| The evolution of many natural and man-made environmental events can be represented as scalar functions of time and space. Examples include the boundary and intensity of wildfires, of waste spills in bodies of water, and of natural emissions of methane from the earth. The difficult task of understanding and monitoring these processes can be accomplished through the use of coordinated groups of vehicles. This thesis devises a method to determine positions of the members of a group of vehicles in the domain of a scalar function which lead to effective sensing of the function. This method involves equating the moments of a scalar function to the moments of a group of positions, which results in a system of polynomial equations to be solved. This methodology also allows for other explicit geometric constraints, in the form of polynomial equations, to be imposed on the vehicles. Several example simulations are shown to demonstrate the advantages and challenges associated with the moment matching technique. |
