1. Random Probabilistic Complete Optimal Formation-Based Multi-Robot Coverage • Coverage: Determine a path that passes the robot over all points in a target region DeWitt T. Latimer IV, Siddhartha Srinivasa, Vincent Lee-Shue, Samuel Sonne, Aaron Hurst, Howie Choset Carnegie Mellon University

2. Multi-Robot Coverage • Assumptions • Unknown space • Static obstacles • Homogenous circular robot • No marking capability • Common coordinate frame • Goals • Complete coverage of space • Coordinated, yet decentralized, among multiple robots • “Minimize” repeat coverage

3. Final (current) Demonstration

4. Challenges • Guaranteeing completeness • Single robot: Hert & Lumelsky, Choset & Acar, Cao • Multi-robot: Butler, Hollis, and Rizzi • Minimize repeat coverage • Planning in a multi-dimensional configuration space • Balch and Arkin, each robot acts independently • Retract methods, Yap, Choset and Burdick, Rao, Kuipers, etc. etc. • Space not known a priori • Single robot: Hert & Lumelsky, Choset & Acar, Cao • Multi-robot: Butler, Hollis, and Rizzi • Scalability

5. Cell Decomposition and Critical Point Sensing At a critical point x,

6. Sensor-based Complete Coverage Goal: Complete coverage of an unknown environment Cell decomposition Incremental construction Time-exposure photo of a coverage experiment

7. Cover Interior of Cell (one corridor at a time) • Two motions • Lapping • Wall follow Wall follow Lap

8. Characterize Critical Points

9. Critical Point Sensing Non-lead Look for parallel vectors during forward wall following, but after a reverse wall follow, lap, and then the forward Look for anti-parallel vectors during reverse wall following Rev convex crit. pt Fwd convex crit. pt Lead Look for parallel vectors during forward wall following Look for parallel vectors during reverse wall following Rev concave crit. pt Fwd Convex crit. pt

10. Action at Critical Points Team divides into two separate teams, each covering a new cell VIRTUAL FRONTIER (Butler) Team finishes cell and then looks for a new cell to cover

11. Virtual Frontier As an attempt to “minimize” repeat coverage, we use the virtual frontier believing that another team will be coming from the “other” cell associated with the forward critical point

12. Team Rejoining (work in progress) • Types of encounters • Two teams covering in opposite slice directions • Both teams finish the current corridor • Two teams covering in same slice direction • Both teams finish the current corridor • One team covering and the other traversing • Since robots only traverse through known space, the covering team stops covering and joins traversing team • Two teams encountering each other on the border of two cells (very hard case) • Combine adjacency graphs

13. Play video Example

14. Future: Distributed Localization and Mapping

15. Acknowledgements • Dave Conner • Ercan Acar • Tucker Balch • Matt Mason and Mike Erdmann

16. Why do the robots jerk back and forth during wall following?Encountering All Critical Points • Conventional back and forth motions are not sufficient • (Cao et al.’88, Hert et al.’97, Lumelsky et al.’90)

17. NOT Occupancy Grid: Less memory, More meaningful, Minimize turns, Completeness Incremental Complete Coverage

18. Critical Point Sensing Look for parallel vectors during forward wall following, but after a reverse wall follow, lap, and then the forward Look for anti-parallel vectors during reverse wall following Look for parallel vectors during forward wall following Look for parallel vectors during reverse wall following