ASAP Kickoff Meeting June 28-29, 2004 Adaptive Sampling Plans: Optimal Mobile Sensor Array Design

1. ASAP Kickoff MeetingJune 28-29, 2004Adaptive Sampling Plans:Optimal Mobile Sensor Array Design Naomi Ehrich Leonard Mechanical and Aerospace Engineering Princeton University and Derek Paley, Francois Lekien, Edward Fiorelli, Pradeep Bhatta

2. Increasing spatial/temporal scales of interest Gliders Propeller-driven AUVs Increasing endurance, decreasing speed Adaptive Sampling Objectives Broad-area Coverage (minimize synoptic error) Feature tracking (sample significant dynamics) Aircraft Ships

3. Top Three Tasks • Plan trajectories. • Adapt trajectories. • 3. Stably coordinate vehicles on trajectories. Increasing frequency of feedback

4. Top Three Tasks For Feature Tracking (eg, with propeller-driven AUVs) • Plan trajectories. • Adapt trajectories. • 3. Stably coordinate vehicles on trajectories. Best tracks for reaching and sampling dynamic “hot spots”. Increasing frequency of feedback Gradient climbing and front tracking. Coordinated formation control.

5. Top Three Tasks For Broad-Area Coverage (with the glider fleet) • Plan trajectories. • Adapt trajectories. • 3. Stably coordinate vehicles on trajectories. Best patterns given a priori statistics for process of interest. Increasing frequency of feedback As statistics change and as # gliders in the water changes. Coordinate relative positions of vehicles on planned patterns.

6. AOSN-II Glider Measurements SIO gliders WHOI gliders

7. Gridded error map computed from - location of measurements taken - assumed measurement error - space-time covariance of process of interest. • Consider Gaussian covariance with - spatial scale s - temporal scale t. • Metric computed from error map • - average error over area. • - percent of area with error below a chosen threshold. Objective Analysis [Gandin, 1965], [Bretherton, Davis and Fandry, 1976]

8. Error Map for SIO and WHOI Gliders During AOSN-II SIO Gliders WHOI Gliders

9. AOSN-II Glider Performance Profile Performance metric is entropic information in the estimate, (negative of entropy of the error). SIO Gliders WHOI Gliders

10. Task 1: Plan Trajectories for Broad-Area Coverage with Glider Fleet • Given statistics and fleet characteristics: • s, t • # gliders = N • glider speed = v • Design periodic trajectories (loops), e.g., transects, racetracks, • that minimize OA error metric: • # loops, # gliders per loop • size, shape and location of each loop

11. e too small, best l best e, best l best e, l too big e too big, l too big Example:

12. Task 2: Adapt Trajectories for Broad-Area Coverage with Glider Fleet • Goal: • Adapt trajectories to changing statistics, inhomogeneities in data, etc. • Adapt trajectories to recovery/deployment of gliders, etc. • Action: • Compute new optimal loops • Determine optimal coordinated transit paths

13. Task 3: Stably Coordinate Gliders on Trajectories • Use real-time feedback control to • ensure optimal coordination of • gliders w.r.t. their loops. • Performance increases with • feedback rate. • Fully automate this task.

14. Requirements for Success • Full fleet of gliders dedicated to optimal coverage • throughout experiment. • Access to changing statistics (covariance function) for • processes of interest. • 3. Automated feedback for lowest level coordinated control • (to maintain gliders on tracks without bunching, etc.) • Requirements for adaptation of propeller-driven vehicles, • airplanes, ships: TBD.

15. Optimal eccentricity and size of ellipse