Optimizing waypoints for monitoring spatiotemporal phenomena

We introduce a graph-based informative path planning algorithm for a mobile robot which explicitly handles time. The objective function must be submodular in the samples taken by the robot, and the samples obtained are allowed to depend on the time at which the robot visits each location. Using a submodular objective function allows our algorithm to handle problems with diminishing returns, e.g. the case when taking a sample provides less utility when other nearby points have already been sampled. We give a formal description of this framework wherein an objective function that maps the path of the robot to the set of samples taken is defined. We also show how this framework can handle the case in which the robot takes samples along the edges of the graph. A proof of the approximation guarantee for the algorithm is given. Finally, quantitative results are shown for three problems: one simple example with a known Gaussian process model, one simulated example for an underwater robot planning problem using data from a well-known ocean modeling system, and one field experiment using an autonomous surface vehicle (ASV) measuring wireless signal strength on a lake.