Multirobot Persistent Monitoring: Minimizing Latency and Number of Robots With Recharging Constraints

In this article, we study multirobot path planning for persistent monitoring tasks. We consider the case where robots have a limited battery capacity with a discharge time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D$</tex-math></inline-formula>. We represent the areas to be monitored as the vertices of a weighted graph. For each vertex, there is a constraint on the maximum allowable time between robot visits, called the latency. The objective is to find the minimum number of robots that can satisfy these latency constraints while also ensuring that the robots periodically charge at a recharging depot. The decision version of this problem is known to be PSPACE-complete. We present a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O\left(\frac{\log D}{\log \log D} h \log \rho\right)$</tex-math></inline-formula> approximation algorithm for the problem where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\rho$</tex-math></inline-formula> is the ratio of the maximum and the minimum latency constraints, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> reflects the ratio of distance of vertices from the depot to their latency constraints. We also present an orienteering-based heuristic to solve the problem and show empirically that it typically provides higher quality solutions than the approximation algorithm. We extend our results to provide an algorithm for the problem of minimizing the maximum weighted latency given a fixed number of robots. We evaluate our algorithms on large problem instances in a patrolling scenario and in a wildfire monitoring application. We also compare the algorithms with an existing solver on benchmark instances.