Environmental Boundary Tracking and Estimation Using Multiple Autonomous Vehicles Andrea Bertozzi University of California, Los Angeles Thanks to Zhipu Jin, Rick Huang, Abhijeet Joshi, Todd Wittman, Trevor Ashley, Zhong Hu, and others This research supported by the Army Research Office, the National Science Foundation, and the Office of Naval Research

2 Outline of Talk Prior Work Local Boundary Tracking Algorithm Formulation for Boundary Estimation Formulation and Optimization Simulation Results Testbed Results

Cooperative boundary tracking with unmanned vehicles Such general problems are of current interest for unmanned vehicle operations with specific applications of tracking  coastal algae blooms  chemical plumes  adaptive ocean sampling  oil spills  hazardous chemicals  Work in the controls literature by Zhang and Leonard, Susca et al, Clark and Fierro, Barat and Rendas, and others. Image of Exxon oil spill from

UUV-gas algorithm Where θ is the heading of the vehicle and ω is the angular rate of change. Dm r Rb *M. Kemp, A Bertozzi, D. Marthaler, 2004, Multi-UUV perimeter surveillance, Autonomous Underwater Vehicles, 2004 IEEE/OES, June 2004 Single vehicle UUV-gas: Assuming that only a binary state sensor is available, the vehicle travels around an arc in a clockwise direction when inside the region of interest and counterclockwise when outside the region of interest. The behavior is described by the following: Multiple vehicles – spaced according to gas law.

Caltech Multi-Vehicle Wireless Testbed boundary tracking implementation Kelly vehicle with 700 Mhz laptop, two ducted fans, 3 casters, gyro, barcoded hat, and body frame. Overhead positioning system tracks in real time and sends information back to vehicles. Chung H. Hsieh, Zhipu Jin, D. Marthaler, B. Q. Nguyen, D. J. Tung, ALB, and R. Murray Proc. American Control Conference, 2005 Testbed implementation without sensor noise.

Individual path of (A) Vehicle 1, (B) Vehicle 2, (C) Vehicle 3 while cooperatively searching the boundary. The square, diamond, circle, and triangle represent 1, 40, 80, 120 seconds respectively of each vehicle’s path. (D) Union of boundary crossing point from the three vehicles over 160 seconds (1 lap). The axes are measured in meters. Boundary Search Result Only works with clean sensor data. Large circular motions are inefficient

7 Advanced Control Law Time-corrected algorithm: Includes time difference between crossing points on boundary, Uses a reference angle,  ref Zhipu Jin and ALB IEEE CDC 2008

8 CUSUM Filter for noisy sensor data Upper Lower Zhipu Jin and ALB IEEE CDC 2008

Hidden Markov Model for Time Dependent Boundary Boundary  (k) is determined by parameters s(k)  (k) = g(s(k)) where s evolves according to a Markov chain. We observe the vehicles’ positions as y i (k) = x i (k) + w i (k) where i {1, · · ·,N}. Actually, there exist an offset  (k) between x i and the real boundary. Recursive Bayesian method: the distribution p(s(k)|Y(k)) is predicted from p(s(k −1)|Y(k −1)) and p(s(k)|s(k −1)), and then corrected by the measurement likelihood p(Y(k))|s(k)).. 9 Zhipu Jin and ALB IEEE CDC 2008

Solve as an Optimization Problem 10

2D Boundary Simplification 11

Matrix  12

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Discussion and Future Work Current problem  Needs a good initial guess  Slow convergence to real parameters  More accurate . Future Work  Using more sophisticated model to approximate boundary  Algorithm for updating   Motion patterns of individual vehicles (d(k)) and possible approximation of the distribution p(Y(k)|s(k)).  Realistic models for environmental tracers in air/ocean. 14

Testbed implementation fixed boundary 15 Raw output from sensor (top) Kalman filtered output (bottom) Car on teal tape 3<t<6 and 9<t<12 Vehicle with IR sensor IR onboard sensors

CUSUM Filtering algorithms without/with Kalman Prefliter Without Kalman prefilterWith Kalman prefilter 16

Comparison Bang-bang controller vs. Zhipu Bang-bang controller, no prefilter Time-correction controller, no prefilter 17

Comparison, without/with Kalman prefilter No Kalman prefilter, with time correction Kalman prefilter, with time correction 18

Boundary Tracking with Noise UCLA testbed implementation, single vehicle Processor will decide state based on noisy sensor data Vision system no longer necessary to track boundary Useful if occlusions block vehicle from cameras or if GPS unavailable. Hidden Markov model for changing boundary and multiple vehicles Thanks to Trevor Ashley Harvey, Mudd College, Rick Huang UCLA

Three car alogrithm Three car algoritmLead car position 20

Gradient Free Boundary Tracking in Images Zhong Hu, Todd Wittman, Victor Mejia, ALB We want to segment a region of interest in a (hypespectral) image. Classical gradient-based segmentation methods like active contours and snakes look at all pixels in the image. Ideally, the number of pixels checked would be proportional to the length of the boundary. The solution is to “walk” the boundary. We propose a gradient-free boundary tracking algorithm inspired by the robotic vehicle tracking algorithm developed by (Kemp-Bertozzi-Marthaler 2004). 21

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Gradient free summary Useful method for both high resolution/low SNR images and robotics applications with noisy sensors Time corrected algorithm improves efficiency while still adequately tracking boundary In very high SNR prefiltering of data can be useful Multiple cooperative trackers can perform tasks such as independent tracking and convoy control Possible use for HSI imagery where pixel identification applications sometimes involve cumbersome lookup tables or computationally intensive manifold learning (e.g. bathymetry calculations from remote sensing – C. Bachmann et al IEEE ). 31