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ACE in the Hole - Adaptive Contour Estimation using Collaborating Mobile Sensors Sumana Srinivasan, Krithi Ramamritham and Purushottam Kulkarni Department of CSE, Indian Institute of Technology Bombay, Mumbai. Contour Estimation Estimation of the boundary formed by connecting a set of points of equal value in a field e.g., temperature, pressure, pollutant concentration Applications: Estimating extent of oil spills - a prerequisite for containment and corrective action (as in figure), tracking pollutant flows, study of plankton assemblages 1. 2. 3. Nest #points on the estimated contour Nact #points on the actual contour Uses image processing for Combine local samples to estimation. form a global estimate. Exploit mobility samples. Low accuracy due to obstructions and inclement weather affect accuracy High density and large number of sensors for high accuracy and coverage + Fewer sensors can yield high accuracy and coverage Large coverage possible + Low sensor cost and energy Higher sensor cost and energy Cannot adapt to dynamic contours, high cost of redeployment f if f (x, y) ) 2 else f (x, y) ACE Algorithm p3 e p 4 yi (x x^ )2 (y y^ )2 Size of contour, . = Area of envelope bounding estimated points on contour Area of field Spread of sensors, S increase + Can adapt to dynamic contours without redeployment p 2 xi S = Area of convex hull of current positions Parameter Contour Sensor Communication Energy Movement 2. Spread Always SA Assumptions Choose direction that minimizes spread function d 2 sf ( ) 2 Continuous Error free,, self-localized Single-hop Mobility+Communication+Computation+ Sensing Step-wise discrete • ACE provides best-of-both-worlds solution • Enables sensors to intelligently choose between direct descent and spread Target Angle ' • Adapts to type of deployment, size of contour and distance from contour • Distributed co-ordination for efficient contour coverage • Performs high precision, low latency and low energy estimation Evaluation Setup and Simulation Parameters Pollutant Field Light Field WQMAP - a tool for simulating pollutant dispersion, Three pollutant load sites, 120 time steps for simulation Measurements taken at every grid point on 15x15 grid with three light sources using Crossbow Mote Parameter Description Value l Length of grid Maximum steps allowed per sensor Number of simulation runs Estimation frequency Sensing radius Transmission range Large Medium Small 500, 140 2000 1000 Every 5 steps √2 √l nmax nsim nest rsense Rtrans Contours Large Medium Small Large Medium Small DD Other Issues • Handle limited transmission range • Support discontinuous contours Latency high when sensors are deployed far and contour is small. Need to spread judiciously!! Estimating centroid Centroid of envelope bounding • estimated points on contour if sensors converge or • estimated convergence points if sensors not converged. > 50% of field area > 10% - 50% of field area < 10% of field area Precision Comparison (Bounded Energy) Latency Comparison (Unbounded Energy) ACE Conclusions Area of field Contours Use wall moving algorithm to trace • Estimate (xˆ, yˆ) such that f((xˆ, yˆ) = • If (x,y) is the current position of the sensor, then STEP 2: Coverage Phase • Use Nonlinear regression to fit (xi, yi,zi) and compute coefficients using Nelder Mead simplex optimization zi p0 p1 e Pi Path length of ith tracing sensor Indicator of energy consumed Mobile Sensors to ) 2 Latency high when sensors are collocated and contour is big. Need to spread!! Nact In-situ Sensing Static Sensors d f (1 | Latency = argmaxi(Pi) tanh( S) 0 1 Choose direction that minimizes the distance function f Distance from Contour, as f d f (1 ) s f 1. Direct Descent DD d f (1 Precision = | Nact Nest Contour Estimation Techniques High deployment cost STEP 1: Converge Phase How do sensors approach and surround the contour efficiently? How do sensors co-ordinate for distributed contour estimation? How do sensors adapt to different deployments, sizes and shapes of contours? Given a scalar field with varying field value, the task is to estimate a contour of a given value with maximum precision and minimum latency 3. Adaptive Contour Estimation ACE Choose direction that minimizes the adaptive spread function System Model and Evaluation Metrics Problem Definition Remote Sensing Movement Strategies Challenges Comparison of Sensors Movement Strategies Feasibility and Energy Characterization on Robotic Test bed SA •11x8 grid with granularity 8 cm with single slit neon source. • ATMEGA 128, 11MHz processor, 2.4GHz CDMA, 3 white line sensors, 2 shaft encoders, 2 ultra low power DC motors, rotating arm with 2 servo motors Deployment Latency CP Latency CP Latency CP Non-clustered 139 2 498 11 248 8 100 100 100 142 2 681 15 268 7 100 71 63 229 4 780 16 319 7 100 78 29 Clustered 375 8 845 23 276 25 100 99 96 441 5 1006 17 319 7 100 31 11 483 5 1119 12 326 11 78 22 4 Convergence Percentage, CP = Number of runs at least one sensor converged on the contour Total number of runs Non-clustered: Large and Small contours: ACE DD Medium contour: ACE < DD by 22% and ACE < SA by 38% Clustered: All contours, ACE < DD by 7-12% and ACE < SA by 4-20% Acknowledgement: We thank Parmesh Ramanathan, Sachitanand Malewar, Amey Apte and GRAM++ team at IITB for their support. Non-clustered deployment (Medium contour) Clustered deployment (Medium contour) Max. steps > 100: • Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30% • Clustered: ACE > DD and SA by 30-45% Sensors directly approach the contour DD Latency = 818 Max. steps ≤ 100: ACE DD for all deployments Sensors only spread around the centroid SA Latency = 623 Contours Sensitivity to Design Parameters Deployment Non-clustered Medium Convergence Percentage is uniformly higher than DD and SA Clustered Distribution of Latency Differences Non-clustered Small Clustered Algorithm ACE DD ACE DD ACE DD ACE DD Total Energy 2030J 2700J 3342J 3890J 1249J 1335J 1417J 1587J Summary of Results Small Contour Non-clustered deployment (Medium contour) Clustered deployment (Medium contour) Very high probability that ACE has lesser latency than DD - Factor of 6 for non-clustered and 8 for clustered deployments Medium Contour ACE adapts best to distance from the contour, size of contour and extent of spread of sensors Sensors 7 and 8 overlap ACE (without redirection) Latency = 451 Sensors 1,5,7,9 redirected without overlap ACE (with redirection) Latency = 383 Adaptive Contour Estimation (ACE) • Minimizes latency 7-22% over DD and 4-38% over SA • Maximizes convergence percentage 8-45% over DD and 30-62% over SA • Maximizes precision by 15-40% for bounded steps • Consumes 7-24% less energy over DD • Latency and prediction error are highly correlated