  This paper studies the problem of reconstructing a two-dimensional scalar
field using a swarm of networked robots with local communication capabilities.
We consider the communication network of the robots to form either a chain or a
grid topology. We formulate the reconstruction problem as an optimization
problem that is constrained by first-order linear dynamics on a large,
interconnected system. To solve this problem, we employ an optimization-based
scheme that uses a gradient-based method with an analytical computation of the
gradient. In addition, we derive bounds on the trace of observability Gramian
of the system, which helps us to quantify and compare the estimation capability
of chain and grid networks. A comparison based on a performance measure related
to the H2 norm of the system is also used to study robustness of the network
topologies. Our resultsare validated using both simulated scalar fields and
actual ocean salinity data.
