  Autonomous exploration of unknown environments using a team of mobile robots
demands distributed perception and planning strategies to enable efficient and
scalable performance. Ideally, each robot should update its map and plan its
motion not only relying on its own observations, but also considering the
observations of its peers. Centralized solutions to multi-robot coordination
are susceptible to central node failure and require a sophisticated
communication infrastructure for reliable operation. Current decentralized
active mapping methods consider simplistic robot models with linear-Gaussian
observations and Euclidean robot states. In this work, we present a distributed
multi-robot mapping and planning method, called Riemannian Optimization for
Active Mapping (ROAM). We formulate an optimization problem over a graph with
node variables belonging to a Riemannian manifold and a consensus constraint
requiring feasible solutions to agree on the node variables. We develop a
distributed Riemannian optimization algorithm that relies only on one-hop
communication to solve the problem with consensus and optimality guarantees. We
show that multi-robot active mapping can be achieved via two applications of
our distributed Riemannian optimization over different manifolds: distributed
estimation of a 3-D semantic map and distributed planning of SE(3) trajectories
that minimize map uncertainty. We demonstrate the performance of ROAM in
simulation and real-world experiments using a team of robots with RGB-D
cameras.
