ASAP Kickoff MeetingJune 28-29, 2004

Adaptive 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

Adaptive Sampling Objectives

Broad-area Coverage(minimize synoptic error)

Feature tracking(sample significant dynamics)

Aircraft Ships

Increasing spatial/temporal scales of interest

Gliders Propeller-driven AUVsIncreasing endurance, decreasing speed

Top Three Tasks

1. Plan trajectories.

2. Adapt trajectories.

3. Stably coordinate vehicles on trajectories.

Increasingfrequency of feedback

Top Three Tasks

1. Plan trajectories.

2. Adapt trajectories.

3. Stably coordinate vehicles on trajectories.

Increasingfrequency of feedback

Best tracks for reaching and sampling dynamic “hot spots”.

Gradient climbing and front tracking.

Coordinated formation control.

For Feature Tracking (eg, with propeller-driven AUVs)

Top Three Tasks

1. Plan trajectories.

2. Adapt trajectories.

3. Stably coordinate vehicles on trajectories.

Increasingfrequency of feedback

Best patterns given a priori statisticsfor process of interest.

As statistics change and as # gliders in the water changes.

Coordinate relative positions of vehicleson planned patterns.

For Broad-Area Coverage (with the glider fleet)

AOSN-II Glider Measurements

SIO gliders WHOI gliders

Objective Analysis[Gandin, 1965], [Bretherton, Davis and Fandry, 1976]

• 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 - temporal scale

• Metric computed from error map

- average error over area. - percent of area with error below a chosen threshold.

Error Map for SIO and WHOI Gliders During AOSN-II

SIO Gliders

WHOI Gliders

AOSN-II Glider Performance Profile

Performance metric is entropic information in the estimate,(negative of entropy of the error).

SIO Gliders WHOI Gliders

Task 1: Plan Trajectories for Broad-Area Coverage with Glider Fleet

Given statistics and fleet characteristics:- - # 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

Example:

e too small, best best e, too big

e too big, too bigbest e, best

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

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.

Requirements for Success

1. Full fleet of gliders dedicated to optimal coverage throughout experiment.

2. 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.

Optimal eccentricity and size of ellipse