Optimal Periodic Multi-Agent Persistent Monitoring of a Finite Set of Targets with Uncertain States

TL;DR

This paper develops a method for optimizing the movement of mobile agents to persistently monitor targets with uncertain states, using periodic trajectories and gradient-based optimization to minimize estimation error.

Contribution

It introduces a novel approach to design periodic agent trajectories constrained to a line, optimizing mean estimation error via stochastic gradient descent and Riccati equation analysis.

Findings

Optimal trajectories involve agents moving at maximum speed or dwelling at fixed points.

Estimation error converges to a steady state under periodic trajectories.

Explicit gradient formulas enable efficient local optimization of agent paths.

Abstract

We investigate the problem of persistently monitoring a finite set of targets with internal states that evolve with linear stochastic dynamics using a finite set of mobile agents. We approach the problem from the infinite-horizon perspective, looking for periodic movement schedules for the agents. Under linear dynamics and some standard assumptions on the noise distribution, the optimal estimator is a Kalman-Bucy filter and the mean estimation error is a function of its covariance matrix, which evolves as a differential Riccati equation. It is shown that when the agents are constrained to move only over a line and they can see at most one target at a time, the movement policy that minimizes the mean estimation error over time is such that the agent is always either moving with maximum speed or dwelling at a fixed position. This type of trajectory can be fully defined by a finite set of parameters. For periodic trajectories, under some observability conditions, the estimation error converges to a steady state condition and the stochastic gradient estimate of the cost with respect to the trajectory parameters of each agent and the global period can be explicitly computed using Infinitesimal Perturbation Analysis. A gradient-descent approach is used to compute locally optimal parameters. This approach allows us to deal with a very long persistent monitoring horizon using a small number of parameters.