Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments

In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at 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 are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment.