# Learning and monitoring of spatio-temporal fields with sensing robots

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Abstract

This thesis proposes new algorithms for a group of sensing robots to learn a para-metric model for a dynamic spatio-temporal field, then based on the learned modeltrajectories are planned for sensing robots to best estimate the field. In this thesiswe call these two parts learning and monitoring, respectively.For the learning, we first introduce a parametric model for the spatio-temporalfield. We then propose a family of motion strategies that can be used by a groupof mobile sensing robots to collect point measurements about the field. Our motionstrategies are designed to collect enough information from enough locations at enough different times for the robots to learn the dynamics of the field. In conjunction withthese motion strategies, we propose a new learning algorithm based on subspaceidentification to learn the parameters of the dynamical model. We prove that as thenumber of data collected by the robots goes to infinity, the parameters learned byour algorithm will converge to the true parameters.For the monitoring, based on the model learned from the learning part, threenew informative trajectory planning algorithms are proposed for the robots to collect the most informative measurements for estimating the field. Kalman filter is usedto calculate the estimate, and to compute the error covariance of the estimate. Thegoal is to find trajectories for sensing robots that minimize a cost metric on theerror covariance matrix. We propose three algorithms to deal with this problem.First, we propose a new randomized path planning algorithm called Rapidly-exploringRandom Cycles RRC and its variant RRC* to find periodic trajectories for thesensing robots that try to minimize the largest eigenvalue of the error covariancematrix over an infinite horizon. The algorithm is proven to find the minimum infinitehorizon cost cycle in a graph, which grows by successively adding random points.Secondly, we apply kinodynamic RRT* to plan continuous trajectories to estimatethe field. We formulate the evolution of the estimation error covariance matrix as adifferential constraint and propose extended state space and task space sampling tofit this problem into classical RRT* setup. Thirdly, Pontryagin’s Minimum Principleis used to find a set of necessary conditions that must be satisfied by the optimaltrajectory to estimate the field.We then consider a real physical spatio-temporal field, the surface water temper-ature in the Caribbean Sea. We first apply the learning algorithm to learn a lineardynamical model for the temperature. Then based on the learned model, RRC andRRC* are used to plan trajectories to estimate the temperature. The estimationperformance of RRC and RRC* trajectories significantly outperform the trajectoriesplanned by random search, greedy and receding horizon algorithms.

Boston University Theses and Dissertations -

Autor: ** Lan, Xiaodong - - **

Fuente: https://open.bu.edu/