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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. 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 optimal movement policy is such that the agent is always either moving with maximum speed or dwelling at a fixed position. Periodic trajectories of this form admit finite parameterization, and we show to compute a stochastic gradient estimate of the performance with respect to the parameters that define the trajectory using Infinitesimal Perturbation Analysis. A gradient-descent scheme 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.
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Multi-agent infinite horizon persistent monitoring of targets with uncertain states in multi-dimensional environments
This paper investigates the problem of persistent monitoring, where a finite set of mobile agents persistently visits a finite set of targets in a multi-dimensional environment. The agents must estimate the targets’ internal states and the goal is to minimize the mean squared estimation error over time. The internal states of the targets evolve with linear stochastic dynamics and thus the optimal estimator is a Kalman-Bucy Filter. We constrain the trajectories of the agents to be periodic and represented by a truncated Fourier series. Taking advantage of the periodic nature of this solution, we define the infinite horizon version of the problem and explore the property that the mean estimation squared error converges to a limit cycle. We present a technique to compute online the gradient of the steady state mean estimation error of the targets’ states with respect to the parameters defining the trajectories and use a gradient descent scheme to obtain locally optimal movement schedules. This scheme allows us to address the infinite horizon problem with only a small number of parameters to be optimized.
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- PAR ID:
- 10171438
- Date Published:
- Journal Name:
- Proc. IFAC World Congress
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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