As mobile robots get deployed to perform sensing tasks (e.g., surveillance, monitoring, scientific exploration), there are usually multiple objectives that must be properly balanced. The general goal is to plan paths and policies that best suit the goal of the mission. Often, it is not clear whether multiple goals can be simultaneously optimized. With the question in mind, we began examining a broad class of problems in which multiple Poisson processes are spatially distributed, mimicking temporally-driven random events to be observed. To observe these events, a mobile robot (observer) must travel to the event site. Because the events are transient (i.e., time sensitive), the longer the robot waits at a particular site, the more likely it will be able to observe the particular event. Therefore, to observe a balanced portfolio of events, the robots must weigh between frequently traveling between different sites and staying at each site longer for making more observations. As it turns out, under proper (and mild) conditions, as established in this paper, there exists a globally optimal policy for scheduling the trip of the robot to (i) maximize the number of events observed and (ii) minimize the delay between consecutive observations of events occurring at the same site. Assuming a cyclic patrol policy is used, we provide a polynomial time approximation scheme (PTAS) that computes for any $\varepsilon > 0$ a $(1+\varepsilon)$-optimal solution for the more general, NP-hard problem. Beside this persistent monitoring problem, we have also studied several related problems including the Correlated Orienteering Problem and the Optimal Tourist Problem.
<a id="links" href="/files/YuAslKarRus15IROS.pdf" target="_">paper</a>
Anytime Planning of Optimal Schedules for a Mobile Sensing Robot. J. Yu, J. Aslam, S. Karaman, and D. Rus. 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2015).
Correlated Orienteering Problem and its Application to Persistent Monitoring Tasks. J. Yu, M. Schwager, and D. Rus. IEEE Transactions on Robotics, 32(5), page(s): 1106 - 1118, 2016.
<a id="links" href="/files/YuKarRus15TOR.pdf" target="_">paper</a>
Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations. J. Yu, S. Karaman, and D. Rus. IEEE Transactions on Robotics, 31(3), page(s): 521-535, 2015.