. 4.3 Map construction: Proposed approach The creation of the measurement map is achieved in two steps. The first step aims at determining, thanks to the function isInside, the set of samples made in each constructed entity Epi. The average of these samples leads to the estimation of one value for each entity Epi, and the uncertainty associated to each entity Epiestimation is determined by computing the variance between the involved measurements. The second step concerns the non-explored entities Epjfor which a neighborhood propagation of the values is proposed. To this end, a neighborhood matrix of the entities Epis built. It aims at determining which entities Epihave common edge. Two examples are provided in Fig. 7, with square and hexagonal entities. For the square Entity Esqr in Fig. 7a, and the hexagonal Entity EHin Fig. 7b, the neighborhood matrices Nsqr and NHare given in Eq. (1), respectively. In Nsqr, all the 1values from the fifth line show that the entity Esqr5has as neighbours the entities Esqr2,Esqr4,Esqr6and Esqr9.InNH, the 1from the second line shows that neighbours of the entity EH2are: EH1,EH3,EH7and EH8. (a) Square Entity Esqr.(b) Hexagonal Entity EH. Fig. 7. Map meshing examples. Nsqr =             110000000 111010000 011001000 000110010 010111001 001011000 000000110 000100111 000010011             NH=             110001100 111000110 011100011 001110001 000110000 100001100 110001110 011000111 001100011             (1) The value that is associated to a non-explored entity Epjis estimated as the average value of each of its neighbours. It is computed as the multiplication of the vector of measurement with the jth line of the associated neighborhood matrix. The limnological map is generated with one mean value of the measured DO concentration for each explored entity EHi. Values for the non-explored entities EHjhave been estimated. The final map of DO is depicted in Fig. 8a. Each entity is associated to a value with rate of DO from 1.43mg/l (dark blue) to 8.41mg/l (yellow). The DO is less concentrated in the top left corner because this area corresponds to the outlet of the river that runs through Lille; this river can be loaded with pollutants. Finally, Fig. 8b shows the variance of the measures given an indication of the uncertainties on the sample. The variance for the DO varies from 0to 10. It is maximum A. Anderson et al. / IFAC PapersOnLine 55-5 (2022) 1–6 5 (a) Final Kriging map of DO. (b) Variance of measures of DO based on Kriging map. Fig. 6. Kriging Map Generation. as circular variogram (see Fig. 5a), ensuring validity (Chiles et al., 1999). Fig. 5b shows as red dots empirical variogram computed from the measurements taken in Ω. The theoretical model used to fit the data is represented as blue dashed line. Note that in Fig. 5b there is a large divergence between the experimental and the theoretical variagrams, specially for small distances. The reason of this divergence is that there are many measurements which, disregarding being very close in distance, are very far in time. Thus, the real value of the parameter can have changed a lot during the time between them. Making use of this theoretical Variogram we can interpolate the mesh of points inside Ω, carried out with hexagonal shape of Sp =5m. Fig. 2 shows the explored area in red. Note that in the top left corner, it can be seen that the USV explored several times the same entities. Meanwhile, in the bottom right corner there are some non-explored entities. With the center of each entity EHi, a limnological map is obtained for every physical parameter analyzed in this work. Fig. 6a shows the map for the DO. Furthermore, by assessing Fig. 6a, it can be seen that the maximal rate of DO in this region comes from 1.1mg/l (dark blue) to 9.09mg/l (yellow). The DO concentration presents smaller values in the top left corner of the set Ω, which corresponds to the river mouth where there is a suspicion of a source of pollution. By means of the generated maps, the gradient of each parameter can be assessed in order to determine if there is a significance pollution source. Lastly, the variance of the measures are depicted in Fig. 6b, with values from 0to 0.51. The variance takes the maximum values at the non-explored area of Ω(see Fig. 2), i.e., the farthest points to the trajectory. 4.3 Map construction: Proposed approach The creation of the measurement map is achieved in two steps. The first step aims at determining, thanks to the function isInside, the set of samples made in each constructed entity Epi. The average of these samples leads to the estimation of one value for each entity Epi, and the uncertainty associated to each entity Epiestimation is determined by computing the variance between the involved measurements. The second step concerns the non-explored entities Epjfor which a neighborhood propagation of the values is proposed. To this end, a neighborhood matrix of the entities Epis built. It aims at determining which entities Epihave common edge. Two examples are provided in Fig. 7, with square and hexagonal entities. For the square Entity Esqr in Fig. 7a, and the hexagonal Entity EHin Fig. 7b, the neighborhood matrices Nsqr and NHare given in Eq. (1), respectively. In Nsqr, all the 1values from the fifth line show that the entity Esqr5has as neighbours the entities Esqr2,Esqr4,Esqr6and Esqr9.InNH, the 1from the second line shows that neighbours of the entity EH2are: EH1,EH3,EH7and EH8. (a) Square Entity Esqr.(b) Hexagonal Entity EH. Fig. 7. Map meshing examples. Nsqr =             110000000 111010000 011001000 000110010 010111001 001011000 000000110 000100111 000010011             NH=             110001100 111000110 011100011 001110001 000110000 100001100 110001110 011000111 001100011             (1) The value that is associated to a non-explored entity Epjis estimated as the average value of each of its neighbours. It is computed as the multiplication of the vector of measurement with the jth line of the associated neighborhood matrix. The limnological map is generated with one mean value of the measured DO concentration for each explored entity EHi. Values for the non-explored entities EHjhave been estimated. The final map of DO is depicted in Fig. 8a. Each entity is associated to a value with rate of DO from 1.43mg/l (dark blue) to 8.41mg/l (yellow). The DO is less concentrated in the top left corner because this area corresponds to the outlet of the river that runs through Lille; this river can be loaded with pollutants. Finally, Fig. 8b shows the variance of the measures given an indication of the uncertainties on the sample. The variance for the DO varies from 0to 10. It is maximum (a) Final Average map of DO. (b) Variance of measures of DO based on Average map. Fig. 8. Average Map Generation. in the top left corner. As well as the Kriging strategy, the average method also show a higher concentration of DO where a source of pollution is suspected. In the next Section, the results obtained by both methods are discussed. 4.4 Comparison of both strategies The two approaches based on average map generation (AMG) and Kriging map generation (KMG) are compared considering the computational load, the values of DO, the variance of measurement. To generate the final map, the computational loads are 74sand 14sfor AMG and KMG respectively 4. The difference comes from AMG which consists in considering each entity EHas surface, instead of KMG which takes into account only dots. This computational load is not really an issue in this work because the map is generated after collecting all the sample and not any dynamical mapping has to be performed. The interval of DO from KMG is a little bigger than AMG, but the difference between both maps is not very big, from 0mg/l to 4.87mg/l, with the exception of some EH(see Fig. 9). The maximum rate of error is located in the top left corner. It is possible that it is due to the number of samples considered in each EH(see Fig. 10), and also the duration between measurements of the first and the last exploration of each EH(see Fig. 11). Indeed, the number of samples and the duration of exploration of these EHare bigger. 4These durations were measured on a PC laptop with Intel(R) Core(TM) i7- 10850H with a 2.70GHz clock, 32 GB of RAM. The Operating System is a 64 bits Windows 10 Professionnel version 21H1. Both implementations were developed using Matlab R2021b Fig. 9. Absolute errors between estimated values from the average and the Kriging approaches for each hexagonal entity. Fig. 10. Number of samples collected during the exploration per hexagonal entity. If the duration between two measurement times is high, the water characteristics may change. This is very likely in this zone of experimentation, with a gradient of concentration due to punctual wastewater output. Depending of the weather or of the river flow, differences in sample values can appear quickly. Also, the number of samples and the duration of exploration of each EHhave a direct impact on the computed measurements variance. The variance of the measurement from the AMG is maximum in the top left corner. In this area, EHare explored with the USV at different times, with a bigger number of samples. It is a way to highlight the importance of the measuring process dynamics. The time and the changes on the parameters could be shown according to the variance. However, this variance is minimum for the non explored area in the bottom right corner. It is mainly due to the step based on neighborhood propagation. This is the main drawback of this approach. At the opposite, as expected, the variance of measurements from the KMG is very much smaller. The variance associated to the non explored EHin the bottom right corner is higher providing implicitly the biggest uncertainties on these measurement. 4.5 Discussion The map extraction from field measurements which consists in detecting the explored area and to discretize it into small entities is very generic. It can be applied to areas with different shapes. Besides, it supports varying the shape of the entity used for discretizing the explored area. However, convex covering shapes, such as triangles, squares or hexagons are preferably used. These shapes share common edges and can be organized to cover the whole area without leaving blanks. Overlapping 6 A. Anderson et al. / IFAC PapersOnLine 55-5 (2022) 1–6 Fig. 11. Duration of exploring each hexagonal entity. between entities is possible, though the usefulness of such overlaps is yet to be investigated. In the case of maps generated to create simulation environments for robots, overlapping entities is a priori not required. Additionally, the size of each entity can be tuned according to the accuracy required for robot navigation. The Kriging approach leads to accurate map with a small variance, even if some estimations seem inaccurate. However, this approach is not suitable to take into account dynamics in the measuring process. In this case spatio-temporal Kriging is required. 5. CONCLUSION AND PERSPECTIVES This paper targets environmental missions to assess water quality by means of aquatic robots. Experiments we have conducted expose critical points related to data collection that can be improved by the study and the implementation of control strategies for Unmanned Surface Vehicles. To this end, a limnological map of the region of interest is necessary to conduct simulations with different scenarios before the field implementation. In this context, and based on validated real data collection, we have provided an estimated parameters map of a region of interest. The proposed map was computed using a known data interpolation method, namely Kriging. Kriging shows some limitations in this kind of non-studied scenario, mainly due to the gap of time between measurements. In future works, in order to improve the parameter estimation of both methodologies, the strategies need to be adapted to a more appropriate dynamic context. 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