  In this paper, we address the problem of autonomous multi-robot mapping,
exploration and navigation in unknown, GPS-denied indoor or urban environments
using a swarm of robots equipped with directional sensors with limited sensing
capabilities and limited computational resources. The robots have no a priori
knowledge of the environment and need to rapidly explore and construct a map in
a distributed manner using existing landmarks, the presence of which can be
detected using onboard senors, although little to no metric information
(distance or bearing to the landmarks) is available. In order to correctly and
effectively achieve this, the presence of a necessary density/distribution of
landmarks is ensured by design of the urban/indoor environment. We thus address
this problem in two phases: 1) During the design/construction of the
urban/indoor environment we can ensure that sufficient landmarks are placed
within the environment. To that end we develop a filtration-based approach for
designing strategic placement of landmarks in an environment. 2) We develop a
distributed algorithm using which a team of robots, with no a priori knowledge
of the environment, can explore such an environment, construct a topological
map requiring no metric/distance information, and use that map to navigate
within the environment. This is achieved using a topological representation of
the environment (called a Landmark Complex), instead of constructing a complete
metric/pixel map. The representation is built by the robot as well as used by
them for navigation through a balance between exploration and exploitation. We
use tools from homology theory for identifying "holes" in the
coverage/exploration of the unknown environment and hence guiding the robots
towards achieving a complete exploration and mapping of the environment.
