We study the problem of planning the motion of an agent such that it maintains indefinitely a highquality estimate of some a priori unknown feature, such as traffic levels in an urban environment. Persistent operation requires that the agent satisfy motion constraints, such as visiting charging stations infinitely often, which are readily described by rich linear temporal logic (LTL) specifications. We propose and evaluate via simulation a two-level dynamic programming algorithm that is

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... ed to satisfy given LTL constraints. The low-level path planner implements a receding horizon algorithm that maximizes the local information gathering rate. The high-level planner selects inputs to the low-level planner based on global performance considerations. I. MOTIVATION In this paper, we address the problem of planning the path of a mobile robot such that it persistently maintains a high-quality estimate of some unknown feature, i.e. persistent monitoring. This describes many real-world applications in which human decision-makers require real-time information about large environments, such as forest rangers monitoring wildfires or traffic engineers monitoring congestion. In order to provide up-to-date information reliably, the robot has to plan its motion such that relevant information is gained, e.g. the agent visits locations that have not recently been visited. This can be formalized as maximizing the expected mutual information rate (MIR) between the environment and the agent's sensor measurements. In addition, the agent's motion must be planned such that it can continue functioning indefinitely, i.e. it must satisfy constraints such as "Regularly visit a recharging station and always avoid obstacles". In this work, we use linear temporal logic (LTL), an extension of Boolean logic that is capable of describing how a system may change over time, to model such constraints. We present a hierarchal stochastic optimal control algorithm that is guaranteed to satisfy the given LTL constraints while attempting to maximize the Austin Jones is with the Division of Systems Engineering, Mac Schwager and Calin Belta are with the Division of Systems Engineering and the MIR. The low-level planner executes a receding horizon algorithm that maximizes the MIR locally. The highlevel planner uses a pre-computed policy to select inputs to the receding horizon algorithm such that the LTL constraints are guaranteed to be met and to maximize the MIR over the long horizon. Our procedure is evaluated via Monte Carlo simulation. Persistent monitoring strategies have recently been considered in the literature. In [21] , the authors demonstrate how to regulate the speed of an agent moving along a fixed path such that the uncertainty about the state of the environment remains below a certain threshold indefinitely. This work is extended to planning trajectories in [16] . The problem of multi-agent persistent monitoring is investigated in [6]. The above works consider a measurement model that is independent of the agent's location in the environment and either completely unconstrained motion or motion along predefined paths. In contrast, we assume that the agent's sensing capability depends on its position in the environment and we incorporate linear temporal logic (LTL) motion constraints. Linear temporal logic [2], [22] can be used to ensure that a system satisfies liveness ("Visit a charging station infinitely often"), fairness ("Ensure a data upload station is visited before visiting a charging station"), and safety ("Always avoid obstacles") properties. Off-theshelf formal synthesis tools exist for planning a robot's trajectory such that it is guaranteed to satisfy a given LTL formula [1], [5], [23] . These tools were applied to the problem of persistent monitoring in [9] in which the goal was to minimize the amount of time between visiting pre-specified surveillance regions. This work did not explicitly represent the agent's sensing model nor the environment model. We previously incorporated information-based planning with temporal logic constraints in [10], [11] . In [11], we considered planning under syntactically co-safe linear temporal logic (scLTL) constraints on the motion of the robot, a finite-time subset of LTL. scLTL can be used to describe reachability and finite-time safety properties, among others. By considering full LTL formulae, the approach in this paper allows us to consider infinitehorizon properties such as visiting different sequences