Hybrid grids and the Homing Robot

In their paper (Inform. Process. Lett. 77 (2001) 261), Wongngamnit and Angluin introduced a memory-efficient robot, called the Homing Robot, which localizes in an occupancy grid. We present a more general class of grids called hybrid grids, and establish the least upper bound for the number of moves the robot takes to localize. We also state analogous results for a hexagonal tiling.