1. Sampling Design: Determine Where to Take Measurements Sampling Design: Determine Where to Take Measurements Empirical Approaches to Sensor Placement: Mobile Sensors and Iterative Deployment Empirical Approaches to Sensor Placement: Mobile Sensors and Iterative Deployment Deployment via Iteration and Mobility Tom Schoellhammer 1, Sameera Poduri 2, Amarjeet Singh 3, Bin Zhang 2 1 CSL – http://lecs.cs.ucla.edu 2 RESL – http://robotics.usc.edu/resl 3 EE http://ee.ucla.edu Sensor Placement with a Limited Sensor Budgets is Difficult Sensor Placement with a Limited Sensor Budgets is Difficult Sensing using Mobile Robots Mobile robots can provide complete coverage for large domains. Traveling and sensing cost demands efficient path planning. Estimation of the phenomenon can be improved by –Maximizing information quality: Initial observations are available by using dense sampling –Minimizing reconstruction Error: Initial estimation on the environment using observations from static sensors Iterative Placement Deployment of Cameras in an outdoor deployment –performance varies depending on obstacles, lighting conditions, background contrast, luminance, etc. –except obstacles, other factors are difficult to model. Deploying sensors belowground –High installation cost –Soils can take weeks to resettle Problem: A sensing environment divided into discrete observation locations (  ) Constraint: Limited budget (B) over the sensing and the traveling cost (C) for each available mobile robot (R i, i 2 N). Objective: Find a set of paths (P i ), one for each robot, such that the total utility: field estimation or collected information (I ( [ P i )) over the visited locations is optimized. Formally: min p µ  (IMSE(P)) subject to C(P) · B – When optimizing reconstruction accuracy max P i µ  I( [ P i ) subject to C(P i ) · B, 8 i · N – When optimizing information quality Optimizing reconstruction accuracy Use Local Linear Regression to minimize the integrated mean square error (IMSE) The IMSE can be estimated by using the sample density and Hessian matrix of the scalar field Associate with each location in , a reward defined as the decrease of the IMSE if more sensor readings taken at x. Static sensor nodes are deployed uniformly and the readings is used to estimate the reward for each location. Center for Embedded Networked Sensing UCLA – UCR – Caltech – USC – UC Merced Optimizing collected information Use mutual information over the set of observed locations as the optimization criterion Provides approximation guarantee of O (logN) Provided a simple sequential allocation approach for multiple robots with strong (near optimal) approximation guarantee: If  is the approximation guarantee for single robot path planning then sequential-allocation provides approximation guarantee of (1+  ) Robot-1 Robot-3 Robot-2 Path for Single RobotA buoy and a robotic boat Path Coverage Problem: Cover a path of arbitrary complexity Constraints: The environment has several obstacles, and the cameras used have limited view Objective: Minimize the number of cameras while ensuring that every point in the path is covered Map obstacles in the environment Start with a uniform deployment Gather detection data and estimate the camera’s detection range at different points (and different directions) along the path. Solve 1D connected set cover to find optimal camera locations Data-Driven Approach Camera set-upObstacle mapOptimal deployment Auditioning Problem: Accurately predict belowground conditions Constraints: Meteorological measurements are available, soil and leaf litter properties are unavailable Objective: Apply automatic fitting techniques to fit in the presence of unknown paramters Auditioning Model belowground temperature from aboveground meteorological measurements, leveraging phenomenon specific knowledge Phenomenon specific models cannot be used directly due to several unknown physical parameters: soil composition, leaf litter thickness, leaf litter composition Apply multivariate adaptive spline regression to automatically choose inputs We address placement in several sensing scenarios using mobility and iterative deployment