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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.

In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of propositions defined on the states of the MDP. We synthesize a control policy such that the MDP satisfies the given specification almost surely, if such a policy exists. In addition, we designate an “optimizing proposition” to be repeatedly satisfied, and we formulate a novel optimization criterion in terms of minimizing the expected cost in between satisfactions of this proposition. We propose a sufficient condition for a policy to be optimal, and develop a dynamic programming algorithm that synthesizes a policy that is optimal under some conditions, and sub-optimal otherwise. This problem is motivated by robotic applications requiring persistent tasks, such as environmental monitoring or data gathering, to be performed.

In this paper we present a method for automatically generating optimal robot trajectories satisfying high level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by a general linear temporal logic formula. In addition, we require that an optimizing proposition must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot trajectory which minimizes the cost function. The problem is motivated by robotic monitoring and data gathering. In this setting, the optimizing proposition is satisfied at locations where data can be uploaded, and the formula specifies a an infinite horizon data collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal logic formula. We then present a graph algorithm which computes a path corresponding to the optimal robot trajectory. We also present an implementation for a robot performing a data gathering mission.

In this paper we present a method for automatically planning optimal paths for a group of robots that satisfy a common high level mission specification. Each robot's motion in the environment is modeled as a weighted transition system. The mission is given as a Linear Temporal Logic formula. In addition, an optimizing proposition must repeatedly be satisfied. The goal is to minimize the maximum time between satisfying instances of the optimizing proposition. Our method is guaranteed to compute an optimal set of robot paths. We utilize a timed automaton representation in order to capture the relative position of the robots in the environment. We then obtain a bisimulation of this timed automaton as a finite transition system that captures the joint behavior of the robots and apply our earlier algorithm for the single robot case to optimize the group motion. We present a simulation of a persistent monitoring task in a road network environment., United States. Office of Naval Research. Multidisciplinary University Research Initiative (N00014-09-1051), United States. Army Research Office (W911NF-09-1-0088), United States. Air Force Office of Scientific Research (YIP FA9550-09-1-020), National Science Foundation (U.S.). (CNS- 0834260)

In this paper we consider the problem of monitoring a known set of stationary features (or locations of interest) in an environment. To observe a feature, a robot must visit its location. Each feature changes over time, and we assume that the currency, or accuracy of an observation decays linearly with time. Thus, robots must repeatedly visit the features to update their observations. Each feature has a known rate of change, and so the frequency of visits to a feature should be proportional to its rate. The goal is to route the robots so as to minimize the maximum change of a feature between observations. We focus on the asymptotic regime of a large number of features distributed according to a probability density function. In this regime we determine a lower bound on the maximum change of a feature between visits, and develop a robot control policy that, with probability one, performs within a factor of two of the optimal. We also provide a single robot lower bound which holds outside of the asymptotic regime, and present a heuristic algorithm motivated by our asymptotic analysis., United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award number N00014-09-1-1051)

Persistent robot tasks such as monitoring and cleaning are concerned with controlling mobile robots to act in a changing environment in a way that guarantees that the uncertainty in the system (due to change and to the actions of the robot) remains bounded for all time. Prior work in persistent robot tasks considered only robot systems with collision-free paths that move following speed controllers. In this paper we describe a solution to multi-robot persistent monitoring, where robots have intersecting trajectories. We develop collision and deadlock avoidance algorithms that are based on stopping policies, and quantify the impact of the stopping times on the overall stability of the speed controllers., United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-09-1-1051), National Science Foundation (U.S.). Graduate Research Fellowship Program (Award 0645960), Boeing Company