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Problem formulation
Problem formulation
9
Connecting the dots
The more concretely one understands the problem, the more likely the person is to come up with a robust solution. Dr. Kshitij Tiwari
Contents 9.1 Relationship between robots and GP 9.2 Scenario 104 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5
Starting configuration 104 Communication strategy 104 Sensing 104 Mission termination conditions Model fusion 105
9.3 Summary
103
105
105
Highlights • • • •
Connection between GPs and robots Nature of observations that can be acquired Starting configuration for robot deployment Requirements for model fusion
Erstwhile chapters have presented non-parametric Bayesian methods, viz., GPs, two classes of robotic path planning, viz., CPP and IPP, and described the various robotic platforms that can be potentially used for monitoring various environments. The aim of this chapter is to connect the dots, i.e., define the roles and interplay of each of these components by explicitly describing the operational setup. Additionally, team deployment configuration and sensing scenario encompassing the potential termination conditions are described.
9.1 Relationship between robots and GP In what follows, each robot is assumed to be a Gaussian Process (GP) expert. What this entails is that the robot is not only capable of deciding where to get the best obMulti-Robot Exploration for Environmental Monitoring. https://doi.org/10.1016/B978-0-12-817607-8.00023-X Copyright © 2020 Elsevier Inc. All rights reserved.
104
Multi-Robot Exploration for Environmental Monitoring
servations from, but is also equally capable of using these observations to train the GP models on-board. Owing to practical and hardware limitations of performing on-board GP inference, most of the results were evaluated in a simulated setup, and thus, sufficient resources were assumed as made available to the robot to carry out its mission. Additionally, the area to be monitored was large, and was covered by multiple robots. This naturally rendered multiple GPs, at the end of mission of each robot.
9.2
Scenario
Most of the environmental phenomena have been traditionally monitored using static sensors placed across the target area. Eventually, this gave rise to discrete datasets which were logged in the format of < Location, Measurement >, making the data discrete in nature. For most simulated testing, these are the datasets that are used to evaluate the model fit, thus, the training data available for GPs becomes inherently discrete in nature. This, in contrast to the real-world, where the data is continuous, is what is fed to the GP experts to train their respective models.
9.2.1 Starting configuration As each robot follows the same objective function which is guided by the amount of information that can be accrued from the candidate locations, they could not be started off from the same start location. Thus, for the most part of this book, the robots were randomly allocated to start locations over multiple trials.
9.2.2 Communication strategy Most of the algorithms were designed for operations under harsh environmental conditions like sub-surface operations in case of marine observations or coal-mine monitoring, etc. In such cases, communication is mostly intermittent or non-existent, so the robots were made independent of their peers. Each robot is an “expert” in the sense that it is a master of its own will and the decisions taken remain unaffected by those of the peers.
9.2.3 Sensing Owing to the discrete nature of the datasets being used for evaluation, each robot was assumed to be equipped with a suitable interoceptive sensor which helps the agent perceive point-samples only where the robot/sensor is located. Additionally, unless specified otherwise, RC-DAS was used for all agents to acquire informative samples by trading off the amount of information to the available resources using a static weight for each component.
Problem formulation
105
9.2.4 Mission termination conditions Two kinds of termination conditions have been discussed in this book, which primarily pertain to the experimental scenario being simulated or real. In case of simulated testing, the robots were allocated a resource budget as a function of “feasible” travel distance that they are expected to cover. This has previously been used in Chap. 8. As opposed to this, for real experiments, an auto-regressive estimator needs to be used to obtain the true residual budget from the robot as the mission progresses. This is described in a greater depth in the upcoming chapters in this part.
9.2.5 Model fusion Upon termination of each respective mission, each GP expert has its respective optimal parameter. A GP model is represented in terms of its mean and covariance functions which can be encoded via the hyper-parameters, meaning that there are multiple models to describe the single environmental phenomenon that each team member was primarily observing. Thus, for a human observer to finally decipher or use these models, there is a need to develop a globally consistent model which begs the question: Who can be trusted amongst the team? This challenge is addressed in a greater detail in Part IV, which focuses on scaling the team size for efficient monitoring, and this aspect is described especially in Chap. 13.
9.3 Summary This is a rather brief chapter which gives a preview of the underlying assumptions and design considerations that govern most of the algorithms that follow suit. Previously, GPs, robots, and path planning mechanisms were discussed separately, but this chapter attempted to connect these components to lay the foundation of a coherent system that will be used for carrying out environmental monitoring operations. In the upcoming chapters (Chaps. 10 and 11) of this part, two pragmatic mission termination criteria for real-world deployments are described before moving on to a discussion on multi-robot teams in Part IV.
9
Connecting the dots
The more concretely one understands the problem, the more likely the person is to come up with a robust solution. Dr. Kshitij Tiwari
Contents 9.1 Relationship between robots and GP 9.2 Scenario 104 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5
Starting configuration 104 Communication strategy 104 Sensing 104 Mission termination conditions Model fusion 105
9.3 Summary
103
105
105
Highlights • • • •
Connection between GPs and robots Nature of observations that can be acquired Starting configuration for robot deployment Requirements for model fusion
Erstwhile chapters have presented non-parametric Bayesian methods, viz., GPs, two classes of robotic path planning, viz., CPP and IPP, and described the various robotic platforms that can be potentially used for monitoring various environments. The aim of this chapter is to connect the dots, i.e., define the roles and interplay of each of these components by explicitly describing the operational setup. Additionally, team deployment configuration and sensing scenario encompassing the potential termination conditions are described.
9.1 Relationship between robots and GP In what follows, each robot is assumed to be a Gaussian Process (GP) expert. What this entails is that the robot is not only capable of deciding where to get the best obMulti-Robot Exploration for Environmental Monitoring. https://doi.org/10.1016/B978-0-12-817607-8.00023-X Copyright © 2020 Elsevier Inc. All rights reserved.
104
Multi-Robot Exploration for Environmental Monitoring
servations from, but is also equally capable of using these observations to train the GP models on-board. Owing to practical and hardware limitations of performing on-board GP inference, most of the results were evaluated in a simulated setup, and thus, sufficient resources were assumed as made available to the robot to carry out its mission. Additionally, the area to be monitored was large, and was covered by multiple robots. This naturally rendered multiple GPs, at the end of mission of each robot.
9.2
Scenario
Most of the environmental phenomena have been traditionally monitored using static sensors placed across the target area. Eventually, this gave rise to discrete datasets which were logged in the format of < Location, Measurement >, making the data discrete in nature. For most simulated testing, these are the datasets that are used to evaluate the model fit, thus, the training data available for GPs becomes inherently discrete in nature. This, in contrast to the real-world, where the data is continuous, is what is fed to the GP experts to train their respective models.
9.2.1 Starting configuration As each robot follows the same objective function which is guided by the amount of information that can be accrued from the candidate locations, they could not be started off from the same start location. Thus, for the most part of this book, the robots were randomly allocated to start locations over multiple trials.
9.2.2 Communication strategy Most of the algorithms were designed for operations under harsh environmental conditions like sub-surface operations in case of marine observations or coal-mine monitoring, etc. In such cases, communication is mostly intermittent or non-existent, so the robots were made independent of their peers. Each robot is an “expert” in the sense that it is a master of its own will and the decisions taken remain unaffected by those of the peers.
9.2.3 Sensing Owing to the discrete nature of the datasets being used for evaluation, each robot was assumed to be equipped with a suitable interoceptive sensor which helps the agent perceive point-samples only where the robot/sensor is located. Additionally, unless specified otherwise, RC-DAS was used for all agents to acquire informative samples by trading off the amount of information to the available resources using a static weight for each component.
Problem formulation
105
9.2.4 Mission termination conditions Two kinds of termination conditions have been discussed in this book, which primarily pertain to the experimental scenario being simulated or real. In case of simulated testing, the robots were allocated a resource budget as a function of “feasible” travel distance that they are expected to cover. This has previously been used in Chap. 8. As opposed to this, for real experiments, an auto-regressive estimator needs to be used to obtain the true residual budget from the robot as the mission progresses. This is described in a greater depth in the upcoming chapters in this part.
9.2.5 Model fusion Upon termination of each respective mission, each GP expert has its respective optimal parameter. A GP model is represented in terms of its mean and covariance functions which can be encoded via the hyper-parameters, meaning that there are multiple models to describe the single environmental phenomenon that each team member was primarily observing. Thus, for a human observer to finally decipher or use these models, there is a need to develop a globally consistent model which begs the question: Who can be trusted amongst the team? This challenge is addressed in a greater detail in Part IV, which focuses on scaling the team size for efficient monitoring, and this aspect is described especially in Chap. 13.
9.3 Summary This is a rather brief chapter which gives a preview of the underlying assumptions and design considerations that govern most of the algorithms that follow suit. Previously, GPs, robots, and path planning mechanisms were discussed separately, but this chapter attempted to connect these components to lay the foundation of a coherent system that will be used for carrying out environmental monitoring operations. In the upcoming chapters (Chaps. 10 and 11) of this part, two pragmatic mission termination criteria for real-world deployments are described before moving on to a discussion on multi-robot teams in Part IV.