We present controllers that enable mobile robots to persistently monitor or
sweep a changing environment. The changing environment is modeled as a field
which grows in locations that are not within range of a robot, and decreases in
locations that are within range of a robot. We assume that the robots travel on
given closed paths. The speed of each robot along its path is controlled to
prevent the field from growing unbounded at any location. We consider the space
of speed controllers that can be parametrized by a finite set of basis
functions. For a single robot, we develop a linear program that is guaranteed
to compute a speed controller in this space to keep the field bounded, if such
a controller exists. Another linear program is then derived whose solution is
the speed controller that minimizes the maximum field value over the
environment. We extend our linear program formulation to develop a multi-robot
controller that keeps the field bounded. The multi-robot controller has the
unique feature that it does not require communication among the robots.
Simulation studies demonstrate the robustness of the controllers to modeling
errors, and to stochasticity in the environment.