Ant Robotics. Terrain Coverage. Motivation. Overview

Transcription

1 Overview Ant Robotics Terrain Coverage Sven Koenig College of Computing Gegia Institute of Technology Overview: One-Time Repeated Coverage of Known Unknown Terrain with Single Ant Robots Teams of Ant Robots f - Mine Sweeping - Surveillance - Surface Inspection - Guarding Terrain Structure: - Motivation - Theetical Results - Real-Time Search - Empirical Results - Simulation - Actual Robots joint wk with: Jonas Svennebring, Boleslaw Szymanski (RPI), and Yaxin Liu Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Motivation cheap limited computational and sensing abilities fault tolerance groups of robots parallelism Motivation DC06 Cye Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Robomow Koala Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; 2003

2 Motivation Approach 1: POMDP-Based Navigation Architecture You want to build a team of robots that cover terrain repeatedly, f example, to guard a museum at night. The terrain could be initially unknown. The terrain could change dynamically. The robots have very noisy actuats senss. The robots can fail. You want to build a team of robots that cover terrain repeatedly, f example, to guard a museum at night. The terrain could be initially unknown. The terrain could change dynamically. The robots have very noisy actuats senss. The robots can fail. Probabilistic Planning R. Simmons and S. Koenig. Probabilistic Robot Navigation in Partially Observable Environments. In Proceedings of the International Joint Conference on Artificial Intelligence, , 199. Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; 2003 Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Approach 1: POMDP-Based Navigation Architecture Approach 1: POMDP-Based Navigation Architecture simulat interface to Xavier Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Xavier Advantages of Navigation with POMDPs - unifm, theetically grounded framewk - maintains arbitrary probability distributions over the poses - explicitly models all uncertainty using probabilities - utilizes all available sens data (landmarks, robot movements) - robust towards sens errs (no explicit exception handling required) Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

3 Approach 2: Ant Robotics Approach 2: Ant Robotics Path Following using Pheromone Traces You want to build a team of robots that cover terrain repeatedly, f example, to guard a museum at night. The terrain could be initially unknown. The terrain could change dynamically. The robots have very noisy actuats senss. The robots can fail. Probabilistic Planning no location estimates! no planning! no direct communication! simpler hardware and software! Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; sht lived traces - alcohol [Sharpe et al.] - heat [Russell] - od [Russell el at.] - virtual traces [Vaughan et al.; Payton et al.] Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Approach 2: Ant Robotics Explation and Coverage using Pheromone Traces Theetical Results (Real-Time Search) - long lived traces [Svennebring and Koenig] Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

4 Initially, the u-values u(s) are zero f all states s. 1. s := start location 2. s := a neighbing location of s with a minimal u-value 3. u(s) := 1 + u(s). move the ant robot to location s. go to time step 0 time step 1 time step 2 time step time step time step time step 6 time step Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; The numbers (= markings) codinate the ant robots! Cover Time (steps) Random Walk random walk 1000 node counting programming: Jonas Svennebring Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Coverage Number coverage number Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

5 The numbers (= markings) codinate the ant robots! 100 Additional Real-Time Search Methods Time (steps) : Shared Markings node counting (individual markings) : Individual Markings node counting (shared markings) Number of Robots number of robots Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Initially, the u-values u(s) are zero f all states s. 1. s := start location 2. s := a neighbing location of s with a minimal u-value 3. u(s) := 1 + u(s) u(s) := 1 + u(s ) Kf s LRTA* (= Wagner s VAW) if u(s) u(s ) then u(s) := 1 + u(s) Wagner s Update Rule u(s) := max(1 + u(s), 1 + u(s )) Thrun s Update Rule. move the ant robot to location s. go to 2. Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Theem: Teams of ant robots that all use the same real-time search method cover all strongly connected graphs repeatedly. Proof: QED Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; time to reach goal (log scale) 1e+12 1e+11 1e+10 1e+09 1e+08 1e+07 1e #vertices/2+1/2-3 [Koenig and Simmons, 1992] number of vertices (n) number of vertices Kf s LRTA* guaranteed to be no wse than O(#vertices diameter) on any strongly connected graph Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; start [Koenig and Simmons, 1992] goal

6 time to reach goal (log scale) 1e+11 1e+10 1e+09 1e+08 1e+07 1e #vertices sqrt((1/6-epsilon)#vertices) [Koenig and Szymanski, 1999] simulation start goal fmula number of vertices (n) number of vertices Kf s LRTA* guaranteed to be no wse than O(#vertices diameter) on any strongly connected graph [Koenig and Simmons, 1992] Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Initially, the u-values u(s) are zero f all states s. 1. s := start location 2. s := a neighbing location of s with a minimal u-value 3. u(s) := 1 + u(s) u(s) := 1 + u(s ) if u(s) u(s ) then u(s) := 1 + u(s) u(s) := max(1 + u(s), 1 + u(s )). move the ant robot to location s. go to 2. exponential polynomial polynomial polynomial Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Is the wst-case of a single ant robot that uses node counting polynomial exponential in the number of vertices (an adversary can choose the graph topology, the start vertex, the goal vertex, and the tie-breaking rule), - if the strongly connected graphs are directed? - if the strongly connected graphs are undirected? - if the strongly connected graphs are undirected grids? yes (see 3 slides ago) yes (see 2 slide2 ago) unknown Wagner s Update Rule Kf s LRTA* Thrun s Update Rule Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; number of robots [Koenig et. al., 2001] Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

7 Kf s LRTA* Empirical Results (Simulation and Actual Robots) BORG Lab [Svennebring and Koenig, 2003] Wagner s Update Rule Thrun s Update Rule [Koenig et. al., 2001] Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Empirical Results (Actual Robots) Empirical Results (Actual Robots) Ant Robot Hardware Ant robots that all use node counting are easy to implement! Thanks to Ashwin Ram f the hardware. A: trail sens B: trail sens C: pen D: micro-controller E: RS232 interface Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

8 Empirical Results (Actual Robots) Empirical Results (Actual Robots) Ant Robot Software our ant robots use a schema-based navigation strategy with an obstacle avoidance behavi and a trail-avoidance behavi Ant Robot Software our ant robots use a schema-based navigation strategy with an obstacle avoidance behavi and a trail-avoidance behavi Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Empirical Results (Actual Robots) Empirical Results (Simulation and Actual Robots) Our ant robots cover closed terrain even if - they don t know the terrain in advance the terrain changes, - some ant robots fail, - some ant robots are moved without realizing this, - some trails are destroyed. destroyed areas of trails low-intensity trails Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

9 Empirical Results (Actual Robots) Empirical Results (Modeling with Real-Time Search) The terrain gets saturated with trails over time randomly drop a drop of ink into this cell increase this number by one with probability (16-)/16 end of first coverage end of third coverage Initially, the u-values u(s) are zero f all states s. 1. s := start location 2. s := a neighbing location of s with a minimal u-value 3. with probability (170-u(s))/170 do: u(s) := 1 + u(s). move the ant robot to location s. go to 2. Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Empirical Results (Simulation) Empirical Results (Simulation) end of first coverage trails after first coverage with one ant robot end of tenth coverage trails after tenth coverage with one ant robot Cover Time (steps) Cover Time (minutes) random walk TeamBots Simualtion of Random Walk Modified modified node counting TeamBots Simulation of Pebbles robot (without trail removal) Coverage Number coverage number Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; with without trail removal trail removal cleaning no cleaning Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

10 Empirical Results (Simulation) Empirical Results (Simulation) 00 0 Cover Time (minutes) TeamBots Simulation of Pebbles without Cleaning robot (without trail removal) robot (with trail removal) TeamBots Simulation of Pebbles with Cleaning Coverage Number coverage number Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; terrain size Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Empirical Results (Simulation) Empirical Results (Simulation) 8 hours without any ant robot getting stuck number of ant robots Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; x 2 meters 10 ant robots Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology;

11 The Future Summary Real-time search methods provide an interesting means f codinating single ant robots teams of ant robots that cover known unknown terrain once repeatedly. They leave markings in the terrain, similar to what some ants do. The ant robots robustly cover terrain even if the robots are moved without realizing this, some robots fail, and some markings get destroyed. The robots do not even need to be localized. small infrared tranceivers as smart markers (similar interesting wk is perfmed at USC and other institutions) Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Selected Publications Ant Robotics [Svennebring and Koenig, 2002] J. Svennebring and S. Koenig. Building Terrain-Covering Ant Robots. Technical Rept, GIT-COGSCI-2002/10, College of Computing, Gegia Institute of Technology, Atlanta (Gegia), 2002 [Koenig et. al., 2001] S. Koenig, B. Szymanski and Y. Liu. Efficient and Inefficient Ant Coverage Methods. Annals of Mathematics and Artificial Intelligence, 31, 1-76, Additional Infmation [Svennebring and Koenig, 2003] J. Svennebring and S. Koenig. Trail-Laying Robots f Robust Terrain Coverage. In Proceedings of the International Conference on Robotics and Automation, Real-Time Search [Koenig and Szymanski, 1999] S. Koenig and B. Szymanski. Value-Update Rules f Real-Time Search. In Proceedings of the National Conference on Artificial Intelligence, , [Koenig and Simmons, 1996a] S. Koenig and R.G. Simmons. Easy and Hard Testbeds f Real-Time Search Algithms. In Proceedings of the National Conference on Artificial Intelligence, , [Koenig and Simmons, 1996b] S. Koenig and R.G. Simmons. The Influence of Domain Properties on the Perfmance of Real-Time Search Algithms. Technical Rept, CMU-CS-96-11, School of Computer Science, Carnegie Mellon University, Pittsburgh (Pennsylvania), [Koenig and Simmons, 199] S. Koenig and R.G. Simmons. Real-Time Search in Non-Deterministic Domains. In Proceedings of the International Joint Conference on Artificial Intelligence, , 199. [Koenig and Simmons, 1992] S. Koenig and R.G. Simmons. Complexity Analysis of Real-Time Reinfcement Learning Applied to Finding Shtest Paths in Deterministic Domains. Technical Rept, CMU-CS , Computer Science Department, Carnegie Mellon University, Pittsburgh (Pennsylvania), Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; Ant Robotics: Terrain Coverage; Sven Koenig; Gegia Institute of Technology; 2003