LIPP: Load-Aware Informative Path Planning with Physical Sampling

TL;DR

This paper forms LIPP as a Mixed-Integer Quadratic Program (MIQP) that jointly optimizes routing, visitation order, and per-location sampling count under an energy budget and shows 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.

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.

Figures (5)

• Figure 1: Illustration of load-aware (LIPP) and load-unaware (C-IPP) planning in a regolith sampling mission in which planetary rovers collect and store physical soil samples. As the rover gathers multiple samples at a scientifically important site, (where minerals are concentrated in the figure) the accumulated payload increases the energy required for the remainder of the journey. C-IPP does not account for this effect during planning, often producing distance-efficient but energy-inefficient paths. In contrast, LIPP explicitly models the evolving load and introduces an additional decision dimension: how much material to collect at each visited location. This added flexibility enables LIPP to allocate more samples to high-value regions while maintaining or even reducing the overall energy budget, resulting in greater information gain per unit of energy expended compared to classical distance-based planning.
• Figure 2: Comparison of sampling strategies on a synthetic scalar field. The heatmap represents the ground-truth (GT) scalar function to be estimated. The numbers inside the white boxes indicate the number of samples taken at each vertex. (left) The Greedy method first moves to vertex e and then to vertex d, as these provide the greatest uncertainty reduction normalized by distance at each iteration. (center) C-IPP considers a global view, budgeting its distance to enable visiting vertex g. However, it visits the important region early in the path, resulting in greater energy usage. (right) LIPP not only visits the important vertices selected by C-IPP, but also chooses an order that allocates less sample-intensive regions earlier in the path, achieving comparable posterior variance while using significantly less energy.
• Figure 3: Posterior variance reduction, total energy used, and posterior variance reduction per unit energy values averaged over 2000 randomly generated graphs with $R_0=1.0$ across different unit sample mass $\lambda$. (a) As the unit sample mass approaches zero, the energy constraint relaxes, and LIPP converges to the same posterior variance reduction as C-IPP. (b) As the unit sample mass increases, LIPP expends energy much more slowly than C-IPP and will be bounded by the threshold 2 energy units. (c) As the unit sample mass increases, LIPP achieves progressively greater reduction in posterior variance per unit energy used compared to C-IPP.
• Figure 4: We evaluate LIPP against C-IPP and Greedy across different budget constraints on 2000 randomly generated graphs, with sample count fixed at $S_{\max} = 3$. For each test instance, we run C-IPP to find a path of length $d$ and compute the energy needed, $B_{CIPP}$, where the robot takes $S_{\max}$ samples at each node. In (a) LIPP is given the same energy budget as C-IPP consumes; it takes longer paths due to the excessive budget allowance. However, in (b) when the energy budget is set to roughly half of C-IPP's consumption, LIPP travels a similar distance while achieving comparable posterior variance. This trend becomes more pronounced in (c) when $B_{LIPP}=0.35B_{CIPP}$ and LIPP matches or improves upon C-IPP in both distance and energy efficiency.
• Figure 5: Runtime comparison of C-IPP and LIPP as a function of graph nodes across density around 15%, measured on 2000 graphs. Solve time is recorded as the time for Gurobi to reach a relative optimality gap below 5%. C-IPP exhibits computationally tractable behavior across all tested densities. However, LIPP exhibits steeper growth than $S_{max}^2 = 9$ times C-IPP, reflecting the increased complexity introduced by a weaker LP relaxation.