Sensor placement~(SP) and informative path planning~(IPP) problems are prevalent in environmental monitoring. These problems require gathering the most informative data from a limited number of sensing locations, but existing solutions face a difficult trade-off. Existing methods are often either computationally efficient but less informative, or more informative but too computationally expensive for practical use, especially on resource-constrained robots. Furthermore, many approaches are limited by requiring discretization of environment or relying on slow, derivative-free optimization techniques.
This paper introduces a novel, computationally efficient variational formulation for the SP problem. Our approach is differentiable with respect to the sensing locations, enabling fast gradient-based optimization in continuous spaces and delivering performance comparable to MI-based methods at a fraction of the computational cost. We establish our formulation as a special case of sparse Gaussian processes~(SGPs). This connection allows us to generalize the method to solve the IPP problem for single and multi-robot systems, efficiently incorporating differentiable path constraints and diverse sensor types. The approach is validated through extensive benchmarks and field experiments with an Autonomous Surface Vehicle~(ASV) and an Autonomous Underwater Vehicle~(AUV). We also provide SGP-Tools—an open-source Python library—and a companion ROS~2 package for Ardupilot-based mobile robots.
