Narges Noori Alessandro Renzaglia Josh Vander Hook PI ... · This work is supported by NSF Awards...
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Narges Noori [email protected] PI: Volkan Isler [email protected] Robotic Sensor Networks http://rsn.cs.umn.edu/ This work is supported by NSF Awards #0916209, #0917676 and #1111638. We gratefully acknowledge the members of Sorensen lab for their help with data collection and field experiments Josh Vander Hook [email protected] Alessandro Renzaglia [email protected] • Carp are suspected to loiter in certain regions of the lake. • We can formulate a search of these regions as a combination of TSPN and coverage. • We present an algorithm that exploits the geometry of the neighborhoods to guarantee coverage in near-optimal time. Once the robot finds the cluster of fish, we use bearing measurements to localize each of them to map out the cluster. The goal is to localize a static target to desired precision as quickly as possible. • We obtain bearing measurements using sampled signal strength by rotating the antenna. • These measurements are fused to improve the estimate of the target location. • Each measurement location is determined by an online, adaptive algorithm. • We provide guarantees on the time to localize any tag • … and prove the near-optimality of the measurement strategy. • Repeated field experiments show the theoretical bounds hold in practice. OPTIMAL Ongoing work is focused on two subjects: Moving Targets, and Coordinated Tracking Using Multiple Robots OPTIMAL log 1) J. Vander Hook, P. Tokekar, V. Isler. Bearing-Only Active Target Localization Strategies for a System of Two Communicating Mobile Robots: Full Technical Report . 2013 2) J. Vander Hook, V. Isler. Pursuit and Evasion with Uncertain Bearing Measurements IEEE Transactions on Robotics. In Review. 1) P. Tokekar, J. Vander Hook, and V. Isler. Active Target Localization for Bearing Based Robotic Telemetry. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2011. 2) J. Vander Hook, P. Tokekar , and V. Isler. Cautious Greedy Strategy for Bearing-based Active Localization: Experiments and Theoretical Analysis. ICRA, 2012. 3) J. Vander Hook, V. Isler. Pursuit and Evasion with Uncertain Bearing Measurements IEEE Transactions on Robotics. In Review. Set of discrete nodes on a line segment [0,1,…,N]. Searcher: can move to left (L), to right (R) or stay (S) Problem Statement: Find the strategy that maximizes the probability of capture given limited time and energy. Only time constraint States: (searcher’s position, searcher’s belief) Belief (B) is not smooth Represent B by uniform bins with exponentially increasing width Uniform Strategies ( ) ( ) Best ( 2 ) ( 2 ) MDP Simulation (red). Closed form (blue) Energy Constraint Optimal strategy is to move then wait How much to move and how much to wait? : moving capture prob : waiting capture prob = −1 +1 + + 1 + ( +1 + 1) 1) N. Noori, A. Renzaglia, J. Vander Hook, V. Isler. Constrained Probabilistic Search for a One-Dimensional Random Walk. Submitted to IEEE Transaction on Robotics (T-RO), 2014. 1) P. Tokekar, D. Bhadauria, A. Studenski, and V. Isler. A Robotic System for Monitoring Carp in Minnesota Lakes. Journal of Field Robotics, 2010. 2) J. Vander Hook, P. Tokekar , E. Branson, P. Bajer, P. Sorensen, and V. Isler. Local Search Strategy for Multi-Modal, Multi-Target Active Localization of Invasive Fish. 13 th ISER, 2012. 3) P. Tokekar, E. Branson, J. Vander Hook, V. Isler. Tracking Aquatic Invaders IEEE Robotics and Automation Magazine. September, 2013. Solution: Capture region of the shortest path polygons with obstacles: Guard two shortest paths. Split the region in between by the third pursuer Evader moves from 1 to 2 . Pursuer moves to the projection of 2 onto the next wavefront. 1 2 1 2 Three pursuers can capture the evader on a polyhedral surface with boundary (Homeomorphic to an open disk) in finite time. A single pursuer can capture the evader on a convex terrain (height maps with no valleys or hills) in finite time. Discretize surface by wavefronts W. Image of the wavefronts onto the 2D plane. Projection of the evader onto the wavefront nontrivial example More than one shortest path between two points. 1) N. Noori, V. Isler. Lion and Man Game on Polyhedral Surfaces with Boundary. Submitted to IROS, 2014. 1) N. Noori, V. Isler. The Lion and Man Game on Convex Terrains. Submitted to the International Workshop on Algorithmic Foundations of Robotics (WAFR), 2014. • Two measurements taken near each other are less informative. • The estimate is more precise when robots separate. • However, hey must meet to communicate and update their collective estimate. • We simultaneously optimize • We provide an approximation of the optimal algorithm for many communicating robots to locate a stationary target Original game: circular arena
Transcript of Narges Noori Alessandro Renzaglia Josh Vander Hook PI ... · This work is supported by NSF Awards...
