LIPP: Load-Aware Informative Path Planning with Physical Sampling

Abstract

In classical Informative Path Planning (C-IPP), robots are typically modeled as mobile sensors that acquire digital measurements such as images or radiation levels. In this model - since making a measurement leaves the robot's physical state unchanged - traversal costs are determined solely by the path taken. This is a natural assumption for many missions, but does not extend to settings involving physical sample collection, where each collected sample adds mass and increases the energy cost of all subsequent motion. As a result, IPP formulations that ignore this coupling between information gain and load-dependent traversal cost can produce plans that are distance-efficient but energy-suboptimal, collecting fewer samples and less data than the energy budget would permit. In this paper, we introduce Load-aware Informative Path Planning (LIPP ), a generalization of C-IPP that explicitly models this coupling and the resulting order-dependent traversal costs. We formulate LIPP as a Mixed-Integer Quadratic Program (MIQP) that jointly optimizes routing, visitation order, and per-location sampling count under an energy budget. We show that LIPP strictly generalizes C-IPP: as sample unit mass $λ\to 0$, the load-dependent energy model reduces exactly to the classical distance budget constraint, recovering C-IPP as a special case. We further derive theoretical bounds on the path-length increase of LIPP relative to C-IPP, characterizing the trade-off for improved energy efficiency. Finally, through extensive simulations across 2000 diverse mission scenarios, we demonstrate that LIPP matches the behavior of C-IPP at zero sample mass and progressively achieves higher uncertainty reduction per unit energy as sample mass increases.