Narges Noori [email protected]
PI: Volkan Isler [email protected]
Robotic Sensor Networks http://rsn.cs.umn.edu/
This work is supported by NSF Awards #0916209, #0917676 and #1111638. We gratefully acknowledge the members of Sorensen lab for their help with data collection and field experiments
Josh Vander Hook [email protected]
Alessandro Renzaglia [email protected]
Not necessarily a terrain
Terrain
• Carp are suspected to loiter in certain regions of the lake. • We can formulate a search of these regions as a combination of TSPN and
coverage. • We present an algorithm that exploits the geometry of the neighborhoods
to guarantee coverage in near-optimal time.
Once the robot finds the cluster of fish, we use bearing measurements to localize each of them to map out the cluster. The goal is to localize a static target to desired precision as quickly as possible. • We obtain bearing measurements using sampled signal strength by rotating the antenna. • These measurements are fused to improve the estimate of the target location. • Each measurement location is determined by an online, adaptive algorithm. • We provide guarantees on the time to localize any tag • … and prove the near-optimality of the measurement strategy. • Repeated field experiments show the theoretical bounds hold in practice.
OPTIMAL
Ongoing work is focused on two subjects: Moving Targets, and Coordinated Tracking Using Multiple Robots
OPTIMAL log 𝜆
1) J. Vander Hook, P. Tokekar, V. Isler. Bearing-Only Active Target Localization Strategies for a System of Two Communicating Mobile Robots: Full Technical Report . 2013 2) J. Vander Hook, V. Isler. Pursuit and Evasion with Uncertain Bearing Measurements IEEE Transactions on Robotics. In Review.
1) P. Tokekar, J. Vander Hook, and V. Isler. Active Target Localization for Bearing Based Robotic Telemetry. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 2011. 2) J. Vander Hook, P. Tokekar , and V. Isler. Cautious Greedy Strategy for Bearing-based Active Localization: Experiments and Theoretical Analysis. ICRA, 2012. 3) J. Vander Hook, V. Isler. Pursuit and Evasion with Uncertain Bearing Measurements IEEE Transactions on Robotics. In Review.
Set of discrete nodes on a line segment [0,1,…,N]. Searcher: can move to left (L), to right (R) or stay (S) Problem Statement: Find the strategy that maximizes the probability of capture given limited time and energy.
Only time constraint States: (searcher’s position, searcher’s belief)
Belief (B) is not smooth Represent B by uniform bins with exponentially increasing width
Uniform Strategies (𝑅𝑘𝑆)𝑀(𝐿𝑘𝑆)𝑛
Best (𝑅2𝑆)𝑀 (𝐿2𝑆)𝑛
MDP
Simulation (red). Closed form (blue)
Energy Constraint Optimal strategy is to move then wait How much to move and how much to wait?
𝑃𝑚: moving capture prob 𝑃𝑠: waiting capture prob
𝑡𝑛 = 𝑝 𝑡𝑛−1 + 1 + 𝑠 𝑡𝑛 + 1 + 𝑞(𝑡𝑛+1 + 1)
1) N. Noori, A. Renzaglia, J. Vander Hook, V. Isler. Constrained Probabilistic Search for a One-Dimensional Random Walk. Submitted to IEEE Transaction on Robotics (T-RO), 2014.
1) P. Tokekar, D. Bhadauria, A. Studenski, and V. Isler. A Robotic System for Monitoring Carp in Minnesota Lakes. Journal of Field Robotics, 2010. 2) J. Vander Hook, P. Tokekar , E. Branson, P. Bajer, P. Sorensen, and V. Isler. Local Search Strategy for Multi-Modal, Multi-Target Active Localization of Invasive Fish. 13th ISER, 2012. 3) P. Tokekar, E. Branson, J. Vander Hook, V. Isler. Tracking Aquatic Invaders IEEE Robotics and Automation Magazine. September, 2013.
Solution: Capture region of the shortest path
polygons with obstacles: Guard two shortest paths. Split the region in between by the third pursuer
Evader moves from 𝑒1 to 𝑒2. Pursuer moves to the projection of 𝑒2 onto the next wavefront.
𝑒1
𝑒2
𝑝1
𝑝2
Three pursuers can capture the evader on a polyhedral surface with boundary (Homeomorphic to an open disk) in finite time.
A single pursuer can capture the evader on a convex terrain (height maps with no valleys or hills) in finite time.
Discretize surface by wavefronts W.
Image of the wavefronts onto the 2D plane.
Projection of the evader onto the wavefront
nontrivial example More than one shortest path between two points.
1) N. Noori, V. Isler. Lion and Man Game on Polyhedral Surfaces with Boundary. Submitted to IROS, 2014.
1) N. Noori, V. Isler. The Lion and Man Game on Convex Terrains. Submitted to the International Workshop on Algorithmic Foundations of Robotics (WAFR), 2014.
• Two measurements taken near each other are less informative. • The estimate is more precise when robots separate. • However, hey must meet to communicate and update their collective estimate. • We simultaneously optimize • We provide an approximation of the optimal algorithm for many communicating robots to
locate a stationary target
Original game: circular arena
